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http://www-ksl.stanford.edu/email-archives/srkb.messages/336.html	# Re: Difference between logics and theories [email protected] Organization: Dipartimento di Informatica - Universita' di Pisa - Italy Date: Tue, 13 Sep 1994 11:59:28 --100 From: [email protected] Message-id: <9409130959.AA04607@omega> To: [email protected] Cc: [email protected], [email protected], [email protected], [email protected], [email protected] Subject: Re: Difference between logics and theories Content-Length: 1592 Sender: [email protected] Precedence: bulk >From [email protected] Sat Sep 10 19:48:13 1994 Date: Sat, 10 Sep 94 13:46:02 -0400 From: [email protected] (John F. Sowa) Cc: [email protected] ... I will certainly admit that we, as definers of KIF and CGs, have a responsibility to demonstrate that our metalanguage is capable of supporting a theory of truth, modality, or whatever. But if anyone writes inconsistent axioms in our formalism, it's not our fault. But the problem is that writing such axioms in a consistent way is very tricky. If you need to invent axioms for every new modality you need, then you have the problem not only of proving the resulting theory consistent, but also of proving it consistent in connection with the axiomatizations of the other modalities that you are also using. This makes the situation completely unmanageable. \begin{commercial} To solve this problem, M. Simi and myself have been developing a framework for expressing and reasoning relativized truth and propositional attitudes, that we call theory of viewpoints (similar to McCarthy contexts), which is first-order, has a model theory and a proof theory and it is proven consistent. The idea is not much different from Sowa "lightweight boxes", but with a full formalization. Using a basic construct for relitivized truth "In(formula, viewpoint)", we show how to express various propositional attitudes: you must supply	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7906283736228943, "perplexity": 9459.111272545288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647649.70/warc/CC-MAIN-20180321121805-20180321141805-00718.warc.gz"}
https://www.opengeosys.org/docs/tools/meshing-submeshes/extract-boundary/	# Extract Boundary ## General The tool extracts either lines in case of a 2D bulk mesh as input or quads/triangles in case of a 3D bulk mesh as input. The input mesh can be given either in the vtu or msh format. Since the algorithm uses the element surface normals a correct node ordering of the element nodes is required. ## Usage ExtractBoundary -i [<file name of input mesh>] [-o <file name of output mesh>] [--face-property-name <string>] [--element-property-name <string>] [--node-property-name <string>] The data arrays added to the boundary mesh by using the options --face-property-name (default value ‘bulk_face_ids’), --element-property-name (default value ‘bulk_element_ids’), and --node-property-name (default value ‘bulk_node_ids’) are used in other tools (for instance in ComputeNodeAreasFromSurfaceMesh) and are required for flux calculations during a simulation run of OpenGeoSys. # Extract the boundary from a quad mesh ExtractBoundary -i square_1x1_quad.vtu -o square_1x1_quad_border.vtu In the figure above the square mesh consists of 16 cells/elements. The numbers in the cells are the cell IDs. The generated boundary grid consists of the somewhat thicker and colored line elements. # Extract the boundary from a tri mesh ExtractBoundary -i square_1x1_tri.vtu -o square_1x1_tri_border.vtu In the figure above the square mesh consists of 32 triangle shaped cells. The numbers in the tri are the cell IDs. The generated boundary grid consists of the somewhat thicker and colored line elements. Previous This article was written by Thomas Fischer. If you are missing something or you find an error please let us know. Generated with Hugo 0.64.1. Last revision: January 17, 2020 Commit: [docu] Docu for the tool ExtractBoundary. cde4e7e90 \| Edit this page on	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5600139498710632, "perplexity": 5136.489398116588}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505731.37/warc/CC-MAIN-20200401130837-20200401160837-00497.warc.gz"}
http://math.stackexchange.com/questions/246974/how-to-prove-that-this-is-an-harmonic-funtion	# How to prove that this is an Harmonic funtion? Let $u$ be an Harmonic function in $B(0,a)$ in $R^3$ we define $I(x)=x\dfrac{a^2}{\|x\|^2}$ Let $w(x) = u(I(x))$. Is there a way to prove that $w$ is harmonic without making too much computation? If not I will make them my self. Thanks for your help! - In fact this are call Kelvin transform, and it work In $R^2$ but it needs a modification for $R^3$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9604790806770325, "perplexity": 269.2855853568272}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119646849.7/warc/CC-MAIN-20141024030046-00267-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.oercommons.org/authoring/48102-greetings-english-foundation/view	# Greetings- English Foundation ## About the Boise State World Languages Resource Center (WLRC) Language Activity Repository The activities provided by the Boise State World Languages Resource Center (WLRC) serve as foundational activities which can be adapted by any language and scaled up or down on the proficiency scale. In other words, the activities are “language-agnostic” to provide language instructors from around the country the platform to remix these instructional materials, infusing them with their target language and culture! This activity was created by upper-division language students working in the World Languages Resource Center at Boise State University. Our activities seek to help students solidify their interpersonal speaking and interpretive listening skills through task-based situations or communicative activities. We recommend using these activities to help reinforce the content students are learning, allowing the students time to feel comfortable using the unit’s vocabulary and grammar structures through application. Further, these activities should be facilitated in approximately 90% (or more) in the target language, per the recommendation of the American Council on the Teaching of Foreign Languages. ### Using the WLRC Repository’s Activities: When you are ready to begin remixing the activity, in order to adapt it for your target language and audience, simply click the “Remix This Resource” button at the top of your screen. The text provided in purple is a suggestion of what you might say to your students and should be changed to the target language. Most activities contain a connected chapter, two to three “NCSSFL-ACTFL Can-Do” statements, a warm-up, main activity, and a wrap-up. In addition to the instructions, some activities may include a “cheat sheet” containing the target vocabulary and grammar structures emphasized in the activity. Though most of the lab materials are provided, a computer, projector, printer, and laminator may also be needed to fully utilize materials. Many of the activities include printable cards and other instructional materials. If you would like to adapt these materials for your language, please email [email protected] and we will provide you with an editable copy. For YouTube videos and other websites, hyperlinks are provided. Enjoy! - Boise State World Languages Resource Center ## Introducing Oneself In this activity students will get the opportunity to practice introducing themselves and asking others their names. They will also practice using greeting appropriate for different times of the day. ### Keywords: Greetings, names, introductions, formal language, informal language, hello, goodbye ### Relevant NCSSFL-ACTFL Can-Do Statements: • I can introduce myself when I meet people. • I can tell my name and ask someone their name. • I can greet and take leave in a polite way. • I can greet and appropriately address someone I meet using polite, rehearsed behaviors. ### Relevant ACTFL World-Readiness Standards Communication Standard 1.1 Students engage in conversations, provide and obtain information, express feelings and emotions, and exchange opinions. ### Materials Needed: Google Slides Presentation Name Game Cards NAME GAME CARDS ## Warm-up 1. Begin by introducing the Can-Dos for today’s activity and displaying Google Slides presentation. “Today, we are going to practice greeting new people and introducing ourselves. We will also discuss common greetings used at different times of the day." ### Relevant NCSSFL-ACTFL Can-Do Statements: • I can introduce myself when I meet people. • I can tell my name and ask someone their name. • I can greet and take leave in a polite way. • I can greet and appropriately address someone I meet using polite, rehearsed behaviors. 2. Proceed through the Google Slides presentation, using each set of photos to introduce students to greetings used at different times of the day. Slides will also allow students to learn and practice basic phrases for introducing oneself and asking someone their name. “During certain times of the day, it is very common to greet people by stating wether is is morning, noon , or night. Additionally, when greeting someone, it is polite to use different expressions when there is a difference of age, authority, or someone has a title. If students need some assistance getting the discussion going, use the questions below: 1. When meeting someone who looks very official, what is the most polite way to greet them? 2. What kinds of words would you use when speaking with someone younger than you? 3. What types of words are appropriate when meeting or greeting friends? Do you need to use formal language? 4. When greeting a teacher, or meeting them for the first time, would you speak formally? 5. How would you introduce yourself to there different people? How would you ask them their names? ## Main Activity 1. Scramble the Name Game cards and lay them out face down. Have each student pick a card. “Next, we are going to practice introducing ourselves by taking on the personas of well known figures and celebrities! Everyone has a card with a photo and a name. ” 2. Tell your students: 1. “We will first start by asking one another for surnames, as this is what is polite when meeting someone for the first time. 2. “After we have all had an opportunity to introduce our surnames, we will practice introducing ourselves and asking someone their name." 3. • Shuffle Cards and place face down on table, students all pick a card • Activity leader starts by showing their card and introducing themselves starting with surnames. Feel free to point to the part of the name card that has the surname if students are unsure of where to look for that information. • Leader then turns to RANDOM students and asks "Excuse me, what is your surname" in the target language. The student then answers by saying their surname, and then asks the same question of another random student. Repeat until all students have asked/responded. • Leader should then ask a random Student "what is your name?" in the target language. Repeat steps as above until all students have had the opportunity to ask/respond. ## Wrap-up After completing the main activity, return to the Google Slides presentation and go over the review slides with students, reinforcing concepts learned in the lesson and giving time for clearing up any confusion or answering questions students have. ### Wrap-up questions (Pick the a few you’d like to ask): • When is it appropriate to use formal/informal language when greeting someone? • What are the different greetings you use at different times of day? ### End of lab: • Read Can-Do statements once more and have students evaluate their confidence. (Use thumbs up/thumbs down or download our student cards.) • Encourage students to be honest in their self-evaluation. • Pay attention, and try to use feedback for future labs! ### Relevant NCSSFL-ACTFL Can-Do Statements: • I can introduce myself when I meet people • I can tell my name and ask someone their name • I can greet and take leave in a polite way • I can greet and appropriately dress someone using polite, rehearsed behaviors Where are we? Rate yourself on the weekly Can-Do Statements using this scale: I get it!, I got it!, I kind of get it..., I don't get it... Return to top	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19384120404720306, "perplexity": 4471.386457004242}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00101.warc.gz"}
https://physics.stackexchange.com/questions/122754/for-what-rare-events-was-the-lhc-built/122764#122764	# For what rare events was the LHC built? I understand that for low cross-section events a very high luminosity is necessary in order to obtain enough data to produce meaningful statistics. That is why the LHC was built. But which are these event which we are interested in? What are the events which would hint at new physics or would confirm theoretical models? • First of all: The Higgs boson. Jul 2 '14 at 14:10 • Related, if not duplicate: physics.stackexchange.com/q/8922 Jul 2 '14 at 14:14 ## 2 Answers The history of high energy physics is in the words "high energy" . There are two ways to get it, building higher and higher energy accelerators or studying cosmic rays, which last has answers in another question. Accelerators are of two types, those creating beams of particles that fall on fixed targets, and colliders, having two beams collide. All studies have yielded the enormous amount of data that one can find in the particle data book, a plethora of resonances and particles that are encapsulated the Standard Model of particle physics. Colliders provide higher center of mass energies and have been for some time the center of studies for the behavior of higher and higher energies at scattering. The reason is that the standard model fits well low energy data but also predicts data for higher energies, as for example the existence of the Higgs. Also the SM is a gauge that will show if something unusual is happening at higher energies like manifestation of supersymmetric particles etc. by checking crossections and branching ratios against SM calculations . Colliders come into two physics types and two geometry types: hadronic, i.e. proton antiproton colliders or proton proton colliders, which is scattering a bag of quarks and gluons (proton) against another bag of antiquarks and gluons (antiproton) or also quarks and gluons (proton), and leptonic, scattering electrons on positrons and watching the fall out. They can be linear one off beam collisions, or circular colliders the beam increasing in energy by a lot of rotations around the ring. Leptonic collisions are much more accurate experimentally and theoretically, as the vertices in the Feynman diagrams are simple and computable with fewer assumptions than for hadronic ones. I have heard that Feynman defended leptonic experiments by saying" if you want to study the interior of a watch you do not throw one watch against another and study the wheels coming out. You take a screw driver ( in this case it was neutrino scattering on a target, I think but it holds for all leptonic collisions). The one of the drawbacks of leptonic circular colliders is also their advantage: the known fixed energy at center of mass can explore systematically a phase space with great accuracy and less modeling but the spread of energies is limited. It is also hard to accelerate electrons and positrons in circular colliders to high enough energies due to synchrotron radiation that degrades the energies of the beams. The drawback of the hadron colliders is that a lot of modelling has to enter since it is a scatter of many on many elementary particles but because of the high luminosity achievable they are great for new discoveries. The Z and W were found at a proton antiproton collider at CERN and then were explored in great detail in the leptonic collider LEP, the results of which nailed the parameters of the SM. Already there are proposals for a higher energy leptonic collider to sit on the Higgs and study with accuracy its branching ratios etc. As well there are plans for an international linear collider at high energies after the LHC gives all the hints it can for where to look for new physics. Hadronic colliders are discovery machines. Leptonic are for nailing down accurately the parameters of the theoretical models. As pfnuessel said in his comment: The first thing to look at was the Higgs - there were hints from LEP and Tevatron, but no evidence, so the LHC was designed that the (SM-)Higgs has to be seen, if it exists. And for everything beyond the Higgs - we don't know! There are various theories, e.g. the different flavors of super-symmetry and others, but they all have different predictions. If any of these theories is right there must be something - havier SUSY-partners of the standard model particles for example. But as there are many different theories it's not a very targeted search, its more a scan over a broad energy range not reachable in pre-LHC-times - we'll see what the experiemnt-collaborations will stumble upon, and which theory will be best to describe the results...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.808179497718811, "perplexity": 488.0610537146031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585916.29/warc/CC-MAIN-20211024081003-20211024111003-00094.warc.gz"}
https://www.physicsforums.com/threads/special-relativity-kinetic-energy.847254/	# Special Relativity -- Kinetic Energy 1. Dec 8, 2015 ### Barry Melby 1. The problem statement, all variables and given/known data An electron e− and positron e+ moving at the same speed in the Earth reference frame collide head-on and produce a proton p and an antiproton p¯. The electron and positron have the same mass. The proton and antiproton also have the same mass. The mass of the proton is 1836.15 times the mass of the electron. Calculate, in the Earth reference frame, the minimum value possible for the ratio of the electron's kinetic energy to its internal energy in order to have the reaction e− + e+ →p + p¯ take place. Want: K/E_internal = ??? 2. Relevant equations K = (y-1)mc^2 --- y = lorentz factor E_internal = mc^2 3. The attempt at a solution I'm not even remotely sure what this question is asking. Can someone offer me some guidance? 2. Dec 8, 2015 ### nrqed You have the correct equations, so you need to figure out the ratio which is simply $\gamma-1$. To find that, the key point is that you want the minimum energies for the e+ and e- to have the reaction take place. This is a special case. What can you say about the proton and antiproton produced then? 3. Dec 8, 2015 ### Barry Melby Well i know that the mass of the proton and the antiproton are 1836.15 times the mass of the electron and positron. Would $\gamma$ = 1/(1-1836.15^2)? 4. Dec 8, 2015 ### Barry Melby No no, never mind. That wouldn't make sense. Where do i go? 5. Dec 8, 2015 ### nrqed As I mentioned earlier, the key point is that you want the minimum energy for the e+ and e- to have the reaction take place. This is a special case. What can you say about the proton and antiproton produced then? 6. Dec 8, 2015 ### Barry Melby I don't really understand what you're saying. Do i have to do something with momentum? 7. Dec 8, 2015 ### nrqed In a general problem, you would have to apply conservation of momentum. Here, you are luckier because that won't be necessary. What is the speed of the proton and antiproton produced, in your question? 8. Dec 8, 2015 ### Barry Melby it doesn't appear that the proton or antiproton are moving at all. 9. Dec 8, 2015 ### nrqed Exactly! Now, what is the total energy of the system after the reaction? 10. Dec 8, 2015 ### Barry Melby The total energy would be zero i would suspect because they have no velocity. How does this relate to $\gamma$? 11. Dec 8, 2015 ### nrqed Not quite. The total energy is not just kinetic energy, in relativity. It includes rest mass energy. So what is the total energy, taking this into account? (Once you find that, you can write an expression for the total energy before. Using conservation of total energy, you will get an equation for gamma that you can then solve for. 12. Dec 8, 2015 ### Ray Vickson $E = M c^2 = 0$ only if $M = 0$. Draft saved Draft deleted Similar Discussions: Special Relativity -- Kinetic Energy	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.895332932472229, "perplexity": 949.2581224335141}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813059.39/warc/CC-MAIN-20180220165417-20180220185417-00699.warc.gz"}
https://cursocomandoseletricos.com.br/anthony-intervention-mttef/viewtopic.php?page=binary-relation-pdf-42478b	are in R for every x in A. The set S is called the domain of the relation and the set T the codomain. Since binary relations are sets, we can apply the classical operations of set theory to them. This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . Example 1.6. We ask that binary relation mathematics example of strict weak orders is related to be restricted to be restricted to the only if a reflexive relation Every set and binary in most ��I7��v7]��҈jt�ۮ]��}��\|qYonc��3at[�P�ct��M�!ǣ��" ��=䑍F��4~G�͐Ii]��מS�=96��G��_J��c0�dD�_�\|>��)��\|V�MTpPn� -��x�Լ�7z�ǋ�'ESF��(��R9�c�bS� ㉇�ڟio��XO��^Fߑ��&��"�;�0 Jyv��&��2��Y,��E��ǫ�DҀ�y�dX2 �)I�k 2.1: Binary Relations - Mathematics LibreTexts Skip to main content Binary Relations November 4, 2003 1 Binary Relations The notion of a relation between two sets of objects is quite common and intuitively clear. Interpretation. Therefore, such a relationship can be viewed as a restricted set of ordered pairs. A binary relation from A to B is a subset of a Cartesian product A x B. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. :��&i�c���ANJ#2�W !jZ�� eT�{}��t�;��]�N��?��ͭ�kM[�xOӷ. 7 Binary Relations • Let A, B be any two sets. The symmetric component Iof a binary relation Ris de ned by xIyif and only if xRyand yRx. stream For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . Reflexivity. learning non-pure binary relations, and demonstrate how the robust nature of WMG can be exploited to handle such noise. Relations and Their Properties 1.1. We express a particular ordered pair, (x, y) R, where R is a binary relation, as xRy. For instance, let X denote the set of all females and Y the set of all males. We implement the above idea in CASREL, an end-to-end cascade binary tagging framework. A binary relation R from A to B, written R : A B, is a subset of the set A B. Complementary Relation Deﬁnition: Let R be the binary relation from A to B. Just as we get a number when two numbers are either added or subtracted or multiplied or are divided. (x, x) R. b. Definition (binary relation): A binary relation from a set A to a set B is a set of ordered pairs where a is an element of A and b is an element of B. We denote this by aRb. The binary operation, : A × A → A. Binary Relations (zyBooks, Chapter 5.1-5.8) Binary Relations • Recall: The Cartesian product of 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. The dual R0of a binary relation Ris de ned by xR0yif and only if yRx. Given a set A and a relation R in A, R is reflexive iff all the ordered pairs of the form are in R for every x in A. Jason Joan Yihui Formally, a binary relation R over a set X is symmetric if: ∀, ∈ (⇔). Binary relation Definition: Let A and B be two sets. The wife-husband relation R can be deﬂned from X to Y. Download Binary Relation In Mathematics With Example doc. Set alert. Basic Methods: We define the Cartesian product of two sets X and Y and use this to define binary relations on X. Abinary relation from A to B is a subset of A B . Chapter 4: Binary Operations and Relations 4.1: Binary Operations DEFINITION 1. In other words, a binary relation R … Binary relation for sets This video is about: Introduction to Binary Relation. endobj A binary relation associates elements of one set called the . Let Aand Bbe sets and deﬁne their Cartesian product to be the set of all pairwise De nition of a Relation. View 5 - Binary Relations.pdf from CS 2212 at Vanderbilt University. Let's see how to prove it. De nition of a Relation. Binary Relations A binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. Binary Relations Any set of ordered pairs defines a binary relation. Binary Relations and Preference Modeling 51 (a,b) 6∈Tor a¬Tb. 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. + : R × R → R e is called identity of * if a * e = e * a = a i.e. <> �6"��f�#��h��uL��$�,ٺ4��h�4 ߑ+�a�z%��і��)�[��WNY��4/y!��U?�Ʌ�w�-� Similarly, R 3 = R 2 R = R R R, and so on. Albert R Meyer February 21, 2011 . Examples: < can be a binary relation over ℕ, ℤ, ℝ, etc. Draw the following: 1. A binary relation over a set $$A$$ is some relation $$R$$ where, for every $$x, y \in A,$$ the statement $$xRy$$ is either true or false. A partial order is an antisymmetric preorder. The arrow diagram representation of the relation. Remark 2.1. (x, x) R. b. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of Let us consider R. The predicate Ris reﬂexive is deﬁned by R is reﬂexive in ﬁeldR. De nition: A binary relation from a set A to a set Bis a subset R A B: If (a;b) 2Rwe say ais related to bby R. Ais the domain of R, and Bis the codomain of R. If A= B, Ris called a binary relation … 9.1 Relations and Their Properties Binary Relation Deﬁnition: Let A, B be any sets. Addition, subtraction, multiplication are binary operations on Z. Introduction to Relations CSE 191, Class Note 09 Computer Sci & Eng Dept SUNY Buffalo c Xin He (University at Buffalo) CSE 191 Descrete Structures 1 / 57 Binary relation Denition: Let A and B be two sets. Binary Relations and Equivalence Relations Intuitively, a binary relation Ron a set A is a proposition such that, for every ordered pair (a;b) 2A A, one can decide if a is related to b or not. Some relations, such as being the same size as and being in the same column as, are reflexive. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Set alert. Brice Mayag (LAMSADE) Preferences as binary relations Chapter 1 7 / 16 0 denotes the empty relation while 1 denoted (prior to the 1950’s)1 the complete relation … Relations and Their Properties 1.1. relation to Paul. 9��D��-��XE��^8� Albert R Meyer . Then R R, the composition of R with itself, is always represented. VG�%�4��슁� The wife-husband relation R can be thought as a relation from X to Y.For a lady A relation which fails to be reflexive is called 2. M��LZ��l�G?v�P:�9Y\��W��c\|_�y�֤#��)>\|��o�ޣ�f{}d�H�9�vnoﺹ��k�I��0Kq)ө�[��C�O;��)�� &�K��ea��Y��IG}��t�)�m�Ú6�R�5g \|1� ܞb�W��9�o�D�He夵�fݸ��-�R�2G�\{�W� �)Ԏ A partial order is an antisymmetric preorder. The wife-husband relation R can be thought as a relation from X to Y.For a lady The predicate Ris … In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Binary relations generalize further to n-ary relations as a set of n-tuples indexed from 1 to n, and yet further to I-ary relations where Iis an arbitrary index set. Binary operations on a set are calculations that combine two elements of the set (called operands) to produce another element of the same set. For example, “less-than” on the real numbers relates every real number, a, to a real number, b, precisely when a> 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. Also, R R is sometimes denoted by R 2. Binary relations. Rsatisﬂes the trichotomy property iﬁ … Introduction to Relations 1. A binary relation R on X is aweak orderor acomplete preorderif R is complete and transitive. Let R is a relation on a set A, that is, R is a relation from a set A to itself. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . 1. A binary relation R on X is apreorderif R is re exive and transitive. A binary relation is a set of pairs of elements assumed to be drawn from an indeterminate but ﬁxed set X. We can also represent relations graphicallyor using a table lec 3T.3 . ��nj]��gw�e��"φ�0)��?]�]��O!��C�s�D�Y}?�? The relation R S is known the composition of R and S; it is sometimes denoted simply by RS. Download as PDF. Preference Relations, Social Decision Rules, Single-Peakedness, and Social Welfare Functions 1 Preference Relations 1.1 Binary Relations A preference relation is a special type of binary relation. A binary operation on a nonempty set Ais a function from A Ato A. Binary Relations De nition: A binary relation between two sets X and Y (or between the elements of X and Y) is a subset of X Y \| i.e., is a set of ordered pairs (x;y) 2X Y. A binary relation A is a poset iff A does not admit an embedding of the following finite relations: The binary relation … ��'y�ijr�r2ܫa{wե)OƌN"��1ƾɘ�@_e��=��R��\|��W�l�xQ~��"��v�R��dk��\\|�a}�>IP!z��>��(�tQ ��t>�r�8T,��]�+�Q�@\�r��X��U �ݵ6�;��0_�M8��fI�zS]��^p �a��. relation to Paul. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Theory of Relations. A symmetric relation is a type of binary relation.An example is the relation "is equal to", because if a = b is true then b = a is also true. We can also represent relations graphicallyor using a table Remark 2.1. ↔ can be a binary relation over V for any undirected graph G = (V, E). Binary Relations Any set of ordered pairs defines a binary relation. %PDF-1.4 <> The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. Finally, The binary operations associate any two elements of a set. Others, such as being in front of or Binary Relations Intuitively speaking: a binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. 5 Binary Relation Wavelet Trees (BRWT) We propose now a special wavelet tree structure to represent binary relations. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Sets are usually denoted by capital letters A B C, , ,K and elements are usually denoted by small letters a b c, , ,... . If (a,b) ∈ R, we say a is in relation R to be b. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . About this page. It consists of a BERT-based encoder module, a sub-ject tagging module, and a relation-speciﬁc object a + e = e + a = a This is only possible if e = 0 Since a + 0 = 0 + a = a ∀ a ∈ R 0 is the identity element for addition on R •A binary relation R from A to B, written (with signature) R:A↔B,is a subset of A×B. Binary Relations - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. stream About this page. View Relation.pdf from COMPUTERSC CS 60-231 at University of Windsor. We can define binary relations by giving a rule, like this: a~b if some property of a and b holds This is the general template for defining a relation. Binary relation Definition: Let A and B be two sets. For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . We consider here certain properties of binary relations. endobj @�d)��7�t�a��M�Y�F�6'{��n \| Find, read and cite all the research you need on ResearchGate This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . /Filter /FlateDecode 2. De nition 1.5. x��T˪�0��+�X��&��tצ��f��. The following de nitions for these properties are not completely standard, in that they mention only those ordered pairs https://www.tutorialspoint.com/.../discrete_mathematics_relations.htm Properties of binary relations Binary relations may themselves have properties. In Studies in Logic and the Foundations of Mathematics, 2000. In other words, a binary relation R … A relation which fails to be reflexive is called << x��[[��~ϯ�("�t� '��-�@�}�w�^&��9$wF��rҼ�#��̹~��ן��{�.G�Kz��r�8��2��Y�-��Sb�\mUow�� #�{zE�A��\|� �V��11\|LjD��oRo&n��-�A��EJ��PD��Z��Z��~�?e��EI��jbW�a��^H��{�ԜD LzJ��U�=�]J��\|CJtw��׍��.C�e��2nJ;�r]n�$\�e�K�u��G墲t��{"��4�0�z;f ��Ř&Y��s��-LN�$��n�P��/��=��W�m5�,�ð���p[T��V$��R�aFG�H�R!�xwS�� ryX�q�� p�p�/��L�#��L�H��N@�:��7�_ҧ�f�qM�[G4:��砈+2��m�T�#!��բJ�U!&'l�( ��ɢi��x�&��Eb����zAz��md�K&Y�ej6 �g��\��Q��SlwmY\uS�cά�u��p�f��5;¬_��z�5r#��G�D��?��:�r��Q$��Q We consider here certain properties of binary relations. ≡ₖ is a binary relation over ℤ for any integer k. Such classes are typically speci ed in terms of the properties required for membership. In Studies in Logic and the Foundations of Mathematics, 2000. 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Implement the above idea in CASREL, an end-to-end cascade binary tagging framework only if xRyand yRx,... 1rk In Karanjade For Rent, Chord Melukis Senja, Aasai Meenamma Athikalayilum, Military Moving Companies, Shaheen Magic 4 Combo, Modern Trade In Retailing, Blue Lagoon Cruises History, Capresso Infinity Vs Infinity Plus, James Horner Death, " /> are in R for every x in A. The set S is called the domain of the relation and the set T the codomain. Since binary relations are sets, we can apply the classical operations of set theory to them. This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . Example 1.6. We ask that binary relation mathematics example of strict weak orders is related to be restricted to be restricted to the only if a reflexive relation Every set and binary in most ��I7��v7]��҈jt�ۮ]��}��\|qYonc��3at[�P�ct��M�!ǣ��" ��=䑍F��4~G�͐Ii]��מS�=96��G��_J��c0�dD�_�\|>��)��\|V�MTpPn� -��x�Լ�7z�ǋ�'ESF��(��R9�c�bS� ㉇�ڟio��XO��^Fߑ��&��"�;�0 Jyv��&��2��Y,��E��ǫ�DҀ�y�dX2 �)I�k 2.1: Binary Relations - Mathematics LibreTexts Skip to main content Binary Relations November 4, 2003 1 Binary Relations The notion of a relation between two sets of objects is quite common and intuitively clear. Interpretation. Therefore, such a relationship can be viewed as a restricted set of ordered pairs. A binary relation from A to B is a subset of a Cartesian product A x B. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. :��&i�c���ANJ#2�W !jZ�� eT�{}��t�;��]�N��?��ͭ�kM[�xOӷ. 7 Binary Relations • Let A, B be any two sets. The symmetric component Iof a binary relation Ris de ned by xIyif and only if xRyand yRx. stream For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . Reflexivity. learning non-pure binary relations, and demonstrate how the robust nature of WMG can be exploited to handle such noise. Relations and Their Properties 1.1. We express a particular ordered pair, (x, y) R, where R is a binary relation, as xRy. For instance, let X denote the set of all females and Y the set of all males. We implement the above idea in CASREL, an end-to-end cascade binary tagging framework. A binary relation R from A to B, written R : A B, is a subset of the set A B. Complementary Relation Deﬁnition: Let R be the binary relation from A to B. Just as we get a number when two numbers are either added or subtracted or multiplied or are divided. (x, x) R. b. Definition (binary relation): A binary relation from a set A to a set B is a set of ordered pairs where a is an element of A and b is an element of B. We denote this by aRb. The binary operation, : A × A → A. Binary Relations (zyBooks, Chapter 5.1-5.8) Binary Relations • Recall: The Cartesian product of 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. The dual R0of a binary relation Ris de ned by xR0yif and only if yRx. Given a set A and a relation R in A, R is reflexive iff all the ordered pairs of the form are in R for every x in A. Jason Joan Yihui Formally, a binary relation R over a set X is symmetric if: ∀, ∈ (⇔). Binary relation Definition: Let A and B be two sets. The wife-husband relation R can be deﬂned from X to Y. Download Binary Relation In Mathematics With Example doc. Set alert. Basic Methods: We define the Cartesian product of two sets X and Y and use this to define binary relations on X. Abinary relation from A to B is a subset of A B . Chapter 4: Binary Operations and Relations 4.1: Binary Operations DEFINITION 1. In other words, a binary relation R … Binary relation for sets This video is about: Introduction to Binary Relation. endobj A binary relation associates elements of one set called the . Let Aand Bbe sets and deﬁne their Cartesian product to be the set of all pairwise De nition of a Relation. View 5 - Binary Relations.pdf from CS 2212 at Vanderbilt University. Let's see how to prove it. De nition of a Relation. Binary Relations A binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. Binary Relations Any set of ordered pairs defines a binary relation. Binary Relations and Preference Modeling 51 (a,b) 6∈Tor a¬Tb. 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. + : R × R → R e is called identity of * if a * e = e * a = a i.e. <> �6"��f�#��h��uL��$�,ٺ4��h�4 ߑ+�a�z%��і��)�[��WNY��4/y!��U?�Ʌ�w�-� Similarly, R 3 = R 2 R = R R R, and so on. Albert R Meyer February 21, 2011 . Examples: < can be a binary relation over ℕ, ℤ, ℝ, etc. Draw the following: 1. A binary relation over a set $$A$$ is some relation $$R$$ where, for every $$x, y \in A,$$ the statement $$xRy$$ is either true or false. A partial order is an antisymmetric preorder. The arrow diagram representation of the relation. Remark 2.1. (x, x) R. b. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of Let us consider R. The predicate Ris reﬂexive is deﬁned by R is reﬂexive in ﬁeldR. De nition: A binary relation from a set A to a set Bis a subset R A B: If (a;b) 2Rwe say ais related to bby R. Ais the domain of R, and Bis the codomain of R. If A= B, Ris called a binary relation … 9.1 Relations and Their Properties Binary Relation Deﬁnition: Let A, B be any sets. Addition, subtraction, multiplication are binary operations on Z. Introduction to Relations CSE 191, Class Note 09 Computer Sci & Eng Dept SUNY Buffalo c Xin He (University at Buffalo) CSE 191 Descrete Structures 1 / 57 Binary relation Denition: Let A and B be two sets. Binary Relations and Equivalence Relations Intuitively, a binary relation Ron a set A is a proposition such that, for every ordered pair (a;b) 2A A, one can decide if a is related to b or not. Some relations, such as being the same size as and being in the same column as, are reflexive. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Set alert. Brice Mayag (LAMSADE) Preferences as binary relations Chapter 1 7 / 16 0 denotes the empty relation while 1 denoted (prior to the 1950’s)1 the complete relation … Relations and Their Properties 1.1. relation to Paul. 9��D��-��XE��^8� Albert R Meyer . Then R R, the composition of R with itself, is always represented. VG�%�4��슁� The wife-husband relation R can be thought as a relation from X to Y.For a lady A relation which fails to be reflexive is called 2. M��LZ��l�G?v�P:�9Y\��W��c\|_�y�֤#��)>\|��o�ޣ�f{}d�H�9�vnoﺹ��k�I��0Kq)ө�[��C�O;��)�� &�K��ea��Y��IG}��t�)�m�Ú6�R�5g \|1� ܞb�W��9�o�D�He夵�fݸ��-�R�2G�\{�W� �)Ԏ A partial order is an antisymmetric preorder. The wife-husband relation R can be thought as a relation from X to Y.For a lady The predicate Ris … In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Binary relations generalize further to n-ary relations as a set of n-tuples indexed from 1 to n, and yet further to I-ary relations where Iis an arbitrary index set. Binary operations on a set are calculations that combine two elements of the set (called operands) to produce another element of the same set. For example, “less-than” on the real numbers relates every real number, a, to a real number, b, precisely when a> 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. Also, R R is sometimes denoted by R 2. Binary relations. Rsatisﬂes the trichotomy property iﬁ … Introduction to Relations 1. A binary relation R on X is aweak orderor acomplete preorderif R is complete and transitive. Let R is a relation on a set A, that is, R is a relation from a set A to itself. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . 1. A binary relation R on X is apreorderif R is re exive and transitive. A binary relation is a set of pairs of elements assumed to be drawn from an indeterminate but ﬁxed set X. We can also represent relations graphicallyor using a table lec 3T.3 . ��nj]��gw�e��"φ�0)��?]�]��O!��C�s�D�Y}?�? The relation R S is known the composition of R and S; it is sometimes denoted simply by RS. Download as PDF. Preference Relations, Social Decision Rules, Single-Peakedness, and Social Welfare Functions 1 Preference Relations 1.1 Binary Relations A preference relation is a special type of binary relation. A binary operation on a nonempty set Ais a function from A Ato A. Binary Relations De nition: A binary relation between two sets X and Y (or between the elements of X and Y) is a subset of X Y \| i.e., is a set of ordered pairs (x;y) 2X Y. A binary relation A is a poset iff A does not admit an embedding of the following finite relations: The binary relation … ��'y�ijr�r2ܫa{wե)OƌN"��1ƾɘ�@_e��=��R��\|��W�l�xQ~��"��v�R��dk��\\|�a}�>IP!z��>��(�tQ ��t>�r�8T,��]�+�Q�@\�r��X��U �ݵ6�;��0_�M8��fI�zS]��^p �a��. relation to Paul. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Theory of Relations. A symmetric relation is a type of binary relation.An example is the relation "is equal to", because if a = b is true then b = a is also true. We can also represent relations graphicallyor using a table Remark 2.1. ↔ can be a binary relation over V for any undirected graph G = (V, E). Binary Relations Any set of ordered pairs defines a binary relation. %PDF-1.4 <> The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. Finally, The binary operations associate any two elements of a set. Others, such as being in front of or Binary Relations Intuitively speaking: a binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. 5 Binary Relation Wavelet Trees (BRWT) We propose now a special wavelet tree structure to represent binary relations. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Sets are usually denoted by capital letters A B C, , ,K and elements are usually denoted by small letters a b c, , ,... . If (a,b) ∈ R, we say a is in relation R to be b. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . About this page. It consists of a BERT-based encoder module, a sub-ject tagging module, and a relation-speciﬁc object a + e = e + a = a This is only possible if e = 0 Since a + 0 = 0 + a = a ∀ a ∈ R 0 is the identity element for addition on R •A binary relation R from A to B, written (with signature) R:A↔B,is a subset of A×B. Binary Relations - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. stream About this page. View Relation.pdf from COMPUTERSC CS 60-231 at University of Windsor. We can define binary relations by giving a rule, like this: a~b if some property of a and b holds This is the general template for defining a relation. Binary relation Definition: Let A and B be two sets. For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . We consider here certain properties of binary relations. endobj @�d)��7�t�a��M�Y�F�6'{��n \| Find, read and cite all the research you need on ResearchGate This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . /Filter /FlateDecode 2. De nition 1.5. x��T˪�0��+�X��&��tצ��f��. The following de nitions for these properties are not completely standard, in that they mention only those ordered pairs https://www.tutorialspoint.com/.../discrete_mathematics_relations.htm Properties of binary relations Binary relations may themselves have properties. In Studies in Logic and the Foundations of Mathematics, 2000. In other words, a binary relation R … A relation which fails to be reflexive is called << x��[[��~ϯ�("�t� '��-�@�}�w�^&��9$wF��rҼ�#��̹~��ן��{�.G�Kz��r�8��2��Y�-��Sb�\mUow�� #�{zE�A��\|� �V��11\|LjD��oRo&n��-�A��EJ��PD��Z��Z��~�?e��EI��jbW�a��^H��{�ԜD LzJ��U�=�]J��\|CJtw��׍��.C�e��2nJ;�r]n�$\�e�K�u��G墲t��{"��4�0�z;f ��Ř&Y��s��-LN�$��n�P��/��=��W�m5�,�ð���p[T��V$��R�aFG�H�R!�xwS�� ryX�q�� p�p�/��L�#��L�H��N@�:��7�_ҧ�f�qM�[G4:��砈+2��m�T�#!��բJ�U!&'l�( ��ɢi��x�&��Eb����zAz��md�K&Y�ej6 �g��\��Q��SlwmY\uS�cά�u��p�f��5;¬_��z�5r#��G�D��?��:�r��Q$��Q We consider here certain properties of binary relations. ≡ₖ is a binary relation over ℤ for any integer k. Such classes are typically speci ed in terms of the properties required for membership. In Studies in Logic and the Foundations of Mathematics, 2000. 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Implement the above idea in CASREL, an end-to-end cascade binary tagging framework only if xRyand yRx,... 1rk In Karanjade For Rent, Chord Melukis Senja, Aasai Meenamma Athikalayilum, Military Moving Companies, Shaheen Magic 4 Combo, Modern Trade In Retailing, Blue Lagoon Cruises History, Capresso Infinity Vs Infinity Plus, James Horner Death, " /> are in R for every x in A. The set S is called the domain of the relation and the set T the codomain. Since binary relations are sets, we can apply the classical operations of set theory to them. This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . Example 1.6. We ask that binary relation mathematics example of strict weak orders is related to be restricted to be restricted to the only if a reflexive relation Every set and binary in most ��I7��v7]��҈jt�ۮ]��}��\|qYonc��3at[�P�ct��M�!ǣ��" ��=䑍F��4~G�͐Ii]��מS�=96��G��_J��c0�dD�_�\|>��)��\|V�MTpPn� -��x�Լ�7z�ǋ�'ESF��(��R9�c�bS� ㉇�ڟio��XO��^Fߑ��&��"�;�0 Jyv��&��2��Y,��E��ǫ�DҀ�y�dX2 �)I�k 2.1: Binary Relations - Mathematics LibreTexts Skip to main content Binary Relations November 4, 2003 1 Binary Relations The notion of a relation between two sets of objects is quite common and intuitively clear. Interpretation. Therefore, such a relationship can be viewed as a restricted set of ordered pairs. A binary relation from A to B is a subset of a Cartesian product A x B. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. :��&i�c���ANJ#2�W !jZ�� eT�{}��t�;��]�N��?��ͭ�kM[�xOӷ. 7 Binary Relations • Let A, B be any two sets. The symmetric component Iof a binary relation Ris de ned by xIyif and only if xRyand yRx. stream For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . Reflexivity. learning non-pure binary relations, and demonstrate how the robust nature of WMG can be exploited to handle such noise. Relations and Their Properties 1.1. We express a particular ordered pair, (x, y) R, where R is a binary relation, as xRy. For instance, let X denote the set of all females and Y the set of all males. We implement the above idea in CASREL, an end-to-end cascade binary tagging framework. A binary relation R from A to B, written R : A B, is a subset of the set A B. Complementary Relation Deﬁnition: Let R be the binary relation from A to B. Just as we get a number when two numbers are either added or subtracted or multiplied or are divided. (x, x) R. b. Definition (binary relation): A binary relation from a set A to a set B is a set of ordered pairs where a is an element of A and b is an element of B. We denote this by aRb. The binary operation, : A × A → A. Binary Relations (zyBooks, Chapter 5.1-5.8) Binary Relations • Recall: The Cartesian product of 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. The dual R0of a binary relation Ris de ned by xR0yif and only if yRx. Given a set A and a relation R in A, R is reflexive iff all the ordered pairs of the form are in R for every x in A. Jason Joan Yihui Formally, a binary relation R over a set X is symmetric if: ∀, ∈ (⇔). Binary relation Definition: Let A and B be two sets. The wife-husband relation R can be deﬂned from X to Y. Download Binary Relation In Mathematics With Example doc. Set alert. Basic Methods: We define the Cartesian product of two sets X and Y and use this to define binary relations on X. Abinary relation from A to B is a subset of A B . Chapter 4: Binary Operations and Relations 4.1: Binary Operations DEFINITION 1. In other words, a binary relation R … Binary relation for sets This video is about: Introduction to Binary Relation. endobj A binary relation associates elements of one set called the . Let Aand Bbe sets and deﬁne their Cartesian product to be the set of all pairwise De nition of a Relation. View 5 - Binary Relations.pdf from CS 2212 at Vanderbilt University. Let's see how to prove it. De nition of a Relation. Binary Relations A binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. Binary Relations Any set of ordered pairs defines a binary relation. Binary Relations and Preference Modeling 51 (a,b) 6∈Tor a¬Tb. 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. + : R × R → R e is called identity of * if a * e = e * a = a i.e. <> �6"��f�#��h��uL��$�,ٺ4��h�4 ߑ+�a�z%��і��)�[��WNY��4/y!��U?�Ʌ�w�-� Similarly, R 3 = R 2 R = R R R, and so on. Albert R Meyer February 21, 2011 . Examples: < can be a binary relation over ℕ, ℤ, ℝ, etc. Draw the following: 1. A binary relation over a set $$A$$ is some relation $$R$$ where, for every $$x, y \in A,$$ the statement $$xRy$$ is either true or false. A partial order is an antisymmetric preorder. The arrow diagram representation of the relation. Remark 2.1. (x, x) R. b. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of Let us consider R. The predicate Ris reﬂexive is deﬁned by R is reﬂexive in ﬁeldR. De nition: A binary relation from a set A to a set Bis a subset R A B: If (a;b) 2Rwe say ais related to bby R. Ais the domain of R, and Bis the codomain of R. If A= B, Ris called a binary relation … 9.1 Relations and Their Properties Binary Relation Deﬁnition: Let A, B be any sets. Addition, subtraction, multiplication are binary operations on Z. Introduction to Relations CSE 191, Class Note 09 Computer Sci & Eng Dept SUNY Buffalo c Xin He (University at Buffalo) CSE 191 Descrete Structures 1 / 57 Binary relation Denition: Let A and B be two sets. Binary Relations and Equivalence Relations Intuitively, a binary relation Ron a set A is a proposition such that, for every ordered pair (a;b) 2A A, one can decide if a is related to b or not. Some relations, such as being the same size as and being in the same column as, are reflexive. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Set alert. Brice Mayag (LAMSADE) Preferences as binary relations Chapter 1 7 / 16 0 denotes the empty relation while 1 denoted (prior to the 1950’s)1 the complete relation … Relations and Their Properties 1.1. relation to Paul. 9��D��-��XE��^8� Albert R Meyer . Then R R, the composition of R with itself, is always represented. VG�%�4��슁� The wife-husband relation R can be thought as a relation from X to Y.For a lady A relation which fails to be reflexive is called 2. M��LZ��l�G?v�P:�9Y\��W��c\|_�y�֤#��)>\|��o�ޣ�f{}d�H�9�vnoﺹ��k�I��0Kq)ө�[��C�O;��)�� &�K��ea��Y��IG}��t�)�m�Ú6�R�5g \|1� ܞb�W��9�o�D�He夵�fݸ��-�R�2G�\{�W� �)Ԏ A partial order is an antisymmetric preorder. The wife-husband relation R can be thought as a relation from X to Y.For a lady The predicate Ris … In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Binary relations generalize further to n-ary relations as a set of n-tuples indexed from 1 to n, and yet further to I-ary relations where Iis an arbitrary index set. Binary operations on a set are calculations that combine two elements of the set (called operands) to produce another element of the same set. For example, “less-than” on the real numbers relates every real number, a, to a real number, b, precisely when a> 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. Also, R R is sometimes denoted by R 2. Binary relations. Rsatisﬂes the trichotomy property iﬁ … Introduction to Relations 1. A binary relation R on X is aweak orderor acomplete preorderif R is complete and transitive. Let R is a relation on a set A, that is, R is a relation from a set A to itself. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . 1. A binary relation R on X is apreorderif R is re exive and transitive. A binary relation is a set of pairs of elements assumed to be drawn from an indeterminate but ﬁxed set X. We can also represent relations graphicallyor using a table lec 3T.3 . ��nj]��gw�e��"φ�0)��?]�]��O!��C�s�D�Y}?�? The relation R S is known the composition of R and S; it is sometimes denoted simply by RS. Download as PDF. Preference Relations, Social Decision Rules, Single-Peakedness, and Social Welfare Functions 1 Preference Relations 1.1 Binary Relations A preference relation is a special type of binary relation. A binary operation on a nonempty set Ais a function from A Ato A. Binary Relations De nition: A binary relation between two sets X and Y (or between the elements of X and Y) is a subset of X Y \| i.e., is a set of ordered pairs (x;y) 2X Y. A binary relation A is a poset iff A does not admit an embedding of the following finite relations: The binary relation … ��'y�ijr�r2ܫa{wե)OƌN"��1ƾɘ�@_e��=��R��\|��W�l�xQ~��"��v�R��dk��\\|�a}�>IP!z��>��(�tQ ��t>�r�8T,��]�+�Q�@\�r��X��U �ݵ6�;��0_�M8��fI�zS]��^p �a��. relation to Paul. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Theory of Relations. A symmetric relation is a type of binary relation.An example is the relation "is equal to", because if a = b is true then b = a is also true. We can also represent relations graphicallyor using a table Remark 2.1. ↔ can be a binary relation over V for any undirected graph G = (V, E). Binary Relations Any set of ordered pairs defines a binary relation. %PDF-1.4 <> The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. Finally, The binary operations associate any two elements of a set. Others, such as being in front of or Binary Relations Intuitively speaking: a binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. 5 Binary Relation Wavelet Trees (BRWT) We propose now a special wavelet tree structure to represent binary relations. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Sets are usually denoted by capital letters A B C, , ,K and elements are usually denoted by small letters a b c, , ,... . If (a,b) ∈ R, we say a is in relation R to be b. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . About this page. It consists of a BERT-based encoder module, a sub-ject tagging module, and a relation-speciﬁc object a + e = e + a = a This is only possible if e = 0 Since a + 0 = 0 + a = a ∀ a ∈ R 0 is the identity element for addition on R •A binary relation R from A to B, written (with signature) R:A↔B,is a subset of A×B. Binary Relations - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. stream About this page. View Relation.pdf from COMPUTERSC CS 60-231 at University of Windsor. We can define binary relations by giving a rule, like this: a~b if some property of a and b holds This is the general template for defining a relation. Binary relation Definition: Let A and B be two sets. For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . We consider here certain properties of binary relations. endobj @�d)��7�t�a��M�Y�F�6'{��n \| Find, read and cite all the research you need on ResearchGate This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . /Filter /FlateDecode 2. De nition 1.5. x��T˪�0��+�X��&��tצ��f��. The following de nitions for these properties are not completely standard, in that they mention only those ordered pairs https://www.tutorialspoint.com/.../discrete_mathematics_relations.htm Properties of binary relations Binary relations may themselves have properties. In Studies in Logic and the Foundations of Mathematics, 2000. 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Implement the above idea in CASREL, an end-to-end cascade binary tagging framework only if xRyand yRx,... 1rk In Karanjade For Rent, Chord Melukis Senja, Aasai Meenamma Athikalayilum, Military Moving Companies, Shaheen Magic 4 Combo, Modern Trade In Retailing, Blue Lagoon Cruises History, Capresso Infinity Vs Infinity Plus, James Horner Death, " /> # binary relation pdf Binary Relations 6 Exercise: Given set A = {r, o, t, p, c} and set B = {discrete, math, proof, proposition}, and corresponding relation R ⊆ A × B such that the tuple (letter, word) is in the relation if that letter occurs somewhere in the word. Knowledge Hypergraphs: Prediction Beyond Binary Relations Bahare Fatemi1; 2y, Perouz Taslakian , David Vazquez2 and David Poole1 1University of British Columbia 2Element AI fbfatemi, [email protected], fperouz,[email protected], Abstract Knowledge graphs store facts using relations … Download as PDF. %�� CS 2212 Discrete Structures 5. 511 CS340-Discrete Structures Section 4.1 Page 1 Section 4.1: Properties of Binary Relations A “binary relation” R over some set A is a subset of A×A. endstream Dynamic binary relations k 2 -tree a b s t r a c t introduce ofa binarydynamic relationsdata ⊆structure × .the compact representation R A B The data structure is a dynamic variant of the k2-tree, a static compact representation that takes advantage of clustering in the binary relation to achieve compression. Reflexivity. 4.4 Binary Relations Binary relations deﬁne relations between two objects. Examples: < can be a binary relation over ℕ, ℤ, ℝ, etc. 6.042 6.003 6.012 6.004 . +\|!��T �MP�o)�K �[��N?��xr_\|��e��t�J��CX��L\�!��H�2ű��b��H=��_n�K+��[��:� �mS�׮x�n��R��x�o�5,��W�>^��-tv5VkX�>$�4�˴�B��jp_6\�fw�ˈ�R�-��u'#2��}�d�4��Υx� �t&[�� 5.2.1 Characterization of posets, chains, trees. ↔ can be a binary relation over V for any undirected graph G = (V, E). A binary relation from A to B is a subset of a Cartesian product A x B. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. The binary operations on a non-empty set A are functions from A × A to A. If R is a relation between X and Y (i.e., if R X Y), we often write xRy instead of (x;y) 2R. Others, such as being in front of or A binary relation A is a poset iff A does not admit an embedding of the following finite relations: The binary relation … M.�G�ٔ�e��!��"ix61��i�ţ��}S\pX%_�hr��u�a�s��X��v�iI�ZWT�� 5 0 obj Consider the binary relation ~defined over the set ℤ: a~b if a+bis even Some examples: 0~4 1~9 2~6 5~5 Turns out, this is an equivalence relation! Similarly, the subset relation relates a set, A, to another set, B, precisely when A B. A binary relation R on X is atotal orderor alinear orderif R is complete, antisymmetric and transitive. Request PDF \| On Jan 1, 2008, Violeta Leoreanu Fotea and others published n-hypergroups and binary relations. Binary relations generalize further to n-ary relations as a set of n-tuples indexed from 1 to n, and yet further to I-ary relations where Iis an arbitrary index set. Since binary relations are sets, we can apply the classical operations of set theory to them. %PDF-1.5 In Section 5 we present our main result. Week 4-5: Binary Relations 1 Binary Relations The concept of relation is common in daily life and seems intuitively clear. Binary Relations and Preference Modeling 51 (a,b) 6∈Tor a¬Tb. Types of Relations • Let R be a binary relation on A: – R is reflexive if xRx for every x in A – R is irreflexive if xRx for every x in A – R is symmetric if xRy implies yRx for every x,y in A – R is antisymmetric if xRy and yRx together imply x=y for every x,y in A – R is transitive if xRy and yRz imply xRz for every x,y,z in A The resultant of the two are in the same set. Introduction to Relations 1. Let X be the set of all living human females and Y the set of all living human males. Given a set A and a relation R in A, R is reflexive iff all the ordered pairs of the form are in R for every x in A. The set S is called the domain of the relation and the set T the codomain. Since binary relations are sets, we can apply the classical operations of set theory to them. This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . Example 1.6. We ask that binary relation mathematics example of strict weak orders is related to be restricted to be restricted to the only if a reflexive relation Every set and binary in most ��I7��v7]��҈jt�ۮ]��}��\|qYonc��3at[�P�ct��M�!ǣ��" ��=䑍F��4~G�͐Ii]��מS�=96��G��_J��c0�dD�_�\|>��)��\|V�MTpPn� -��x�Լ�7z�ǋ�'ESF��(��R9�c�bS� ㉇�ڟio��XO��^Fߑ��&��"�;�0 Jyv��&��2��Y,��E��ǫ�DҀ�y�dX2 �)I�k 2.1: Binary Relations - Mathematics LibreTexts Skip to main content Binary Relations November 4, 2003 1 Binary Relations The notion of a relation between two sets of objects is quite common and intuitively clear. Interpretation. Therefore, such a relationship can be viewed as a restricted set of ordered pairs. A binary relation from A to B is a subset of a Cartesian product A x B. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. :��&i�c���ANJ#2�W !jZ�� eT�{}��t�;��]�N��?��ͭ�kM[�xOӷ. 7 Binary Relations • Let A, B be any two sets. The symmetric component Iof a binary relation Ris de ned by xIyif and only if xRyand yRx. stream For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . Reflexivity. learning non-pure binary relations, and demonstrate how the robust nature of WMG can be exploited to handle such noise. Relations and Their Properties 1.1. We express a particular ordered pair, (x, y) R, where R is a binary relation, as xRy. For instance, let X denote the set of all females and Y the set of all males. We implement the above idea in CASREL, an end-to-end cascade binary tagging framework. A binary relation R from A to B, written R : A B, is a subset of the set A B. Complementary Relation Deﬁnition: Let R be the binary relation from A to B. Just as we get a number when two numbers are either added or subtracted or multiplied or are divided. (x, x) R. b. Definition (binary relation): A binary relation from a set A to a set B is a set of ordered pairs where a is an element of A and b is an element of B. We denote this by aRb. The binary operation, : A × A → A. Binary Relations (zyBooks, Chapter 5.1-5.8) Binary Relations • Recall: The Cartesian product of 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. The dual R0of a binary relation Ris de ned by xR0yif and only if yRx. Given a set A and a relation R in A, R is reflexive iff all the ordered pairs of the form are in R for every x in A. Jason Joan Yihui Formally, a binary relation R over a set X is symmetric if: ∀, ∈ (⇔). Binary relation Definition: Let A and B be two sets. The wife-husband relation R can be deﬂned from X to Y. Download Binary Relation In Mathematics With Example doc. Set alert. Basic Methods: We define the Cartesian product of two sets X and Y and use this to define binary relations on X. Abinary relation from A to B is a subset of A B . Chapter 4: Binary Operations and Relations 4.1: Binary Operations DEFINITION 1. In other words, a binary relation R … Binary relation for sets This video is about: Introduction to Binary Relation. endobj A binary relation associates elements of one set called the . Let Aand Bbe sets and deﬁne their Cartesian product to be the set of all pairwise De nition of a Relation. View 5 - Binary Relations.pdf from CS 2212 at Vanderbilt University. Let's see how to prove it. De nition of a Relation. Binary Relations A binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. Binary Relations Any set of ordered pairs defines a binary relation. Binary Relations and Preference Modeling 51 (a,b) 6∈Tor a¬Tb. 1.1.2 Preorders A preorder or ordered set is a pair (X,≤) where Xis a set and ≤ is a reﬂexive transitive binary relation on X. + : R × R → R e is called identity of * if a * e = e * a = a i.e. <> �6"��f�#��h��uL��$�,ٺ4��h�4 ߑ+�a�z%��і��)�[��WNY��4/y!��U?�Ʌ�w�-� Similarly, R 3 = R 2 R = R R R, and so on. Albert R Meyer February 21, 2011 . Examples: < can be a binary relation over ℕ, ℤ, ℝ, etc. Draw the following: 1. A binary relation over a set $$A$$ is some relation $$R$$ where, for every $$x, y \in A,$$ the statement $$xRy$$ is either true or false. A partial order is an antisymmetric preorder. The arrow diagram representation of the relation. Remark 2.1. (x, x) R. b. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of Let us consider R. The predicate Ris reﬂexive is deﬁned by R is reﬂexive in ﬁeldR. De nition: A binary relation from a set A to a set Bis a subset R A B: If (a;b) 2Rwe say ais related to bby R. Ais the domain of R, and Bis the codomain of R. If A= B, Ris called a binary relation … 9.1 Relations and Their Properties Binary Relation Deﬁnition: Let A, B be any sets. Addition, subtraction, multiplication are binary operations on Z. Introduction to Relations CSE 191, Class Note 09 Computer Sci & Eng Dept SUNY Buffalo c Xin He (University at Buffalo) CSE 191 Descrete Structures 1 / 57 Binary relation Denition: Let A and B be two sets. Binary Relations and Equivalence Relations Intuitively, a binary relation Ron a set A is a proposition such that, for every ordered pair (a;b) 2A A, one can decide if a is related to b or not. Some relations, such as being the same size as and being in the same column as, are reflexive. Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets.A binary relation from A to B is a subset of A ×B. Set alert. Brice Mayag (LAMSADE) Preferences as binary relations Chapter 1 7 / 16 0 denotes the empty relation while 1 denoted (prior to the 1950’s)1 the complete relation … Relations and Their Properties 1.1. relation to Paul. 9��D��-��XE��^8� Albert R Meyer . Then R R, the composition of R with itself, is always represented. VG�%�4��슁� The wife-husband relation R can be thought as a relation from X to Y.For a lady A relation which fails to be reflexive is called 2. M��LZ��l�G?v�P:�9Y\��W��c\|_�y�֤#��)>\|��o�ޣ�f{}d�H�9�vnoﺹ��k�I��0Kq)ө�[��C�O;��)�� &�K��ea��Y��IG}��t�)�m�Ú6�R�5g \|1� ܞb�W��9�o�D�He夵�fݸ��-�R�2G�\{�W� �)Ԏ A partial order is an antisymmetric preorder. The wife-husband relation R can be thought as a relation from X to Y.For a lady The predicate Ris … In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Binary relations generalize further to n-ary relations as a set of n-tuples indexed from 1 to n, and yet further to I-ary relations where Iis an arbitrary index set. Binary operations on a set are calculations that combine two elements of the set (called operands) to produce another element of the same set. For example, “less-than” on the real numbers relates every real number, a, to a real number, b, precisely when a> 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. Also, R R is sometimes denoted by R 2. Binary relations. Rsatisﬂes the trichotomy property iﬁ … Introduction to Relations 1. A binary relation R on X is aweak orderor acomplete preorderif R is complete and transitive. Let R is a relation on a set A, that is, R is a relation from a set A to itself. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . 1. A binary relation R on X is apreorderif R is re exive and transitive. A binary relation is a set of pairs of elements assumed to be drawn from an indeterminate but ﬁxed set X. We can also represent relations graphicallyor using a table lec 3T.3 . ��nj]��gw�e��"φ�0)��?]�]��O!��C�s�D�Y}?�? The relation R S is known the composition of R and S; it is sometimes denoted simply by RS. Download as PDF. Preference Relations, Social Decision Rules, Single-Peakedness, and Social Welfare Functions 1 Preference Relations 1.1 Binary Relations A preference relation is a special type of binary relation. A binary operation on a nonempty set Ais a function from A Ato A. Binary Relations De nition: A binary relation between two sets X and Y (or between the elements of X and Y) is a subset of X Y \| i.e., is a set of ordered pairs (x;y) 2X Y. A binary relation A is a poset iff A does not admit an embedding of the following finite relations: The binary relation … ��'y�ijr�r2ܫa{wե)OƌN"��1ƾɘ�@_e��=��R��\|��W�l�xQ~��"��v�R��dk��\\|�a}�>IP!z��>��(�tQ ��t>�r�8T,��]�+�Q�@\�r��X��U �ݵ6�;��0_�M8��fI�zS]��^p �a��. relation to Paul. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Theory of Relations. A symmetric relation is a type of binary relation.An example is the relation "is equal to", because if a = b is true then b = a is also true. We can also represent relations graphicallyor using a table Remark 2.1. ↔ can be a binary relation over V for any undirected graph G = (V, E). Binary Relations Any set of ordered pairs defines a binary relation. %PDF-1.4 <> The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. Finally, The binary operations associate any two elements of a set. Others, such as being in front of or Binary Relations Intuitively speaking: a binary relation over a set A is some relation R where, for every x, y ∈ A, the statement xRy is either true or false. 5 Binary Relation Wavelet Trees (BRWT) We propose now a special wavelet tree structure to represent binary relations. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. If a R b, we say a is related to b by R. Sets are usually denoted by capital letters A B C, , ,K and elements are usually denoted by small letters a b c, , ,... . If (a,b) ∈ R, we say a is in relation R to be b. Except when explicitly mentioned otherwise, we will suppose in all what follows that the set Ais ﬁnite . About this page. It consists of a BERT-based encoder module, a sub-ject tagging module, and a relation-speciﬁc object a + e = e + a = a This is only possible if e = 0 Since a + 0 = 0 + a = a ∀ a ∈ R 0 is the identity element for addition on R •A binary relation R from A to B, written (with signature) R:A↔B,is a subset of A×B. Binary Relations - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The logical operations treat a binary relation purely as a set, ignoring the nature of its ele-ments. 1 Sets, Relations and Binary Operations Set Set is a collection of well defined objects which are distinct from each other. stream About this page. View Relation.pdf from COMPUTERSC CS 60-231 at University of Windsor. We can define binary relations by giving a rule, like this: a~b if some property of a and b holds This is the general template for defining a relation. Binary relation Definition: Let A and B be two sets. For example, if a relation R is such that everything stands in the relation R to itself, R is said to be reflexive . We consider here certain properties of binary relations. endobj @�d)��7�t�a��M�Y�F�6'{��n \| Find, read and cite all the research you need on ResearchGate This wavelet tree contains two bitmaps per level at each node v, Bvl and Bvr . /Filter /FlateDecode 2. De nition 1.5. x��T˪�0��+�X��&��tצ��f��. The following de nitions for these properties are not completely standard, in that they mention only those ordered pairs https://www.tutorialspoint.com/.../discrete_mathematics_relations.htm Properties of binary relations Binary relations may themselves have properties. In Studies in Logic and the Foundations of Mathematics, 2000. In other words, a binary relation R … A relation which fails to be reflexive is called << x��[[��~ϯ�("�t� '��-�@�}�w�^&��9$wF��rҼ�#��̹~��ן��{�.G�Kz��r�8��2��Y�-��Sb�\mUow�� #�{zE�A��\|� �V��11\|LjD��oRo&n��-�A��EJ��PD��Z��Z��~�?e��EI��jbW�a��^H��{�ԜD LzJ��U�=�]J��\|CJtw��׍��.C�e��2nJ;�r]n�$\�e�K�u��G墲t��{"��4�0�z;f ��Ř&Y��s��-LN�$��n�P��/��=��W�m5�,�ð���p[T��V$��R�aFG�H�R!�xwS�� ryX�q�� p�p�/��L�#��L�H��N@�:��7�_ҧ�f�qM�[G4:��砈+2��m�T�#!��բJ�U!&'l�( ��ɢi��x�&��Eb����zAz��md�K&Y�ej6 �g��\��Q��SlwmY\uS�cά�u��p�f��5;¬_��z�5r#��G�D��?��:�r��Q`\$��Q We consider here certain properties of binary relations. ≡ₖ is a binary relation over ℤ for any integer k. Such classes are typically speci ed in terms of the properties required for membership. In Studies in Logic and the Foundations of Mathematics, 2000. Properties Properties of a binary relation R on a set X: a. reflexive: if for every x X, xRx holds, i.e. If a is an element of a set A, then we write a A∈ and say a belongs to A or a is in A or a is a member of A.If a does not belongs to A, we write 3 0 obj Interpretation. Knowledge Hypergraphs: Prediction Beyond Binary Relations Bahare Fatemi1; 2y, Perouz Taslakian , David Vazquez2 and David Poole1 1University of British Columbia 2Element AI fbfatemi, [email protected], fperouz,[email protected], Abstract Knowledge graphs store facts using relations … All these properties apply only to relations in (on) a (single) set, i.e., in A ¥ A for example. Let us consider R. the predicate Ris reﬂexive is deﬁned by R 2 R = R! Size as and being in the same size as and being in the same as. Ignoring the nature of its ele-ments front of or Interpretation themselves have.! Life and seems intuitively clear nature of its ele-ments such as being in front of or.. 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Implement the above idea in CASREL, an end-to-end cascade binary tagging framework only if xRyand yRx,... 0 Comentários	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8750322461128235, "perplexity": 1628.3164884684406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150067.51/warc/CC-MAIN-20210723210216-20210724000216-00579.warc.gz"}
http://oni.bungie.org/forum/viewtopic.php?id=2744	# Oni Central Forum A forum for the Oni community You are not logged in. ## #1 14/6/14 9:10 loveoni12 Member Registered: 14/6/14 ### Ae?nstal 2 does not install!! it does not install the anniversary edition friends. Error: Unable to access jarfile bin/AEInstaller2.jar Offline ## #2 14/6/14 9:41 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Hi there. In your Oni installation, do you have the file AE\AEInstaller\updater_output.log? If so, can you post its contents here? byproducts are fine, but where's the beef? Offline ## #3 14/6/14 9:52 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! none. You send them to me. Offline ## #4 14/6/14 10:06 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! Did you send the file? Offline ## #5 14/6/14 10:15 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! That's a log file, so it won't help if I send it to you You need to get the AEI2Updater to run. It's at AE\AEInstaller\AEInstaller2Updater.jar. You can try double-clicking it, but if that doesn't work, you need to open the Command Prompt in Windows and type "java -jar C:\[path to Oni]\AE\AEInstaller\AEInstaller2Updater.jar" and then tell us what is printed as output in the window. byproducts are fine, but where's the beef? Offline ## #6 14/6/14 10:22 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! Here you can send me. Offline ## #7 14/6/14 10:27 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Sorry, but I don't think you understand -- I can't send you anything. You have to get the AE Installer to run on your computer, in order to be able to play AE Oni. To do that, you need to either: 1. Double-click on the AEInstaller2Updater.jar. 2. Type "java -jar C:\[path to Oni]\AE\AEInstaller\AEInstaller2Updater.jar" in the Command Prompt window. If neither of those work: 3. Type "cd C:\[path to Oni]\AE\AEInstaller; jre\bin\java -jar AEInstaller2Updater.jar" and tell us the output in the window. byproducts are fine, but where's the beef? Offline ## #8 14/6/14 10:28 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! Thank you.I'm trying it. Let me open my jar file with WinRAR or slide? Offline ## #9 14/6/14 10:34 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Hmm, you don't want to open it with those programs. I think you'll need to use option 3 above (enter that in the Command Prompt window). byproducts are fine, but where's the beef? Offline ## #10 14/6/14 10:41 loveoni12 Member Registered: 14/6/14 Thank you. Offline ## #11 14/6/14 10:50 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! Unfortunately we can not be trimmed.AEInstaller2Updater.jar does not open Offline ## #12 14/6/14 10:58 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Did you try the command I gave in option 3? Did the Command Prompt give you an error message? byproducts are fine, but where's the beef? Offline ## #13 14/6/14 11:06 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! C: \ Users \ ahmetenes> Local Disk (C > Program Files) Oni) AE) of aeınstal) aeınstaller2 . jar 'Local' internal or external command, operable program or batch file as unknown. Gives such an error. Offline ## #14 14/6/14 11:11 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! yes. give me an error message. Offline ## #15 14/6/14 11:19 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Hmm, I'm not sure what that error is referring to. If you have Oni installed at C:\Program Files\Oni, then ``cd C:\Program Files\Oni\AE\AEInstaller; jre\bin\java -jar AEInstaller2Updater.jar`` should work. You can directly copy-paste that text into the Command Prompt window. Do you have the folder C:\Program Files\Oni\AE\AEInstaller\jre\? byproducts are fine, but where's the beef? Offline ## #16 14/6/14 11:31 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! hey iritscen something came to my mind. Could you send me the installed AE files? Offline ## #17 14/6/14 11:34 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! YES.gives the same mistake again. Offline ## #18 14/6/14 11:35 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! C: \ Program Files \ Oni \ AE \ AE Installer \ jre \? There are in this folder. Offline ## #19 14/6/14 11:41 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Sorry, I made a syntax mistake (I'm on a Mac, with a different command line). The command should be: ``cd "C:\Program Files\Oni\AE\AEInstaller" & jre\bin\java -jar AEInstaller2Updater.jar`` Let me know how that works. byproducts are fine, but where's the beef? Offline ## #20 14/6/14 11:43 loveoni12 Member Registered: 14/6/14 Yes, now what? Offline ## #21 14/6/14 11:47 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! Well, that command should have opened a small window that performed an initial installation and then proceeded to open the AE Installer. If that didn't happen, did you get an error on the command line? Please note that I changed the command shortly after posting it, so you might want to try copy-pasting the command again. I'm not accustomed to people posting so rapidly on the forum. P.S.: The reason I can't send you the AE's installed files is: 1. They're large. 2. It's illegal. The data needs to be based on your copy of Oni. 3. You wouldn't be able to install mods. You need the AE Installer to run in order to be able to choose what mods to install. P.P.S.: We could try sending you the AE Installer itself, if it doesn't get installed by the AE2InstallerUpdater, but first let's find out why the command I gave you is not working. byproducts are fine, but where's the beef? Offline ## #22 14/6/14 11:48 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! Something came to my mind, no net framework on my computer. Offline ## #23 14/6/14 11:51 Iritscen Moderator From: NC, USA Registered: 22/10/07 ### Re: Ae?nstal 2 does not install!! I see; that will be an issue if the AE Installer tries to run. But it shouldn't prevent you from running the Installer Updater. After that, though, you should make sure to install .NET 2.0 or higher. byproducts are fine, but where's the beef? Offline ## #24 14/6/14 11:53 loveoni12 Member Registered: 14/6/14 All right. Offline ## #25 14/6/14 12:02 loveoni12 Member Registered: 14/6/14 ### Re: Ae?nstal 2 does not install!! I want to send you a photo. Offline	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9240477085113525, "perplexity": 15898.737690323182}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203021.14/warc/CC-MAIN-20190323201804-20190323223804-00466.warc.gz"}
https://quics.umd.edu/research/publications?s=year&amp%3Bf%5Bag%5D=N&amp%3Bf%5Bauthor%5D=2086&o=asc&f%5Bauthor%5D=1692	# Publications Export 1 results: Author Title Type [ Year] Filters: Author is Ron Taylor [Clear All Filters] 2017 , Domination with decay in triangular matchstick arrangement graphs, Involve, a Journal of Mathematics, vol. 10, no. 5, pp. 749 - 766, 2017.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8713756203651428, "perplexity": 4217.177271155851}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487621699.22/warc/CC-MAIN-20210616001810-20210616031810-00001.warc.gz"}
https://www.projecteuclid.org/search_result?type=index&q.a.keyword=Gibbs+sampler&linkedSearch=1	## Search results Showing 1-10 of 60 results Select/deselect all • Export citations ### Bayesian Effect Fusion for Categorical Predictors Pauger, Daniela and Wagner, Helga Bayesian Analysis Volume 14, Number 2 (June 2019), 341-369. Journal article ### On the mixing time of Kac’s walk and other high-dimensional Gibbs samplers with constraints S. Pillai, Natesh and Smith, Aaron The Annals of Probability Volume 46, Number 4 (July 2018), 2345-2399. Journal article ### Bayesian Analysis of the Stationary MAP2 Ramírez-Cobo, P., Lillo, R. E., and Wiper, M. P. Bayesian Analysis Volume 12, Number 4 (December 2017), 1163-1194. Journal article ### Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves Tak, Hyungsuk, Mandel, Kaisey, van Dyk, David A., Kashyap, Vinay L., Meng, Xiao-Li, and Siemiginowska, Aneta The Annals of Applied Statistics Volume 11, Number 3 (September 2017), 1309-1348. Journal article ### Bayesian Inference of C-AR(1) Time Series Model with Structural Break Kumar, Jitendra, Kumar, Ashok, Agiwal, Varun, and Shangodoyin, Dahud Kehinde Afrika Statistika Volume 12, Number 3 (August 2017), 1467-1479. Journal article ### $G$ method in action: Fast exact sampling from set of permutations of order $n$ according to Mallows model through Cayley metric Păun, Udrea Brazilian Journal of Probability and Statistics Volume 31, Number 2 (May 2017), 338-352. Journal article ### The General Projected Normal Distribution of Arbitrary Dimension: Modeling and Bayesian Inference Hernandez-Stumpfhauser, Daniel, Breidt, F. Jay, and van der Woerd, Mark J. Bayesian Analysis Volume 12, Number 1 (March 2017), 113-133. Journal article ### Convergence rates for a hierarchical Gibbs sampler Bernoulli Volume 23, Number 1 (February 2017), 603-625. Journal article ### Kac’s walk on $n$-sphere mixes in $n\log n$ steps Pillai, Natesh S. and Smith, Aaron The Annals of Applied Probability Volume 27, Number 1 (February 2017), 631-650. Journal article ### Convergence rates of the random scan Gibbs sampler under the Dobrushin’s uniqueness condition Wang, Neng-Yi Electronic Communications in Probability Volume 22, (2017). Journal article Select/deselect all	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15654778480529785, "perplexity": 16967.066661453227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540491491.18/warc/CC-MAIN-20191206222837-20191207010837-00116.warc.gz"}
https://worldwidescience.org/topicpages/c/configuration+interaction.html	#### Sample records for configuration interaction 1. Kramers Pairs in configuration interaction DEFF Research Database (Denmark) Avery, John Scales; Avery, James Emil 2003-01-01 The theory of symmetry-preserving Kramers pair creation operators is reviewed and formulas for applying these operators to configuration interaction calculations are derived. A new and more general type of symmetry-preserving pair creation operator is proposed and shown to commute with the total ... 2. Industrial requirements for interactive product configurators DEFF Research Database (Denmark) Queva, Matthieu Stéphane Benoit; Probst, Christian W.; Vikkelsøe, Per 2009-01-01 The demand for highly customized products at low cost is driving the industry towards Mass Customization. Interactive product configurators play an essential role in this new trend, and must be able to support more and more complex features. The purpose of this paper is, firstly, to identify...... requirements for modern interactive configurators. Existing modeling and solving technologies for configuration are then reviewed and their limitations discussed. Finally, a proposition for a future product configuration system is described.... 3. Interactive Cost Configuration Over Decision Diagrams DEFF Research Database (Denmark) Andersen, Henrik Reif; Hadzic, Tarik; Pisinger, David 2010-01-01 interaction online. In particular,binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDD-based configuration to scenarios involving cost functions which express user preferences. We first show...... that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multi-valued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is non-additive or if it is encoded explicitly into MDD. We...... then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiple-cost configuration is NP-hard in the input MDD. However, for solving two-cost configuration we develop a pseudo-polynomial scheme and a fully polynomial approximation scheme... 4. Co-Configuration in Interaction Work DEFF Research Database (Denmark) Fischer, Louise Harder; Pries-Heje, Lene 2015-01-01 How to increase knowledge workers productivity is still a puzzle. While knowledge work has become increasingly virtual, collaborative and interactive, we still witness challenges in the area of productivity. We challenge the widespread perception of the causal relationship between high autonomy...... and high productivity in knowledge work and the fact that configuration and standardization for improving productivity is logical impossible. With a hermeneutical approach we describe and interpret “what is going on” in two different context of interaction knowledge work. Findings suggests that knowledge...... workers often feel caught in counter-productive practices with technology, due to the autonomous use of Interaction-IT and the challenge of configuring work. We witness different behaviors related to “the autonomy paradox” and we see something interesting happening, when introducing Interaction IT. While... 5. Pushing configuration-interaction to the limit DEFF Research Database (Denmark) Vogiatzis, Konstantinos D.; Ma, Dongxia; Olsen, Jeppe 2017-01-01 A new large-scale parallel multiconfigurational self-consistent field (MCSCF) implementation in the open-source NWChem computational chemistry code is presented. The generalized active space (GAS) approach is used to partition large configuration interaction (CI) vectors and generate a sufficient... 6. Improving the Performance of Interactive Configuration with Regular String Constraints DEFF Research Database (Denmark) Hansen, Esben Rune; Tiedemann, Peter 2008-01-01 A generalization of the problem of interactive configuration has previously been presented in [1]. This generalization utilized decomposition to extend the standard finite domain interactive configuration framework to deal with unbounded string variables and provided features such as prefix auto... 7. Configuration interaction wave functions: A seniority number approach International Nuclear Information System (INIS) Alcoba, Diego R.; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B. 2014-01-01 This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure 8. Configuration interaction wave functions: A seniority number approach Energy Technology Data Exchange (ETDEWEB) Alcoba, Diego R. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Torre, Alicia; Lain, Luis, E-mail: [email protected] [Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao (Spain); Massaccesi, Gustavo E. [Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Oña, Ofelia B. [Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata (Argentina) 2014-06-21 This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure. 9. Configuration interaction in LTE spectra of heavy elements International Nuclear Information System (INIS) Bar-Shalom, A.; Oreg, J.; Goldstein, W. 1992-11-01 We present a method for including the effects of configuration interaction (CI) between relativistic subconfigurations of an electron configuration in the calculation of emission and absorption spectra of plasmas in local thermodynamic equilibrium (LTE). Analytical expressions for the correction to the intensities, owing to Cl, of an unresolved transition array (UTA) and of a supertransition array (STA) are obtained when the correction is small compared to the spin-orbit splitting, bypassing the need to diagonalize energy matrices. These expressions serve as working formulas in the STA model and, in addition, reveal a priori the conditions under which CI effects are significant. Examples of the effect are presented 10. Configuration interaction calculations of positron binding to Be(3P ) International Nuclear Information System (INIS) Bromley, M.W.J.; Mitroy, J. 2006-01-01 The configuration interaction method is applied to investigate the possibility of positron binding to the metastable beryllium (1s 2 2s2p 3 P ) state. The largest calculation obtained an estimated energy that was unstable by 0.00014 Hartree with respect to the Ps + Be + (2s) lowest dissociation channel. It is likely that positron binding to parent states with non-zero angular momentum is inhibited by centrifugal barriers 11. Configuration mixing in the sdg interacting boson model International Nuclear Information System (INIS) Bouldjedri, A; Van Isacker, P; Zerguine, S 2005-01-01 A wavefunction analysis of the strong-coupling limits of the sdg interacting boson model is presented. The analysis is carried out for two-boson states and allows us to characterize the boson configuration mixing in the different limits. Based on these results and those of a shell-model analysis of the sdg IBM, qualitative conclusions are drawn about the range of applicability of each limit 12. Configuration mixing in the sdg interacting boson model Energy Technology Data Exchange (ETDEWEB) Bouldjedri, A [Department of Physics, Faculty of Science, University of Batna, Avenue Boukhelouf M El Hadi, 05000 Batna (Algeria); Van Isacker, P [GANIL, BP 55027, F-14076 Caen cedex 5 (France); Zerguine, S [Department of Physics, Faculty of Science, University of Batna, Avenue Boukhelouf M El Hadi, 05000 Batna (Algeria) 2005-11-01 A wavefunction analysis of the strong-coupling limits of the sdg interacting boson model is presented. The analysis is carried out for two-boson states and allows us to characterize the boson configuration mixing in the different limits. Based on these results and those of a shell-model analysis of the sdg IBM, qualitative conclusions are drawn about the range of applicability of each limit. 13. Effects of configuration interaction on photoabsorption spectra in the continuum International Nuclear Information System (INIS) Komninos, Yannis; Nicolaides, Cleanthes A. 2004-01-01 It is pointed out that the proper interpretation of a recently published experimental spectrum from the multilaser photoionization of Sr [Eichmann et al., Phys. Rev. Lett. 90, 233004 (2003)] must account for a radiative transition between two autoionizing states. The application of orthonormality selection rules and of configuration-interaction theory involving the continuous spectrum and the quasicontinuum of the upper part of Rydberg series explains quantitatively the appearance, the shape, and the variation of heights of the observed peaks of resonances 14. Electric dipole moment of diatomic molecules by configuration interaction. IV. Science.gov (United States) Green, S. 1972-01-01 The theory of basis set dependence in configuration interaction calculations is discussed, taking into account a perturbation model which is valid for small changes in the self-consistent field orbitals. It is found that basis set corrections are essentially additive through first order. It is shown that an error found in a previously published dipole moment calculation by Green (1972) for the metastable first excited state of CO was indeed due to an inadequate basis set as claimed. 15. Determination of orbitals for use in configuration interaction calculations International Nuclear Information System (INIS) Dunning, T.H. Jr.; Davidson, E.R.; Ruedenberg, K.; Hinze, J. 1978-01-01 For a full configuration interaction (CI) calculation the choice of orbitals is completely irrelevant, i.e., the calculated wavefunction is unaffected by an arbitrary unitary transformation of the orbitals; it depends only on the space spanned by the original basis set. For most chemical systems it is not possible to realistically carry out a full CI calculation, so that specification of the orbital set is important. Even for less-than-full CI calculations, it can be shown, however, that for certain types of calculations the wavefunction is unaffected by restricted transformations among the orbital set. For example, for CI calculations based on a single configuration plus a complete set of excitations of a given type (single, double, etc.), the calculated wavefunction is independent of transformations among the set of occupied orbitals and among the set of virtual orbitals. The wavefunction does, however, depend on transformations which mix the occupied and virtual orbitals 16. Nuclear deformation in the configuration-interaction shell model Science.gov (United States) Alhassid, Y.; Bertsch, G. F.; Gilbreth, C. N.; Mustonen, M. T. 2018-02-01 We review a method that we recently introduced to calculate the finite-temperature distribution of the axial quadrupole operator in the laboratory frame using the auxiliary-field Monte Carlo technique in the framework of the configuration-interaction shell model. We also discuss recent work to determine the probability distribution of the quadrupole shape tensor as a function of intrinsic deformation β,γ by expanding its logarithm in quadrupole invariants. We demonstrate our method for an isotope chain of samarium nuclei whose ground states describe a crossover from spherical to deformed shapes. 17. Variational configuration interaction methods and comparison with perturbation theory International Nuclear Information System (INIS) Pople, J.A.; Seeger, R.; Krishnan, R. 1977-01-01 A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Moller-Plesset perturbation results to second and third order are obtained in the first CI iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final CI energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory 18. Configuration interaction calculations for the region of 76Ge Science.gov (United States) Brown, Alex 2017-09-01 I will present a short history of the configuration interaction Hamiltonians that have been developed for the (0f5 / 2 , 1p3 / 2 , 1p1 / 2 , 0g9 / 2) (jj 44) model space. This model space is appropriate for the region of nuclei bounded by the nickel isotopes for Z = 28 and the isotones with N = 50 . I will discuss results for the double-beta decay of 76Ge that lies in the jj 44 region. I will show results for the structure of nuclei around 76Ge for some selected data from gamma decay, Gamow-Teller beta decay, charge-exchange reactions, one-nucleon transfer reactions, and two-nucleon transfer reactions. This work was supported by NSF Grant PHY-1404442. 19. Accelerating Full Configuration Interaction Calculations for Nuclear Structure International Nuclear Information System (INIS) Yang, Chao; Sternberg, Philip; Maris, Pieter; Ng, Esmond; Sosonkina, Masha; Le, Hung Viet; Vary, James; Yang, Chao 2008-01-01 One of the emerging computational approaches in nuclear physics is the full configuration interaction (FCI) method for solving the many-body nuclear Hamiltonian in a sufficiently large single-particle basis space to obtain exact answers - either directly or by extrapolation. The lowest eigenvalues and corresponding eigenvectors for very large, sparse and unstructured nuclear Hamiltonian matrices are obtained and used to evaluate additional experimental quantities. These matrices pose a significant challenge to the design and implementation of efficient and scalable algorithms for obtaining solutions on massively parallel computer systems. In this paper, we describe the computational strategies employed in a state-of-the-art FCI code MFDn (Many Fermion Dynamics - nuclear) as well as techniques we recently developed to enhance the computational efficiency of MFDn. We will demonstrate the current capability of MFDn and report the latest performance improvement we have achieved. We will also outline our future research directions 20. Watermelon configurations with wall interaction: exact and asymptotic results Energy Technology Data Exchange (ETDEWEB) Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France) 2006-06-15 We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature. 1. Watermelon configurations with wall interaction: exact and asymptotic results International Nuclear Information System (INIS) Krattenthaler, C 2006-01-01 We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature 2. Watermelon configurations with wall interaction: exact and asymptotic results Science.gov (United States) Krattenthaler, C. 2006-06-01 We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature. 3. Particle-two particle interaction in configuration space International Nuclear Information System (INIS) Kuzmichev, V.E. 1982-07-01 The problem if three indentical particles with zero-range two-particle interaction is considered. An explicit expression for the effective potential between one particle and the remaining two-particle system is obtained in the coordinate representation. It is shown that for arbitrary energies, at small and, for zero energy, at large distances rho between the one particle and centre of mass of the other two particles the diagonal matrix element of the effective potential is attractive and proportional to 1/rho 2 . This property of the effective potenial explains both the Thomas singularity and the Efimov effect. In the case of zero total energy of the system the general form of the solution of the three-particle integral equation is found in configuration space. (orig.) 4. Configuration interaction in charge exchange spectra of tin and xenon Science.gov (United States) D'Arcy, R.; Morris, O.; Ohashi, H.; Suda, S.; Tanuma, H.; Fujioka, S.; Nishimura, H.; Nishihara, K.; Suzuki, C.; Kato, T.; Koike, F.; O'Sullivan, G. 2011-06-01 Charge-state-specific extreme ultraviolet spectra from both tin ions and xenon ions have been recorded at Tokyo Metropolitan University. The electron cyclotron resonance source spectra were produced from charge exchange collisions between the ions and rare gas target atoms. To identify unknown spectral lines of tin and xenon, atomic structure calculations were performed for Sn14+-Sn17+ and Xe16+-Xe20+ using the Hartree-Fock configuration interaction code of Cowan (1981 The Theory of Atomic Structure and Spectra (Berkeley, CA: University of California Press)). The energies of the capture states involved in the single-electron process that occurs in these slow collisions were estimated using the classical over-barrier model. 5. Leadership Class Configuration Interaction Code - Status and Opportunities Science.gov (United States) Vary, James 2011-10-01 With support from SciDAC-UNEDF (www.unedf.org) nuclear theorists have developed and are continuously improving a Leadership Class Configuration Interaction Code (LCCI) for forefront nuclear structure calculations. The aim of this project is to make state-of-the-art nuclear structure tools available to the entire community of researchers including graduate students. The project includes codes such as NuShellX, MFDn and BIGSTICK that run a range of computers from laptops to leadership class supercomputers. Codes, scripts, test cases and documentation have been assembled, are under continuous development and are scheduled for release to the entire research community in November 2011. A covering script that accesses the appropriate code and supporting files is under development. In addition, a Data Base Management System (DBMS) that records key information from large production runs and archived results of those runs has been developed (http://nuclear.physics.iastate.edu/info/) and will be released. Following an outline of the project, the code structure, capabilities, the DBMS and current efforts, I will suggest a path forward that would benefit greatly from a significant partnership between researchers who use the codes, code developers and the National Nuclear Data efforts. This research is supported in part by DOE under grant DE-FG02-87ER40371 and grant DE-FC02-09ER41582 (SciDAC-UNEDF). 6. Relativistic configuration interaction treatment of generalized oscillator strength for krypton International Nuclear Information System (INIS) Wang Huangchun; Qu Yizhi; Liu Chunhua 2007-01-01 A fully relativistic configuration interaction method is developed to investigate the transition energies and general oscillator strengths of the lower lying states of krypton, for both optically allowed and optically forbidden transitions. The calculated results are in agreement with the recent experimental measurements. The calculated transition energies for the 5s and 5s' transitions are 9.970 and 10.717 eV, which agree with the experimental data of 10.033 and 10.643 eV. The calculated oscillator strengths are 0.211 and 0.170, comparable with the experimental results 0.214(±0.012) and 0.194 (±0.012), respectively. The momentum transfer positions (K 2 in a.u.) of the minimum and maximum GOSs in the 4s 2 4p 6 →4s 2 4p 5 (5s + 5s') transitions are 1.105 and 2.225, comparable with the measurements results 1.24 and 2.97. (authors) 7. A sparse matrix based full-configuration interaction algorithm International Nuclear Information System (INIS) Rolik, Zoltan; Szabados, Agnes; Surjan, Peter R. 2008-01-01 We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers 8. Relativistic Configuration Interaction Treatment of Generalized Oscillator Strength for Krypton Institute of Scientific and Technical Information of China (English) WANG Huang-Chun; QU Yi-Zhi; LIU Chun-Hua 2007-01-01 A fully relativistic configuration interaction method is developed to investigate the transition energies and general oscillator strengths of the lower lying states of krypton, for both optically allowed and optically forbidden transitions. The calculated results are in agreement with the recent experimental measurements. The calculated transition energies for the 5s and 5s' transitions are 9.970 and 10.717eV, which agree with the experimental data of 10.033 and 10.643 eV. The calculated oscillator strengths are 0.211 and 0.170, comparable with the experimental results 0.214(±0.012) and 0.194 (±0.012), respectively. The momentum transfer positions ( K2 in a.u.) of the minimum and maximum GOSs in the 4s24p6 → 4s24p5 (5s + 5s') transitions are 1.105 and 2.225, comparable with the measurements results 1.24 and 2.97 [Phys. Rev. A 67 (2003) 062708]. 9. Photoabsorption in sodium clusters: first principles configuration interaction calculations Science.gov (United States) Priya, Pradip Kumar; Rai, Deepak Kumar; Shukla, Alok 2017-05-01 We present systematic and comprehensive correlated-electron calculations of the linear photoabsorption spectra of small neutral closed- and open-shell sodium clusters (Nan, n = 2 - 6), as well as closed-shell cation clusters (Nan+, n = 3, 5). We have employed the configuration interaction (CI) methodology at the full CI (FCI) and quadruple CI (QCI) levels to compute the ground, and the low-lying excited states of the clusters. For most clusters, besides the minimum energy structures, we also consider their energetically close isomers. The photoabsorption spectra were computed under the electric-dipole approximation, employing the dipole-matrix elements connecting the ground state with the excited states of each isomer. Our calculations were tested rigorously for convergence with respect to the basis set, as well as with respect to the size of the active orbital space employed in the CI calculations. These calculations reveal that as far as electron-correlation effects are concerned, core excitations play an important role in determining the optimized ground state geometries of various clusters, thereby requiring all-electron correlated calculations. But, when it comes to low-lying optical excitations, only valence electron correlation effects play an important role, and excellent agreement with the experimental results is obtained within the frozen-core approximation. For the case of Na6, the largest cluster studied in this work, we also discuss the possibility of occurrence of plasmonic resonance in the optical absorption spectrum. Supplementary material in the form of one pdf file available from the Journal web page at http://https://doi.org/10.1140/epjd/e2017-70728-3 10. A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations International Nuclear Information System (INIS) Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel; Buluc, Aydin; Shao, Meiyue 2017-01-01 As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using the compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor. 11. Robust and Efficient Spin Purification for Determinantal Configuration Interaction. Science.gov (United States) Fales, B Scott; Hohenstein, Edward G; Levine, Benjamin G 2017-09-12 The limited precision of floating point arithmetic can lead to the qualitative and even catastrophic failure of quantum chemical algorithms, especially when high accuracy solutions are sought. For example, numerical errors accumulated while solving for determinantal configuration interaction wave functions via Davidson diagonalization may lead to spin contamination in the trial subspace. This spin contamination may cause the procedure to converge to roots with undesired ⟨Ŝ 2 ⟩, wasting computer time in the best case and leading to incorrect conclusions in the worst. In hopes of finding a suitable remedy, we investigate five purification schemes for ensuring that the eigenvectors have the desired ⟨Ŝ 2 ⟩. These schemes are based on projection, penalty, and iterative approaches. All of these schemes rely on a direct, graphics processing unit-accelerated algorithm for calculating the S 2 c matrix-vector product. We assess the computational cost and convergence behavior of these methods by application to several benchmark systems and find that the first-order spin penalty method is the optimal choice, though first-order and Löwdin projection approaches also provide fast convergence to the desired spin state. Finally, to demonstrate the utility of these approaches, we computed the lowest several excited states of an open-shell silver cluster (Ag 19 ) using the state-averaged complete active space self-consistent field method, where spin purification was required to ensure spin stability of the CI vector coefficients. Several low-lying states with significant multiply excited character are predicted, suggesting the value of a multireference approach for modeling plasmonic nanomaterials. 12. Isotope shift and configuration interaction in U I International Nuclear Information System (INIS) King, W.H. 1979-01-01 Recent calculations by Rajnak and Fred (J. Opt. Soc. Am.; 67:1314 (1977)) show that the transitions studied by Gagne et al (J. Opt. Soc. Am.; 66:1415 (1976)) have upper levels of mixed configurations. The amount of mixing and the probability of mass shifts due to 5f electrons is discussed. (author) 13. Convergence of configuration-interaction single-center calculations of positron-atom interactions International Nuclear Information System (INIS) Mitroy, J.; Bromley, M. W. J. 2006-01-01 The configuration interaction (CI) method using orbitals centered on the nucleus has recently been applied to calculate the interactions of positrons interacting with atoms. Computational investigations of the convergence properties of binding energy, phase shift, and annihilation rate with respect to the maximum angular momentum of the orbital basis for the e + Cu and PsH bound states, and the e + -H scattering system were completed. The annihilation rates converge very slowly with angular momentum, and moreover the convergence with radial basis dimension appears to be slower for high angular momentum. A number of methods of completing the partial wave sum are compared; an approach based on a ΔX J =a(J+(1/2)) -n +b(J+(1/2)) -(n+1) form [with n=4 for phase shift (or energy) and n=2 for the annihilation rate] seems to be preferred on considerations of utility and underlying physical justification 14. Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction International Nuclear Information System (INIS) Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E. 2016-01-01 Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure. 15. New developments in multireference and complete configuration interaction calculations International Nuclear Information System (INIS) Knowles, P.J.; Werner, H.J. 1987-01-01 Some recently developed techniques for the calculation of Hamiltonian matrix elements in molecular electronic structure calculations are described. These techniques allow the very rapid calculation, in any desired order, of one particle coupling coefficients between spin symmetry adapted basis functions of arbitrary structure. The matrix elements that are required, for either internally contracted multireference CI calculations, or full CI calculations, are then obtainable from suitable summations over resolutions of the identity, which has been shown previously to be rather efficient; this is especially true on vector computers, since all arithmetic can be formulated as matrix multiplications. These ideas have culminated in the preparation of a new multireference CI program which is capable of handling very large numbers of reference configurations. Application of the new techniques to full CI calculations are also presented 16. Configurable Input Devices for 3D Interaction using Optical Tracking NARCIS (Netherlands) A.J. van Rhijn (Arjen) 2007-01-01 textabstractThree-dimensional interaction with virtual objects is one of the aspects that needs to be addressed in order to increase the usability and usefulness of virtual reality. Human beings have difficulties understanding 3D spatial relationships and manipulating 3D user interfaces, which 17. Configurable input devices for 3D interaction using optical tracking NARCIS (Netherlands) Rhijn, van A.J. 2007-01-01 Three-dimensional interaction with virtual objects is one of the aspects that needs to be addressed in order to increase the usability and usefulness of virtual reality. Human beings have difficulties understanding 3D spatial relationships and manipulating 3D user interfaces, which require the 18. An Interaction Measure for Control Configuration Selection for Multivariable Bilinear Systems DEFF Research Database (Denmark) Shaker, Hamid Reza; Stoustrup, Jakob 2013-01-01 are needed to be controlled, are nonlinear and linear models are insufficient to describe the behavior of the processes. The focus of this paper is on the problem of control configuration selection for a class of nonlinear systems which is known as bilinear systems. A gramian-based interaction measure...... for control configuration selection of MIMO bilinear processes is described. In general, most of the results on the control configuration selection, which have been proposed so far, can only support linear systems. The proposed gramian-based interaction measure not only supports bilinear processes but also... 19. Chemical interactions and configurational disorder in silicate melts Directory of Open Access Journals (Sweden) G. Ottonello 2005-06-01 Full Text Available The Thermodynamics of quasi-chemical and polymeric models are briefly reviewed. It is shown that the two classes are mutually consistent, and that opportune conversion of the existing quasi-chemical parameterization of binary interactions in MO-SiO2 joins to polymeric models may be afforded without substantial loss of precision. It is then shown that polymeric models are extremely useful in deciphering the structural and reactive properties of silicate melts and glasses. They not only allow the Lux-Flood character of the dissolved oxides to be established, but also discriminate subordinate strain energy contributions to the Gibbs free energy of mixing from the dominant chemical interaction terms. This discrimination means that important information on the short-, medium- and long-range periodicity of this class of substances can be retrieved from thermodynamic analysis. Lastly, it is suggested that an important step forward in deciphering the complex topology of the inhomogeneity ranges observed at high SiO2 content can be performed by applying SCMF theory and, particularly, Matsen-Schick spectral analysis, hitherto applied only to rubberlike materials. 20. An Activity-Centric Approach to Configuration Work in Distributed Interaction DEFF Research Database (Denmark) Houben, Steven The widespread introduction of new types of computing devices, such as smartphones, tablet computers, large interactive displays or even wearable devices, has led to setups in which users are interacting with a rich ecology of devices. These new device ecologies have the potential to introduce...... and captures the problems and challenges of distributed interaction. Using both empirical data and related work, I argue that configuration work is composed of: curation work, task resumption lag, mobility work, physical handling and articulation work. Using configuration work as a problem description, I... 1. Control configuration selection for bilinear systems via generalised Hankel interaction index array DEFF Research Database (Denmark) 2015-01-01 configuration selection. It is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control. In this paper the problem of control configuration selection for multiple-input and multiple-output (MIMO) bilinear processes is addressed. First...... way, an iterative method for solving the generalised Sylvester equation is proposed. The generalised cross-gramian is used to form the generalised Hankel interaction index array. The generalised Hankel interaction index array is used for control configuration selection of MIMO bilinear processes. Most......Decentralised and partially decentralised control strategies are very popular in practice. To come up with a suitable decentralised or partially decentralised control structure, it is important to select the appropriate input and output pairs for control design. This procedure is called control... 2. A hybrid configuration interaction treatment based on seniority number and excitation schemes International Nuclear Information System (INIS) Alcoba, Diego R.; Capuzzi, Pablo; Torre, Alicia; Lain, Luis; Oña, Ofelia B.; Van Raemdonck, Mario; Bultinck, Patrick; Van Neck, Dimitri 2014-01-01 We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method 3. A hybrid configuration interaction treatment based on seniority number and excitation schemes Energy Technology Data Exchange (ETDEWEB) Alcoba, Diego R.; Capuzzi, Pablo [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Torre, Alicia; Lain, Luis, E-mail: [email protected] [Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644 E-48080 Bilbao (Spain); Oña, Ofelia B. [Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata (Argentina); Van Raemdonck, Mario; Bultinck, Patrick [Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent (Belgium); Van Neck, Dimitri [Center for Molecular Modelling, Ghent University, Technologiepark 903, 9052 Zwijnaarde (Belgium) 2014-12-28 We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method. 4. CONFIGURATION-INTERACTION IN NI METAL AND NI-ALLOYS AND HIGH-ENERGY SPECTROSCOPY NARCIS (Netherlands) TANAKA, A; JO, T; SAWATZKY, GA We discuss the electronic state of Ni atoms in Ni metal and of Ni impurity in Cu and Au metals from the viewpoint of 3d configuration interaction (CI) using the Anderson impurity model including atomic multiplets. On the basis of the discussion, we give an interpretation for the Ni 2p-core X-ray 5. Higher-order resonant electronic recombination as a manifestation of configuration interaction International Nuclear Information System (INIS) Beilmann, C; Amaro, P; Tashenov, S; Bekker, H; Harman, Z; Crespo López-Urrutia, J R 2013-01-01 Theoretical and experimental investigations of higher-order electron–ion recombination resonances including inter-shell excitations are presented for L-shell ions of Kr with the aim of examining details of atomic structure calculations. The particular importance of electron–electron interaction and configuration mixing effects for these recombination processes enables their use for detailed tests of electron correlation effects. A test of the required level of considered mixing configurations is presented and further experiments involving higher-order recombination channels are motivated. (paper) 6. Multireference configuration interaction calculations of the first six ionization potentials of the uranium atom Energy Technology Data Exchange (ETDEWEB) Bross, David H.; Parmar, Payal; Peterson, Kirk A., E-mail: [email protected] [Department of Chemistry, Washington State University, Pullman, Washington 99164-4630 (United States) 2015-11-14 The first 6 ionization potentials (IPs) of the uranium atom have been calculated using multireference configuration interaction (MRCI+Q) with extrapolations to the complete basis set limit using new all-electron correlation consistent basis sets. The latter was carried out with the third-order Douglas-Kroll-Hess Hamiltonian. Correlation down through the 5s5p5d electrons has been taken into account, as well as contributions to the IPs due to the Lamb shift. Spin-orbit coupling contributions calculated at the 4-component Kramers restricted configuration interaction level, as well as the Gaunt term computed at the Dirac-Hartree-Fock level, were added to the best scalar relativistic results. The final ionization potentials are expected to be accurate to at least 5 kcal/mol (0.2 eV) and thus more reliable than the current experimental values of IP{sub 3} through IP{sub 6}. 7. Nuclear structure calculations in $^{20}$Ne with No-Core Configuration-Interaction model OpenAIRE Konieczka, Maciej; Satuła, Wojciech 2016-01-01 Negative parity states in $^{20}$Ne and Gamow-Teller strength distribution for the ground-state beta-decay of $^{20}$Na are calculated for the very first time using recently developed No-Core Configuration-Interaction model. The approach is based on multi-reference density functional theory involving isospin and angular-momentum projections. Advantages and shortcomings of the method are briefly discussed. 8. Interaction potentials for multiquark states from instantons and other background gauge field configurations International Nuclear Information System (INIS) Warner, R.C.; Joshi, G.C. 1979-01-01 A simple rule is presented for calculating the contributions to the interaction potentials between constituent particles for a family of multiquark states, due to the presence of a semi-classical gauge field configuration which exists in a single SU(2) subgroup of colour SU(3). In multiquark states beyond the baryon many-body potential terms are found. The static (Wilson loop) limit is sufficient to elucidate the dependence of the potential on the colour structure of the multiquark state 9. Configuration interaction calculations of positron binding to Be({sup 3}P ) Energy Technology Data Exchange (ETDEWEB) Bromley, M.W.J. [Department of Physics, San Diego State University, San Diego, CA 92182 (United States)]. E-mail: [email protected]; Mitroy, J. [Faculty of Technology, Charles Darwin University, Darwin, NT 0909 (Australia)]. E-mail: [email protected] 2006-06-15 The configuration interaction method is applied to investigate the possibility of positron binding to the metastable beryllium (1s{sup 2}2s2p {sup 3}P ) state. The largest calculation obtained an estimated energy that was unstable by 0.00014 Hartree with respect to the Ps + Be{sup +}(2s) lowest dissociation channel. It is likely that positron binding to parent states with non-zero angular momentum is inhibited by centrifugal barriers. 10. Relativistic configuration-interaction calculation of the correlation energies of heliumlike ions. Revision 1 International Nuclear Information System (INIS) Cheng, K.T.; Chen, M.H.; Johnson, W.R. 1994-04-01 A new relativistic configuration-interaction (CI) method using B-spline basis functions has been developed to study the correlation energies of two-electron heliumlike ions. Based on the relativistic no-pair Hamiltonian, the CI equation leads to a symmetric eigenvalue problem involving large, dense matrices. Davidson's method is used to obtain the lowest few eigenenergies and eigenfunctions. Results on transition energies and finite structure splittings for heliumlike ions are in very good agreement with experiment throughout the periodic table 11. Threshold and channel interaction in cochlear implant users: evaluation of the tripolar electrode configuration. Science.gov (United States) Bierer, Julie Arenberg 2007-03-01 The efficacy of cochlear implants is limited by spatial and temporal interactions among channels. This study explores the spatially restricted tripolar electrode configuration and compares it to bipolar and monopolar stimulation. Measures of threshold and channel interaction were obtained from nine subjects implanted with the Clarion HiFocus-I electrode array. Stimuli were biphasic pulses delivered at 1020 pulses/s. Threshold increased from monopolar to bipolar to tripolar stimulation and was most variable across channels with the tripolar configuration. Channel interaction, quantified by the shift in threshold between single- and two-channel stimulation, occurred for all three configurations but was largest for the monopolar and simultaneous conditions. The threshold shifts with simultaneous tripolar stimulation were slightly smaller than with bipolar and were not as strongly affected by the timing of the two channel stimulation as was monopolar. The subjects' performances on clinical speech tests were correlated with channel-to-channel variability in tripolar threshold, such that greater variability was related to poorer performance. The data suggest that tripolar channels with high thresholds may reveal cochlear regions of low neuron survival or poor electrode placement. 12. Deterministic alternatives to the full configuration interaction quantum Monte Carlo method for strongly correlated systems Science.gov (United States) Tubman, Norm; Whaley, Birgitta The development of exponential scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, allows exact diagonalization through stochastically sampling of determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, together with a stochastic projected wave function, which are used to explore the important parts of Hilbert space. However, a stochastic representation of the wave function is not required to search Hilbert space efficiently and new deterministic approaches have recently been shown to efficiently find the important parts of determinant space. We shall discuss the technique of Adaptive Sampling Configuration Interaction (ASCI) and the related heat-bath Configuration Interaction approach for ground state and excited state simulations. We will present several applications for strongly correlated Hamiltonians. This work was supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. 13. High pressure studies of configuration interaction and crystal field effects in Sm2+ International Nuclear Information System (INIS) Shen, Y.; Bray, K.L. 1998-01-01 Full text: Divalent rare earth ions are interesting luminescence centres because of the low energy of the excited 4f n-1 5d 1 configuration relative to the 4f n ground configuration. The low energy difference between these two configurations leads to two principle effects which distinguish the luminescence properties of divalent rare earth ions from those of trivalent rare earth ions. First, a significant amount of 5d state mixing into the electronic states of the 4f n configuration occurs and second, the thermal activation barrier to 4f n → 4f n-1 5d 1 crossing is greatly reduced. The first effect introduces opposite parity character into the emitting levels of divalent rare earth ions and acts to shorten lifetimes and increase f-f luminescence intensity, while the second effect acts to enhance thermal quenching of 4f n excited electronic states closest in energy to the 4f n-1 5d 1 configuration. The interaction between the 4f n and 4f n-1 5d 1 configurations and crystal field properties are typically studied by considering the luminescence properties of divalent rare earth ions in a series of host crystals. We are currently developing a new approach, based on high pressure luminescence spectroscopy, for understanding con-figuration interaction and crystal field properties of divalent rare earth ions. The strategy of our approach is to use high pressure as a tool of structural perturbation. By applying hydrostatic pressure to solids, we have an opportunity to continuously vary the nearest neighbour coordination environment of divalent rare earth dopants. Our general goal is to correlate pressure-induced changes in local structure with pressure-induced changes in luminescence properties in an attempt to better understand structure-property-composition relations in solid state luminescent materials. In this paper we present recent results on Sm 2+ in a series of MFCl (M = Sr, Ba, Ca) host lattices. Luminescence spectra and decay properties as a function of 14. Configurational energies and effective cluster interactions in substitutionally disordered binary alloys International Nuclear Information System (INIS) Gonis, A.; Zhang, X.h.; Freeman, A.J.; Turchi, P.; Stocks, G.M.; Nicholson, D.M. 1987-01-01 The determination of configurational energies in terms of effective cluster interactions in substitutionally disordered alloys from a knowledge of the alloy electronic structure is examined within the methods of concentration waves (CW) and the generalized perturbation method (GPM), and for the first time within the embedded-cluster method (ECM). It is shown that the ECM provides the exact summation to all orders of the effective cluster interaction expansions obtained in the partially renormalized GPM. The connection between the various methods (CW, GPM, and ECM) is discussed and illustrated by means of numerical calculations for model one-dimensional tight-binding (TB) systems and for TB Hamiltonians chosen to describe Pd-V alloys. These calculations, and the formal considerations presented in the body of the paper, show the complete equivalence of converged GPM summations within specific clusters and the ECM. In addition, it is shown that an exact expansion of the configurational energy can be obtained in terms of fully renormalized effective cluster interactions. In principle, these effective cluster interactions can be used in conjunction with statistical models to determine stable ordered structures at low temperatures and alloy phase diagrams 15. Nanoscale multireference quantum chemistry: full configuration interaction on graphical processing units. Science.gov (United States) Fales, B Scott; Levine, Benjamin G 2015-10-13 Methods based on a full configuration interaction (FCI) expansion in an active space of orbitals are widely used for modeling chemical phenomena such as bond breaking, multiply excited states, and conical intersections in small-to-medium-sized molecules, but these phenomena occur in systems of all sizes. To scale such calculations up to the nanoscale, we have developed an implementation of FCI in which electron repulsion integral transformation and several of the more expensive steps in σ vector formation are performed on graphical processing unit (GPU) hardware. When applied to a 1.7 × 1.4 × 1.4 nm silicon nanoparticle (Si72H64) described with the polarized, all-electron 6-31G** basis set, our implementation can solve for the ground state of the 16-active-electron/16-active-orbital CASCI Hamiltonian (more than 100,000,000 configurations) in 39 min on a single NVidia K40 GPU. 16. Spin--orbit configuration-interaction study of valence and Rydberg states of LiBe International Nuclear Information System (INIS) Marino, M.M.; Ermler, W.C.; Kern, C.W.; Bondybey, V.E. 1992-01-01 Ab initio spin--orbit full configuration-interaction calculations in the context of relativistic effective core potentials are reported for the weakly bound metal dimer LiBe, a three-valence-electron system. The effects of basis set on the energies of valence and Rydberg states of the cluster are discussed, as are the effects of configuration space selection on the energy of the latter states. Results at the dissociative limit are compared to the experimental atomic spectra. Potential-energy curves and spectroscopic constants are presented for the ground state and fourteen excited states, which includes the Li and Be 2p valence states, the Li 3s, 3p, 3d, and 4s Rydberg states, as well as three low-lying states of the molecular cation 17. Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo. Science.gov (United States) Vigor, W A; Spencer, J S; Bearpark, M J; Thom, A J W 2016-03-07 Within full configuration interaction quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per time step and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree-Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem. 18. Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo Energy Technology Data Exchange (ETDEWEB) Vigor, W. A.; Bearpark, M. J. [Department of Chemistry, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Spencer, J. S. [Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Thom, A. J. W. [Department of Chemistry, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW (United Kingdom) 2016-03-07 Within full configuration interaction quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per time step and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree–Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem. 19. Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy Energy Technology Data Exchange (ETDEWEB) Schriber, Jeffrey B.; Evangelista, Francesco A. [Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 (United States) 2016-04-28 We introduce a new procedure for iterative selection of determinant spaces capable of describing highly correlated systems. This adaptive configuration interaction (ACI) determines an optimal basis by an iterative procedure in which the determinant space is expanded and coarse grained until self-consistency. Two importance criteria control the selection process and tune the ACI to a user-defined level of accuracy. The ACI is shown to yield potential energy curves of N{sub 2} with nearly constant errors, and it predicts singlet-triplet splittings of acenes up to decacene that are in good agreement with the density matrix renormalization group. 20. Evaluation of the Stillinger-Weber classical interaction potential for tetragonal semiconductors in nonideal atomic configurations International Nuclear Information System (INIS) Dodson, B.W. 1986-01-01 A classical potential incorporating two- and three-body interaction terms has recently been introduced by Stillinger and Weber (SW) for simulation of the liquefaction transition of silicon. The equilibrium mechanical properties of this potential are determined and found to agree well with experimental values. The potential also seems to be adequate for problems involving computation of defect energies, such as the stability of strained-layer superlattice interfaces. However, inadequate treatment of configurations with low coordination number makes modeling of the epitaxial growth of (111) silicon impossible. Simple modifications of the SW potential form do allow for (111) epitaxial growth, but the earliest stages of growth then become unphysical 1. Non-orthogonal configuration interaction for the calculation of multielectron excited states Energy Technology Data Exchange (ETDEWEB) Sundstrom, Eric J., E-mail: [email protected]; Head-Gordon, Martin [Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States) 2014-03-21 We apply Non-orthogonal Configuration Interaction (NOCI) to molecular systems where multielectron excitations, in this case double excitations, play a substantial role: the linear polyenes and β-carotene. We demonstrate that NOCI when applied to systems with extended conjugation, provides a qualitatively correct wavefunction at a fraction of the cost of many other multireference treatments. We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree-Fock Slater determinants and the details for computing 〈S{sup 2}〉 for the ground and excited states. 2. Electronic spectra of DyF studied by four-component relativistic configuration interaction methods Energy Technology Data Exchange (ETDEWEB) Yamamoto, Shigeyoshi, E-mail: [email protected] [School of International Liberal Studies, Chukyo University, 101-2 Yagoto-Honmachi, Showa-ku, Nagoya 466-8666 (Japan); Tatewaki, Hiroshi [Institute of Advanced Studies in Artificial Intelligence, Chukyo University, Toyota 470-0393 (Japan); Graduate School of Natural Sciences, Nagoya City University, Aichi 467-8501 (Japan) 2015-03-07 The electronic states of the DyF molecule below 3.0 eV are studied using 4-component relativistic CI methods. Spinors generated by the average-of-configuration Hartree-Fock method with the Dirac-Coulomb Hamiltonian were used in CI calculations by the KRCI (Kramers-restricted configuration interaction) program. The CI reference space was generated by distributing 11 electrons among the 11 Kramers pairs composed mainly of Dy [4f], [6s], [6p] atomic spinors, and double excitations are allowed from this space to the virtual molecular spinors. The CI calculations indicate that the ground state has the dominant configuration (4f{sup 9})(6s{sup 2})(Ω = 7.5). Above this ground state, 4 low-lying excited states (Ω = 8.5, 7.5, 7.5, 7.5) are found with dominant configurations (4f{sup 10})(6s). These results are consistent with the experimental studies of McCarthy et al. Above these 5 states, 2 states were observed at T{sub 0} = 2.39 eV, 2.52 eV by McCarthy et al. and were named as [19.3]8.5 and [20.3]8.5. McCarthy et al. proposed that both states have dominant configurations (4f{sup 9})(6s)(6p), but these configurations are not consistent with the large R{sub e}’s (∼3.9 a.u.) estimated from the observed rotational constants. The present CI calculations provide near-degenerate states of (4f{sup 10})(6p{sub 3/2,1/2}), (4f{sup 10})(6p{sub 3/2,3/2}), and (4f{sup 9})(6s)(6p{sub 3/2,1/2}) at around 3 eV. The former two states have larger R{sub e} (3.88 a.u.) than the third, so that it is reasonable to assign (4f{sup 10})(6p{sub 3/2,1/2}) to [19.3]8.5 and (4f{sup 10})(6p{sub 3/2,3/2}) to [20.3]8.5. 3. Contextual interactions in grating plaid configurations are explained by natural image statistics and neural modeling Directory of Open Access Journals (Sweden) Udo Alexander Ernst 2016-10-01 Full Text Available Processing natural scenes requires the visual system to integrate local features into global object descriptions. To achieve coherent representations, the human brain uses statistical dependencies to guide weighting of local feature conjunctions. Pairwise interactions among feature detectors in early visual areas may form the early substrate of these local feature bindings. To investigate local interaction structures in visual cortex, we combined psychophysical experiments with computational modeling and natural scene analysis. We first measured contrast thresholds for 2x2 grating patch arrangements (plaids, which differed in spatial frequency composition (low, high or mixed, number of grating patch co-alignments (0, 1 or 2, and inter-patch distances (1° and 2° of visual angle. Contrast thresholds for the different configurations were compared to the prediction of probability summation (PS among detector families tuned to the four retinal positions. For 1° distance the thresholds for all configurations were larger than predicted by PS, indicating inhibitory interactions. For 2° distance, thresholds were significantly lower compared to PS when the plaids were homogeneous in spatial frequency and orientation, but not when spatial frequencies were mixed or there was at least one misalignment. Next, we constructed a neural population model with horizontal laminar structure, which reproduced the detection thresholds after adaptation of connection weights. Consistent with prior work, contextual interactions were medium-range inhibition and long-range, orientation-specific excitation. However, inclusion of orientation-specific, inhibitory interactions between populations with different spatial frequency preferences were crucial for explaining detection thresholds. Finally, for all plaid configurations we computed their likelihood of occurrence in natural images. The likelihoods turned out to be inversely related to the detection thresholds obtained 4. Large-scale ab initio configuration interaction calculations for light nuclei International Nuclear Information System (INIS) Maris, Pieter; Potter, Hugh; Vary, James P; Aktulga, H Metin; Ng, Esmond G; Yang Chao; Caprio, Mark A; Çatalyürek, Ümit V; Saule, Erik; Oryspayev, Dossay; Sosonkina, Masha; Zhou Zheng 2012-01-01 In ab-initio Configuration Interaction calculations, the nuclear wavefunction is expanded in Slater determinants of single-nucleon wavefunctions and the many-body Schrodinger equation becomes a large sparse matrix problem. The challenge is to reach numerical convergence to within quantified numerical uncertainties for physical observables using finite truncations of the infinite-dimensional basis space. We discuss strategies for constructing and solving the resulting large sparse matrix eigenvalue problems on current multicore computer architectures. Several of these strategies have been implemented in the code MFDn, a hybrid MPI/OpenMP Fortran code for ab-initio nuclear structure calculations that can scale to 100,000 cores and more. Finally, we will conclude with some recent results for 12 C including emerging collective phenomena such as rotational band structures using SRG evolved chiral N3LO interactions. 5. A full-configuration-interaction nuclear orbital approach and application for small doped He clusters Energy Technology Data Exchange (ETDEWEB) Lara-Castells, M. P. de, E-mail: [email protected]; Aguirre, N. F., E-mail: [email protected]; Delgado-Barrio, G., E-mail: [email protected]; Villarreal, P., E-mail: [email protected] [Instituto de Física Fundamental (CSIC), Serrano 123, 28006 Madrid (Spain); Mitrushchenkov, A. O. [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France) 2015-01-22 An efficient full-configuration-interaction 'nuclear orbital' treatment was developed as a benchmark quantum-chemistry-like method to calculate, ground and excited, fermionic 'solvent' wave-functions and applied to {sup 3}He{sub N} clusters with atomic or molecular impurities [J. Chem. Phys. (Communication) 125, 221101 (2006)]. The main difficulty in handling doped {sup 3}He{sub N} clusters lies in the Fermi-Dirac nuclear statistics, the wide amplitudes of the He-dopant and He-He motions, and the hard-core He-He interaction at short distances. This paper overviews the theoretical approach and its recent applications to energetic, structural and spectroscopic aspects of different dopant-{sup 3}He{sub N} clusters. Preliminary results by using the latest version of the FCI-NO computational implementation, to bosonic Cl{sub 2}(X)-({sup 4}He){sub N} clusters, are also shown. 6. Distinct configurations of protein complexes and biochemical pathways revealed by epistatic interaction network motifs LENUS (Irish Health Repository) Casey, Fergal 2011-08-22 Abstract Background Gene and protein interactions are commonly represented as networks, with the genes or proteins comprising the nodes and the relationship between them as edges. Motifs, or small local configurations of edges and nodes that arise repeatedly, can be used to simplify the interpretation of networks. Results We examined triplet motifs in a network of quantitative epistatic genetic relationships, and found a non-random distribution of particular motif classes. Individual motif classes were found to be associated with different functional properties, suggestive of an underlying biological significance. These associations were apparent not only for motif classes, but for individual positions within the motifs. As expected, NNN (all negative) motifs were strongly associated with previously reported genetic (i.e. synthetic lethal) interactions, while PPP (all positive) motifs were associated with protein complexes. The two other motif classes (NNP: a positive interaction spanned by two negative interactions, and NPP: a negative spanned by two positives) showed very distinct functional associations, with physical interactions dominating for the former but alternative enrichments, typical of biochemical pathways, dominating for the latter. Conclusion We present a model showing how NNP motifs can be used to recognize supportive relationships between protein complexes, while NPP motifs often identify opposing or regulatory behaviour between a gene and an associated pathway. The ability to use motifs to point toward underlying biological organizational themes is likely to be increasingly important as more extensive epistasis mapping projects in higher organisms begin. 7. Configuration interaction calculations and excitation rates of X-ray and EUV transitions in sulfurlike manganese Energy Technology Data Exchange (ETDEWEB) El-Maaref, A.A., E-mail: [email protected]; Saddeek, Y.B.; Abou halaka, M.M. 2017-02-15 Highlights: • Fine-structure calculations of sulfurlike Mn have been performed using configuration interaction technique, CI. • The relativistic effects, Breit-Pauli Hameltonian, have been correlated to the CI calculations. • Excitation rates by electron impact of the Mn X ion have been evaluated up to ionization potential. - Abstract: Fine-structure calculations of energies and transition parameters have been performed using the configuration interaction technique (CI) as implemented in CIV3 code for sulfurlike manganese, Mn X. The calculations are executed in an intermediate coupling scheme using the Breit-Pauli Hamiltonian. As well as, energy levels and oscillator strengths are calculated using LANL code, where the calculations by LANL have been used to estimate the accuracy of the present CI calculations. The calculated energy levels, oscillator strengths, and lifetimes are in reasonable agreement with the published experimental and theoretical values. Electron impact excitation rates of the transitions emit soft X-ray and extreme ultraviolet (EUV) wavelengths have been evaluated. The level population densities are calculated using the collisional radiative model (CRM), as well. The collisional excitation rates and collision strengths have been calculated in the electron temperature range ≤ the ionization potential, ∼1–250 eV. 8. Parallel implementation and performance optimization of the configuration-interaction method Energy Technology Data Exchange (ETDEWEB) Shan, H; Williams, S; Johnson, C; McElvain, K; Ormand, WE 2015-11-20 The configuration-interaction (CI) method, long a popular approach to describe quantum many-body systems, is cast as a very large sparse matrix eigenpair problem with matrices whose dimension can exceed one billion. Such formulations place high demands on memory capacity and memory bandwidth - - two quantities at a premium today. In this paper, we describe an efficient, scalable implementation, BIGSTICK, which, by factorizing both the basis and the interaction into two levels, can reconstruct the nonzero matrix elements on the fly, reduce the memory requirements by one or two orders of magnitude, and enable researchers to trade reduced resources for increased computational time. We optimize BIGSTICK on two leading HPC platforms - - the Cray XC30 and the IBM Blue Gene/Q. Specifically, we not only develop an empirically-driven load balancing strategy that can evenly distribute the matrix-vector multiplication across 256K threads, we also developed techniques that improve the performance of the Lanczos reorthogonalization. Combined, these optimizations improved performance by 1.3-8× depending on platform and configuration. 9. Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo International Nuclear Information System (INIS) Thomas, Robert E.; Overy, Catherine; Opalka, Daniel; Alavi, Ali; Knowles, Peter J.; Booth, George H. 2015-01-01 Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation 10. Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver Science.gov (United States) Shao, Meiyue; Aktulga, H. Metin; Yang, Chao; Ng, Esmond G.; Maris, Pieter; Vary, James P. 2018-01-01 We describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. We also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system. 11. Electric dipole moment of diatomic molecules by configuration interaction. V - Two states of /2/Sigma/+/ symmetry in CN. Science.gov (United States) Green, S. 1972-01-01 Previous accurate dipole moment calculation techniques are modified to be applicable to higher excited states of symmetry. The self-consistent fields and configuration interactions are calculated for the X(2)Sigma(+) and B(2)Sigma(+) states of CN. Spin hyperfine constants and spin density at the nucleus are considered in the context of one-electron operator properties. The values of the self-consistent field and configuration interaction for the spin density are compared with experimental values for several diatomic molecules. 12. Optical spectroscopy and system–bath interactions in molecular aggregates with full configuration interaction Frenkel exciton model Energy Technology Data Exchange (ETDEWEB) Seibt, Joachim; Sláma, Vladislav; Mančal, Tomáš, E-mail: [email protected] 2016-12-20 Highlights: • Standard Frenkel exciton model is extended to include inter-band coupling. • It is formally linked with configuration interaction method of quantum chemistry. • Spectral shifts due to inter-band coupling are found in molecular aggregates. • Effects of peak amplitude redistribution in two-dimensional spectra are found. - Abstract: Standard application of the Frenkel exciton model neglects resonance coupling between collective molecular aggregate states with different number of excitations. These inter-band coupling terms are, however, of the same magnitude as the intra-band coupling between singly excited states. We systematically derive the Frenkel exciton model from quantum chemical considerations, and identify it as a variant of the configuration interaction method. We discuss all non-negligible couplings between collective aggregate states, and provide compact formulae for their calculation. We calculate absorption spectra of molecular aggregate of carotenoids and identify significant band shifts as a result of inter-band coupling. The presence of inter-band coupling terms requires renormalization of the system–bath coupling with respect to standard formulation, but renormalization effects are found to be weak. We present detailed discussion of molecular dimer and calculate its time-resolved two-dimensional Fourier transformed spectra to find weak but noticeable effects of peak amplitude redistribution due to inter-band coupling. 13. Improving the iterative Linear Interaction Energy approach using automated recognition of configurational transitions. Science.gov (United States) Vosmeer, C Ruben; Kooi, Derk P; Capoferri, Luigi; Terpstra, Margreet M; Vermeulen, Nico P E; Geerke, Daan P 2016-01-01 Recently an iterative method was proposed to enhance the accuracy and efficiency of ligand-protein binding affinity prediction through linear interaction energy (LIE) theory. For ligand binding to flexible Cytochrome P450s (CYPs), this method was shown to decrease the root-mean-square error and standard deviation of error prediction by combining interaction energies of simulations starting from different conformations. Thereby, different parts of protein-ligand conformational space are sampled in parallel simulations. The iterative LIE framework relies on the assumption that separate simulations explore different local parts of phase space, and do not show transitions to other parts of configurational space that are already covered in parallel simulations. In this work, a method is proposed to (automatically) detect such transitions during the simulations that are performed to construct LIE models and to predict binding affinities. Using noise-canceling techniques and splines to fit time series of the raw data for the interaction energies, transitions during simulation between different parts of phase space are identified. Boolean selection criteria are then applied to determine which parts of the interaction energy trajectories are to be used as input for the LIE calculations. Here we show that this filtering approach benefits the predictive quality of our previous CYP 2D6-aryloxypropanolamine LIE model. In addition, an analysis is performed of the gain in computational efficiency that can be obtained from monitoring simulations using the proposed filtering method and by prematurely terminating simulations accordingly. 14. Interaction of ICRF power and edge plasma in Tore Supra ergodic divertor configuration International Nuclear Information System (INIS) Nguyen, F.; Grosman, A.; Basiuk, V.; Fraboulet, D.; Beaumont, B.; Becoulet, A.; Ghendrih, Ph.; Ladurelle, L.; Meslin, B. 2000-01-01 The coupling of ICRF power to plasma is a crucial problem in Tore Supra for high power and long pulse operations and depends greatly on the edge parameters, in particular on the edge density. Conversely, the behaviour of the bulk plasma is related to the edge conditions and the injection of RF power also induces major modifications on the edge plasma. Moreover, the Ergodic Divertor (ED) of Tore Supra imposes a complex configuration at the edge due to the presence of the magnetic perturbation. Several diagnostics are available to study the interaction of ICRF power with the edge plasma: Langmuir probes on the ED modules, infra red (IR) cameras, charge exchange neutral analysers. In minority heating scheme, the edge density is very sensitive to any perturbation in the high recycling regime which is always found in the ED configuration for relevant plasma parameters. Partially detached regimes, with or without inhomogeneities of density and temperature induced by the flux tubes of the laminar layer, are obtained for high resistance coupling values. The coupling is then not very robust and feedback control or antenna automatic matching techniques are developed. In fast wave electron heating scheme with ED, various fast wave absorption mechanisms (minority heating, Mode Conversion, Alfven resonance) are present at the plasma edge due to the large size of the plasma. The ICRF coupling is difficult due to the low fast wave direct electron damping, even with high hydrogen minority scheme. An increase of the injected ICRF power could improve this situation 15. Interaction of Fast Ions with Global Plasma Modes in the C-2 Field Reversed Configuration Experiment Science.gov (United States) Smirnov, Artem; Dettrick, Sean; Clary, Ryan; Korepanov, Sergey; Thompson, Matthew; Trask, Erik; Tuszewski, Michel 2012-10-01 A high-confinement operating regime [1] with plasma lifetimes significantly exceeding past empirical scaling laws was recently obtained by combining plasma gun edge biasing and tangential Neutral Beam Injection (NBI) in the C-2 field-reversed configuration (FRC) experiment [2, 3]. We present experimental and computational results on the interaction of fast ions with the n=2 rotational and n=1 wobble modes in the C-2 FRC. It is found that the n=2 mode is similar to quadrupole magnetic fields in its detrimental effect on the fast ion transport due to symmetry breaking. The plasma gun generates an inward radial electric field, thus stabilizing the n=2 rotational instability without applying the quadrupole magnetic fields. The resultant FRCs are nearly axisymmetric, which enables fast ion confinement. The NBI further suppresses the n=2 mode, improves the plasma confinement characteristics, and increases the plasma configuration lifetime [4]. The n=1 wobble mode has relatively little effect on the fast ion transport, likely due to the approximate axisymmetry about the displaced plasma column. [4pt] [1] M. Tuszewski et al., Phys. Rev. Lett. 108, 255008 (2012).[0pt] [2] M. Binderbauer et al., Phys. Rev. Lett. 105, 045003 (2010).[0pt] [3] H.Y. Guo et al., Phys. Plasmas 18, 056110 (2011).[0pt] [4] M. Tuszewski et al., Phys. Plasmas 19, 056108 (2012) 16. An excited-state approach within full configuration interaction quantum Monte Carlo International Nuclear Information System (INIS) Blunt, N. S.; Smart, Simon D.; Booth, George H.; Alavi, Ali 2015-01-01 We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available 17. Photochemistry of ethylene: A multireference configuration interaction investigation of the excited-state energy surfaces International Nuclear Information System (INIS) Barbatti, M.; Paier, J.; Lischka, H. 2004-01-01 Multireference configuration interaction with singles and doubles (MR-CISD) calculations have been performed for the optimization of conical intersections and stationary points on the ethylene excited-state energy surfaces using recently developed methods for the computation of analytic gradients and nonadiabatic coupling terms. Basis set dependence and the effect of various choices of reference spaces for the MR-CISD calculations have been investigated. The crossing seam between the S 0 and S 1 states has been explored in detail. This seam connects all conical intersections presently known for ethylene. Major emphasis has been laid on the hydrogen-migration path. Starting in the V state of twisted-orthogonal ethylene, a barrierless path to ethylidene was found. The feasibility of ethylidene formation will be important for the explanation of the relative yield of cis and trans H 2 elimination 18. Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo International Nuclear Information System (INIS) Overy, Catherine; Blunt, N. S.; Shepherd, James J.; Booth, George H.; Cleland, Deidre; Alavi, Ali 2014-01-01 Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems 19. Ab initio/interpolated quantum dynamics on coupled electronic states with full configuration interaction wave functions International Nuclear Information System (INIS) Thompson, K.; Martinez, T.J. 1999-01-01 We present a new approach to first-principles molecular dynamics that combines a general and flexible interpolation method with ab initio evaluation of the potential energy surface. This hybrid approach extends significantly the domain of applicability of ab initio molecular dynamics. Use of interpolation significantly reduces the computational effort associated with the dynamics over most of the time scale of interest, while regions where potential energy surfaces are difficult to interpolate, for example near conical intersections, are treated by direct solution of the electronic Schroedinger equation during the dynamics. We demonstrate the concept through application to the nonadiabatic dynamics of collisional electronic quenching of Li(2p). Full configuration interaction is used to describe the wave functions of the ground and excited electronic states. The hybrid approach agrees well with full ab initio multiple spawning dynamics, while being more than an order of magnitude faster. copyright 1999 American Institute of Physics 20. Fast vibrational configuration interaction using generalized curvilinear coordinates and self-consistent basis. Science.gov (United States) Scribano, Yohann; Lauvergnat, David M; Benoit, David M 2010-09-07 In this paper, we couple a numerical kinetic-energy operator approach to the direct-vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) method for the calculation of vibrational anharmonic frequencies. By combining this with fast-VSCF, an efficient direct evaluation of the ab initio potential-energy surface (PES), we introduce a general formalism for the computation of vibrational bound states of molecular systems exhibiting large-amplitude motion such as methyl-group torsion. We validate our approach on an analytical two-dimensional model and apply it to the methanol molecule. We show that curvilinear coordinates lead to a significant improvement in the VSCF/VCI description of the torsional frequency in methanol, even for a simple two-mode coupling expansion of the PES. Moreover, we demonstrate that a curvilinear formulation of the fast-VSCF/VCI scheme improves its speed by a factor of two and its accuracy by a factor of 3. 1. Coupled-Cluster and Configuration-Interaction Calculations for Heavy Nuclei International Nuclear Information System (INIS) Horoi, M.; Gour, J. R.; Wloch, M.; Lodriguito, M. D.; Brown, B. A.; Piecuch, P. 2007-01-01 We compare coupled-cluster (CC) and configuration-interaction (CI) results for 56 Ni obtained in the pf-shell basis, focusing on practical CC approximations that can be applied to systems with dozens or hundreds of correlated fermions. The weight of the reference state and the strength of correlation effects are controlled by the gap between the f 7/2 orbit and the f 5/2 , p 3/2 , p 1/2 orbits. Independent of the gap, the CC method with 1p-1h and 2p-2h clusters and a noniterative treatment of 3p-3h clusters is as accurate as the more demanding CI approach truncated at the 4p-4h level 2. Hylleraas-Configuration Interaction study of the 1S ground state of the negative Li ion. Science.gov (United States) Sims, James S 2017-12-28 In a previous work Sims and Hagstrom [J. Chem. Phys. 140, 224312 (2014)] reported Hylleraas-Configuration Interaction (Hy-CI) method variational calculations for the neutral atom and positive ion 1 S ground states of the beryllium isoelectronic sequence. The Li - ion, nominally the first member of this series, has a decidedly different electronic structure. This paper reports the results of a large, comparable calculation for the Li - ground state to explore how well the Hy-CI method can represent the more diffuse L shell of Li - which is representative of the Be(2sns) excited states as well. The best non-relativistic energy obtained was -7.500 776 596 hartree, indicating that 10 - 20 nh accuracy is attainable in Hy-CI and that convergence of the r 12 r 34 double cusp is fast and that this correlation type can be accurately represented within the Hy-CI model. 3. On the performance of atomic natural orbital basis sets: A full configuration interaction study International Nuclear Information System (INIS) Illas, F.; Ricart, J.M.; Rubio, J.; Bagus, P.S. 1990-01-01 The performance of atomic natural orbital (ANO) basis sets has been studied by comparing self-consistant field (SCF) and full configuration interaction (CI) results obtained for the first row atoms and hydrides. The ANO results have been compared with those obtained using a segmented basis set containing the same number of contracted basis functions. The total energies obtained with the ANO basis sets are always lower than the one obtained by using the segmented one. However, for the hydrides, differential electronic correlation energy obtained with the ANO basis set may be smaller than the one recovered with the segmented set. We relate this poorer differential correlation energy for the ANO basis set to the fact that only one contracted d function is used for the ANO and segmented basis sets 4. Large-dimension configuration-interaction calculations of positron binding to the group-II atoms International Nuclear Information System (INIS) Bromley, M. W. J.; Mitroy, J. 2006-01-01 The configuration-interaction (CI) method is applied to the calculation of the structures of a number of positron binding systems, including e + Be, e + Mg, e + Ca, and e + Sr. These calculations were carried out in orbital spaces containing about 200 electron and 200 positron orbitals up to l=12. Despite the very large dimensions, the binding energy and annihilation rate converge slowly with l, and the final values do contain an appreciable correction obtained by extrapolating the calculation to the l→∞ limit. The binding energies were 0.00317 hartree for e + Be, 0.0170 hartree for e + Mg, 0.0189 hartree for e + Ca, and 0.0131 hartree for e + Sr 5. Neutron star equilibrium configurations within a fully relativistic theory with strong, weak, electromagnetic, and gravitational interactions International Nuclear Information System (INIS) Belvedere, Riccardo; Pugliese, Daniela; Rueda, Jorge A.; Ruffini, Remo; Xue, She-Sheng 2012-01-01 We formulate the equations of equilibrium of neutron stars taking into account strong, weak, electromagnetic, and gravitational interactions within the framework of general relativity. The nuclear interactions are described by the exchange of the σ, ω, and ρ virtual mesons. The equilibrium conditions are given by our recently developed theoretical framework based on the Einstein–Maxwell–Thomas–Fermi equations along with the constancy of the general relativistic Fermi energies of particles, the “Klein potentials”, throughout the configuration. The equations are solved numerically in the case of zero temperatures and for selected parameterizations of the nuclear models. The solutions lead to a new structure of the star: a positively charged core at supranuclear densities surrounded by an electronic distribution of thickness ∼ℏ/(m e c)∼10 2 ℏ/(m π c) of opposite charge, as well as a neutral crust at lower densities. Inside the core there is a Coulomb potential well of depth ∼m π c 2 /e. The constancy of the Klein potentials in the transition from the core to the crust, imposes the presence of an overcritical electric field ∼(m π /m e ) 2 E c , the critical field being E c =m e 2 c 3 /(eℏ). The electron chemical potential and the density decrease, in the boundary interface, until values μ e crust e core and ρ crust core . For each central density, an entire family of core–crust interface boundaries and, correspondingly, an entire family of crusts with different mass and thickness, exist. The configuration with ρ crust =ρ drip ∼4.3×10 11 gcm −3 separates neutron stars with and without inner crust. We present here the novel neutron star mass–radius for the especial case ρ crust =ρ drip and compare and contrast it with the one obtained from the traditional Tolman–Oppenheimer–Volkoff treatment. 6. Evaluation of Early Ground Control Station Configurations for Interacting with a UAS Traffic Management (UTM) System Science.gov (United States) Dao, Arik-Quang V.; Martin, Lynne; Mohlenbrink, Christoph; Bienert, Nancy; Wolte, Cynthia; Gomez, Ashley; Claudatos, Lauren; Mercer, Joey 2017-01-01 The purpose of this paper is to report on a human factors evaluation of ground control station design concepts for interacting with an unmanned traffic management system. The data collected for this paper comes from recent field tests for NASA's Unmanned Traffic Management (UTM) project, and covers the following topics; workload, situation awareness, as well as flight crew communication, coordination, and procedures. The goal of this evaluation was to determine if the various software implementations for interacting with the UTM system can be described and classified into design concepts to provide guidance for the development of future UTM interfaces. We begin with a brief description of NASA's UTM project, followed by a description of the test range configuration related to a second development phase. We identified (post hoc) two classes in which the ground control stations could be grouped. This grouping was based on level of display integration. The analysis was exploratory and informal. It was conducted to compare ground stations across those two classes and against the aforementioned topics. Herein, we discuss the results. 7. Rabi like angular splitting in Surface Plasmon Polariton - Exciton interaction in ATR configuration Science.gov (United States) Hassan, Heba; Abdallah, T.; Negm, S.; Talaat, H. 2018-05-01 We have studied the coupling of propagating Surface Plasmon Polaritons (SPP) on silver films and excitons in CdS quantum dots (QDs). We employed the Kretschmann-Raether configuration of the attenuated total reflection (ATR) to propagate the SPP on silver film of thickness 47.5 nm at three different wavelengths. The CdS QD have been chemically synthesized with particular size such that its exciton of energy would resonate with SPP. High resolution transmission electron microscopy (HRTEM) and scan tunneling microscopy (STM) were used to measure the corresponding QDs size and confirm its shape. Further confirmation of the size has been performed by the effective mass approximation (EMA) model utilizing the band gap of the prepared QDs. The band gaps have been measured through UV-vis absorption spectra as well as scan tunneling spectroscopy (STS). The coupling has been observed as two branching dips in the ATR spectra indicating Rabi like splitting. To the best of our knowledge, this is the first time that Rabi interaction is directly observed in an ATR angular spectra. This observation is attributed to the use a high resolution angular scan (±0.005°), in addition to the Doppler width of the laser line as well as the energy distribution of the excitons. The effect of three different linker molecules (TOPO, HDA), (Pyridine) and (Tri-butylamine) as surface ligands, on SPP-Exciton interaction has been examined. 8. Magnetization reversal in magnetic dot arrays: Nearest-neighbor interactions and global configurational anisotropy Energy Technology Data Exchange (ETDEWEB) Van de Wiele, Ben [Department of Electrical Energy, Systems and Automation, Ghent University, Technologiepark 913, B-9052 Ghent-Zwijnaarde (Belgium); Fin, Samuele [Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, 44122 Ferrara (Italy); Pancaldi, Matteo [CIC nanoGUNE, E-20018 Donostia-San Sebastian (Spain); Vavassori, Paolo [CIC nanoGUNE, E-20018 Donostia-San Sebastian (Spain); IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao (Spain); Sarella, Anandakumar [Physics Department, Mount Holyoke College, 211 Kendade, 50 College St., South Hadley, Massachusetts 01075 (United States); Bisero, Diego [Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, 44122 Ferrara (Italy); CNISM, Unità di Ferrara, 44122 Ferrara (Italy) 2016-05-28 Various proposals for future magnetic memories, data processing devices, and sensors rely on a precise control of the magnetization ground state and magnetization reversal process in periodically patterned media. In finite dot arrays, such control is hampered by the magnetostatic interactions between the nanomagnets, leading to the non-uniform magnetization state distributions throughout the sample while reversing. In this paper, we evidence how during reversal typical geometric arrangements of dots in an identical magnetization state appear that originate in the dominance of either Global Configurational Anisotropy or Nearest-Neighbor Magnetostatic interactions, which depends on the fields at which the magnetization reversal sets in. Based on our findings, we propose design rules to obtain the uniform magnetization state distributions throughout the array, and also suggest future research directions to achieve non-uniform state distributions of interest, e.g., when aiming at guiding spin wave edge-modes through dot arrays. Our insights are based on the Magneto-Optical Kerr Effect and Magnetic Force Microscopy measurements as well as the extensive micromagnetic simulations. 9. Comparison of fully internally and strongly contracted multireference configuration interaction procedures Science.gov (United States) Sivalingam, Kantharuban; Krupicka, Martin; Auer, Alexander A.; Neese, Frank 2016-08-01 Multireference (MR) methods occupy an important class of approaches in quantum chemistry. In many instances, for example, in studying complex magnetic properties of transition metal complexes, they are actually the only physically satisfactory choice. In traditional MR approaches, single and double excitations are performed with respect to all reference configurations (or configuration state functions, CSFs), which leads to an explosive increase of computational cost for larger reference spaces. This can be avoided by the internal contraction scheme proposed by Meyer and Siegbahn, which effectively reduces the number of wavefunction parameters to their single-reference counterpart. The "fully internally contracted" scheme (FIC) is well known from the popular CASPT2 approach. An even shorter expansion of the wavefunction is possible with the "strong contraction" (SC) scheme proposed by Angeli and Malrieu in their NEVPT2 approach. Promising multireference configuration interaction formulations (MRCI) employing internal contraction and strong contraction have been reported by several authors. In this work, we report on the implementation of the FIC-MRCI and SC-MRCI methodologies, using a computer assisted implementation strategy. The methods are benchmarked against the traditional uncontracted MRCI approach for ground and excited states of small molecules (N2, O2, CO, CO+, OH, CH, and CN). For ground states, the comparison includes the "partially internally contracted" MRCI based on the Celani-Werner ansatz (PC-MRCI). For the three contraction schemes, the average errors range from 2% to 6% of the uncontracted MRCI correlation energies. Excitation energies are reproduced with ˜0.2 eV accuracy. In most cases, the agreement is better than 0.2 eV, even in cases with very large differential correlation contributions as exemplified for the d-d and ligand-to-metal charge transfer transitions of a Cu [NH 3 ] 4 2 + model complex. The benchmark is supplemented with the 10. Density matrix-based time-dependent configuration interaction approach to ultrafast spin-flip dynamics Science.gov (United States) Wang, Huihui; Bokarev, Sergey I.; Aziz, Saadullah G.; Kühn, Oliver 2017-08-01 Recent developments in attosecond spectroscopy yield access to the correlated motion of electrons on their intrinsic timescales. Spin-flip dynamics is usually considered in the context of valence electronic states, where spin-orbit coupling is weak and processes related to the electron spin are usually driven by nuclear motion. However, for core-excited states, where the core-hole has a nonzero angular momentum, spin-orbit coupling is strong enough to drive spin-flips on a much shorter timescale. Using density matrix-based time-dependent restricted active space configuration interaction including spin-orbit coupling, we address an unprecedentedly short spin-crossover for the example of L-edge (2p→3d) excited states of a prototypical Fe(II) complex. This process occurs on a timescale, which is faster than that of Auger decay (∼4 fs) treated here explicitly. Modest variations of carrier frequency and pulse duration can lead to substantial changes in the spin-state yield, suggesting its control by soft X-ray light. 11. Gauge-Invariant Formulation of Time-Dependent Configuration Interaction Singles Method Directory of Open Access Journals (Sweden) Takeshi Sato 2018-03-01 Full Text Available We propose a gauge-invariant formulation of the channel orbital-based time-dependent configuration interaction singles (TDCIS method [Phys. Rev. A, 74, 043420 (2006], one of the powerful ab initio methods to investigate electron dynamics in atoms and molecules subject to an external laser field. In the present formulation, we derive the equations of motion (EOMs in the velocity gauge using gauge-transformed time-dependent, not fixed, orbitals that are equivalent to the conventional EOMs in the length gauge using fixed orbitals. The new velocity-gauge EOMs avoid the use of the length-gauge dipole operator, which diverges at large distance, and allows us to exploit computational advantages of the velocity-gauge treatment over the length-gauge one, e.g., a faster convergence in simulations with intense and long-wavelength lasers, and the feasibility of exterior complex scaling as an absorbing boundary. The reformulated TDCIS method is applied to an exactly solvable model of one-dimensional helium atom in an intense laser field to numerically demonstrate the gauge invariance. We also discuss the consistent method for evaluating the time derivative of an observable, which is relevant, e.g., in simulating high-harmonic generation. 12. Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations Energy Technology Data Exchange (ETDEWEB) Aktulga, Hasan Metin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Buluc, Aydin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States) 2014-08-14 Obtaining highly accurate predictions on the properties of light atomic nuclei using the configuration interaction (CI) approach requires computing a few extremal Eigen pairs of the many-body nuclear Hamiltonian matrix. In the Many-body Fermion Dynamics for nuclei (MFDn) code, a block Eigen solver is used for this purpose. Due to the large size of the sparse matrices involved, a significant fraction of the time spent on the Eigen value computations is associated with the multiplication of a sparse matrix (and the transpose of that matrix) with multiple vectors (SpMM and SpMM-T). Existing implementations of SpMM and SpMM-T significantly underperform expectations. Thus, in this paper, we present and analyze optimized implementations of SpMM and SpMM-T. We base our implementation on the compressed sparse blocks (CSB) matrix format and target systems with multi-core architectures. We develop a performance model that allows us to understand and estimate the performance characteristics of our SpMM kernel implementations, and demonstrate the efficiency of our implementation on a series of real-world matrices extracted from MFDn. In particular, we obtain 3-4 speedup on the requisite operations over good implementations based on the commonly used compressed sparse row (CSR) matrix format. The improvements in the SpMM kernel suggest we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn. 13. A deterministic alternative to the full configuration interaction quantum Monte Carlo method Energy Technology Data Exchange (ETDEWEB) Tubman, Norm M.; Lee, Joonho; Takeshita, Tyler Y.; Head-Gordon, Martin; Whaley, K. Birgitta [University of California, Berkeley, Berkeley, California 94720 (United States) 2016-07-28 Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. However, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method that can achieve chemical accuracy for a wide range of systems, including the difficult Cr{sub 2} molecule. We demonstrate for systems like Cr{sub 2} that such calculations can be performed in just a few cpu hours which makes it one of the most efficient and accurate methods that can attain chemical accuracy for strongly correlated systems. In addition our method also allows efficient calculation of excited state energies, which we illustrate with benchmark results for the excited states of C{sub 2}. 14. Relativistic configuration interaction calculation on the ground and excited states of iridium monoxide International Nuclear Information System (INIS) Suo, Bingbing; Yu, Yan-Mei; Han, Huixian 2015-01-01 We present the fully relativistic multi-reference configuration interaction calculations of the ground and low-lying excited electronic states of IrO for individual spin-orbit component. The lowest-lying state is calculated for Ω = 1/2, 3/2, 5/2, and 7/2 in order to clarify the ground state of IrO. Our calculation suggests that the ground state is of Ω = 1/2, which is highly mixed with 4 Σ − and 2 Π states in Λ − S notation. The two low-lying states 5/2 and 7/2 are nearly degenerate with the ground state and locate only 234 and 260 cm −1 above, respectively. The equilibrium bond length 1.712 Å and the harmonic vibrational frequency 903 cm −1 of the 5/2 state are close to the experimental measurement of 1.724 Å and 909 cm −1 , which suggests that the 5/2 state should be the low-lying state that contributes to the experimental spectra. Moreover, the electronic states that give rise to the observed transition bands are assigned for Ω = 5/2 and 7/2 in terms of the obtained excited energies and oscillator strengths 15. Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format. Science.gov (United States) Böhm, Karl-Heinz; Auer, Alexander A; Espig, Mike 2016-06-28 In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms. 16. Charge transfer dynamics from adsorbates to surfaces with single active electron and configuration interaction based approaches Energy Technology Data Exchange (ETDEWEB) Ramakrishnan, Raghunathan, E-mail: [email protected] [Institute of Physical Chemistry, National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel (Switzerland); Nest, Mathias [Theoretische Chemie, Technische Universität München, Lichtenbergstr. 4, 85747 Garching (Germany) 2015-01-13 Highlights: • We model electron dynamics across cyano alkanethiolates attached to gold cluster. • We present electron transfer time scales from TD-DFT and TD-CI based simulations. • Both DFT and CI methods qualitatively predict the trend in time scales. • TD-CI predicts the experimental relative time scale very accurately. - Abstract: We employ wavepacket simulations based on many-body time-dependent configuration interaction (TD-CI), and single active electron theories, to predict the ultrafast molecule/metal electron transfer time scales, in cyano alkanethiolates bonded to model gold clusters. The initial states represent two excited states where a valence electron is promoted to one of the two virtual π{sup ∗} molecular orbitals localized on the cyanide fragment. The ratio of the two time scales indicate the efficiency of one charge transfer channel over the other. In both our one-and many-electron simulations, this ratio agree qualitatively with each other as well as with the previously reported experimental time scales (Blobner et al., 2012), measured for a macroscopic metal surface. We study the effect of cluster size and the description of electron correlation on the charge transfer process. 17. Exponentially more precise quantum simulation of fermions in the configuration interaction representation Science.gov (United States) Babbush, Ryan; Berry, Dominic W.; Sanders, Yuval R.; Kivlichan, Ian D.; Scherer, Artur; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán 2018-01-01 We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in Babbush et al (2016 New Journal of Physics 18, 033032), we employ a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require \\widetilde{{ O }}(N) qubits, where N is the number of single-particle spin-orbitals, the CI matrix representation requires \\widetilde{{ O }}(η ) qubits, where η \\ll N is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as \\widetilde{{ O }}({η }2{N}3t). 18. Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy. Science.gov (United States) Bytautas, Laimutis; Henderson, Thomas M; Jiménez-Hoyos, Carlos A; Ellis, Jason K; Scuseria, Gustavo E 2011-07-28 We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electron correlation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N(2) and CO(2) molecules, as well as the symmetric dissociation of an H(8) hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction. © 2011 American Institute of Physics 19. Competition between intermolecular interaction and configuration entropy as the structure-determining factor for inclusion compounds Energy Technology Data Exchange (ETDEWEB) Subbotin, O.; Belosludov, V.; Adamova, T. [Russian Academy of Science, Novosibirsk (Russian Federation). Nikolaev Inst. of Inorganic Chemistry; Belosludov, R.; Kawazoe, Y. [Tohoku Univ., Aoba-ku, Sendai (Japan). Inst. for Materials Research; Kudoh, J.I. [Tohoku Univ., Aoba-ku, Sendai (Japan). Center for Northeast Asia Studies 2008-07-01 This paper presented a newly developed method to accurately predict the thermodynamic properties of clathrate hydrates, particularly their structural phase transitions under pressure. The method is based on the theory of Van-der-Waals and Platteeuw with some modifications that include the influence of guest molecules on the host lattice. The model was used to explain the exception from the established rule that small guest molecules form structure s1 and large molecules form structure s2 hydrates. In this study, the thermodynamic properties of argon (Ar) hydrate and methane hydrate, each in both cubic structure s1 and s2 were modelled. The model showed that two competing factors play a role in the formation of inclusions, notably the intermolecular interaction of guest molecules with water molecules, and the configuration entropy. Competition of these 2 factors determines the structure of hydrate formed at different pressures. The model provides an accurate description of the thermodynamic properties of gas hydrates and how they behave under pressure. For the argon hydrates, the structural phase transition from structure s2 to s1 at high pressure was predicted, while methane hydrates were predicted to be metastable in the s2 structure. The model can be used for other inclusion compounds with the same type of composition such as clathrate silicon, zeolites, and inclusion compounds of semiconductor elements. 17 refs., 5 figs. 20. Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method Energy Technology Data Exchange (ETDEWEB) Lötstedt, Erik, E-mail: [email protected]; Kato, Tsuyoshi; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan) 2016-04-21 An approximate implementation of the multiconfiguration time-dependent Hartree-Fock method is proposed, in which the matrix of configuration-interaction coefficients is decomposed into a product of matrices of smaller dimension. The applicability of this method in which all the configurations are kept in the expansion of the wave function, while the configuration-interaction coefficients are approximately calculated, is discussed by showing the results on three model systems: a one-dimensional model of a beryllium atom, a one-dimensional model of a carbon atom, and a one-dimensional model of a chain of four hydrogen atoms. The time-dependent electronic dynamics induced by a few-cycle, long-wavelength laser pulse is found to be well described at a lower computational cost compared to the standard multiconfiguration time-dependent Hartree-Fock treatment. Drawbacks of the method are also discussed. 1. Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction DEFF Research Database (Denmark) Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A. 2008-01-01 Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole... 2. Criticality in the configuration-mixed interacting boson model: (1) U(5)-Q(χ)Q(χ) mixing International Nuclear Information System (INIS) Hellemans, V.; Van Isacker, P.; De Baerdemacker, S.; Heyde, K. 2007-01-01 The case of U(5)-Q(χ)Q(χ) mixing in the configuration-mixed interacting boson model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively 3. Large-scale parallel configuration interaction. I. Nonrelativisticand scalar-relativistic general active space implementationwith application to (Rb-Ba)+ DEFF Research Database (Denmark) Knecht, Stefan; Jensen, Hans Jørgen Aagaard; Fleig, Timo 2008-01-01 We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation... 4. Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields. Science.gov (United States) 2016-05-14 In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN. 5. Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields Energy Technology Data Exchange (ETDEWEB) Klinkusch, Stefan; Tremblay, Jean Christophe [Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin (Germany) 2016-05-14 In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN. 6. An atomistic geometrical model of the B-DNA configuration for DNA-radiation interaction simulations Science.gov (United States) Bernal, M. A.; Sikansi, D.; Cavalcante, F.; Incerti, S.; Champion, C.; Ivanchenko, V.; Francis, Z. 2013-12-01 In this paper, an atomistic geometrical model for the B-DNA configuration is explained. This model accounts for five organization levels of the DNA, up to the 30 nm chromatin fiber. However, fragments of this fiber can be used to construct the whole genome. The algorithm developed in this work is capable to determine which is the closest atom with respect to an arbitrary point in space. It can be used in any application in which a DNA geometrical model is needed, for instance, in investigations related to the effects of ionizing radiations on the human genetic material. Successful consistency checks were carried out to test the proposed model. Catalogue identifier: AEPZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1245 No. of bytes in distributed program, including test data, etc.: 6574 Distribution format: tar.gz Programming language: FORTRAN. Computer: Any. Operating system: Multi-platform. RAM: 2 Gb Classification: 3. Nature of problem: The Monte Carlo method is used to simulate the interaction of ionizing radiation with the human genetic material in order to determine DNA damage yields per unit absorbed dose. To accomplish this task, an algorithm to determine if a given energy deposition lies within a given target is needed. This target can be an atom or any other structure of the genetic material. Solution method: This is a stand-alone subroutine describing an atomic-resolution geometrical model of the B-DNA configuration. It is able to determine the closest atom to an arbitrary point in space. This model accounts for five organization levels of the human genetic material, from the nucleotide pair up to the 30 nm chromatin fiber. This subroutine carries out a series of coordinate transformations 7. Light-matter interaction in the strong coupling regime: configurations, conditions, and applications. Science.gov (United States) Dovzhenko, D S; Ryabchuk, S V; Rakovich, Yu P; Nabiev, I R 2018-02-22 Resonance interaction between a molecular transition and a confined electromagnetic field can reach the coupling regime where coherent exchange of energy between light and matter becomes reversible. In this case, two new hybrid states separated in energy are formed instead of independent eigenstates, which is known as Rabi splitting. This modification of the energy spectra of the system offers new possibilities for controlled impact on various fundamental properties of coupled matter (such as the rate of chemical reactions and the conductivity of organic semiconductors). To date, the strong coupling regime has been demonstrated in many configurations under different ambient conditions. However, there is still no comprehensive approach to determining parameters for achieving the strong coupling regime for a wide range of practical applications. In this review, a detailed analysis of various systems and corresponding conditions for reaching strong coupling is carried out and their advantages and disadvantages, as well as the prospects for application, are considered. The review also summarizes recent experiments in which the strong coupling regime has led to new interesting results, such as the possibility of collective strong coupling between X-rays and matter excitation in a periodic array of Fe isotopes, which extends the applications of quantum optics; a strong amplification of the Raman scattering signal from a coupled system, which can be used in surface-enhanced and tip-enhanced Raman spectroscopy; and more efficient second-harmonic generation from the low polaritonic state, which is promising for nonlinear optics. The results reviewed demonstrate great potential for further practical applications of strong coupling in the fields of photonics (low-threshold lasers), quantum communications (switches), and biophysics (molecular fingerprinting). 8. Gamow-Teller response in the configuration space of a density-functional-theory-rooted no-core configuration-interaction model Science.gov (United States) Konieczka, M.; Kortelainen, M.; Satuła, W. 2018-03-01 Background: The atomic nucleus is a unique laboratory in which to study fundamental aspects of the electroweak interaction. This includes a question concerning in medium renormalization of the axial-vector current, which still lacks satisfactory explanation. Study of spin-isospin or Gamow-Teller (GT) response may provide valuable information on both the quenching of the axial-vector coupling constant as well as on nuclear structure and nuclear astrophysics. Purpose: We have performed a seminal calculation of the GT response by using the no-core configuration-interaction approach rooted in multireference density functional theory (DFT-NCCI). The model treats properly isospin and rotational symmetries and can be applied to calculate both the nuclear spectra and transition rates in atomic nuclei, irrespectively of their mass and particle-number parity. Methods: The DFT-NCCI calculation proceeds as follows: First, one builds a configuration space by computing relevant, for a given physical problem, (multi)particle-(multi)hole Slater determinants. Next, one applies the isospin and angular-momentum projections and performs the isospin and K mixing in order to construct a model space composed of linearly dependent states of good angular momentum. Eventually, one mixes the projected states by solving the Hill-Wheeler-Griffin equation. Results: The method is applied to compute the GT strength distribution in selected N ≈Z nuclei including the p -shell 8Li and 8Be nuclei and the s d -shell well-deformed nucleus 24Mg. In order to demonstrate a flexibility of the approach we present also a calculation of the superallowed GT β decay in doubly-magic spherical 100Sn and the low-spin spectrum in 100In. Conclusions: It is demonstrated that the DFT-NCCI model is capable of capturing the GT response satisfactorily well by using a relatively small configuration space, exhausting simultaneously the GT sum rule. The model, due to its flexibility and broad range of applicability, may 9. Fish-robot interactions in a free-swimming environment: Effects of speed and configuration of robots on live fish Science.gov (United States) Butail, Sachit; Polverino, Giovanni; Phamduy, Paul; Del Sette, Fausto; Porfiri, Maurizio 2014-03-01 We explore fish-robot interactions in a comprehensive set of experiments designed to highlight the effects of speed and configuration of bioinspired robots on live zebrafish. The robot design and movement is inspired by salient features of attraction in zebrafish and includes enhanced coloration, aspect ratio of a fertile female, and carangiform/subcarangiformlocomotion. The robots are autonomously controlled to swim in circular trajectories in the presence of live fish. Our results indicate that robot configuration significantly affects both the fish distance to the robots and the time spent near them. 10. Mixing of the lowest-lying qqq configurations with JP =1/2- in different hyperfine interaction models Science.gov (United States) Chen, Jia; An, Chunsheng; Chen, Hong 2018-02-01 We investigate mixing of the lowest-lying qqq configurations with JP = 1/2- caused by the hyperfine interactions between quarks mediated by Goldstone Boson Exchange, One Gluon Exchange, and both Goldstone Boson and One Gluon exchange, respectively. The first orbitally excited nucleon, Σ, Λ and Ξ states are considered. Contributions of both the contact term and tensor term are taken into account. Our numerical results show that mixing of the studied configurations in the two employed hyperfine interaction models are very different. Therefore, the present results, which should affect the strong and electromagnetic decays of baryon resonances, may be used to examine the present employed hyperfine interaction models. Supported by National Natural Science Foundation of China (11675131,11645002), Chongqing Natural Science Foundation (cstc2015jcyjA00032) and Fundamental Research Funds for the Central Universities (SWU115020) 11. Configuration Management International Nuclear Information System (INIS) Morcos, A.; Taylor, H. S. 1989-01-01 This paper will briefly discuss the reason for and content of configuration management both for new plants and, when adapted, for older plants. It will then address three types of activities a utility may undertake as part of a nuclear CAM program and with which Sargent and Leyden has been actively involved. The first activity is a methodology for preparing design-basis documentation. The second is the identification of essential data required to be kept by the utility in support of the operation of a nuclear plant. The third activity is a computerized classification system of plant components, allowing ready identification of plant functional and physical characteristics. Plant configuration documentation describes plant components, the ways they arranged to interact, and the ways they are enabled to interact. Configuration management, on the other hand, is more than the control of such documentation. It is a dynamic process for ensuring that a plant configuration meets all relevant requirements for safety and economy, even while the configuration changes and even while the requirements change. Configuration management for a nuclear plant is so complex that it must be implemented in phases and modules. It takes advantage of and integrates existing programs. Managing complexity and streamlining the change process become important additional objectives of configuration management. The example activities fulfill essential goals of an overall CAM program: definition of design baseline, definition of essential plant data, and classification of plant components 12. Parallel multireference configuration interaction calculations on mini-β-carotenes and β-carotene Science.gov (United States) Kleinschmidt, Martin; Marian, Christel M.; Waletzke, Mirko; Grimme, Stefan 2009-01-01 We present a parallelized version of a direct selecting multireference configuration interaction (MRCI) code [S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999)]. The program can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRCI). We have investigated the efficiency of the parallelization in case studies on carotenoids and porphyrins. The performance is found to depend heavily on the cluster architecture. While the speed-up on the older Intel Netburst technology is close to linear for up to 12-16 processes, our results indicate that it is not favorable to use all cores of modern Intel Dual Core or Quad Core processors simultaneously for memory intensive tasks. Due to saturation of the memory bandwidth, we recommend to run less demanding tasks on the latter architectures in parallel to two (Dual Core) or four (Quad Core) MRCI processes per node. The DFT/MRCI branch has been employed to study the low-lying singlet and triplet states of mini-n-β-carotenes (n =3, 5, 7, 9) and β-carotene (n =11) at the geometries of the ground state, the first excited triplet state, and the optically bright singlet state. The order of states depends heavily on the conjugation length and the nuclear geometry. The B1u+ state constitutes the S1 state in the vertical absorption spectrum of mini-3-β-carotene but switches order with the 2 A1g- state upon excited state relaxation. In the longer carotenes, near degeneracy or even root flipping between the B1u+ and B1u- states is observed whereas the 3 A1g- state is found to remain energetically above the optically bright B1u+ state at all nuclear geometries investigated here. The DFT/MRCI method is seen to underestimate the absolute excitation energies of the longer mini-β-carotenes but the energy gaps between the excited states are reproduced well. In addition to singlet data, triplet-triplet absorption energies are presented. For β-carotene, where these transition 13. Parallel multireference configuration interaction calculations on mini-beta-carotenes and beta-carotene. Science.gov (United States) Kleinschmidt, Martin; Marian, Christel M; Waletzke, Mirko; Grimme, Stefan 2009-01-28 We present a parallelized version of a direct selecting multireference configuration interaction (MRCI) code [S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999)]. The program can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRCI). We have investigated the efficiency of the parallelization in case studies on carotenoids and porphyrins. The performance is found to depend heavily on the cluster architecture. While the speed-up on the older Intel Netburst technology is close to linear for up to 12-16 processes, our results indicate that it is not favorable to use all cores of modern Intel Dual Core or Quad Core processors simultaneously for memory intensive tasks. Due to saturation of the memory bandwidth, we recommend to run less demanding tasks on the latter architectures in parallel to two (Dual Core) or four (Quad Core) MRCI processes per node. The DFT/MRCI branch has been employed to study the low-lying singlet and triplet states of mini-n-beta-carotenes (n=3, 5, 7, 9) and beta-carotene (n=11) at the geometries of the ground state, the first excited triplet state, and the optically bright singlet state. The order of states depends heavily on the conjugation length and the nuclear geometry. The (1)B(u) (+) state constitutes the S(1) state in the vertical absorption spectrum of mini-3-beta-carotene but switches order with the 2 (1)A(g) (-) state upon excited state relaxation. In the longer carotenes, near degeneracy or even root flipping between the (1)B(u) (+) and (1)B(u) (-) states is observed whereas the 3 (1)A(g) (-) state is found to remain energetically above the optically bright (1)B(u) (+) state at all nuclear geometries investigated here. The DFT/MRCI method is seen to underestimate the absolute excitation energies of the longer mini-beta-carotenes but the energy gaps between the excited states are reproduced well. In addition to singlet data, triplet-triplet absorption energies are 14. Critical comparison between equation of motion-Green's function methods and configuration interaction methods: analysis of methods and applications International Nuclear Information System (INIS) Freed, K.F.; Herman, M.F.; Yeager, D.L. 1980-01-01 A description is provided of the common conceptual origins of many-body equations of motion and Green's function methods in Liouville operator formulations of the quantum mechanics of atomic and molecular electronic structure. Numerical evidence is provided to show the inadequacies of the traditional strictly perturbative approaches to these methods. Nonperturbative methods are introduced by analogy with techniques developed for handling large configuration interaction calculations and by evaluating individual matrix elements to higher accuracy. The important role of higher excitations is exhibited by the numerical calculations, and explicit comparisons are made between converged equations of motion and configuration interaction calculations for systems where a fundamental theorem requires the equality of the energy differences produced by these different approaches. (Auth.) 15. Patterns in the Pythagorean Configuration and Some Extensions: The Power of Interactive Geometry Software Science.gov (United States) Contreras, José 2015-01-01 In this paper I describe classroom experiences with pre-service secondary mathematics teachers (PSMTs) investigating and extending patterns embedded in the Pythagorean configuration. This geometric figure is a fruitful source of mathematical tasks to help students, including PSMTs, further develop habits of mind such as visualization,… 16. Configuration interaction effect on open M shell Fe and Ni LTE spectral opacities, Rosseland and Planck means International Nuclear Information System (INIS) Gilles, D; Busquet, M; Gilleron, F; Pain, J-C; Klapisch, M 2016-01-01 We have recently shown that iron and nickel open M-shell opacity spectra, up to Δn = 2 are very sensitive to Configuration Interaction (CI) treatments at temperature around 15 eV and for various densities. To do so we had compared extensive CI calculations obtained with two opacity codes HULLAC-v9 and SCO-RCG. In this work we extend these comparisons to a first evaluation of CI effects on Rosseland and Planck means. (paper) 17. Simulation of Molten Core-Concrete Interaction in oxide/metal stratified configuration with the TOLBIAC-ICB code International Nuclear Information System (INIS) Tourniaire, B.; Spindler, B. 2005-01-01 The frame of this work is the validation of the TOLBIAC-ICB code which is devoted to the simulation of Molten Core-Concrete Interaction (MCCI) for reactor safety analysis. Attention focuses here on the validation of TOLBIAC-ICB in configurations expected to be representative of the long term phase of MCCI i.e. during an interaction between an oxide/metal stratified corium melt and a concrete structure. Up to now the BETA tests performed at the Forschungszentrum Karlsruhe (FzK) are the only tests available to study such kind of interaction. The BETA tests are first described and the operating conditions are reminded. The TOLBIAC-ICB code is then briefly described, with emphasis on the models used for stratified configurations. The results of the simulations are discussed. A sensitivity study is also performed with the power generated in the oxide layer instead of the metal layer as in the test. This last calculation shows that the large axial ablation observed in the tests is probably due to the peculiar configuration of the test with input power in the bottom metal layer. Since in the reactor case the residual power would be mainly concentrated in the upper oxide layer, the conclusions of the BETA tests for the reactor applications, in term of axial ablation, must be derived with caution. (author) 18. Theoretical studies on CH+ ion molecule using configuration interaction method and its spectroscopic properties International Nuclear Information System (INIS) 1985-01-01 The use of the configuration (CI) method for the calculation of very accurate potential energy curves and dipole moment functions, and then their use in the comprehension of spectroscopic properties of diatomic molecules is presented. The spectroscopic properties of CH + and CD + such as: vibrational levels, spectroscopic constants, averaged dipole moments for all vibrational levels, radiative transition probabilities for emission and absorption, and radiative lifetimes are verificated. (M.J.C.) [pt 19. Global characteristics of atomic spectra and their use for the analysis of spectra. IV. Configuration interaction effects International Nuclear Information System (INIS) Kucas, S.; Jonauskas, V.; Karazija, R. 1997-01-01 For pt.III see ibid., vol.52, p.639, 1995. Changes of the moments of atomic spectrum due to configuration interaction (CI), the CI strength, the average shift of the energy of a level due to its interaction with all levels of distant configuration and other global characteristics of CI effects in atoms are systematised and their expressions presented. The results of the calculation of those characteristics for the energy level spectra of the 3s3p 3 + 3s 2 3p3d configurations in Si isoelectronic series, 3p 5 3d N + 3p 6 3d N-2 4p + 3p 6 3d N-2 4f (N = 5, 6, 7, 8) in Cr, Mn, Fe and Co isoelectronic series, ns 2 np N + np N+2 at n = 2 - 5 and N = 2 - 4 in neutral atoms as well as for the characteristic emission spectra corresponding to the 3p 5 3d 9 + 3d 7 4p → 3d 8 transitions as well as for the Auger M 4.3 N 1 N 2.3 spectra in Kr and N 4.5 O 1 O 2.3 in Xe are given and compared with the same characteristics of the more complete experimental spectra. (orig.) 20. Nanomechanics modeling of carbon nanotubes interacting with surfaces in various configurations Science.gov (United States) Wu, Yu-Chiao Carbon nanotubes (CNTs) have been widely used as potential components in reported nanoelectromechanical (NEM) devices due to their excellent mechanical and electrical properties. This thesis models the experiments by the continuum mechanics in two distinct scenarios. In the first situation, measurements are made of CNT configurations after manipulations. Modeling is then used to determine the interfacial properties during the manipulation which led to the observed configuration. This technique is used to determine the shear stress between a SWNT bundle and other materials. During manipulation, a SWNT bundle slipped on two micro-cantilevers. According to the slack due to the slippage after testing and the device configuration, the shear stress between a SWNT bundle and other materials can be determined. In another model, the work of adhesion was determined on two accidentally fabricated devices. Through the configuration of two SWNT adhered bundles and the force-distance curves measured by an atomic force microscope (AFM), modeling was used to determine the work of adhesion between two bundles and the shear stress at the SWNT-substrate interface. In the second situation, modeling is used in a more traditional fashion to make theoretical predictions as to how a device will operate. Using this technique, the actuation mechanism of a single-trench SWNT-based switch was investigated. During the actuation, the deflection-induced tension causes the SWNT bundle to slip on both platforms and to be partially peeled from two side recessed electrodes. These effects produce a slack which reduces the threshold voltages subsequent to the first actuation. The result shows excellent agreement between the theory and the measurement. Furthermore, the operation of a double-trenched SWNT-based switch was investigated. A slack is produced in the 1st actuated trench region by the slip and peeling effects. This slack reduces the 2nd actuation voltage in the neighbor trench. Finally, the 1. Ab initio configuration interaction description of excitation energy transfer between closely packed molecules International Nuclear Information System (INIS) Fink, R.F.; Pfister, J.; Schneider, A.; Zhao, H.; Engels, B. 2008-01-01 We present new, generally applicable protocols for the computation of the coupling parameter, J, of excitation energy transfer with quantum chemical ab initio methods. The protocols allow to select the degree of approximation and computational demand such that they are applicable for realistic systems and still allow to control the quality of the approach. We demonstrate the capabilities of the different protocols using the CO dimer as a first example. Correlation effects are found to scale J by a factor of about 0.7 which is in good agreement to earlier results obtained for the ethene dimer. The various levels of the protocol allow to assess the influence of ionic configurations and the polarisation within the dimer. Further, the interplay between the Foerster and Dexter contribution to J is investigated. The computations also show error compensation within approximations that are widely used for extended systems as in particular the transition density cube method 2. Vortex configuration and vortex-vortex interaction in nano-structured superconductors International Nuclear Information System (INIS) Kato, Masaru; Niwa, Yuhei; Suematsu, Hisataka; Ishida, Takekazu 2012-01-01 We study the vortex structures and quasi-particle structures in nano-structured superconductors. We used the Bogoliubov-de Gennes equation and the finite element method and obtained stable magnetic flux structures and the quasi-particle states. We found the vortex configurations are affected by the interference of the quasi-particle bound states around the vortices. In order to clarify the interference between the quasi-particle wave-functions around two vortices we have developed a numerical method using the elliptic coordinates and the Mathieu functions. We apply this method to two singly quantized vortex state in a conventional s-wave superconductor and a pair of half-quantum vortices in a chiral p-wave superconductor. 3. Ab initio configuration interaction description of excitation energy transfer between closely packed molecules Energy Technology Data Exchange (ETDEWEB) Fink, R.F. [University of Wuerzburg, Institute of Organic Chemistry, Am Hubland, D-97074 Wuerzburg (Germany)], E-mail: [email protected]; Pfister, J.; Schneider, A.; Zhao, H.; Engels, B. [University of Wuerzburg, Institute of Organic Chemistry, Am Hubland, D-97074 Wuerzburg (Germany) 2008-01-29 We present new, generally applicable protocols for the computation of the coupling parameter, J, of excitation energy transfer with quantum chemical ab initio methods. The protocols allow to select the degree of approximation and computational demand such that they are applicable for realistic systems and still allow to control the quality of the approach. We demonstrate the capabilities of the different protocols using the CO dimer as a first example. Correlation effects are found to scale J by a factor of about 0.7 which is in good agreement to earlier results obtained for the ethene dimer. The various levels of the protocol allow to assess the influence of ionic configurations and the polarisation within the dimer. Further, the interplay between the Foerster and Dexter contribution to J is investigated. The computations also show error compensation within approximations that are widely used for extended systems as in particular the transition density cube method. 4. The Relationship Between Spatial Configuration and Social Interaction in High-Rise Flats: A Case Study On The Jatinegara Barat in Jakarta. Directory of Open Access Journals (Sweden) Ridwana Rifan 2018-01-01 The results of this study indicate that: (1 the relationship of spatial configuration to social interaction level in Jatinegara Barat flats can be positive or negative. (2 Positive relationships are found on the1st and 2ndfloor areas. High configuration values with high interaction levels are found in shared spaces on the 1st and 2nd floors with characteristics such as open space, large space, and availability of interaction supporting elements, while low configuration values with low interaction levels are found in more confined spaces such as private spaces and narrow corridors. (3 Negative relationships are found in the corridor and shared space in front of the elevator on each typical floors. Shared space in front of the elevator that has high spatial configuration value with large area show a low level of social interaction. While corridor with lower configuration value with the narrow area but have supporting elements such as chairs, mats, and shops have a higher level of social interaction. (4 This study shows that in the case of the relationship between spatial configuration and social interaction, availability of interaction supporting elements has greater influence rather than any other spatial factors. 5. Simulations of two sedimenting-interacting spheres with different sizes and initial configurations using immersed boundary method Science.gov (United States) Liao, Chuan-Chieh; Hsiao, Wen-Wei; Lin, Ting-Yu; Lin, Chao-An 2015-06-01 Numerical investigations are carried out for the drafting, kissing and tumbling (DKT) phenomenon of two freely falling spheres within a long container by using an immersed-boundary method. The method is first validated with flows induced by a sphere settling under gravity in a small container for which experimental data are available. The hydrodynamic interactions of two spheres are then studied with different sizes and initial configurations. When a regular sphere is placed below the larger one, the duration of kissing decreases in pace with the increase in diameter ratio. On the other hand, the time duration of the kissing stage increases in tandem with the increase in diameter ratio as the large sphere is placed below the regular one, and there is no DKT interactions beyond threshold diameter ratio. Also, the gap between homogeneous spheres remains constant at the terminal velocity, whereas the gaps between the inhomogeneous spheres increase due to the differential terminal velocity. 6. The ionic states of iodobenzene studied by photoionization and ab initio configuration interaction and DFT computations International Nuclear Information System (INIS) Palmer, Michael H.; Ridley, Trevor; Hoffmann, Søren Vrønning; Jones, Nykola C.; Coreno, Marcello; Simone, Monica de; Grazioli, Cesare; Biczysko, Malgorzata; Baiardi, Alberto 2015-01-01 New valence electron photoelectron spectra of iodobenzene obtained using synchrotron radiation have been recorded. Ionization energies (IEs) determined using multi-configuration SCF calculation (MCSCF) procedures confirmed the adiabatic IE order as: X 2 B 1 7. International Nuclear Information System (INIS) Chouh, Hamza 2016-01-01 In order to fulfill increasing reliability and safety requirements, non-destructive testing techniques are constantly evolving and so does their complexity. Consequently, simulation is an essential part of their design. We developed a tool for the simulation of the ultrasonic field radiated by any planar probes into non-destructive testing configurations involving meshed geometries without prominent edges, isotropic and anisotropic, homogeneous and heterogeneous materials, and wave trajectories that can include reflections and transmissions. We approximate the ultrasonic wave fronts by using polynomial interpolators that are local to ultrasonic ray pencils. They are obtained using a surface research algorithm based on pencil tracing and successive subdivisions. Their interpolators enable the computation of the necessary quantities for the impulse responses on each point of a sampling of the transducer surface that fulfills the Shannon criterion. By doing so, we can compute a global impulse response which, when convolved with the excitation signal of the transducer, results in the ultrasonic field. The usage of task parallelism and of SIMD instructions on the most computationally expensive steps yields an important performance boost. Finally, we developed a tool for progressive visualization of field images. It benefits from an image reconstruction technique and schedules field computations in order to accelerate convergence towards the final image. (author) [fr 8. Adaptive vibrational configuration interaction (A-VCI): A posteriori error estimation to efficiently compute anharmonic IR spectra Science.gov (United States) Garnier, Romain; Odunlami, Marc; Le Bris, Vincent; Bégué, Didier; Baraille, Isabelle; Coulaud, Olivier 2016-05-01 A new variational algorithm called adaptive vibrational configuration interaction (A-VCI) intended for the resolution of the vibrational Schrödinger equation was developed. The main advantage of this approach is to efficiently reduce the dimension of the active space generated into the configuration interaction (CI) process. Here, we assume that the Hamiltonian writes as a sum of products of operators. This adaptive algorithm was developed with the use of three correlated conditions, i.e., a suitable starting space, a criterion for convergence, and a procedure to expand the approximate space. The velocity of the algorithm was increased with the use of a posteriori error estimator (residue) to select the most relevant direction to increase the space. Two examples have been selected for benchmark. In the case of H2CO, we mainly study the performance of A-VCI algorithm: comparison with the variation-perturbation method, choice of the initial space, and residual contributions. For CH3CN, we compare the A-VCI results with a computed reference spectrum using the same potential energy surface and for an active space reduced by about 90%. 9. Spin-flip configuration interaction singles with exact spin-projection: Theory and applications to strongly correlated systems. Science.gov (United States) Tsuchimochi, Takashi 2015-10-14 Spin-flip approaches capture static correlation with the same computational scaling as the ordinary single reference methods. Here, we extend spin-flip configuration interaction singles (SFCIS) by projecting out intrinsic spin-contamination to make it spin-complete, rather than by explicitly complementing it with spin-coupled configurations. We give a general formalism of spin-projection for SFCIS, applicable to any spin states. The proposed method is viewed as a natural unification of SFCIS and spin-projected CIS to achieve a better qualitative accuracy at a low computational cost. While our wave function ansatz is more compact than previously proposed spin-complete SF approaches, it successfully offers more general static correlation beyond biradicals without sacrificing good quantum numbers. It is also shown that our method is invariant with respect to open-shell orbital rotations, due to the uniqueness of spin-projection. We will report benchmark calculations to demonstrate its qualitative performance on strongly correlated systems, including conical intersections that appear both in ground-excited and excited-excited degeneracies. 10. Two-electron states of a group-V donor in silicon from atomistic full configuration interactions Science.gov (United States) Tankasala, Archana; Salfi, Joseph; Bocquel, Juanita; Voisin, Benoit; Usman, Muhammad; Klimeck, Gerhard; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.; Rogge, Sven; Rahman, Rajib 2018-05-01 Two-electron states bound to donors in silicon are important for both two-qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multielectron exchange and correlation effects taking into account the full band structure of silicon and the atomic-scale granularity of a nanoscale device. Excited s -like states of A1 symmetry are found to strongly influence the charging energy of a negative donor center. We apply the technique on subsurface dopants subjected to gate electric fields and show that bound triplet states appear in the spectrum as a result of decreased charging energy. The exchange energy, obtained for the two-electron states in various confinement regimes, may enable engineering electrical control of spins in donor-dot hybrid qubits. 11. Laser-induced electron dynamics including photoionization: A heuristic model within time-dependent configuration interaction theory. Science.gov (United States) Klinkusch, Stefan; Saalfrank, Peter; Klamroth, Tillmann 2009-09-21 We report simulations of laser-pulse driven many-electron dynamics by means of a simple, heuristic extension of the time-dependent configuration interaction singles (TD-CIS) approach. The extension allows for the treatment of ionizing states as nonstationary states with a finite, energy-dependent lifetime to account for above-threshold ionization losses in laser-driven many-electron dynamics. The extended TD-CIS method is applied to the following specific examples: (i) state-to-state transitions in the LiCN molecule which correspond to intramolecular charge transfer, (ii) creation of electronic wave packets in LiCN including wave packet analysis by pump-probe spectroscopy, and, finally, (iii) the effect of ionization on the dynamic polarizability of H(2) when calculated nonperturbatively by TD-CIS. 12. Propulsion and airframe aerodynamic interactions of supersonic V/STOL configurations. Volume 2: Wind tunnel test force and moment data report Science.gov (United States) Zilz, D. E. 1985-01-01 A wind tunnel model of a supersonic V/STOL fighter configuration has been tested to measure the aerodynamic interaction effects which can result from geometrically close-coupled propulsion system/airframe components. The approach was to configure the model to represent two different test techniques. One was a conventional test technique composed of two test modes. In the Flow-Through mode, absolute configuration aerodynamics are measured, including inlet/airframe interactions. In the Jet-Effects mode, incremental nozzle/airframe interactions are measured. The other test technique is a propulsion simulator approach, where a sub-scale, externally powered engine is mounted in the model. This allows proper measurement of inlet/airframe and nozzle/airframe interactions simultaneously. This is Volume 2 of 2: Wind Tunnel Test Force and Moment Data Report. 13. Interactive effects of size, contrast, intensity and configuration of background objects in evoking disruptive camouflage in cuttlefish. Science.gov (United States) Chiao, Chuan-Chin; Chubb, Charles; Hanlon, Roger T 2007-07-01 Disruptive body coloration is a primary camouflage tactic of cuttlefish. Because rapid changeable coloration of cephalopods is guided visually, we can present different visual backgrounds (e.g., computer-generated, two-dimensional prints) and video record the animal's response by describing and grading its body pattern. We showed previously that strength of cuttlefish disruptive patterning depends on the size, contrast, and density of discrete light elements on a homogeneous dark background. Here we report five experiments on the interactions of these and other features. Results show that Weber contrast of light background elements is--in combination with element size--a powerful determinant of disruptive response strength. Furthermore, the strength of disruptive patterning decreases with increasing mean substrate intensity (with other factors held constant). Interestingly, when element size, Weber contrast and mean substrate intensity are kept constant, strength of disruptive patterning depends on the configuration of clusters of small light elements. This study highlights the interactions of multiple features of natural microhabitats that directly influence which camouflage pattern a cuttlefish will choose. 14. Positron-attachment to small molecules: Vibrational enhancement of positron affinities with configuration interaction level of multi-component molecular orbital approach Energy Technology Data Exchange (ETDEWEB) Tachikawa, Masanori [Quantum Chemistry Division, Graduate School of NanoBioScience, Yokohama City University, 22-2 Seto, Kanazawa, Yokohama 236-0027 (Japan) 2015-12-31 To theoretically demonstrate the binding of a positron to small polarized molecules, we have calculated the vibrational averaged positron affinity (PA) values along the local vibrational contribution with the configuration interaction level of multi-component molecular orbital method. This method can take the electron-positron correlation contribution into account through single electronic - single positronic excitation configurations. The PA values are enhanced by including the local vibrational contribution from vertical PA values due to the anharmonicity of the potential. 15. Loop-driven graphical unitary group approach to the electron correlation problem, including configuration interaction energy gradients International Nuclear Information System (INIS) Brooks, B.R. 1979-09-01 The Graphical Unitary Group Approach (GUGA) was cast into an extraordinarily powerful form by restructuring the Hamiltonian in terms of loop types. This restructuring allows the adoption of the loop-driven formulation which illuminates vast numbers of previously unappreciated relationships between otherwise distinct Hamiltonian matrix elements. The theoretical/methodological contributions made here include the development of the loop-driven formula generation algorithm, a solution of the upper walk problem used to develop a loop breakdown algorithm, the restriction of configuration space employed to the multireference interacting space, and the restructuring of the Hamiltonian in terms of loop types. Several other developments are presented and discussed. Among these developments are the use of new segment coefficients, improvements in the loop-driven algorithm, implicit generation of loops wholly within the external space adapted within the framework of the loop-driven methodology, and comparisons of the diagonalization tape method to the direct method. It is also shown how it is possible to implement the GUGA method without the time-consuming full (m 5 ) four-index transformation. A particularly promising new direction presented here involves the use of the GUGA methodology to obtain one-electron and two-electron density matrices. Once these are known, analytical gradients (first derivatives) of the CI potential energy are easily obtained. Several test calculations are examined in detail to illustrate the unique features of the method. Also included is a calculation on the asymmetric 2 1 A' state of SO 2 with 23,613 configurations to demonstrate methods for the diagonalization of very large matrices on a minicomputer. 6 figures, 6 tables 16. Relativistic configuration-interaction calculations of electric dipole n=2−n=3 transitions for medium-charge Li-like ions Energy Technology Data Exchange (ETDEWEB) Deng, Banglin, E-mail: [email protected] [Department of Applied Physics, Chengdu University of Technology, Chengdu 610059, Sichuan (China); Jiang, Gang [Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, Sichuan (China); Zhang, Chuanyu [Department of Applied Physics, Chengdu University of Technology, Chengdu 610059, Sichuan (China) 2014-09-15 In this work, the multi-configuration Dirac–Fock and relativistic configuration-interaction methods have been used to calculate the transition wavelengths, electric dipole transition probabilities, line strengths, and absorption oscillator strengths for the 2s–3p, 2p–3s, and 2p–3d transitions in Li-like ions with nuclear charge Z=7–30. Our calculated values are in good agreement with previous experimental and theoretical results. We took the contributions from Breit interaction, finite nuclear mass corrections, and quantum electrodynamics corrections to the initial and final levels into account, and also found that the contributions from Breit interaction, self-energy, and vacuum polarization grow fast with increasing nuclear charge for a fixed configuration. The ratio of the velocity to length form of the transition rate (A{sub v}/A{sub l}) was used to estimate the accuracy of our calculations. 17. New Advancements in the Study of the Uniform Electron Gas with Full Configuration Interaction Quantum Monte Carlo Science.gov (United States) Ruggeri, Michele; Luo, Hongjun; Alavi, Ali Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is able to give remarkably accurate results in the study of atoms and molecules. The study of the uniform electron gas (UEG) on the other hand has proven to be much harder, particularly in the low density regime. The source of this difficulty comes from the strong interparticle correlations that arise at low density, and essentially forbid the study of the electron gas in proximity of Wigner crystallization. We extend a previous study on the three dimensional electron gas computing the energy of a fully polarized gas for N=27 electrons at high and medium density (rS = 0 . 5 to 5 . 0). We show that even when dealing with a polarized UEG the computational cost of the study of systems with rS > 5 . 0 is prohibitive; in order to deal with correlations and to extend the density range that to be studied we introduce a basis of localized states and an effective transcorrelated Hamiltonian. 18. Configuration-interaction relativistic-many-body-perturbation-theory calculations of photoionization cross sections from quasicontinuum oscillator strengths International Nuclear Information System (INIS) Savukov, I. M.; Filin, D. V. 2014-01-01 Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreement with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. As a result, the demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions 19. Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory International Nuclear Information System (INIS) Zhang, Xing; Herbert, John M. 2014-01-01 We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H 3 near its D 3h geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state 20. An open-source framework for analyzing N-electron dynamics. II. Hybrid density functional theory/configuration interaction methodology. Science.gov (United States) Hermann, Gunter; Pohl, Vincent; Tremblay, Jean Christophe 2017-10-30 In this contribution, we extend our framework for analyzing and visualizing correlated many-electron dynamics to non-variational, highly scalable electronic structure method. Specifically, an explicitly time-dependent electronic wave packet is written as a linear combination of N-electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time-dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open-source Python program detCI@ORBKIT, which extends the capabilities of our recently published post-processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom-centered Gaussian-type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one-electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser-driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher-level method provided a judicious choice of functional is made. Broadband excitation of a medium-sized organic chromophore further demonstrates the scalability of the method. In addition, the time-dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc. 1. The 3d8-(3d74p + 3p53d9) transitions in Br X: A striking case of configuration interaction International Nuclear Information System (INIS) Kleef, T.A.M. van; Uylings, P.H.M.; Ryabtsev, A.N.; Podobedova, L.I.; Joshi, Y.N. 1988-01-01 The spectrum of nine times ionized bromine (Br X) was photographed in the 90-120 A wavelength region on a variety of grazing incidence spectrographs using an open spark and a triggered spark as light sources. The analysis of the 3d 8 -(3d 7 4p + 3p 5 3d 9 ) transitions has resulted in establishing all 9 levels of the 3d 8 configuration, all 12 levels of the 3p 5 3d 9 configuration and 99 out of 110 levels of the 3d 7 4p configuration. The excitation probability of the 3p inner-shell electron increases with nuclear charge and in Br X is comparable with the excitation probability of the optical electrons resulting in a very strong configuration interaction between the 3p 5 3d 9 and 3d 7 4p configurations. Parametric calculations treating these configurations as one super configuration support the analysis. Two hundred and thirty two lines have been classified in this spectrum. (orig.) 2. Large-scale parallel configuration interaction. II. Two- and four-component double-group general active space implementation with application to BiH DEFF Research Database (Denmark) Knecht, Stefan; Jensen, Hans Jørgen Aagaard; Fleig, Timo 2010-01-01 We present a parallel implementation of a large-scale relativistic double-group configuration interaction CIprogram. It is applicable with a large variety of two- and four-component Hamiltonians. The parallel algorithm is based on a distributed data model in combination with a static load balanci... 3. Criticality in the configuration-mixed interacting boson model (1) $U(5)-\\hat{Q}(\\chi)\\cdot\\hat{Q}(\\chi)$ mixing CERN Document Server Hellemans, V; De Baerdemacker, S; Heyde, K 2008-01-01 The case of U(5)--$\\hat{Q}(\\chi)\\cdot\\hat{Q}(\\chi)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively. 4. Electronic spectra of azaindole and its excited state mixing: A symmetry-adapted cluster configuration interaction study Energy Technology Data Exchange (ETDEWEB) Arulmozhiraja, Sundaram, E-mail: [email protected]; Coote, Michelle L. [ARC Centre of Excellence for Electromaterials Science, Research School of Chemistry, The Australian National University, Canberra, 2601 ACT (Australia); Hasegawa, Jun-ya [Institute for Catalysis, Hokkaido University, Kita 21, Nishi 10, Kita-Ku, Sapporo 001-0021 (Japan) 2015-11-28 Electronic structures of azaindole were studied using symmetry-adapted cluster configuration interaction theory utilizing Dunning’s cc-pVTZ basis set augmented with appropriate Rydberg spd functions on carbon and nitrogen atoms. The results obtained in the present study show good agreement with the available experimental values. Importantly, and contrary to previous theoretical studies, the excitation energy calculated for the important n–π{sup ∗} state agrees well with the experimental value. A recent study by Pratt and co-workers concluded that significant mixing of π-π{sup ∗} and n-π{sup ∗} states leads to major change in the magnitude and direction of the dipole moment of the upper state vibrational level in the 0,0 + 280 cm{sup −1} band in the S{sub 1}←S{sub 0} transition when compared to that of the zero-point level of the S{sub 1} state. The present study, however, shows that all the four lowest lying excited states, {sup 1}L{sub b} π-π{sup ∗}, {sup 1}L{sub a} π-π{sup ∗}, n-π{sup ∗}, and π-σ{sup ∗}, cross each other in one way or another, and hence, significant state mixing between them is likely. The upper state vibrational level in the 0,0 + 280 cm{sup −1} band in the S{sub 1}←S{sub 0} transition benefits from this four-state mixing and this can explain the change in magnitude and direction of the dipole moment of the S{sub 1} excited vibrational level. This multistate mixing, and especially the involvement of π-σ{sup ∗} state in mixing, could also provide a route for hydrogen atom detachment reactions. The electronic spectra of benzimidazole, a closely related system, were also investigated in the present study. 5. Interpretation of the photoelectron, ultraviolet, and vacuum ultraviolet photoabsorption spectra of bromobenzene by ab initio configuration interaction and DFT computations Energy Technology Data Exchange (ETDEWEB) Palmer, Michael H., E-mail: [email protected]; Ridley, Trevor, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh EH9 3FJ, Scotland (United Kingdom); Hoffmann, Søren Vrønning, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected]; Jones, Nykola C., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [ISA, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C (Denmark); Coreno, Marcello, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [CNR-IMIP, Montelibretti, c/o Laboratorio Elettra, Trieste (Italy); Simone, Monica de, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [CNR-IOM Laboratorio TASC, Trieste (Italy); Grazioli, Cesare [CNR-IOM Laboratorio TASC, Trieste (Italy); Department of Chemical and Pharmaceutical Sciences, University of Trieste, Trieste (Italy); Zhang, Teng [Department of Physics and Astronomy, University of Uppsala, Uppsala (Sweden); and others 2015-10-28 New photoelectron, ultraviolet (UV), and vacuum UV (VUV) spectra have been obtained for bromobenzene by synchrotron study with higher sensitivity and resolution than previous work. This, together with use of ab initio calculations with both configuration interaction and time dependent density functional theoretical methods, has led to major advances in interpretation. The VUV spectrum has led to identification of a considerable number of Rydberg states for the first time. The Franck-Condon (FC) analyses including both hot and cold bands lead to identification of the vibrational structure of both ionic and electronically excited states including two Rydberg states. The UV onset has been interpreted in some detail, and an interpretation based on the superposition of FC and Herzberg-Teller contributions has been performed. In a similar way, the 6 eV absorption band which is poorly resolved is analysed in terms of the presence of two ππ* states of {sup 1}A{sub 1} (higher oscillator strength) and {sup 1}B{sub 2} (lower oscillator strength) symmetries, respectively. The detailed analysis of the vibrational structure of the 2{sup 2}B{sub 1} ionic state is particularly challenging, and the best interpretation is based on equation-of-motion-coupled cluster with singles and doubles computations. A number of equilibrium structures of the ionic and singlet excited states show that the molecular structure is less subject to variation than corresponding studies for iodobenzene. The equilibrium structures of the 3b{sub 1}3s and 6b{sub 2}3s (valence shell numbering) Rydberg states have been obtained and compared with the corresponding ionic limit structures. 6. Multireference configuration interaction study on spectroscopic properties of low-lying electronic states of As2 molecule International Nuclear Information System (INIS) Wang Jie-Min; Liu Qiang 2013-01-01 The potential energy curves (PECs) of four electronic states (X 1 Σ g + , e 3 Δ u , a 3 Σ u − , and d 3 Π g ) of an As 2 molecule are investigated employing the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV5Z basis set. The effect on PECs by the relativistic correction is taken into account. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian approximation. The correction is made at the level of a cc-pV5Z basis set. The PECs of the electronic states involved are extrapolated to the complete basis set limit. With the PECs, the spectroscopic parameters (T e , R e , ω e , ω e x e , ω e y e , α e , β e , γ e , and B e ) of these electronic states are determined and compared in detail with those reported in the literature. Excellent agreement is found between the present results and the experimental data. The first 40 vibrational states are studied for each electronic state when the rotational quantum number J equals zero. In addition, the vibrational levels, inertial rotation and centrifugal distortion constants of d 3 Π g electronic state are reported which are in excellent agreement with the available measurements. Comparison with the experimental data shows that the present results are both reliable and accurate. (atomic and molecular physics) 7. Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function. Science.gov (United States) Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi 2013-07-28 We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals. 8. Analysis of the half-projected Hartree--Fock function: density matrix, natural orbitals, and configuration interaction equivalence International Nuclear Information System (INIS) 1976-01-01 The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized 9. New Theoretical Developments in Exploring Electronically Excited States: Including Localized Configuration Interaction Singles and Application to Large Helium Clusters Science.gov (United States) Closser, Kristina Danielle This thesis presents new developments in excited state electronic structure theory. Contrasted with the ground state, the electronically excited states of atoms and molecules often are unstable and have short lifetimes, exhibit a greater diversity of character and are generally less well understood. The very unusual excited states of helium clusters motivated much of this work. These clusters consist of large numbers of atoms (experimentally 103--109 atoms) and bands of nearly degenerate excited states. For an isolated atom the lowest energy excitation energies are from 1s → 2s and 1s → 2 p transitions, and in clusters describing the lowest energy band minimally requires four states per atom. In the ground state the clusters are weakly bound by van der Waals interactions, however in the excited state they can form well-defined covalent bonds. The computational cost of quantum chemical calculations rapidly becomes prohibitive as the size of the systems increase. Standard excited-state methods such as configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) can be used with ≈100 atoms, and are optimized to treat only a few states. Thus, one of our primary aims is to develop a method which can treat these large systems with large numbers of nearly degenerate excited states. Additionally, excited states are generally formed far from their equilibrium structures. Vertical excitations from the ground state induce dynamics in the excited states. Thus, another focus of this work is to explore the results of these forces and the fate of the excited states. Very little was known about helium cluster excited states when this work began, thus we first investigated the excitations in small helium clusters consisting of 7 or 25 atoms using CIS. The character of these excited states was determined using attachment/detachment density analysis and we found that in the n = 2 manifold the excitations could generally be interpreted as 10. Multireference configuration interaction treatment of potential energy surfaces: symmetric dissociation of H/sub 2/O in a double-zeta basis Energy Technology Data Exchange (ETDEWEB) Brown, F B; Shavitt, I; Shepard, R 1984-03-23 Multiconfiguration self-consistent fields (SCF) and multireference configurational interaction (CI) calculations have been performed for the H/sub 2/O molecule in a double-zeta basis for four symmetric geometries, for comparison with full CI results. Unlike single-reference results, the energy errors are almost independent of geometry, allowing unbiased treatments of potential energy surfaces. 35 references, 1 figure, 2 tables. 11. The electronic states of 1,2,3-triazole studied by vacuum ultraviolet photoabsorption and ultraviolet photoelectron spectroscopy, and a comparison with ab initio configuration interaction methods DEFF Research Database (Denmark) Palmer, Michael H.; Hoffmann, Søren Vrønning; Jones, Nykola C. 2011-01-01 The Rydberg states in the vacuum ultraviolet photoabsorption spectrum of 1,2,3-triazole have been measured and analyzed with the aid of comparison to the UV valence photoelectron ionizations and the results of ab initio configuration interaction (CI) calculations. Calculated electronic ionization...... and excitation energies for singlet, triplet valence, and Rydberg states were obtained using multireference multiroot CI procedures with an aug-cc-pVTZ [5s3p3d1f] basis set and a set of Rydberg [4s3p3d3f] functions. Adiabatic excitation energies obtained for several electronic states using coupled...... are the excitations consistent with an f-series.... 12. Thermomechanical interactions of particle bed-structural wall in a layered configuration. Pt. 1. Effect of particle bed thermal expansions International Nuclear Information System (INIS) Tehranian, F. 1995-01-01 Materials in the form of particle beds have been considered for shielding and tritium breeding as well as neutron multiplication in many of the conceptual reactor design studies. As the level of effort of the fusion blanket community in the area of out-of-pile and in-pile (ITER) testing of integrated test modules increases, so does the need for modelling capability for predicting the thermomechanical responses of the test modules under reactor environment.In this study, the thermomechanical responses of a particle bed-structural wall system in a layered configuration, subjected to bed temperature rise and/or external coolant pressure, were considered. Equations were derived which represent the dependence of the particle-to-particle and particle-to-wall contact forces and areas on the structural wall deformations and in turn on the thermomechanical loads. Using the derived equations, parametric analyses were performed to study the variations in the thermomechanical response quantities of a beryllium particle bed-stainless steel structural wall when subjected to thermomechanical loads. The results are presented in two parts. In Part I, presented in this paper, the derivation of the analytical equations and the effects of bed temperature rise are discussed. In Part II of this study, also presented in this symposium, the effects of external coolant pressure as well as the combined effects of bed temperature rise and coolant pressure on the thermomechanical responses are given.It is shown that, depending on the stiffness of the structural walls, uniform bed temperature rises in the range 100-400 C result in non-uniform effective thermal properties through the prticle bed and could increase the bed effective thermal conductivity by a factor of 2-5 and the bed-wall interface thermal conductance by even a larger factor. (orig.) 13. Configuration management International Nuclear Information System (INIS) Beavers, R.R.; Sumiec, K.F. 1989-01-01 Increasing regulatory and industry attention has been focused on properly controlling electrical design changes. These changes can be controlled by using configuration management techniques. Typically, there are ongoing modifications to various process systems or additions due to new requirements at every power plant. Proper control of these changes requires that an organized method be used to ensure that all important parameters of the electrical auxiliary systems are analyzed and that these parameters are evaluated accurately. This process, commonly referred to as configuration management, is becoming more important on both fossil and nuclear plants. Recent NRC- and utility-initiated inspections have identified problems due to incomplete analysis of changes to electrical auxiliary systems at nuclear stations 14. Electronic excitation of molecules in solution calculated using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model International Nuclear Information System (INIS) Fukuda, Ryoichi; Ehara, Masahiro 2015-01-01 The effects from solvent environment are specific to the electronic states; therefore, a computational scheme for solvent effects consistent with the electronic states is necessary to discuss electronic excitation of molecules in solution. The PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (configuration interaction) methods are developed for such purposes. The PCM SAC-CI adopts the state-specific (SS) solvation scheme where solvent effects are self-consistently considered for every ground and excited states. For efficient computations of many excited states, we develop a perturbative approximation for the PCM SAC-CI method, which is called corrected linear response (cLR) scheme. Our test calculations show that the cLR PCM SAC-CI is a very good approximation of the SS PCM SAC-CI method for polar and nonpolar solvents 15. Symmetries of cluster configurations International Nuclear Information System (INIS) Kramer, P. 1975-01-01 A deeper understanding of clustering phenomena in nuclei must encompass at least two interrelated aspects of the subject: (A) Given a system of A nucleons with two-body interactions, what are the relevant and persistent modes of clustering involved. What is the nature of the correlated nucleon groups which form the clusters, and what is their mutual interaction. (B) Given the cluster modes and their interaction, what systematic patterns of nuclear structure and reactions emerge from it. Are there, for example, families of states which share the same ''cluster parents''. Which cluster modes are compatible or exclude each other. What quantum numbers could characterize cluster configurations. There is no doubt that we can learn a good deal from the experimentalists who have discovered many of the features relevant to aspect (B). Symmetries specific to cluster configurations which can throw some light on both aspects of clustering are discussed 16. Compensation of the long-range beam-beam interactions as a path towards new configurations for the high luminosity LHC Directory of Open Access Journals (Sweden) Stéphane Fartoukh 2015-12-01 Full Text Available Colliding bunch trains in a circular collider demands a certain crossing angle in order to separate the two beams transversely after the collision. The magnitude of this crossing angle is a complicated function of the bunch charge, the number of long-range beam-beam interactions, of β^{} and type of optics (flat or round, and possible compensation or additive effects between several low-β insertions in the ring depending on the orientation of the crossing plane at each interaction point. About 15 years ago, the use of current bearing wires was proposed at CERN in order to mitigate the long-range beam-beam effects [J. P. Koutchouk, CERN Report No. LHC-Project-Note 223, 2000], therefore offering the possibility to minimize the crossing angle with all the beneficial effects this might have: on the luminosity performance by reducing the need for crab-cavities or lowering their voltage, on the required aperture of the final focus magnets, on the strength of the orbit corrector involved in the crossing bumps, and finally on the heat load and radiation dose deposited in the final focus quadrupoles. In this paper, a semianalytical approach is developed for the compensation of the long-range beam-beam interactions with current wires. This reveals the possibility of achieving optimal correction through a careful adjustment of the aspect ratio of the β functions at the wire position. We consider the baseline luminosity upgrade plan of the Large Hadron Collider (HL-LHC project, and compare it to alternative scenarios, or so-called “configurations,” where modifications are applied to optics, crossing angle, or orientation of the crossing plane in the two low-β insertions of the ring. For all these configurations, the beneficial impact of beam-beam compensation devices is then demonstrated on the tune footprint, the dynamical aperture, and/or the frequency map analysis of the nonlinear beam dynamics as the main figures of merit. 17. A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: Application to transition metal L-edge X-ray absorption spectroscopy Energy Technology Data Exchange (ETDEWEB) Roemelt, Michael; Maganas, Dimitrios; Neese, Frank [Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Muelheim an der Ruhr (Germany); DeBeer, Serena [Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Muelheim an der Ruhr (Germany); Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853 (United States) 2013-05-28 A novel restricted-open-shell configuration interaction with singles (ROCIS) approach for the calculation of transition metal L-edge X-ray absorption spectra is introduced. In this method, one first calculates the ground state and a number of excited states of the non-relativistic Hamiltonian. By construction, the total spin is a good quantum number in each of these states. For a ground state with total spin S excited states with spin S Prime = S, S - 1, and S + 1 are constructed. Using Wigner-Eckart algebra, all magnetic sublevels with M{sub S}= S, Horizontal-Ellipsis , -S for each multiplet of spin S are obtained. The spin-orbit operator is represented by a mean-field approximation to the full Breit-Pauli spin-orbit operator and is diagonalized over this N-particle basis. This is equivalent to a quasi-degenerate treatment of the spin-orbit interaction to all orders. Importantly, the excitation space spans all of the molecular multiplets that arise from the atomic Russell-Saunders terms. Hence, the method represents a rigorous first-principles approach to the complicated low-symmetry molecular multiplet problem met in L-edge X-ray absorption spectroscopy. In order to gain computational efficiency, as well as additional accuracy, the excitation space is restricted to single excitations and the configuration interaction matrix is slightly parameterized in order to account for dynamic correlation effects in an average way. To this end, it is advantageous to employ Kohn-Sham rather than Hartree-Fock orbitals thus defining the density functional theory/ROCIS method. However, the method can also be used in an entirely non-empirical fashion. Only three global empirical parameters are introduced and have been determined here for future application of the method to any system containing any transition metal. The three parameters were carefully calibrated using the L-edge X-ray absorption spectroscopy spectra of a test set of coordination complexes containing first row 18. A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions. Science.gov (United States) van Meer, R; Gritsenko, O V; Baerends, E J 2018-03-14 Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH 4 , NH 3 , H 2 O, FH, and N 2 ) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron. 19. A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions Science.gov (United States) van Meer, R.; Gritsenko, O. V.; Baerends, E. J. 2018-03-01 Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH4, NH3, H2O, FH, and N2) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron. 20. Intersystem-crossing and phosphorescence rates in fac-Ir{sup III}(ppy){sub 3}: A theoretical study involving multi-reference configuration interaction wavefunctions Energy Technology Data Exchange (ETDEWEB) Kleinschmidt, Martin; Marian, Christel M., E-mail: [email protected] [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany); Wüllen, Christoph van [Fachbereich Chemie and Forschungszentrum OPTIMAS, Technical University of Kaiserslautern, Erwin-Schrödinger-Straße 52, 67663 Kaiserslautern (Germany) 2015-03-07 We have employed combined density functional theory and multi-reference configuration interaction methods including spin–orbit coupling (SOC) effects to investigate the photophysics of the green phosphorescent emitter fac-tris-(2-phenylpyridine)iridium (fac-Ir(ppy){sub 3}). A critical evaluation of our quantum chemical approaches shows that a perturbational treatment of SOC is the method of choice for computing the UV/Vis spectrum of this heavy transition metal complex while multi-reference spin–orbit configuration interaction is preferable for calculating the phosphorescence rates. The particular choice of the spin–orbit interaction operator is found to be of minor importance. Intersystem crossing (ISC) rates have been determined by Fourier transformation of the time correlation function of the transition including Dushinsky rotations. In the electronic ground state, fac-Ir(ppy){sub 3} is C{sub 3} symmetric. The calculated UV/Vis spectrum is in excellent agreement with experiment. The effect of SOC is particularly pronounced for the metal-to-ligand charge transfer (MLCT) band in the visible region of the absorption spectrum which does not only extend its spectral onset towards longer wavelengths but also experiences a blue shift of its maximum. Pseudo-Jahn-Teller interaction leads to asymmetric coordinate displacements in the lowest MLCT states. Substantial electronic SOC and a small energy gap make ISC an ultrafast process in fac-Ir(ppy){sub 3}. For the S{sub 1}↝T{sub 1} non-radiative transition, we compute a rate constant of k{sub ISC} = 6.9 × 10{sup 12} s{sup −1} which exceeds the rate constant of radiative decay to the electronic ground state by more than six orders of magnitude, in agreement with the experimental observation of a subpicosecond ISC process and a triplet quantum yield close to unity. As a consequence of the geometric distortion in the T{sub 1} state, the T{sub 1} → S{sub 0} transition densities are localized on one of the 1. Tensor contraction engine: Abstraction and automated parallel implementation of configuration-interaction, coupled-cluster, and many-body perturbation theories International Nuclear Information System (INIS) Hirata, So 2003-01-01 We develop a symbolic manipulation program and program generator (Tensor Contraction Engine or TCE) that automatically derives the working equations of a well-defined model of second-quantized many-electron theories and synthesizes efficient parallel computer programs on the basis of these equations. Provided an ansatz of a many-electron theory model, TCE performs valid contractions of creation and annihilation operators according to Wick's theorem, consolidates identical terms, and reduces the expressions into the form of multiple tensor contractions acted by permutation operators. Subsequently, it determines the binary contraction order for each multiple tensor contraction with the minimal operation and memory cost, factorizes common binary contractions (defines intermediate tensors), and identifies reusable intermediates. The resulting ordered list of binary tensor contractions, additions, and index permutations is translated into an optimized program that is combined with the NWChem and UTChem computational chemistry software packages. The programs synthesized by TCE take advantage of spin symmetry, Abelian point-group symmetry, and index permutation symmetry at every stage of calculations to minimize the number of arithmetic operations and storage requirement, adjust the peak local memory usage by index range tiling, and support parallel I/O interfaces and dynamic load balancing for parallel executions. We demonstrate the utility of TCE through automatic derivation and implementation of parallel programs for various models of configuration-interaction theory (CISD, CISDT, CISDTQ), many-body perturbation theory[MBPT(2), MBPT(3), MBPT(4)], and coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, and CCSDTQ) 2. Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study Energy Technology Data Exchange (ETDEWEB) Schönborn, Jan Boyke; Saalfrank, Peter; Klamroth, Tillmann, E-mail: [email protected] [Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam-Golm (Germany) 2016-01-28 We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization. 3. The landscape configuration of zoonotic transmission of Ebola virus disease in West and Central Africa: interaction between population density and vegetation cover Directory of Open Access Journals (Sweden) Michael G. Walsh 2015-01-01 Full Text Available Ebola virus disease (EVD is an emerging infectious disease of zoonotic origin that has been responsible for high mortality and significant social disruption in West and Central Africa. Zoonotic transmission of EVD requires contact between susceptible human hosts and the reservoir species for Ebolaviruses, which are believed to be fruit bats. Nevertheless, features of the landscape that may facilitate such points of contact have not yet been adequately identified. Nor have spatial dependencies between zoonotic EVD transmission and landscape structures been delineated. This investigation sought to describe the spatial relationship between zoonotic EVD transmission events, or spillovers, and population density and vegetation cover. An inhomogeneous Poisson process model was fitted to all precisely geolocated zoonotic transmissions of EVD in West and Central Africa. Population density was strongly associated with spillover; however, there was significant interaction between population density and green vegetation cover. In areas of very low population density, increasing vegetation cover was associated with a decrease in risk of zoonotic transmission, but as population density increased in a given area, increasing vegetation cover was associated with increased risk of zoonotic transmission. This study showed that the spatial dependencies of Ebolavirus spillover were associated with the distribution of population density and vegetation cover in the landscape, even after controlling for climate and altitude. While this is an observational study, and thus precludes direct causal inference, the findings do highlight areas that may be at risk for zoonotic EVD transmission based on the spatial configuration of important features of the landscape. 4. Free electrons and ionic liquids: study of excited states by means of electron-energy loss spectroscopy and the density functional theory multireference configuration interaction method. Science.gov (United States) Regeta, Khrystyna; Bannwarth, Christoph; Grimme, Stefan; Allan, Michael 2015-06-28 The technique of low energy (0-30 eV) electron impact spectroscopy, originally developed for gas phase molecules, is applied to room temperature ionic liquids (IL). Electron energy loss (EEL) spectra recorded near threshold, by collecting 0-2 eV electrons, are largely continuous, assigned to excitation of a quasi-continuum of high overtones and combination vibrations of low-frequency modes. EEL spectra recorded by collecting 10 eV electrons show predominantly discrete vibrational and electronic bands. The vibrational energy-loss spectra correspond well to IR spectra except for a broadening (∼0.04 eV) caused by the liquid surroundings, and enhanced overtone activity indicating a contribution from resonant excitation mechanism. The spectra of four representative ILs were recorded in the energy range of electronic excitations and compared to density functional theory multireference configuration interaction (DFT/MRCI) calculations, with good agreement. The spectra up to about 8 eV are dominated by π-π transitions of the aromatic cations. The lowest bands were identified as triplet states. The spectral region 2-8 eV was empty in the case of a cation without π orbitals. The EEL spectrum of a saturated solution of methylene green in an IL band showed the methylene green EEL band at 2 eV, indicating that ILs may be used as a host to study nonvolatile compounds by this technique in the future. 5. Gaussian-2 theory: Use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Moller--Plesset zero-point energies International Nuclear Information System (INIS) Curtiss, L.A.; Raghavachari, K.; Pople, J.A. 1995-01-01 The performance of Gaussian-2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero-point energies. A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)]. The use of geometries optimized at the QCISD level rather than the second-order Moller--Plesset level (MP2) and the use of scaled MP2 zero-point energies rather than scaled Hartree--Fock (HF) zero-point energies have also been examined. The set of 125 energies used for validation of G2 theory [J. Chem. Phys. 94, 7221 (1991)] is used to test out these variations of G2 theory. Inclusion of higher levels of correlation treatment has little effect except in the cases of multiply-bonded systems. In these cases better agreement is obtained in some cases and poorer agreement in others so that there is no improvement in overall performance. The use of QCISD geometries yields significantly better agreement with experiment for several cases including the ionization potentials of CS and O 2 , electron affinity of CN, and dissociation energies of N 2 , O 2 , CN, and SO 2 . This leads to a slightly better agreement with experiment overall. The MP2 zero-point energies gives no overall improvement. These methods may be useful for specific systems 6. Ab initio configuration interaction study on the energetics and electronic structure of the 1-52Σ+ and 1-32Π states of CS+ International Nuclear Information System (INIS) Honjou, Nobumitsu 2006-01-01 The energetics and electronic structure of the 1-5 2 Σ + and 1-3 2 Π states of CS + at and around the equilibrium internuclear distance R e for the CS X 1 Σ + state are studied by carrying out ab initio configuration interaction (CI) calculations. The spectroscopic constants of T e , ω e , and R e for the 1-4 2 Σ + , 1 2 Π, and 3 2 Π states are evaluated from the CI potential energy curves (PECs). The avoided crossing between the 2-3 2 Σ + PECs causes the 3 2 Σ + minimum and explains the observed high intensities for the photoionization from the CS X 1 Σ + state to both the 2-3 2 Σ + states. The avoided crossing between the 3-4 2 Σ + PECs produces the 3 2 Σ + maximum and 4 2 Σ + well minimum. The avoided crossing between the 2-3 2 Π PECs results in the 3 2 Π minimum and a small minimum spacing (0.14 eV) between the PECs 7. Numerical investigation of the effect of the configuration of ExoMars landing platform propulsion system on the interaction of supersonic jets with the surface of Mars Science.gov (United States) Kagenov, Anuar; Glazunov, Anatoliy; Kostyushin, Kirill; Eremin, Ivan; Shuvarikov, Vladimir 2017-10-01 This paper presents the results of numerical investigations of the interaction with the Mars surface of four supersonic jets of ExoMars landing platform propulsion system. The cases of impingement of supersonic jets on a curved surface are considered depending on the values of propulsion system thrust. According to the results of numerical studies are obtained the values of normal stresses on the surface of Mars at altitudes of 1.0, 0.5 and 0.3 meter to the surface of the landing. To define the occurring shear stresses Mohr-Coulomb theory was used. The maximum values of shear stresses were defined for the following types of soil of Mars: drift material, crusty to cloddy material, blocky material, sand and Mojave Mars simulant. The conducted evaluations showed, regardless of the propulsion system configuration, that when the final stage of the controlled landing of the ExoMars landing platform, the erosion of the Mars regolith would be insignificant. The estimates are consistent with the available data from previous Mars missions. 8. A Managerial Perspective on Common Identity-based and Common Bond-based Groups in Non-governmental Organizations. Patterns of Interaction, Attachment and Social Network Configuration Directory of Open Access Journals (Sweden) Elena - Mădălina VĂTĂMĂNESCU 2014-10-01 Full Text Available The paper approaches the common identity and common bond theories in analyzing the group patterns of interaction, their causes, processes and outcomes from a managerial perspective. The distinction between identity and bond referred to people’s different reasons for being in a group, stressing out whether they like the group as a whole — identity-based attachment, or they like individuals in the group — bond-based attachment. While members of the common identity groups reported feeling more attached to their group as a whole than to their fellow group members and tended to perceive others in the group as interchangeable, in bond-based attachment, people felt connected to each other and less to the group as a whole, loyalty or attraction to the group stemming from their attraction primarily to certain members in the group. At this level, the main question concerned with the particularities of common identity-based or common bond-based groups regarding social interaction, the participatory architecture of the group, the levels of personal and work engagement in acting like a cohesive group. In order to address pertinently this issue, the current work was focused on a qualitative research which comprised in-depth (semi-structured interviews with several project coordinators from non-governmental organizations (NGOs. Also, to make the investigation more complex and clear, the research relied on the social network analysis which was indicative of the group dynamics and configuration, highlighting the differences between common identity-based and common bond-based groups. 9. Avoided crossings, conical intersections, and low-lying excited states with a single reference method: the restricted active space spin-flip configuration interaction approach. Science.gov (United States) Casanova, David 2012-08-28 The restricted active space spin-flip CI (RASCI-SF) performance is tested in the electronic structure computation of the ground and the lowest electronically excited states in the presence of near-degeneracies. The feasibility of the method is demonstrated by analyzing the avoided crossing between the ionic and neutral singlet states of LiF along the molecular dissociation. The two potential energy surfaces (PESs) are explored by means of the energies of computed adiabatic and approximated diabatic states, dipole moments, and natural orbital electronic occupancies of both states. The RASCI-SF methodology is also used to study the ground and first excited singlet surface crossing involved in the double bond isomerization of ethylene, as a model case. The two-dimensional PESs of the ground (S(0)) and excited (S(1)) states are calculated for the complete configuration space of torsion and pyramidalization molecular distortions. The parameters that define the state energetics in the vicinity of the S(0)/S(1) conical intersection region are compared to complete active space self-consistent field (CASSCF) results. These examples show that it is possible to describe strongly correlated electronic states using a single reference methodology without the need to expand the wavefunction to high levels of collective excitations. Finally, RASCI is also examined in the electronic structure characterization of the ground and 2(1)A(g)(-), 1(1)B(u)(+), 1(1)B(u)(-), and 1(3)B(u)(-) states of all-trans polyenes with two to seven double bonds and beyond. Transition energies are compared to configuration interaction singles, time-dependent density functional theory (TDDFT), CASSCF, and its second-order perturbation correction calculations, and to experimental data. The capability of RASCI-SF to describe the nature and properties of each electronic state is discussed in detail. This example is also used to expose the properties of different truncations of the RASCI wavefunction and to 10. The electronic states of 1,2,4-triazoles: A study of 1H- and1-methyl-1,2,4-triazole by vacuum ultraviolet photoabsorption and ultraviolet photoelectron spectroscopy and a comparison with ab initio configuration interaction computations DEFF Research Database (Denmark) Palmer, Michael H.; Camp, Philip J.; Hoffmann, Søren Vrønning 2012-01-01 The first vacuum ultraviolet absorption spectrum of a 1,2,4-triazole has been obtained and analyzed in detail, with assistance from both an enhanced UV photoelectron spectroscopic study and ab initio multi-reference multi-root configuration interaction procedures. For both 1H- and 1-methyl-1,2... 11. Symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster studies of electronically excited states of copper tetrachloride and copper tetrabromide dianions International Nuclear Information System (INIS) Ehara, Masahiro; Piecuch, Piotr; Lutz, Jesse J.; Gour, Jeffrey R. 2012-01-01 Graphical abstract: Electronically excited states of CuCl 4 2- and CuBr 4 2- are determined using the scalar relativistic symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster calculations. The results are compared with experimental spectra. Highlights: ► Electronic spectra of CuCl 4 2- and CuBr 4 2- are examined by SAC-CI and EOMCC methods. ► Relativistic SAC-CI and EOMCC results are compared with experimental spectra. ► An assignment of bands in the CuCl 4 2- and CuBr 4 2- absorption spectra is obtained. ► Relativistic effects affect excitation energies and ground-state geometries. ► The effect of relativity on the oscillator strengths is generally small. - Abstract: The valence excitation spectra of the copper tetrachloride and copper tetrabromide open-shell dianions, CuCl 4 2- and CuBr 4 2- , respectively, are investigated by a variety of symmetry-adapted-cluster configuration-interaction (SAC-CI) and equation-of-motion coupled-cluster (EOMCC) methods. The valence excited states of the CuCl 4 2- and CuBr 4 2- species that correspond to transitions from doubly occupied molecular orbitals (MOs) to a singly occupied MO (SOMO), for which experimental spectra are available, are examined with the ionized (IP) variants of the SAC-CI and EOMCC methods. The higher-energy excited states of CuCl 4 2- and CuBr 4 2- that correspond to transitions from SOMO to unoccupied MOs, which have not been characterized experimentally, are determined using the electron-attached (EA) SAC-CI and EOMCC approaches. An emphasis is placed on the scalar relativistic SAC-CI and EOMCC calculations based on the spin-free part of the second-order Douglass–Kroll–Hess Hamiltonian (DKH2) and on a comparison of the results of the IP and EA SAC-CI and EOMCC calculations with up to 2-hole-1-particle (2h-1p) and 2-particle-1-hole (2p-1h) excitations, referred to as the IP-SAC-CI SD-R and IP-EOMCCSD(2h-1p) methods in the IP case and EA-SAC-CI SD-R and EA 12. The role of Rydberg and continuum levels in computing high harmonic generation spectra of the hydrogen atom using time-dependent configuration interaction International Nuclear Information System (INIS) 2013-01-01 We study the role of Rydberg bound-states and continuum levels in the field-induced electronic dynamics associated with the High-Harmonic Generation (HHG) spectroscopy of the hydrogen atom. Time-dependent configuration-interaction (TD-CI) is used with very large atomic orbital (AO) expansions (up to L= 4 with sextuple augmentation and off-center functions) to describe the bound Rydberg levels, and some continuum levels. To address the lack of ionization losses in TD-CI with finite AO basis sets, we employed a heuristic lifetime for energy levels above the ionization potential. The heuristic lifetime model is compared against the conventional atomic orbital treatment (infinite lifetimes), and a third approximation which is TD-CI using only the bound levels (continuum lifetimes go to zero). The results suggest that spectra calculated using conventional TD-CI do not converge with increasing AO basis set size, while the zero lifetime and heuristic lifetime models converge to qualitatively similar spectra, with implications for how best to apply bound state electronic structure methods to simulate HHG. The origin of HHG spectral features including the cutoff and extent of interference between peaks is uncovered by separating field-induced coupling between different types of levels (ground state, bound Rydberg levels, and continuum) in the simulated electronic dynamics. Thus the origin of deviations between the predictions of the semi-classical three step model and the full simulation can be associated with particular physical contributions, which helps to explain both the successes and the limitations of the three step model 13. Configuration and local elastic interaction of ferroelectric domains and misfit dislocation in PbTiO3/SrTiO3 epitaxial thin films Directory of Open Access Journals (Sweden) Takanori Kiguchi, Kenta Aoyagi, Yoshitaka Ehara, Hiroshi Funakubo, Tomoaki Yamada, Noritaka Usami and Toyohiko J Konno 2011-01-01 Full Text Available We have studied the strain field around the 90° domains and misfit dislocations in PbTiO3/SrTiO3 (001 epitaxial thin films, at the nanoscale, using the geometric phase analysis (GPA combined with high-resolution transmission electron microscopy (HRTEM and high-angle annular dark field––scanning transmission electron microscopy (HAADF-STEM. The films typically contain a combination of a/c-mixed domains and misfit dislocations. The PbTiO3 layer was composed from the two types of the a-domain (90° domain: a typical a/c-mixed domain configuration where a-domains are 20–30 nm wide and nano sized domains with a width of about 3 nm. In the latter case, the nano sized a-domain does not contact the film/substrate interface; it remains far from the interface and stems from the misfit dislocation. Strain maps obtained from the GPA of HRTEM images show the elastic interaction between the a-domain and the dislocations. The normal strain field and lattice rotation match each other between them. Strain maps reveal that the a-domain nucleation takes place at the misfit dislocation. The lattice rotation around the misfit dislocation triggers the nucleation of the a-domain; the normal strains around the misfit dislocation relax the residual strain in a-domain; then, the a-domain growth takes place, accompanying the introduction of the additional dislocation perpendicular to the misfit dislocation and the dissociation of the dislocations into two pairs of partial dislocations with an APB, which is the bottom boundary of the a-domain. The novel mechanism of the nucleation and growth of 90° domain in PbTiO3/SrTiO3 epitaxial system has been proposed based on above the results. 14. Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations) Science.gov (United States) Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M. 1987-01-01 The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated. 15. Pair Natural Orbital Restricted Open-Shell Configuration Interaction (PNO-ROCIS) Approach for Calculating X-ray Absorption Spectra of Large Chemical Systems. Science.gov (United States) Maganas, Dimitrios; DeBeer, Serena; Neese, Frank 2018-02-08 In this work, the efficiency of first-principles calculations of X-ray absorption spectra of large chemical systems is drastically improved. The approach is based on the previously developed restricted open-shell configuration interaction singles (ROCIS) method and its parametrized version, based on a density functional theory (DFT) ground-state determinant ROCIS/DFT. The combination of the ROCIS or DFT/ROCIS methods with the well-known machinery of the pair natural orbitals (PNOs) leads to the new PNO-ROCIS and PNO-ROCIS/DFT variants. The PNO-ROCIS method can deliver calculated metal K-, L-, and M-edge XAS spectra orders of magnitude faster than ROCIS while maintaining an accuracy with calculated spectral parameters better than 1% relative to the original ROCIS method (referred to as canonical ROCIS). The method is of a black box character, as it does not require any user adjustments, while it scales quadratically with the system size. It is shown that for large systems, the size of the virtual molecular orbital (MO) space is reduced by more than 90% with respect to the canonical ROCIS method. This allows one to compute the X-ray absorption spectra of a variety of large "real-life" chemical systems featuring hundreds of atoms using a first-principles wave-function-based approach. Examples chosen from the fields of bioinorganic and solid-state chemistry include the Co K-edge XAS spectrum of aquacobalamin [H 2 OCbl] + , the Fe L-edge XAS spectrum of deoxymyoglobin (DMb), the Ti L-edge XAS spectrum of rutile TiO 2 , and the Fe M-edge spectrum of α-Fe 2 O 3 hematite. In the largest calculations presented here, molecules with more than 700 atoms and cluster models with more than 50 metal centers were employed. In all the studied cases, very good to excellent agreement with experiment is obtained. It will be shown that the PNO-ROCIS method provides an unprecedented performance of wave-function-based methods in the field of computational X-ray spectroscopy. 16. Software configuration management International Nuclear Information System (INIS) Arribas Peces, E.; Martin Faraldo, P. 1993-01-01 Software Configuration Management is directed towards identifying system configuration at specific points of its life cycle, so as to control changes to the configuration and to maintain the integrity and traceability of the configuration throughout its life. SCM functions and tasks are presented in the paper 17. Conceptualizing Embedded Configuration DEFF Research Database (Denmark) Oddsson, Gudmundur Valur; Hvam, Lars; Lysgaard, Ole 2006-01-01 and services. The general idea can be named embedded configuration. In this article we intend to conceptualize embedded configuration, what it is and is not. The difference between embedded configuration, sales configuration and embedded software is explained. We will look at what is needed to make embedded...... configuration systems. That will include requirements to product modelling techniques. An example with consumer electronics will illuminate the elements of embedded configuration in settings that most can relate to. The question of where embedded configuration would be relevant is discussed, and the current... 18. Groundwater in the Boreal Plains: How Climate and Geology Interact to Control Water Table Configurations in a Sub-Humid, Low-Relief Region Science.gov (United States) Hokanson, K. J.; Devito, K.; Mendoza, C. A. 2017-12-01 The Boreal Plain (BP) region of Canada, a landscape characterized by low-relief, a sub-humid climate and heterogeneous glacial landforms, is experiencing unprecedented anthropogenic and natural disturbance, including climate change and oil & gas operations. Understanding the controls on and the natural variability of water table position, and subsequently predicting changes in water table position under varying physical and climatic scenarios will become important as water security becomes increasingly threatened. The BP is composed of a mosaic of forestland, wetland, and aquatic land covers that contrast in dominant vegetation cover, evapotranspiration, and soil storage that, in turn, influence water table configurations. Additionally, these land-covers overlie heterogeneous glacial landforms with large contrasts in storage and hydraulic properties which, when coupled with wet-dry climate cycles, result in complex water table distributions in time and space. Several forestland-wetland-pond complexes were selected at the Utikuma Research Study Area (URSA) over three distinct surficial geologic materials (glacial fluvial outwash, stagnant ice moraine, lacustrine clay plain) to explore the roles of climate (cumulative departure from the long term yearly mean precipitation), geology, topographic position, and land cover on water table configurations over 15 years (2002 - 2016). In the absence of large groundwater flow systems, local relief and shallow low conductivity substrates promote the formation of near-surface water tables that are less susceptible to climate variation, regardless of topography. Furthermore, in areas of increased storage, wet and dry climate conditions can result in appreciably different water table configurations over time, ranging from mounds to hydraulic depressions, depending on the arrangement of land-covers, dominant surficial geology, and substrate layering. 19. A unix configuration engine International Nuclear Information System (INIS) Burgess, M. 1994-06-01 A high level description language is presented for the purpose of automatically configuring large heterogeneous networked unix environments, based on class-oriented abstractions. The configuration engine is portable and easily extensible 20. MICROCONTROLLER PIN CONFIGURATION TOOL OpenAIRE Bhaskar Joshi; F. Mohammed Rizwan; Dr. Rajashree Shettar 2012-01-01 Configuring the micro controller with large number of pins is tedious. Latest Infine on microcontroller contains more than 200 pins and each pin has classes of signals. Therefore the complexity of the microcontroller is growing. It evolves looking into thousands of pages of user manual. For a user it will take days to configure the microcontroller with the peripherals. We need an automated tool to configure the microcontroller so that the user can configure the microcontroller without having ... 1. Operational Dynamic Configuration Analysis Science.gov (United States) Lai, Chok Fung; Zelinski, Shannon 2010-01-01 Sectors may combine or split within areas of specialization in response to changing traffic patterns. This method of managing capacity and controller workload could be made more flexible by dynamically modifying sector boundaries. Much work has been done on methods for dynamically creating new sector boundaries [1-5]. Many assessments of dynamic configuration methods assume the current day baseline configuration remains fixed [6-7]. A challenging question is how to select a dynamic configuration baseline to assess potential benefits of proposed dynamic configuration concepts. Bloem used operational sector reconfigurations as a baseline [8]. The main difficulty is that operational reconfiguration data is noisy. Reconfigurations often occur frequently to accommodate staff training or breaks, or to complete a more complicated reconfiguration through a rapid sequence of simpler reconfigurations. Gupta quantified a few aspects of airspace boundary changes from this data [9]. Most of these metrics are unique to sector combining operations and not applicable to more flexible dynamic configuration concepts. To better understand what sort of reconfigurations are acceptable or beneficial, more configuration change metrics should be developed and their distribution in current practice should be computed. This paper proposes a method to select a simple sequence of configurations among operational configurations to serve as a dynamic configuration baseline for future dynamic configuration concept assessments. New configuration change metrics are applied to the operational data to establish current day thresholds for these metrics. These thresholds are then corroborated, refined, or dismissed based on airspace practitioner feedback. The dynamic configuration baseline selection method uses a k-means clustering algorithm to select the sequence of configurations and trigger times from a given day of operational sector combination data. The clustering algorithm selects a simplified 2. Valence ionized states of iron pentacarbonyl and eta5-cyclopentadienyl cobalt dicarbonyl studied by symmetry-adapted cluster-configuration interaction calculation and collision-energy resolved Penning ionization electron spectroscopy. Science.gov (United States) Fukuda, Ryoichi; Ehara, Masahiro; Nakatsuji, Hiroshi; Kishimoto, Naoki; Ohno, Koichi 2010-02-28 Valence ionized states of iron pentacarbonyl Fe(CO)(5) and eta(5)-cyclopentadienyl cobalt dicarbonyl Co(eta(5)-C(5)H(5))(CO)(2) have been studied by ultraviolet photoelectron spectroscopy, two-dimensional Penning ionization electron spectroscopy (2D-PIES), and symmetry-adapted cluster-configuration interaction calculations. Theory provided reliable assignments for the complex ionization spectra of these molecules, which have metal-carbonyl bonds. Theoretical ionization energies agreed well with experimental observations and the calculated wave functions could explain the relative intensities of PIES spectra. The collision-energy dependence of partial ionization cross sections (CEDPICS) was obtained by 2D-PIES. To interpret these CEDPICS, the interaction potentials between the molecules and a Li atom were examined in several coordinates by calculations. The relation between the slope of the CEDPICS and the electronic structure of the ionized states, such as molecular symmetry and the spatial distribution of ionizing orbitals, was analyzed. In Fe(CO)(5), an attractive interaction was obtained for the equatorial CO, while the interaction for the axial CO direction was repulsive. For Co(eta(5)-C(5)H(5))(CO)(2), the interaction potential in the direction of both Co-C-O and Co-Cp ring was attractive. These anisotropic interactions and ionizing orbital distributions consistently explain the relative slopes of the CEDPICS. 3. HLT configuration management system CERN Document Server Daponte, Vincenzo 2015-01-01 The CMS High Level Trigger (HLT) is implemented running a streamlined version of the CMS offline reconstruction software running on thousands of CPUs. The CMS software is written mostly in C++, using Python as its configuration language through an embedded CPython interpreter. The configuration of each process is made up of hundreds of modules, organized in sequences and paths. As an example, the HLT configurations used for 2011 data taking comprised over 2200 different modules, organized in more than 400 independent trigger paths. The complexity of the HLT configurations and the large number of configuration produced require the design of a suitable data management system. The present work describes the designed solution to manage the considerable number of configurations developed and to assist the editing of new configurations. The system is required to be remotely accessible and OS-independent as well as easly maintainable easy to use. To meet these requirements a three-layers architecture has been choose... 4. Software configuration management CERN Document Server Keyes, Jessica 2004-01-01 Software Configuration Management discusses the framework from a standards viewpoint, using the original DoD MIL-STD-973 and EIA-649 standards to describe the elements of configuration management within a software engineering perspective. Divided into two parts, the first section is composed of 14 chapters that explain every facet of configuration management related to software engineering. The second section consists of 25 appendices that contain many valuable real world CM templates. Energy Technology Data Exchange (ETDEWEB) Mahnke, Lisa K.; Naether, Christian; Bensch, Wolfgang [Institut fuer Anorganische Chemie, Christian-Albrechts-Universitaet, Kiel (Germany); Kondinski, Aleksandar; Van Leusen, Jan; Monakhov, Kirill Yu.; Koegerler, Paul [Institut fuer Anorganische Chemie, RWTH Aachen University (Germany); Warzok, Ulrike; Schalley, Christoph A. [Institut fuer Chemie und Biochemie, Freie Universitaet Berlin (Germany) 2018-03-05 A water-soluble derivative of the polyoxovanadate {V_1_5E_6O_4_2} (E=semimetal) archetype enables the study of cluster shell rearrangements driven by supramolecular interactions. A reaction unique to E=Sb, induced exclusively by ligand metathesis in peripheral [Ni(ethylenediamine){sub 3}]{sup 2+} counterions, results in the formation of the metastable α{sub 1}* configurational isomer of the {V_1_4Sb_8O_4_2} cluster type. Contrary to all other polyoxovanadate shell architectures, this isomer comprises an inward-oriented vanadyl group and is ca. 50 and 12 kJ mol{sup -1} higher in energy than the previously isolated α and β isomers, respectively. We discuss this unexpected reaction in light of supramolecular Sb-O..V and Sb-O..Sb contacts manifested in {V_1_4Sb_8O_4_2}{sub 2} dimers detected in the solid state. ESI MS experiments confirm the stability of these dimers also in solution and in the gas phase. DFT calculations indicate that other, as of yet elusive isomers of {V_1_4Sb_8}, might be accessible as well. (copyright 2018 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim) 6. CONFIGURATION GENERATOR MODEL International Nuclear Information System (INIS) Alsaed, A. 2004-01-01 ''The Disposal Criticality Analysis Methodology Topical Report'' prescribes an approach to the methodology for performing postclosure criticality analyses within the monitored geologic repository at Yucca Mountain, Nevada. An essential component of the methodology is the ''Configuration Generator Model for In-Package Criticality'' that provides a tool to evaluate the probabilities of degraded configurations achieving a critical state. The configuration generator model is a risk-informed, performance-based process for evaluating the criticality potential of degraded configurations in the monitored geologic repository. The method uses event tree methods to define configuration classes derived from criticality scenarios and to identify configuration class characteristics (parameters, ranges, etc.). The probabilities of achieving the various configuration classes are derived in part from probability density functions for degradation parameters. The NRC has issued ''Safety Evaluation Report for Disposal Criticality Analysis Methodology Topical Report, Revision 0''. That report contained 28 open items that required resolution through additional documentation. Of the 28 open items, numbers 5, 6, 9, 10, 18, and 19 were concerned with a previously proposed software approach to the configuration generator methodology and, in particular, the k eff regression analysis associated with the methodology. However, the use of a k eff regression analysis is not part of the current configuration generator methodology and, thus, the referenced open items are no longer considered applicable and will not be further addressed 7. Ansible configuration management CERN Document Server Hall, Daniel 2013-01-01 Ansible Configuration Management"" is a step-by-step tutorial that teaches the use of Ansible for configuring Linux machines.This book is intended for anyone looking to understand the basics of Ansible. It is expected that you will have some experience of how to set up and configure Linux machines. In parts of the book we cover configuration files of BIND, MySQL, and other Linux daemons, therefore a working knowledge of these would be helpful but are certainly not required. 8. Configuration management at NEK International Nuclear Information System (INIS) 1999-01-01 Configuration Management (CM) objectives at NEK are to ensure consistency between Design Requirements, Physical Plant Configuration and Configuration Information. Software applications, supporting Design Change, Work Control and Document Control Processes, are integrated in one module-oriented Management Information System (MIS). Master Equipment Component List (MECL) database is central MIS module. Through a combination of centralized database and process migrated activities it is ensured that the CM principles and requirements (accurate, current design data matching plant's physical configuration while complying to applicable requirements), are followed and fulfilled.(author) 9. Compensation of the long-range beam-beam interactions as a path towards new configurations for the High Luminosity LHC CERN Document Server AUTHOR\|(SzGeCERN)390904; Papaphilippou, Yannis; Shatilov, Dmitry 2015-01-01 Colliding bunch trains in a circular collider demands a certain crossing angle in order to separate the two beams transversely after the collision. The magnitude of this crossing angle is a complicated function of the bunch charge, the number of long-range beam-beam interactions, of β* and type of optics (flat or round), and possible compensation or additive effects between several low-β insertions in the ring depending on the orientation of the crossing plane at each interaction point. About 15 years ago, the use of current bearing wires was proposed at CERN in order to mitigate the longrange beam-beam effects, therefore offering the possibility to minimize the crossing angle with all the beneficial effects this might have: on the luminosity performance by reducing the need for crab-cavities or lowering their voltage, on the required aperture of the final focus magnets, on the strength of the orbit corrector involved in the crossing bumps, and finally on the heat load and radiation dose deposited in the fi... 10. Simulator configuration maintenance International Nuclear Information System (INIS) 2006-01-01 Requirements and recommendations of this section defines NPP personnel activity aimed to the provision of the simulator configuration compliance with the current configuration of the power-generating unit-prototype, standard and technical requirements and describe a monitoring procedure for a set of simulator software and hardware, training, organizational and technical documents 11. PIV Logon Configuration Guidance Energy Technology Data Exchange (ETDEWEB) Lee, Glen Alan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States) 2016-03-04 This document details the configurations and enhancements implemented to support the usage of federal Personal Identity Verification (PIV) Card for logon on unclassified networks. The guidance is a reference implementation of the configurations and enhancements deployed at the Los Alamos National Laboratory (LANL) by Network and Infrastructure Engineering – Core Services (NIE-CS). DEFF Research Database (Denmark) Taran, Yariv; Nielsen, Christian; Thomsen, Peter 2015-01-01 , by developing (inductively) an ontological classification framework, in view of the BM process configurations typology developed. Design/methodology/approach – Given the inconsistencies found in the business model studies (e.g. definitions, configurations, classifications) we adopted the analytical induction... 13. Risk-based configuration control International Nuclear Information System (INIS) Szikszai, T. 1997-01-01 The presentation discusses the following issues: The Configuration Control; The Risk-based Configuration Control (during power operation mode, and during shutdown mode). PSA requirements. Use of Risk-based Configuration Control System. Configuration Management (basic elements, benefits, information requirements) 14. Experimental study of a RF plasma source with helicon configuration in the mix Ar/H_2. Application to the chemical etching of carbon materials surfaces in the framework of the plasma-wall interactions studies of ITER's divertor International Nuclear Information System (INIS) Bieber, T. 2012-01-01 The issue of the interaction wall-plasma is important in thermonuclear devices. The purpose of this work is to design a very low pressure atomic plasma source in order to study chemical etching of carbon surfaces in the same conditions as edge plasma in tokamaks. The experimental work has consisted in 2 stages: first, the characterisation of the new helicon configuration reactor developed for this research and secondly the atomic hydrogen source used for the chemical etching. The first chapter recalls what thermonuclear fusion is. The helicon configuration reactor as well as its diagnostics (optical emission spectroscopy, laser induced fluorescence - LIF, and Langmuir probe) are described in the second chapter. The third chapter deals with the different coupling modes (RF power and plasma) identified in pure argon plasmas and how they are obtained by setting experimental parameters such as injected RF power, magnetic fields or pressure. The fourth chapter is dedicated to the study of the difference in behavior between the electronic density and the relative density of metastable Ar"+ ions. The last chapter presents the results in terms of mass losses of the carbon material surfaces obtained with the atomic hydrogen source. (A.C.) 15. Interaction of 4p54dN+1 and 4p64dN-14f configurations and its influence on the photoexcitation and emission spectra in the isoelectronic and isonuclear sequences International Nuclear Information System (INIS) Kucas, S; Karazija, R; Jonauskas, V; Momkauskaite, A 2009-01-01 The strong interaction of 4p 5 4d N+1 + 4p 6 4d N-1 4f configurations and its influence on the photoexcitation and emission spectra corresponding to the excitations from the ground level of 4p 6 4d N have been considered. The results are presented for the isoelectronic sequences from the ionization degree q = 5 up to q = 29-37 as well as for the isonuclear sequences of Sn q+ and W q+ . It is shown that depending on the number of 4d electrons, the variation of spectra in the isoelectronic sequences corresponds to three different types. At N = 4 and N = 6-9, the strong concentration of lines takes place in the whole isoelectronic sequence, except for small ionization degrees. At N ≤ 3, the width of photoexcitation and emission spectra also obtains a relatively larger value at small ionization degrees, decreases with ionization degree rising, but tends to increase again at large ionization degrees. In the whole isoelectronic sequence, a very narrow group of a few intense lines is obtained for N = 5. The transitions from the excited levels mainly proceed to the lowest level of the ground configuration; it is the reason for the similarity of photoexcitation and emission spectra. The quenching of many lines and the concentration of line strengths in a few transitions indicate the existence of some wavefunction basis with strict selection rules for dipole transitions. 16. Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins. Science.gov (United States) Li Manni, Giovanni; Smart, Simon D; Alavi, Ali 2016-03-08 A novel stochastic Complete Active Space Self-Consistent Field (CASSCF) method has been developed and implemented in the Molcas software package. A two-step procedure is used, in which the CAS configuration interaction secular equations are solved stochastically with the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) approach, while orbital rotations are performed using an approximated form of the Super-CI method. This new method does not suffer from the strong combinatorial limitations of standard MCSCF implementations using direct schemes and can handle active spaces well in excess of those accessible to traditional CASSCF approaches. The density matrix formulation of the Super-CI method makes this step independent of the size of the CI expansion, depending exclusively on one- and two-body density matrices with indices restricted to the relatively small number of active orbitals. No sigma vectors need to be stored in memory for the FCIQMC eigensolver--a substantial gain in comparison to implementations using the Davidson method, which require three or more vectors of the size of the CI expansion. Further, no orbital Hessian is computed, circumventing limitations on basis set expansions. Like the parent FCIQMC method, the present technique is scalable on massively parallel architectures. We present in this report the method and its application to the free-base porphyrin, Mg(II) porphyrin, and Fe(II) porphyrin. In the present study, active spaces up to 32 electrons and 29 orbitals in orbital expansions containing up to 916 contracted functions are treated with modest computational resources. Results are quite promising even without accounting for the correlation outside the active space. The systems here presented clearly demonstrate that large CASSCF calculations are possible via FCIQMC-CASSCF without limitations on basis set size. 17. A configural dominant account of contextual cueing: Configural cues are stronger than colour cues. Science.gov (United States) Kunar, Melina A; John, Rebecca; Sweetman, Hollie 2014-01-01 Previous work has shown that reaction times to find a target in displays that have been repeated are faster than those for displays that have never been seen before. This learning effect, termed "contextual cueing" (CC), has been shown using contexts such as the configuration of the distractors in the display and the background colour. However, it is not clear how these two contexts interact to facilitate search. We investigated this here by comparing the strengths of these two cues when they appeared together. In Experiment 1, participants searched for a target that was cued by both colour and distractor configural cues, compared with when the target was only predicted by configural information. The results showed that the addition of a colour cue did not increase contextual cueing. In Experiment 2, participants searched for a target that was cued by both colour and distractor configuration compared with when the target was only cued by colour. The results showed that adding a predictive configural cue led to a stronger CC benefit. Experiments 3 and 4 tested the disruptive effects of removing either a learned colour cue or a learned configural cue and whether there was cue competition when colour and configural cues were presented together. Removing the configural cue was more disruptive to CC than removing colour, and configural learning was shown to overshadow the learning of colour cues. The data support a configural dominant account of CC, where configural cues act as the stronger cue in comparison to colour when they are presented together. 18. The LHCb configuration database CERN Document Server Abadie, Lana; Gaspar, Clara; Jacobsson, Richard; Jost, Beat; Neufeld, Niko 2005-01-01 The Experiment Control System (ECS) will handle the monitoring, configuration and operation of all the LHCb experimental equipment. All parameters required to configure electronics equipment under the control of the ECS will reside in a configuration database. The database will contain two kinds of information: 1.\tConfiguration properties about devices such as hardware addresses, geographical location, and operational parameters associated with particular running modes (dynamic properties). 2.\tConnectivity between devices : this consists of describing the output and input connections of a device (static properties). The representation of these data using tables must be complete so that it can provide all the required information to the ECS and must cater for all the subsystems. The design should also guarantee a fast response time, even if a query results in a large volume of data being loaded from the database into the ECS. To fulfil these constraints, we apply the following methodology: Determine from the d... 19. Drupal 8 configuration management CERN Document Server Borchert, Stefan 2015-01-01 Drupal 8 Configuration Management is intended for people who use Drupal 8 to build websites, whether you are a hobbyist using Drupal for the first time, a long-time Drupal site builder, or a professional web developer. 20. Configuration by Modularisation DEFF Research Database (Denmark) 1998-01-01 Globally operating companies have realized that locally customized products and services are today the prerequisite for the success. The capability or the paradigm to act locally in global markets is called Mass Customization [Victor 1997]. The prerequisite for Mass Customization is Configuration...... Management and i Configuration Management the most important means is Modularisation.The goal of this paper is to show Configuration Management as a contribution to the Mass Customisation and Modularisation as a contribution to the industrialisation of the design area [Andreasen 1997]. A basic model...... for the creation of a structured product family is presented and examples are given. The concepts of a novel Dynamic Modularisation method, Metrics for Modularisation and Design for Configurability are presented.... 1. Configuration Management Automation (CMA) - Data.gov (United States) Department of Transportation — Configuration Management Automation (CMA) will provide an automated, integrated enterprise solution to support CM of FAA NAS and Non-NAS assets and investments. CMA... 2. Computer software configuration management International Nuclear Information System (INIS) Pelletier, G. 1987-08-01 This report reviews the basic elements of software configuration management (SCM) as defined by military and industry standards. Several software configuration management standards are evaluated given the requirements of the nuclear industry. A survey is included of available automated tools for supporting SCM activities. Some information is given on the experience of establishing and using SCM plans of other organizations that manage critical software. The report concludes with recommendations of practices that would be most appropriate for the nuclear power industry in Canada 3. Control Configuration Selection for Multivariable Descriptor Systems DEFF Research Database (Denmark) Shaker, Hamid Reza; Stoustrup, Jakob 2012-01-01 Control configuration selection is the procedure of choosing the appropriate input and output pairs for the design of SISO (or block) controllers. This step is an important prerequisite for a successful industrial control strategy. In industrial practices it is often the case that the system, whi...... is that it can be used to propose a richer sparse or block diagonal controller structure. The interaction measure is used for control configuration selection of the linearized CSTR model with descriptor from.... 4. X-ray M4,5 Resonant Raman Scattering from La metal with final 4p hole: Calculations with 4p-4d-4f configuration interaction in the final state and comparison with the experiment International Nuclear Information System (INIS) Taguchi, M.; Braicovich, L.; Tagliaferri, A.; Dallera, C.; Giarda, K.; Ghiringhelli, G.; Brookes, N.B.; Borgatti, F. 2001-03-01 We consider the X-Ray Resonant Raman Scattering (RRS) in La in the whole M 4,5 region ending with a state with a 4p hole, along the sequence 3d 10 4f 0 →3d 9 4f 1 →3d 10 4p 5 4f 1 . The final state configuration mixes with that with two 4d holes i.e. 3d 10 4d 8 4f n+2 having almost the same energy. Thus RRS must be described by introducing final state Configuration Interaction (CI) between states with one 4p hole and with two 4d holes. This approach allows detailed experimental data on La-metal to be interpreted on the basis of a purely ionic approach. It is shown that the inclusion of CI is crucial and has very clear effects. The calculations with the Kramers-Heisenberg formula describe all measured spectral features appearing in the strict Raman regime i.e. dispersing with the incident photon energy. In the experiment also a nondispersive component is present when the excitation energy is greater than about 2 eV above the M 5 peak. The shape and position of this component is well accounted for by a model based on all possible partitions of the excitation energy between localised and extended states. However, the intensity of the nondispersive component is greater in the measurements, suggesting a rearrangement in the intermediate excited state. The comparison of ionic calculations with the metal measurements is legitimate, as shown by the comparison between the measurements on La-metal and on LaF 3 with M 5 excitation, giving the same spectrum within the experimental accuracy. Moreover, the experiment shows that the final lifetime broadening is much greater in the final states corresponding to lower outgoing photon energies than in the states corresponding to higher outgoing photon energies. (author) 5. Reference frame for Product Configuration DEFF Research Database (Denmark) Ladeby, Klaes Rohde; Oddsson, Gudmundur Valur 2011-01-01 a reference frame for configuration that permits 1) a more precise understanding of a configuration system, 2) a understanding of how the configuration system relate to other systems, and 3) a definition of the basic concepts in configuration. The total configuration system, together with the definition... 6. Remembering facial configurations. Science.gov (United States) Bruce, V; Doyle, T; Dench, N; Burton, M 1991-02-01 Eight experiments are reported showing that subjects can remember rather subtle aspects of the configuration of facial features to which they have earlier been exposed. Subjects saw several slightly different configurations (formed by altering the relative placement of internal features of the face) of each of ten different faces, and they were asked to rate the apparent age and masculinity-femininity of each. Afterwards, subjects were asked to select from pairs of faces the configuration which was identical to one previously rated. Subjects responded strongly to the central or "prototypical" configuration of each studied face where this was included as one member of each test pair, whether or not it had been studied (Experiments 1, 2 and 4). Subjects were also quite accurate at recognizing one of the previously encountered extremes of the series of configurations that had been rated (Experiment 3), but when unseen prototypes were paired with seen exemplars subjects' performance was at chance (Experiment 5). Prototype learning of face patterns was shown to be stronger than that for house patterns, though both classes of patterns were affected equally by inversion (Experiment 6). The final two experiments demonstrated that preferences for the prototype could be affected by instructions at study and by whether different exemplars of the same face were shown consecutively or distributed through the study series. The discussion examines the implications of these results for theories of the representation of faces and for instance-based models of memory. 7. Configuration Control Office CERN Multimedia Beltramello, O In order to enable Technical Coordination to manage the detector configuration and to be aware of all changes in this configuration, a baseline of the envelopes has been created in April 2001. Fifteen system and multi-system envelope drawings have been approved and baselined. An EDMS file is associated with each approved envelope, which provides a list of the current known unsolved conflicts related to the envelope and a list of remaining drawing inconsistencies to be corrected. The envelope status with the associated drawings and EDMS file can be found on the web at this adress: http://atlasinfo.cern.ch/Atlas/TCOORD/Activities/Installation/Configuration/ Any modification in the baseline has to be requested via the Engineering Change Requests. The procedure can be found under: http://atlasinfo.cern.ch/Atlas/TCOORD/Activities/TcOffice/Quality/ECR/ TC will review all the systems envelopes in the near future and manage conflict resolution with the collaboration of the systems. 8. The LHCb configuration database CERN Document Server Abadie, L; Van Herwijnen, Eric; Jacobsson, R; Jost, B; Neufeld, N 2005-01-01 The aim of the LHCb configuration database is to store information about all the controllable devices of the detector. The experiment's control system (that uses PVSS ) will configure, start up and monitor the detector from the information in the configuration database. The database will contain devices with their properties, connectivity and hierarchy. The ability to store and rapidly retrieve huge amounts of data, and the navigability between devices are important requirements. We have collected use cases to ensure the completeness of the design. Using the entity relationship modelling technique we describe the use cases as classes with attributes and links. We designed the schema for the tables using relational diagrams. This methodology has been applied to the TFC (switches) and DAQ system. Other parts of the detector will follow later. The database has been implemented using Oracle to benefit from central CERN database support. The project also foresees the creation of tools to populate, maintain, and co... 9. Oxygen configurations in silica International Nuclear Information System (INIS) Chelikowsky, James R.; Chadi, D. J.; Binggeli, N. 2000-01-01 We propose a transition state for oxygen in silica. This state is produced by the insertion of an oxygen molecule into the Si-O-Si bond, i.e., it consists of producing a Si-O-O-O-Si bond. This state allows molecular oxygen diffusion in silica without breaking the molecular O 2 bond and it is energetically more stable than a peroxy configuration. This configuration may allow for exchange of molecular oxygen with the oxygen in the silica framework. (c) 2000 The American Physical Society 10. Control of divertor configuration in JT-60 International Nuclear Information System (INIS) Yoshino, R.; Kukuchi, M.; Ninomiya, H.; Yoshida, H.; Tsuji, S.; Hosogane, N.; Seki, S. 1985-01-01 The control algorithm of JT-60 divertor configuration is presented. JT-60 has five types of poloidal magnetic field coil with each power supply in order to regulate the control objectives mentioned above. However, if one controls each objective by each coil current independently, there must inevitably occur large interaction between control objectives. Because the relation between control objectives and coil currents is complicated. This situation may be the same with a fusion reactor device. For making it possible to control each objective independently without causing large interaction, the authors adopt the noninteracting control algorithm. Hence, this report demonstrates the availability of this method to the control of JT-60 divertor configuration 11. Stirling Engine Configuration Selection Directory of Open Access Journals (Sweden) Jose Egas 2018-03-01 Full Text Available Unlike internal combustion engines, Stirling engines can be designed to work with many drive mechanisms based on the three primary configurations, alpha, beta and gamma. Hundreds of different combinations of configuration and mechanical drives have been proposed. Few succeed beyond prototypes. A reason for poor success is the use of inappropriate configuration and drive mechanisms, which leads to low power to weight ratio and reduced economic viability. The large number of options, the lack of an objective comparison method, and the absence of a selection criteria force designers to make random choices. In this article, the pressure—volume diagrams and compression ratios of machines of equal dimensions, using the main (alpha, beta and gamma crank based configurations as well as rhombic drive and Ross yoke mechanisms, are obtained. The existence of a direct relation between the optimum compression ratio and the temperature ratio is derived from the ideal Stirling cycle, and the usability of an empirical low temperature difference compression ratio equation for high temperature difference applications is tested using experimental data. It is shown that each machine has a different compression ratio, making it more or less suitable for a specific application, depending on the temperature difference reachable. 12. Global Value Chain Configuration DEFF Research Database (Denmark) Hernandez, Virginia; Pedersen, Torben 2017-01-01 modes chosen and the different ways of coordinating them. We also examine the outcomes of a global value chain configuration in terms of performance and upgrading. Our aim is to review the state of the art of these issues, identify research gaps and suggest new lines for future research that would... 13. Inclusive Services Innovation Configuration Science.gov (United States) Holdheide, Lynn R.; Reschly, Daniel J. 2011-01-01 Teacher preparation to deliver inclusive services to students with disabilities is increasingly important because of changes in law and policy emphasizing student access to, and achievement in, the general education curriculum. This innovation configuration identifies the components of inclusive services that should be incorporated in teacher… 14. Ansible configuration management CERN Document Server Hall, Daniel 2015-01-01 This book is intended for anyone who wants to learn Ansible starting from the basics. Some experience of how to set up and configure Linux machines and a working knowledge of BIND, MySQL, and other Linux daemons is expected. 15. Configuring the development space for conceptualization DEFF Research Database (Denmark) Brønnum, Louise; Clausen, Christian 2013-01-01 This paper addresses issues of conceptualization in the early stages of concept development noted as the Front End of Innovation [FEI]. We examine this particular development space as a socio technical space where a diversity of technological knowledge, user perspectives and organizational agendas...... meet and interact. Based on a case study from an industrial medical company, the paper addresses and analyses the configuration of the development space in a number of projects aiming to take up user oriented perspectives in their activities. It presents insights on how the FEI was orchestrated...... and staged and how different elements and objects contributed to the configuration of the space in order to make it perform in a certain way. The analysis points at the importance of the configuration processes and indicate how these configurations often may act as more or less hidden limitations on concept... 16. Analyzing Visibility Configurations. Science.gov (United States) Dachsbacher, C 2011-04-01 Many algorithms, such as level of detail rendering and occlusion culling methods, make decisions based on the degree of visibility of an object, but do not analyze the distribution, or structure, of the visible and occluded regions across surfaces. We present an efficient method to classify different visibility configurations and show how this can be used on top of existing methods based on visibility determination. We adapt co-occurrence matrices for visibility analysis and generalize them to operate on clusters of triangular surfaces instead of pixels. We employ machine learning techniques to reliably classify the thus extracted feature vectors. Our method allows perceptually motivated level of detail methods for real-time rendering applications by detecting configurations with expected visual masking. We exemplify the versatility of our method with an analysis of area light visibility configurations in ray tracing and an area-to-area visibility analysis suitable for hierarchical radiosity refinement. Initial results demonstrate the robustness, simplicity, and performance of our method in synthetic scenes, as well as real applications. 17. Mechanical configuration and maintenance International Nuclear Information System (INIS) Brown, T.G.; Casini, G.; Churakov, G.F. 1982-01-01 The INTOR engineering design has been strongly influenced by considerations for assembly and maintenance. A maintenance philosophy was established at the outset of the conceptual design to insure that the tokamak configuration would be developed to accommodate maintenance requirements. The main features of the INTOR design are summarized in this paper with primary emphasis on the impact of maintenance considerations. The most apparent configuration design feature is the access provided for torus maintenance. Particular attention was given to the size and location of superconducting magnets and the location of vacuum boundaries. All of the poloidal field (PF) coils are placed outside of the bore of the toroidal field (TF) coils and located above and below an access opening between adjacent TF coils through which torus sectors are removed. A magnet structural configuration consisting of mechanically attached reinforcing members has been designed which facilitates the open access space for torus sector removal. For impurity control, a single null poloidal divertor was selected over a double null design in order to maintain sufficient access for pumping and maintenance of the collector. A double null divertor was found to severely limit access to the torus with the addition of divertor collectors and pumping at the top. For this reason, a single null concept was selected in spite of the more difficult design problems associated with the required asymmetric PF system and higher particle loadings 18. Lessons Learned in Designing User-configurable Modular Robotics DEFF Research Database (Denmark) Lund, Henrik Hautop 2013-01-01 User-configurable robotics allows users to easily configure robotic systems to perform task-fulfilling behaviors as desired by the users. With a user configurable robotic system, the user can easily modify the physical and func-tional aspect in terms of hardware and software components of a robotic...... with the semi-autonomous com-ponents of the user-configurable robotic system in interaction with the given environment. Components constituting such a user-configurable robotic system can be characterized as modules in a modular robotic system. Several factors in the definition and implementation... 19. Computational methods for stellerator configurations International Nuclear Information System (INIS) Betancourt, O. 1992-01-01 This project had two main objectives. The first one was to continue to develop computational methods for the study of three dimensional magnetic confinement configurations. The second one was to collaborate and interact with researchers in the field who can use these techniques to study and design fusion experiments. The first objective has been achieved with the development of the spectral code BETAS and the formulation of a new variational approach for the study of magnetic island formation in a self consistent fashion. The code can compute the correct island width corresponding to the saturated island, a result shown by comparing the computed island with the results of unstable tearing modes in Tokamaks and with experimental results in the IMS Stellarator. In addition to studying three dimensional nonlinear effects in Tokamaks configurations, these self consistent computed island equilibria will be used to study transport effects due to magnetic island formation and to nonlinearly bifurcated equilibria. The second objective was achieved through direct collaboration with Steve Hirshman at Oak Ridge, D. Anderson and R. Talmage at Wisconsin as well as through participation in the Sherwood and APS meetings 20. Valence configurations in 214Rn International Nuclear Information System (INIS) Dracoulis, G.D.; Byrne, A.P.; Stuchbery, A.E.; Bark, R.A.; Poletti, A.R. 1987-01-01 Excited states of 214 Rn, up to spins of ≅ 24 ℎ have been studied using γ-ray and electron spectroscopy following the 208 Pb( 9 Be,3n) 214 Rn reaction. The level scheme (which differs substantially from earlier work) is compared with the results of a semi-empirical shell model calculation. The availability of high-spin orbitals for the four valence protons and two valence neutrons, and the effect of the attractive proton-neutron interaction, leads to the prediction of high-spin states at an unusually low excitation energy. Experimentally, the high level density leads to difficulties in the level scheme assignments at high spin. Nevertheless, configuration assignments, supported by transition strengths deduced from the measured lifetimes (in the nanosecond region) are suggested for the main yrast states. The decay properties also suggest that configuration mixing is important. The possibility of a gradual transition to octupole deformation, implied by the decay properties of the 11 - and 10 + yrast states is also discussed. (orig.) 1. Configuration Management Program Plan International Nuclear Information System (INIS) 1991-01-01 Westinghouse Savannah River Company (WSRC) has established a configuration management (CM) plan to execute the SRS CM Policy and the requirements of the DOE Order 4700.1. The Reactor Restart Division (RRD) has developed its CM Plan under the SRS CM Program and is implementing it via the RRD CM Program Plan and the Integrated Action Plan. The purpose of the RRD CM program is to improve those processes which are essential to the safe and efficient operation of SRS production reactors. This document provides details of this plan 2. Ames Optimized TCA Configuration Science.gov (United States) Cliff, Susan E.; Reuther, James J.; Hicks, Raymond M. 1999-01-01 Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the 3. Gas/liquid flow configurations International Nuclear Information System (INIS) Bonin, Jacques; Fitremann, J.-M. 1978-01-01 Prediction of flow configurations (morphology) for gas/liquid or liquid/vapour mixtures is an important industrial problem which is not yet fully understood. The ''Flow Configurations'' Seminar of Societe Hydrotechnique de France has framed recommendations for investigation of potential industrial applications for flow configurations [fr 4. Software Configurable Multichannel Transceiver Science.gov (United States) Freudinger, Lawrence C.; Cornelius, Harold; Hickling, Ron; Brooks, Walter 2009-01-01 Emerging test instrumentation and test scenarios increasingly require network communication to manage complexity. Adapting wireless communication infrastructure to accommodate challenging testing needs can benefit from reconfigurable radio technology. A fundamental requirement for a software-definable radio system is independence from carrier frequencies, one of the radio components that to date has seen only limited progress toward programmability. This paper overviews an ongoing project to validate the viability of a promising chipset that performs conversion of radio frequency (RF) signals directly into digital data for the wireless receiver and, for the transmitter, converts digital data into RF signals. The Software Configurable Multichannel Transceiver (SCMT) enables four transmitters and four receivers in a single unit the size of a commodity disk drive, programmable for any frequency band between 1 MHz and 6 GHz. 5. Configuring the autism epidemic DEFF Research Database (Denmark) Seeberg, Jens; Christensen, Fie Lund Lindegaard 2017-01-01 Autism has been described as an epidemic, but this claim is contested and may point to an awareness epidemic, i.e. changes in the definition of what autism is and more attention being invested in diagnosis leading to a rise in registered cases. The sex ratio of children diagnosed with autism...... is skewed in favour of boys, and girls with autism tend to be diagnosed much later than boys. Building and further developing the notion of ‘configuration’ of epidemics, this article explores the configuration of autism in Denmark, with a particular focus on the health system and social support to families...... with children diagnosed with autism, seen from a parental perspective. The article points to diagnostic dynamics that contribute to explaining why girls with autism are not diagnosed as easily as boys. We unfold these dynamics through the analysis of a case of a Danish family with autism.... 6. Deployable reflector configurations Science.gov (United States) Meinel, A. B.; Meinel, M. P.; Woolf, N. J. Both the theoretical reasons for considering a non-circular format for the Large Deployable Reflector, and a potentially realizable concept for such a device, are discussed. The optimum systems for diffraction limited telescopes with incoherent detection have either a single filled aperture, or two such apertures as an interferometer to synthesize a larger aperture. For a single aperture of limited area, a reflector in the form of a slot can be used to give increased angular resolution. It is shown how a 20 x 8 meter telescope can be configured to fit the Space Shuttle bay, and deployed with relatively simple operations. The relationship between the sunshield design and the inclination of the orbit is discussed. The possible use of the LDR as a basic module to permit the construction of supergiant space telescopes and interferometers both for IR/submm studies and for the entire ultraviolet through mm wave spectral region is discussed. 7. A Configuration Model of Organizational Culture Directory of Open Access Journals (Sweden) Daniel Dauber 2012-01-01 Full Text Available The article proposes a configuration model of organizational culture, which explores dynamic relationships between organizational culture, strategy, structure, and operations of an organization (internal environment and maps interactions with the external environment (task and legitimization environment. A major feature of the configuration model constitutes its well-defined processes, which connect the elements of the model systematically to each other, such as single- and double-loop learning, operationalization of strategies, legitimization management, and so on. The model is grounded in a large review of literature in different research areas and builds on widely recognized models in the field of organization and culture theory. It constitutes a response to the call for new models, which are able to explain and facilitate the exploration of the empirical complexity that organizations face today. The configuration model of organizational culture is of particular interest to scholars who investigate into cultural phenomena and change over time. 8. Application of Configurators in Networks DEFF Research Database (Denmark) Malis, Martin; Hvam, Lars 2003-01-01 Shorter lead-time, improved quality of product specifications and better communication with customers and suppliers are benefits derived from the application of configurators. Configurators are knowledge-based IT-systems that can be applied to deal with product knowledge and to support different...... processes in a company. Traditionally, configurators have been used as an internal tool. In this paper focus will be on the application of configurators in a network of companies, and a procedure for developing product configurators in a network of companies will be presented. The aim is to present...... a structured guideline, tools and methods on how to successfully develop configurators in a network perspective. Findings presented in this paper are supported by research in a case company. The results from the empirical work show a huge potential for the application of configurators in networks of companies.... 9. INTERACT DEFF Research Database (Denmark) Jochum, Elizabeth; Borggreen, Gunhild; Murphey, TD This paper considers the impact of visual art and performance on robotics and human-computer interaction and outlines a research project that combines puppetry and live performance with robotics. Kinesics—communication through movement—is the foundation of many theatre and performance traditions ... 10. Integrating configuration workflows with project management system International Nuclear Information System (INIS) Nilsen, Dimitri; Weber, Pavel 2014-01-01 The complexity of the heterogeneous computing resources, services and recurring infrastructure changes at the GridKa WLCG Tier-1 computing center require a structured approach to configuration management and optimization of interplay between functional components of the whole system. A set of tools deployed at GridKa, including Puppet, Redmine, Foreman, SVN and Icinga, provides the administrative environment giving the possibility to define and develop configuration workflows, reduce the administrative effort and improve sustainable operation of the whole computing center. In this presentation we discuss the developed configuration scenarios implemented at GridKa, which we use for host installation, service deployment, change management procedures, service retirement etc. The integration of Puppet with a project management tool like Redmine provides us with the opportunity to track problem issues, organize tasks and automate these workflows. The interaction between Puppet and Redmine results in automatic updates of the issues related to the executed workflow performed by different system components. The extensive configuration workflows require collaboration and interaction between different departments like network, security, production etc. at GridKa. Redmine plugins developed at GridKa and integrated in its administrative environment provide an effective way of collaboration within the GridKa team. We present the structural overview of the software components, their connections, communication protocols and show a few working examples of the workflows and their automation. International Nuclear Information System (INIS) Payne, G.L.; Klink, W.H.; Ployzou, W.N. 1991-01-01 The detailed study of few-body systems provides one of the most precise tools for studying the dynamics of nuclei. Our research program consists of a careful theoretical study of the nuclear few-body systems. During the past year we have completed several aspects of this program. We have continued our program of using the trinucleon system to investigate the validity of various realistic nucleon-nucleon potentials. Also, the effects of meson-exchange currents in nuclear systems have been studied. Initial calculations using the configuration-space Faddeev equations for nucleon-deuteron scattering have been completed. With modifications to treat relativistic systems, few-body methods can be applied to phenomena that are sensitive to the structure of the individual hadrons. We have completed a review of Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics for Advances in Nuclear Physics. Although it is called a review, it is a large document that contains a significant amount of new research 12. Simulator configuration management system International Nuclear Information System (INIS) Faulent, J.; Brooks, J.G. 1990-01-01 The proposed revisions to ANS 3.5-1985 (Section 5) require Utilities to establish a simulator Configuration Management System (CMS). The proposed CMS must be capable of: Establishing and maintaining a simulator design database. Identifying and documenting differences between the simulator and its reference plant. Tracking the resolution of identified differences. Recording data to support simulator certification, testing and maintenance. This paper discusses a CMS capable of meeting the proposed requirements contained in ANS 3.5. The system will utilize a personal computer and a relational database management software to construct a simulator design database. The database will contain records to all reference nuclear plant data used in designing the simulator, as well as records identifying all the software, hardware and documentation making up the simulator. Using the relational powers of the database management software, reports will be generated identifying the impact of reference plant changes on the operation of the simulator. These reports can then be evaluated in terms of training needs to determine if changes are required for the simulator. If a change is authorized, the CMS will track the change through to its resolution and then incorporate the change into the simulator design database 13. Configurable software for satellite graphics Energy Technology Data Exchange (ETDEWEB) Hartzman, P D 1977-12-01 An important goal in interactive computer graphics is to provide users with both quick system responses for basic graphics functions and enough computing power for complex calculations. One solution is to have a distributed graphics system in which a minicomputer and a powerful large computer share the work. The most versatile type of distributed system is an intelligent satellite system in which the minicomputer is programmable by the application user and can do most of the work while the large remote machine is used for difficult computations. At New York University, the hardware was configured from available equipment. The level of system intelligence resulted almost completely from software development. Unlike previous work with intelligent satellites, the resulting system had system control centered in the satellite. It also had the ability to reconfigure software during realtime operation. The design of the system was done at a very high level using set theoretic language. The specification clearly illustrated processor boundaries and interfaces. The high-level specification also produced a compact, machine-independent virtual graphics data structure for picture representation. The software was written in a systems implementation language; thus, only one set of programs was needed for both machines. A user can program both machines in a single language. Tests of the system with an application program indicate that is has very high potential. A major result of this work is the demonstration that a gigantic investment in new hardware is not necessary for computing facilities interested in graphics. 14. Configuration studies of LHD plasmas International Nuclear Information System (INIS) Okamoto, M. 1997-01-01 Configuration studies are performed on the plasmas of The Large Helical Device (LHD), the construction of which is almost completed at the National Institute for Fusion Science. The LHD has flexibility as an experimental device and can have various configurations by changing the poloidal magnetic fields, the pitch of the helical coils (pitch parameter), and the ratio of currents flowing in the two helical coils. Characteristics of the plasma are investigated for the standard configuration, the change in the pitch parameter, and the helical axis configuration 15. Configuration studies of LHD plasmas Energy Technology Data Exchange (ETDEWEB) Okamoto, Masao 1997-03-01 Configuration studies are performed on the plasmas of The Large Helical Device (LHD), the construction of which is almost completed at the National Institute for Fusion Science. The LHD has flexibility as an experimental device and can have various configurations by changing the poloidal magnetic fields, the pitch of the helical coils (pitch parameter), and the ratio of currents flowing in the two helical coils. Characteristics of the plasma are investigated for the standard configuration, the change in the pitch parameter, and the helical axis configuration. (author) International Nuclear Information System (INIS) Payne, G.L.; Klink, W.H.; Polyzou, W.N. 1989-01-01 The detailed study of few-body systems provides one of the most effective means for studying nuclear physics at subnucleon distance scales. For few-body systems the model equations can be solved numerically with errors less than the experimental uncertainties. We have used such systems to investigate the size of relativistic effects, the role of meson-exchange currents, and the importance of quark degrees of freedom in the nucleus. Complete calculations for momentum-dependent potentials have been performed, and the properties of the three-body bound state for these potentials have been studied. Few-body calculations of the electromagnetic form factors of the deuteron and pion have been carried out using a front-form formulation of relativistic quantum mechanics. The decomposition of the operators transforming convariantly under the Poincare group into kinematical and dynamical parts has been studies. New ways for constructing interactions between particles, as well as interactions which lead to the production of particles, have been constructed in the context of a relativistic quantum mechanics. To compute scattering amplitudes in a nonperturbative way, classes of operators have been generated out of which the phase operator may be constructed. Finally, we have worked out procedures for computing Clebsch-Gordan and Racah coefficients on a computer, as well as giving procedures for dealing with the multiplicity problem 17. Configurational entropy of glueball states Energy Technology Data Exchange (ETDEWEB) Bernardini, Alex E., E-mail: [email protected] [Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP (Brazil); Braga, Nelson R.F., E-mail: [email protected] [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 (Brazil); Rocha, Roldão da, E-mail: [email protected] [CMCC, Universidade Federal do ABC, UFABC, 09210-580, Santo André (Brazil) 2017-02-10 The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton–dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states. 18. The benefits of ITER for the portfolio of fusion configurations International Nuclear Information System (INIS) Goldston, R.J. 2002-01-01 Recent plasma science challenges are 1) what limits the pressure in plasmas? (macroscopic stability), 2) how do hot particles and plasma waves interact in the non-linear regime? (wave-particle interactions), 3) what causes plasma transport? (microscopic turbulence and transport) and 4) how can high-temperature plasma and material surface co-exist? (plasma-material interactions). This fusion plasma science is addressed using a 'Portfolio' of configurations, like Stellarator, Tokamak, Spherical Torus, Reversed Field Pinch, Spheromak, and Field Reversed Configuration. Namely, the scientific results from one configuration benefit progress in others. Recent example of this effort can be found in NCSX, NSTX and RFP. ITER will provide very significant benefits to the development of the full fusion portfolio; macroscopic stability, wave-particle interactions, microturbulence and transport, plasma-material interactions, and technical demonstration of an integrated fusion system. (author) 19. The benefits of ITER for the portfolio of fusion configurations Energy Technology Data Exchange (ETDEWEB) Goldston, R.J. [Princeton Plasma Physics Lab., NJ (United States) 2002-10-01 Recent plasma science challenges are 1) what limits the pressure in plasmas? (macroscopic stability), 2) how do hot particles and plasma waves interact in the non-linear regime? (wave-particle interactions), 3) what causes plasma transport? (microscopic turbulence and transport) and 4) how can high-temperature plasma and material surface co-exist? (plasma-material interactions). This fusion plasma science is addressed using a 'Portfolio' of configurations, like Stellarator, Tokamak, Spherical Torus, Reversed Field Pinch, Spheromak, and Field Reversed Configuration. Namely, the scientific results from one configuration benefit progress in others. Recent example of this effort can be found in NCSX, NSTX and RFP. ITER will provide very significant benefits to the development of the full fusion portfolio; macroscopic stability, wave-particle interactions, microturbulence and transport, plasma-material interactions, and technical demonstration of an integrated fusion system. (author) 20. Viscous Design of TCA Configuration Science.gov (United States) Krist, Steven E.; Bauer, Steven X. S.; Campbell, Richard L. 1999-01-01 The goal in this effort is to redesign the baseline TCA configuration for improved performance at both supersonic and transonic cruise. Viscous analyses are conducted with OVERFLOW, a Navier-Stokes code for overset grids, using PEGSUS to compute the interpolations between overset grids. Viscous designs are conducted with OVERDISC, a script which couples OVERFLOW with the Constrained Direct Iterative Surface Curvature (CDISC) inverse design method. The successful execution of any computational fluid dynamics (CFD) based aerodynamic design method for complex configurations requires an efficient method for regenerating the computational grids to account for modifications to the configuration shape. The first section of this presentation deals with the automated regridding procedure used to generate overset grids for the fuselage/wing/diverter/nacelle configurations analysed in this effort. The second section outlines the procedures utilized to conduct OVERDISC inverse designs. The third section briefly covers the work conducted by Dick Campbell, in which a dual-point design at Mach 2.4 and 0.9 was attempted using OVERDISC; the initial configuration from which this design effort was started is an early version of the optimized shape for the TCA configuration developed by the Boeing Commercial Airplane Group (BCAG), which eventually evolved into the NCV design. The final section presents results from application of the Natural Flow Wing design philosophy to the TCA configuration. 1. Qualtiy Issues in Project configured Supply Chains DEFF Research Database (Denmark) Koch, Christian; Larsen, Casper Schultz by configuration by project. In such a setting creating value for the customers and the enterprises becomes dependent of the ability to organise and coordinate in the supply chains. That the configuration is not always successful can be demonstrated by studying the emergence of failures occurring in the supply...... observation period. These were compiled and analysed. The economic consequences are calculated to be 8% of the production costs. The analysis of relations in the supply chain both show relations to materials and knowledge chains and their interaction. Most of the failures were generated in the knowledge...... stream and then occasionally transform into the material stream. The paper proposes initiatives to strengthen partnerships in supply chains and especially at engineer to order production. The contradiction between the permanent enterprise organisation potentially capable of handling purchasing... 2. Stable configurations in social networks Science.gov (United States) Bronski, Jared C.; DeVille, Lee; Ferguson, Timothy; Livesay, Michael 2018-06-01 We present and analyze a model of opinion formation on an arbitrary network whose dynamics comes from a global energy function. We study the global and local minimizers of this energy, which we call stable opinion configurations, and describe the global minimizers under certain assumptions on the friendship graph. We show a surprising result that the number of stable configurations is not necessarily monotone in the strength of connection in the social network, i.e. the model sometimes supports more stable configurations when the interpersonal connections are made stronger. 3. A Software Configuration Management Course DEFF Research Database (Denmark) 2003-01-01 Software Configuration Management has been a big success in research and creation of tools. There are also many vendors in the market of selling courses to companies. However, in the education sector Software Configuration Management has still not quite made it - at least not into the university...... curriculum. It is either not taught at all or is just a minor part of a general course in software engineering. In this paper, we report on our experience with giving a full course entirely dedicated to Software Configuration Management topics and start a discussion of what ideally should be the goal... 4. Device configuration-management system International Nuclear Information System (INIS) Nowell, D.M. 1981-01-01 The Fusion Chamber System, a major component of the Magnetic Fusion Test Facility, contains several hundred devices which report status to the Supervisory Control and Diagnostic System for control and monitoring purposes. To manage the large number of diversity of devices represented, a device configuration management system was required and developed. Key components of this software tool include the MFTF Data Base; a configuration editor; and a tree structure defining the relationships between the subsystem devices. This paper will describe how the configuration system easily accomodates recognizing new devices, restructuring existing devices, and modifying device profile information 5. Airport Configuration Prediction, Phase I Data.gov (United States) National Aeronautics and Space Administration — There is presently poor knowledge throughout the National Airspace System (NAS) of the airport configurations currently in use at each airport. There is even less... 6. Belene NPP project configuration management International Nuclear Information System (INIS) Matveev, A. 2009-01-01 The configuration management includes: change identification; change assessment; change coordination; change approval or rejection; Change introduction. One of the main tasks while implementing the above processes is the analysis of the effect of one change upon all the related elements 7. Configurational Information as Potentially Negative Entropy: The Triple Helix Model Directory of Open Access Journals (Sweden) Loet Leydesdorff 2008-10-01 Full Text Available Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth dimension of a regime 8. Bayesian image restoration, using configurations OpenAIRE Thorarinsdottir, Thordis 2006-01-01 In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the re... 9. Network configuration of global R&D networks DEFF Research Database (Denmark) Hansen, Zaza Nadja Lee; Srai, Jagjit Singh 2011-01-01 , network configuration of global R&D has tended to focus on strategic elements with limited attention given operational effectiveness, or to interfaces with downstream manufacturing operations. Within OM literature, the drivers of configuration of global networks within, engineering, production, supply...... to R&D networks emerged, e.g. product features were more prominent in R&D networks. Furthermore, the study has shown extensive interaction with other operations, including many downstream manufacturing operations. By extending the OM configuration concepts to the configuration of R&D networks......Companies are increasingly globalising their R&D activities, both within the firms and with external partners, with consequent implications for their interaction with manufacturing operations. Previous research in R&D networks has focused on coordination, governance and support elements. However... 10. Knowledge Based Product Configuration - a documentatio tool for configuration projects DEFF Research Database (Denmark) Hvam, Lars; Malis, Martin 2003-01-01 . A lot of knowledge isput into these systems and many domain experts are involved. This calls for an effective documentation system in order to structure this knowledge in a way that fits to the systems. Standard configuration systems do not support this kind of documentation. The chapter deals...... with the development of a Lotus Notes application that serves as a knowledge based documentation tool for configuration projects. A prototype has been developed and tested empirically in an industrial case-company. It has proved to be a succes.... 11. Moderator Configuration Options for ESS DEFF Research Database (Denmark) Zanini, L.; Batkov, K.; Klinkby, Esben Bryndt 2016-01-01 The current, still evolving status of the design and the optimization work for the moderator configuration for the European Spallation Source is described. The moderator design has been strongly driven by the low-dimensional moderator concept recently proposed for use in spallation neutron sources...... or reactors. Quasi-two dimensional, disc- or tube-shaped moderators,can provide strong brightness increase (factor of 3 or more) with respect to volume para-H2moderators, which constitute the reference, state-of-the-art technology for high-intensity coupled moderators. In the design process other, more...... conventional, principles were also considered,such as the importance of moderator positioning, of the premoderator, and beam extraction considerations. Different design and configuration options are evaluated and compared with the reference volume moderator configuration described in the ESS Technical Design... 12. Development of Simulator Configuration Tool International Nuclear Information System (INIS) Nedrelid, Olav; Pettersen, Geir 1996-01-01 The main objective of the development of a Simulator Configuration Tool (SCT) is to achieve faster and more efficient production of dynamic simulators. Through application of versatile graphical interfaces, the simulator builder should be able to configure different types of simulators including full-scope process simulators. The SCT should be able to serve different simulator environments. The configuration tool communicates with simulator execution environments through a TCP/IP-based interface, Communication with a Model Server System developed at Institutt for energiteknikk has been established and used as test case. The system consists of OSF/Motif dialogues for operations requiring textual input, list selections etc., and uses the Picasso-3 User Interface Management System to handle presentation of static and dynamic graphical information. (author) 13. BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS Directory of Open Access Journals (Sweden) Thordis Linda Thorarinsdottir 2011-05-01 Full Text Available In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given. 14. Calculations of configurations of doubly ionized copper (Cu III) International Nuclear Information System (INIS) Sugar, J.; Martin, W.C. 1976-01-01 The energy levels belonging to the configurations 3d 7 4s 2 and 3d 8 nl (nl = 4s, 5s, 4p, 5p, 4d, 5d, 4f, and 5g) have been calculated. The radial energy integrals were treated as parameters and adjusted to give a least-squares fit to the observed levels. Two- and three-body effective electrostatic interactions for equivalent electrons were included, as well as two-body effective interactions for inequivalent electrons. Strong configuration interaction between 3d 7 4s 2 and 3d 8 4d was taken into account. Values of the parameters are given for all the above configurations, and the calculated levels are given for all except 3d 8 4s and 3d 8 4p (for which essentially equivalent results have been published). Leading eigenvector percentages are given in appropriate coupling schemes 15. Projective configurations in projectivegeometrical drawings Directory of Open Access Journals (Sweden) Ivashchenko Andrey Viktorovich 2015-05-01 Full Text Available The article focuses on the optimization of the earlier discussed computer method of obtaining new forms of polyhedra based on projective geometry drawings (trace Diagrams.While working on getting new multifaceted forms by projective geometry methods based on the well-known models of polyhedra on the first stage of the work it is required to calculate the parameters of projective geometry drawings, and then to build them. This is an often used apparatus of analytical geometry. According to it, at first the parameters of the polyhedron (core system of planes are calculated, then we obtain the equation of the plane of the face of the polyhedron, and finally we obtain the equations of lines the next plane faces on the selected curve plane. At each stage of application such a method requires the use of the algorithms of floating point arithmetic, on the one hand, leads to some loss of accuracy of the results and, on the other hand, the large amount of computer time to perform these operations in comparison with integer arithmetic operations.The proposed method is based on the laws existing between the lines that make up the drawing - the known configurations of projective geometry (complete quadrilaterals, configuration of Desargues, Pappus et al..The authors discussed in detail the analysis procedure of projective geometry drawing and the presence of full quadrilaterals, Desargues and Pappus configurations in it.Since the composition of these configurations is invariant with respect to projective change of the original nucleus, knowing them, you can avoid the calculations when solving the equations for finding direct projective geometry drawing analytically, getting them on the basis of belonging to a particular configuration. So you can get a definite advantage in accuracy of the results, and in the cost of computer time. Finding these basic configurations significantly enriches the set of methods and the use of projective geometry drawings. 16. Instance-specific algorithm configuration CERN Document Server Malitsky, Yuri 2014-01-01 This book presents a modular and expandable technique in the rapidly emerging research area of automatic configuration and selection of the best algorithm for the instance at hand. The author presents the basic model behind ISAC and then details a number of modifications and practical applications. In particular, he addresses automated feature generation, offline algorithm configuration for portfolio generation, algorithm selection, adaptive solvers, online tuning, and parallelization. The author's related thesis was honorably mentioned (runner-up) for the ACP Dissertation Award in 2014, 17. Quantum communication in spin star configuration International Nuclear Information System (INIS) Deng Hongliang; Fang Ximing 2008-01-01 This paper considers a generalized spin star system which can be solved exactly, with the central spin-½ system embedded in an outer ring of N spin-½ particles(denoted as spin bath). In this model, in addition to the central-outer interaction, each pair of nearest neighbour of the bath interacts within themselves. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of the symmetries of system. It analyses the quantum state transfer and the dynamical behaviour of entanglement created during quantum communication. It also analyses the efficiency of the configuration regarded as quantum phase covariant clone or decoherence model. Some interesting results are discovered concerning the properties of quantum communication in this model 18. Aerodynamic interactions from reaction controls for lateral control of the M2-F2 lifting-body entry configuration at transonic and supersonic and supersonic Mach numbers. [wind tunnel tests Science.gov (United States) Bailey, R. O.; Brownson, J. J. 1979-01-01 Tests were conducted in the Ames 6 by 6 foot wind tunnel to determine the interaction of reaction jets for roll control on the M2-F2 lifting-body entry vehicle. Moment interactions are presented for a Mach number range of 0.6 to 1.7, a Reynolds number range of 1.2 x 10 to the 6th power to 1.6 x 10 to the 6th power (based on model reference length), an angle-of-attack range of -9 deg to 20 deg, and an angle-of-sideslip range of -6 deg to 6 deg at an angle of attack of 6 deg. The reaction jets produce roll control with small adverse yawing moment, which can be offset by horizontal thrust component of canted jets. 19. Interactive baby feeding bottle NARCIS (Netherlands) 2013-01-01 An interactive baby bottle with an electronic unit is disclosed. The electronic unit comprises a sensor unit configured to sense the heart beat of a person bottle feeding a baby and an actuator unit configured to transmit the sensed heart beat to the baby. The disclosed interactive baby bottle can 20. NCCDS configuration management process improvement Science.gov (United States) Shay, Kathy 1993-01-01 By concentrating on defining and improving specific Configuration Management (CM) functions, processes, procedures, personnel selection/development, and tools, internal and external customers received improved CM services. Job performance within the section increased in both satisfaction and output. Participation in achieving major improvements has led to the delivery of consistent quality CM products as well as significant decreases in every measured CM metrics category. 1. Bayesian image restoration, using configurations DEFF Research Database (Denmark) Thorarinsdottir, Thordis configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed... 2. Bayesian image restoration, using configurations DEFF Research Database (Denmark) Thorarinsdottir, Thordis Linda 2006-01-01 configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed... 3. Equilibrium: three-dimensional configurations International Nuclear Information System (INIS) Anon. 1987-01-01 This chapter considers toroidal MHD configurations that are inherently three-dimensional. The motivation for investigation such complicated equilibria is that they possess the potential for providing toroidal confinement without the need of a net toroidal current. This leads to a number of advantages with respect to fusion power generation. First, the attractive feature of steady-state operation becomes more feasible since such configurations no longer require a toroidal current transformer. Second, with zero net current, one potentially dangerous class of MHD instabilities, the current-driven kink modes, is eliminated. Finally, three-dimensional configurations possess nondegenerate flux surfaces even in the absence of plasma pressure and plasma current. Although there is an enormous range of possible three-dimensional equilibria, the configurations of interest are accurately described as axisymmetric tori with superimposed helical fields; furthermore, they possess no net toroidal current. Instead, two different and less obvious restoring forces are developed: the helical sideband force and the toroidal dipole current force. Each is discussed in detail in Chapter 7. A detailed discussion of the parallel current constraint, including its physical significance, is given in section 7.2. A general analysis of helical sideband equilibria, along with a detailed description of the Elmo bumpy torus, is presented in sections 7.3 and 7.4. A general description of toroidal dipole-current equilibria, including a detailed discussion of stellarators, heliotrons, and torsatrons, is given in sections 7.5 and 7.6 4. Product Configuration Systems and Productivity DEFF Research Database (Denmark) Pedersen, Jørgen Lindgaard; Edwards, Kasper 2004-01-01 Twelve companies have been interviewed with the purpose to get information about technical, economic and organisational matters in respect of Product Configuration Systems (PCS).Combinations of qualitative interviews and quantitative scoring have been used in ranking expected and realized results... 5. Environmental restoration project configuration control International Nuclear Information System (INIS) Hutterman, L.L. 1991-01-01 This paper provides an overview of the approach that Westinghouse Idaho Nuclear Company, Inc. (WINCO) is using for the implementation of the configuration control requirements for a major system acquisition under the guidance of US Department of Energy (DOE) Order 4700.1, open-quotes Project Management System,close quotes for environmental restoration. The two major features of the WINCO environmental restoration approach relate to (1) the product and (2) the maintenance of the baseline for many sites in different phases at the same time. Historically, a project has typically produced a product. Environmental restoration in some ways produces no typical project product. Essentially, what is produced and what configuration control management is exercised on is one of the following: (1) the development of clean dirt, (2) the documentation to support clean dirt, or (3) the track record of each of the sites. It is the latter approach that this paper deals with. This approach is unique in that there are four baselines [cost, schedule, scope, and technical (the track record product)] rather than the typical three. This is essential in configuration management due to the lack of a uniquely identifiable product for each site. Essentially, the philosophy behind the four-part configuration controls allows the technical baseline to fulfill the function typically met by the identifiable product 6. Software control and system configuration management - A process that works Science.gov (United States) Petersen, K. L.; Flores, C., Jr. 1983-01-01 A comprehensive software control and system configuration management process for flight-crucial digital control systems of advanced aircraft has been developed and refined to insure efficient flight system development and safe flight operations. Because of the highly complex interactions among the hardware, software, and system elements of state-of-the-art digital flight control system designs, a systems-wide approach to configuration control and management has been used. Specific procedures are implemented to govern discrepancy reporting and reconciliation, software and hardware change control, systems verification and validation testing, and formal documentation requirements. An active and knowledgeable configuration control board reviews and approves all flight system configuration modifications and revalidation tests. This flexible process has proved effective during the development and flight testing of several research aircraft and remotely piloted research vehicles with digital flight control systems that ranged from relatively simple to highly complex, integrated mechanizations. 7. Configuring Symantec AntiVirus CERN Document Server Shimonski, Robert 2003-01-01 This is the only book that will teach system administrators how to configure, deploy, and troubleshoot Symantec Enterprise Edition in an enterprise network. The book will reflect Symantec''s philosophy of "Centralized Antivirus Management." For the same reasons that Symantec bundled together these previously separate products, the book will provide system administrators with a holistic approach to defending their networks from malicious viruses. This book will also serve as a Study Guide for those pursuing Symantec Product Specialist Certifications.Configuring Symantec AntiVirus Enterprise Edition contains step-by-step instructions on how to Design, implement and leverage the Symantec Suite of products in the enterprise.ØFirst book published on market leading product and fast-growing certification. Despite the popularity of Symantec''s products and Symantec Product Specialist certifications, there are no other books published or announced.ØLess expensive substitute for costly on-sight training. Symantec off... 8. Snowflake Divertor Configuration in NSTX International Nuclear Information System (INIS) Soukhanovskii, V.A.; Ahn, Joonwook; Bell, R.E.; Gates, D.A.; Gerhardt, S.; Kaita, R.; Kolemen, E.; Kugel, H.W.; LeBlanc, B.; Maingi, Rajesh; Maqueda, R.J.; McLean, Adam G.; Menard, J.E.; Mueller, D.; Paul, S.F.; Raman, R.; Roquemore, L.; Ryutov, D.D.; Scott, H.A. 2011-01-01 Steady-state handling of divertor heat flux is a critical issue for present and future conventional and spherical tokamaks with compact high power density divertors. A novel 'snowflake' divertor (SFD) configuration that takes advantage of magnetic properties of a second-order poloidal null has been predicted to have a larger plasma-wetted area and a larger divertor volume, in comparison with a standard first-order poloidal X-point divertor configuration. The SFD was obtained in 0.8 MA, 4-6 MW NBI-heated H-mode discharges in NSTX using two divertor magnetic coils. The SFD led to a partial detachment of the outer strike point even in low-collisionality scrape-off layer plasma obtained with lithium coatings in NSTX. Significant divertor peak heat flux reduction and impurity screening have been achieved simultaneously with good core confinement and MHD properties. 9. 'Snowflake' divertor configuration in NSTX International Nuclear Information System (INIS) Soukhanovskii, V.A.; Ahn, J.-W.; Bell, R.E.; Gates, D.A.; Gerhardt, S.; Kaita, R.; Kolemen, E.; Kugel, H.W.; LeBlanc, B.P.; Maingi, R.; Maqueda, R.; McLean, A.; Menard, J.E.; Mueller, D.M.; Paul, S.F.; Raman, R.; Roquemore, A.L.; Ryutov, D.D.; Scott, H.A. 2011-01-01 Steady-state handling of divertor heat flux is a critical issue for present and future conventional and spherical tokamaks with compact high power density divertors. A novel 'snowflake' divertor (SFD) configuration that takes advantage of magnetic properties of a second-order poloidal null has been predicted to have a larger plasma-wetted area and a larger divertor volume, in comparison with a standard first-order poloidal X-point divertor configuration. The SFD was obtained in 0.8 MA, 4-6 MW NBI-heated H-mode discharges in NSTX using two divertor magnetic coils. The SFD led to a partial detachment of the outer strike point even in low-collisionality scrape-off layer plasma obtained with lithium coatings in NSTX. Significant divertor peak heat flux reduction and impurity screening have been achieved simultaneously with good core confinement and MHD properties. 10. "Snowflake" divertor configuration in NSTX Science.gov (United States) Soukhanovskii, V. A.; Ahn, J.-W.; Bell, R. E.; Gates, D. A.; Gerhardt, S.; Kaita, R.; Kolemen, E.; Kugel, H. W.; Leblanc, B. P.; Maingi, R.; Maqueda, R.; McLean, A.; Menard, J. E.; Mueller, D. M.; Paul, S. F.; Raman, R.; Roquemore, A. L.; Ryutov, D. D.; Scott, H. A. 2011-08-01 Steady-state handling of divertor heat flux is a critical issue for present and future conventional and spherical tokamaks with compact high power density divertors. A novel "snowflake" divertor (SFD) configuration that takes advantage of magnetic properties of a second-order poloidal null has been predicted to have a larger plasma-wetted area and a larger divertor volume, in comparison with a standard first-order poloidal X-point divertor configuration. The SFD was obtained in 0.8 MA, 4-6 MW NBI-heated H-mode discharges in NSTX using two divertor magnetic coils. The SFD led to a partial detachment of the outer strike point even in low-collisionality scrape-off layer plasma obtained with lithium coatings in NSTX. Significant divertor peak heat flux reduction and impurity screening have been achieved simultaneously with good core confinement and MHD properties. 11. Automatic creation of simulation configuration International Nuclear Information System (INIS) Oudot, G.; Poizat, F. 1993-01-01 SIPA, which stands for 'Simulator for Post Accident', includes: 1) a sophisticated software oriented workshop SWORD (which stands for 'Software Workshop Oriented towards Research and Development') designed in the ADA language including integrated CAD system and software tools for automatic generation of simulation software and man-machine interface in order to operate run-time simulation; 2) a 'simulator structure' based on hardware equipment and software for supervision and communications; 3) simulation configuration generated by SWORD, operated under the control of the 'simulator structure' and run on a target computer. SWORD has already been used to generate two simulation configurations (French 900 MW and 1300 MW nuclear power plants), which are now fully operational on the SIPA training simulator. (Z.S.) 1 ref 12. Microsoft System Center Configuration Manager CERN Document Server Sandbu, Marius 2013-01-01 This book is a step-by-step tutorial that guides you through the key steps in implementing best solutions for high availability and performance tuning. It is split into two distinct approaches: client and site side HA and optimization.Microsoft SCCM High Availability and Performance Tuning is for IT professionals and consultants working with Configuration Manager who wish to learn the skills to deploy a redundant and scalable solution. 13. Safe Configuration of TLS Connections Science.gov (United States) 2013-10-16 comparison with observed flows to flag inconsistencies. Keywords: Transport Layer Security ( TLS ), Secure Socket Layer ( SSL ), configuration, secure...servers. SSL / TLS has evolved over 18 years from SSL 1.0 to TLS 1.2 and has been widely deployed and accepted across Internet servers. This has made...and provides a large-scale view of TLS properties across Internet web sites. The guidance provided in [10] describes best practices for SSL / TLS 14. Theory of field reversed configurations International Nuclear Information System (INIS) Steinhauer, L.C. 1990-01-01 This final report surveys the results of work conducted on the theory of field reversed configurations. This project has spanned ten years, beginning in early 1980. During this period, Spectra Technology was one of the leading contributors to the advances in understanding FRC. The report is organized into technical topic areas, FRC formation, equilibrium, stability, and transport. Included as an appendix are papers published in archival journals that were generated in the course of this report. 33 refs 15. Drupal 7 Multi Sites Configuration CERN Document Server Butcher, Matt 2012-01-01 Follow the creation of a multi-site instance with Drupal. The practical examples and accompanying screenshots will help you to get multiple Drupal sites set up in no time. This book is for Drupal site builders. It is assumed that readers are familiar with Drupal already, with a basic grasp of its concepts and components. System administration concepts, such as configuring Apache, MySQL, and Vagrant are covered but no previous knowledge of these tools is required. 16. Records of Migration in the Exoplanet Configurations Science.gov (United States) Michtchenko, Tatiana A.; Rodriguez Colucci, A.; Tadeu Dos Santos, M. 2013-05-01 Abstract (2,250 Maximum Characters): When compared to our Solar System, many exoplanet systems exhibit quite unusual planet configurations; some of these are hot Jupiters, which orbit their central stars with periods of a few days, others are resonant systems composed of two or more planets with commensurable orbital periods. It has been suggested that these configurations can be the result of a migration processes originated by tidal interactions of the planets with disks and central stars. The process known as planet migration occurs due to dissipative forces which affect the planetary semi-major axes and cause the planets to move towards to, or away from, the central star. In this talk, we present possible signatures of planet migration in the distribution of the hot Jupiters and resonant exoplanet pairs. For this task, we develop a semi-analytical model to describe the evolution of the migrating planetary pair, based on the fundamental concepts of conservative and dissipative dynamics of the three-body problem. Our approach is based on an analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces needs to be invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the stationary solutions of the conservative problem (Birkhoff, Dynamical systems, 1966). The ultimate convergence and the evolution of the system along one of these modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the roper frequencies of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states, and consequently to constrain the parameters of the physical processes involved. 17. Low emittance configuration for spear International Nuclear Information System (INIS) Blumberg, L.N.; Harris, J.; Stege, R.; Cerino, J.; Hettel, R.; Hofmann, A.; Liu, R.Z.; Wiedemann, H.; Winick, H. 1985-01-01 The quality of synchrotron radiation beams from SPEAR, in particular the brilliance of undulator radiation, can be improved significantly by reducing the emittance of the stored electron beam. A reduction of the horizontal emittance by a factor of 3.5 to a value of 130 nanometer-radians (nm-r) at 3 GeV has been achieved by using stronger focussing, mainly in the horizontal plane. The low emittance configuration also reduces the dispersion and vertical beta functions in the straight sections, making them more suitable for wigglers. The higher betatron tunes lead to a larger phase advance between the two kickers, which has to be corrected during injection by shunting current from some quadrupoles. The configuration was optimized within SPEAR hardware limitations and tested for dynamic aperture with the tracking program PATRICIA. After implementation of this scheme, beam was successfully injected and accumulated. The measured emittance of the stored beam was in agreement with calculations. Presently the configuration is being made operational 18. Configuration Management Process Assessment Strategy Science.gov (United States) 2014-01-01 Purpose: To propose a strategy for assessing the development and effectiveness of configuration management systems within Programs, Projects, and Design Activities performed by technical organizations and their supporting development contractors. Scope: Various entities CM Systems will be assessed dependent on Project Scope (DDT&E), Support Services and Acquisition Agreements. Approach: Model based structured against assessing organizations CM requirements including best practices maturity criteria. The model is tailored to the entity being assessed dependent on their CM system. The assessment approach provides objective feedback to Engineering and Project Management of the observed CM system maturity state versus the ideal state of the configuration management processes and outcomes(system). center dot Identifies strengths and risks versus audit gotcha's (findings/observations). center dot Used "recursively and iteratively" throughout program lifecycle at select points of need. (Typical assessments timing is Post PDR/Post CDR) center dot Ideal state criteria and maturity targets are reviewed with the assessed entity prior to an assessment (Tailoring) and is dependent on the assessed phase of the CM system. center dot Supports exit success criteria for Preliminary and Critical Design Reviews. center dot Gives a comprehensive CM system assessment which ultimately supports configuration verification activities.* 19. RINGED ACCRETION DISKS: EQUILIBRIUM CONFIGURATIONS Energy Technology Data Exchange (ETDEWEB) Pugliese, D.; Stuchlík, Z., E-mail: [email protected], E-mail: [email protected] [Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava (Czech Republic) 2015-12-15 We investigate a model of a ringed accretion disk, made up by several rings rotating around a supermassive Kerr black hole attractor. Each toroid of the ringed disk is governed by the general relativity hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. Properties of the tori can then be determined by an appropriately defined effective potential reflecting the background Kerr geometry and the centrifugal effects. The ringed disks could be created in various regimes during the evolution of matter configurations around supermassive black holes. Therefore, both corotating and counterrotating rings have to be considered as being a constituent of the ringed disk. We provide constraints on the model parameters for the existence and stability of various ringed configurations and discuss occurrence of accretion onto the Kerr black hole and possible launching of jets from the ringed disk. We demonstrate that various ringed disks can be characterized by a maximum number of rings. We present also a perturbation analysis based on evolution of the oscillating components of the ringed disk. The dynamics of the unstable phases of the ringed disk evolution seems to be promising in relation to high-energy phenomena demonstrated in active galactic nuclei. 20. Isobar configurations in nuclei and short range correlations CERN Document Server Weber, H J 1979-01-01 Recent results on short range correlations and isobar configurations are reviewed, and in particular a unitary version of the isobar model, coupling constants and rho -meson transition potentials, a comparison with experiments, the CERN N-knockout from /sup 4/He, QCD and the NN interaction of short range. (42 refs). 1. BPHZ renormalization in configuration space for the A4-model Science.gov (United States) Pottel, Steffen 2018-02-01 Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated. 2. A configural dominant account of contextual cueing : configural cues are stronger than colour cues OpenAIRE Kunar, Melina A.; Johnston, Rebecca; Sweetman, Hollie 2013-01-01 Previous work has shown that reaction times to find a target in displays that have been repeated are faster than those for displays that have never been seen before. This learning effect, termed “contextual cueing” (CC), has been shown using contexts such as the configuration of the distractors in the display and the background colour. However, it is not clear how these two contexts interact to facilitate search. We investigated this here by comparing the strengths of these two cues when they... 3. Experiment Simulation Configurations Used in DUNE CDR Energy Technology Data Exchange (ETDEWEB) Alion, T. [Univ. of South Carolina, Columbia, SC (United States); Black, J. J. [Univ. of Warwick, Coventry (United Kingdom); Bashyal, A. [Oregon State Univ., Corvallis, OR (United States); Bass, M. [Univ. of Oxford (United Kingdom); Bishai, M. [Brookhaven National Lab. (BNL), Upton, NY (United States); Cherdack, D. [Colorado State Univ., Fort Collins, CO (United States); Diwan, M. [Brookhaven National Lab. (BNL), Upton, NY (United States); Djurcic, Z. [Argonne National Lab. (ANL), Argonne, IL (United States); Evans, J. [Univ. of Manchester (United Kingdom); Fernandez-Martinez, E. [Madrid Autonama Univ. (Spain); Fields, L. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Fleming, B. [Yale Univ., New Haven, CT (United States); Gran, R. [Univ. of Minnesota, Duluth, MN (United States); Guenette, R. [Univ. of Oxford (United Kingdom); Hewes, J. [Univ. of Manchester (United Kingdom); Hogan, M. [Colorado State Univ., Fort Collins, CO (United States); Hylen, J. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Junk, T. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Kohn, S. [Univ. of California, Berkeley, CA (United States); LeBrun, P. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Lundberg, B. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Marchionni, A. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Morris, C. [Univ. of California, Berkeley, CA (United States); Papadimitriou, V. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Rameika, R. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Rucinski, R. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Soldner-Rembold, S. [Univ. of Manchester (United Kingdom); Sorel, M. [Spanish National Research Council (CSIC), Valencia (Spain). Univ. of Valencia (UV), Inst. de Fisica Corpuscular; Urheim, J. [Indiana Univ., Bloomington, IN (United States); Viren, B. [Brookhaven National Lab. (BNL), Upton, NY (United States); Whitehead, L. [Univ. of Houston, TX (United States); Wilson, R. [Colorado State Univ., Fort Collins, CO (United States); Worcester, E. [Brookhaven National Lab. (BNL), Upton, NY (United States); Zeller, G. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States) 2016-06-30 The LBNF/DUNE CDR describes the proposed physics program and experimental design at the conceptual design phase. Volume 2, entitled The Physics Program for DUNE at LBNF, outlines the scientific objectives and describes the physics studies that the DUNE collaboration will perform to address these objectives. The long-baseline physics sensitivity calculations presented in the DUNE CDR rely upon simulation of the neutrino beam line, simulation of neutrino interactions in the far detector, and a parameterized analysis of detector performance and systematic uncertainty. The purpose of this posting is to provide the results of these simulations to the community to facilitate phenomenological studies of long-baseline oscillation at LBNF/DUNE. Additionally, this posting includes GDML of the DUNE single-phase far detector for use in simulations. DUNE welcomes those interested in performing this work as members of the collaboration, but also recognizes the benefit of making these configurations readily available to the wider community. 4. Transport modelling for ergodic configurations International Nuclear Information System (INIS) Runov, A.; Kasilov, S.V.; McTaggart, N.; Schneider, R.; Bonnin, X.; Zagorski, R.; Reiter, D. 2004-01-01 The effect of ergodization, either by additional coils like in TEXTOR-dynamic ergodic divertor (DED) or by intrinsic plasma effects like in W7-X, defines the need for transport models that are able to describe the ergodic configuration properly. A prerequisite for this is the concept of local magnetic coordinates allowing a correct discretization with minimized numerical errors. For these coordinates the appropriate full metric tensor has to be known. To study the transport in complex edge geometries (in particular for W7-X) two possible methods are used. First, a finite-difference discretization of the transport equations on a custom-tailored grid in local magnetic coordinates is used. This grid is generated by field-line tracing to guarantee an exact discretization of the dominant parallel transport (thus also minimizing the numerical diffusion problem). The perpendicular fluxes are then interpolated in a plane (a toroidal cut), where the interpolation problem for a quasi-isotropic system has to be solved by a constrained Delaunay triangulation (keeping the structural information for magnetic surfaces if they exist) and discretization. All toroidal terms are discretized by finite differences. Second, a Monte Carlo transport model originally developed for the modelling of the DED configuration of TEXTOR is used. A generalization and extension of this model was necessary to be able to handle W7-X. The model solves the transport equations with Monte Carlo techniques making use of mappings of local magnetic coordinates. The application of this technique to W7-X in a limiter-like configuration is presented. The decreasing dominance of parallel transport with respect to radial transport for electron heat, ion heat and particle transport results in increasingly steep profiles for the respective quantities within the islands. (author) 5. Variable configuration plasmas in TCV International Nuclear Information System (INIS) Lister, J.B.; Hofmann, F.; Anton, M. 1994-01-01 During its first year of operation, TCV has achieved a wide variety of plasma shapes, limited and diverted, attaining 810 kA plasma current and elongation over 2.0. Ohmic H-Modes have been regularly produced, with a maximum confinement time of 80 msec and maximum normalised β N of 1.9. The conditions for the H-Mode transition differ from other experiments. The transitions from ELM-free to ELMy H-Modes and back have been selectively triggered for configurations close to a Double-Null. (author) 3 figs., 5 refs 6. Variable configuration plasmas in TCV International Nuclear Information System (INIS) Lister, J.B.; Hofmann, F.; Anton, M. 1995-01-01 During its first year of operation, TCV has achieved a wide variety of plasma shapes, limited and diverted, attaining 810 kA plasma current and elongation over 2.0. Ohmic H modes have been regularly produced, with a maximum confinement time of 80 ms and a maximum normalized β N of 1.9. The conditions for the H mode transition differ from other experiments. The transitions from ELM free to ELMy H modes and back have been selectively triggered for configurations close to a double-null. (author). 5 refs, 3 figs 7. FED pumped limiter configuration issues International Nuclear Information System (INIS) Haines, J.R.; Fuller, G.M. 1983-01-01 Impurity control in the Fusion Engineering Device (FED) is provided by a toroidal belt pumped limiter. Limiter design issues addressed in this paper are (1) poloidal location of the limiter belt, (2) shape of the limiter surface facing the plasma, and (3) whether the belt is pumped from one or both sides. The criteria used for evaluation of limiter configuration features were sensitivity to plasma-edge conditions and ease of maintenance and fabrication. The evaluation resulted in the selection of a baseline FED limiter that is located at the bottom of the device and has a flat surface with a single leading edge 8. FED pumped limiter configuration issues International Nuclear Information System (INIS) Haines, J.R.; Fuller, G.M. 1983-01-01 Impurity control in the Fusion Engineering Device (FED) is provided by a toroidal belt pumped limiter. Limiter design issues addressed in this paper are (1) poloidal location of the limiter belt, (2) shape of the limiter surface facing the plasma, and (3) whether the belt is pumped from one or both sides. The criteria used for evaluation of limiter configuration features were sensitivity to plasma edge conditions and ease of maintenance and fabrication. The evaluation resulted in the selection of a baseline FED limiter that is located at the bottom of the device and has a flat surface with a single leading edge 9. Dimensional regularization in configuration space International Nuclear Information System (INIS) Bollini, C.G.; Giambiagi, J.J. 1995-09-01 Dimensional regularization is introduced in configuration space by Fourier transforming in D-dimensions the perturbative momentum space Green functions. For this transformation, Bochner theorem is used, no extra parameters, such as those of Feynman or Bogoliubov-Shirkov are needed for convolutions. The regularized causal functions in x-space have ν-dependent moderated singularities at the origin. They can be multiplied together and Fourier transformed (Bochner) without divergence problems. The usual ultraviolet divergences appear as poles of the resultant functions of ν. Several example are discussed. (author). 9 refs 10. Example of software configuration management model International Nuclear Information System (INIS) Roth, P. 2006-01-01 Software configuration management is the mechanism used to track and control software changes and may include the following actions: A tracking system should be established for any changes made to the existing software configuration. Requirement of the configuration management system are the following: - Backup the different software configuration; - Record the details (the date, the subject, the filenames, the supporting documents, the tests, ...) of the changes introduced in the new configuration; - Document all the differences between the different versions. Configuration management allows simultaneous exploitation of one specific version and development of the next version. Minor correction can be perform in the current exploitation version 11. Vertical and horizontal access configurations International Nuclear Information System (INIS) Spampinato, P.T. 1987-01-01 A number of configuration features and maintenance operations are influenced by the choice of whether a design is based on vertical or horizontal access for replacing reactor components. The features which are impacted most include the first wall/blanket segmentation, the poloidal field coil locations, the toroidal field coil number and size, access port size for in-vessel components, and facilities. Since either configuration can be made to work, the choice between the two is not clear cut because both have certain advantages. It is apparent that there are large cost benefits in the poloidal field coil system for ideal coil locations for high elongation plasmas and marginal savings for the INTOR case. If we assume that a new tokamak design will require a higher plasma elongation, the recommendation is to arrange the poloidal field coils in a cost-effective manner while providing reasonable midplane access for heating interfaces and test modules. If a new design study is not based on a high elongation plasma, it still appears prudent to consider this approach so that in-vessel maintenance can be accomplished without moving very massive structures such as the bulk shield. 10 refs., 29 figs., 3 tabs 12. Equilibrium: two-dimensional configurations International Nuclear Information System (INIS) Anon. 1987-01-01 In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7 13. Tank waste remediation system configuration management plan International Nuclear Information System (INIS) Vann, J.M. 1998-01-01 The configuration management program for the Tank Waste Remediation System (TWRS) Project Mission supports management of the project baseline by providing the mechanisms to identify, document, and control the functional and physical characteristics of the products. This document is one of the tools used to develop and control the mission and work. It is an integrated approach for control of technical, cost, schedule, and administrative information necessary to manage the configurations for the TWRS Project Mission. Configuration management focuses on five principal activities: configuration management system management, configuration identification, configuration status accounting, change control, and configuration management assessments. TWRS Project personnel must execute work in a controlled fashion. Work must be performed by verbatim use of authorized and released technical information and documentation. Application of configuration management will be consistently applied across all TWRS Project activities and assessed accordingly. The Project Hanford Management Contract (PHMC) configuration management requirements are prescribed in HNF-MP-013, Configuration Management Plan (FDH 1997a). This TWRS Configuration Management Plan (CMP) implements those requirements and supersedes the Tank Waste Remediation System Configuration Management Program Plan described in Vann, 1996. HNF-SD-WM-CM-014, Tank Waste Remediation System Configuration Management Implementation Plan (Vann, 1997) will be revised to implement the requirements of this plan. This plan provides the responsibilities, actions and tools necessary to implement the requirements as defined in the above referenced documents 14. Hanford Environmental Information System Configuration Management Plan International Nuclear Information System (INIS) 1996-06-01 The Hanford Environmental Information System (HEIS) Configuration Management Plan establishes the software and data configuration control requirements for the HEIS and project-related databases maintained within the Environmental Restoration Contractor's data management department 15. Configurations and level structure of 219Rn International Nuclear Information System (INIS) Sheline, R.K.; Liang, C.F.; Paris, P. 1998-01-01 The level structure of 219 Rn has been studied using the alpha decay of 223 Ra and coincident gamma rays. While only modest changes are required in the level structure, and only above 342.8 keV, severe changes are required throughout the level scheme in the spin assigments. These changes allow the assignment of two sets of anomalous bands with K=5/2 ± and K=3/2 ± . The K=5/2 ± bands have configurations intermediate between the reflection asymmetric configuration and the g 9/2 shell model configuration, while the K=3/2 ± bands have configurations intermediate between the mixed reflection asymmetric configuration and the i 11/2 shell model configuration. Comparison of the systematics of 219 Rn with neighboring isotones, isobars, and isotopes shows clearly the collapse of the quadrupole-octupole-type configurations into the less degenerate shell model configurations. copyright 1998 The American Physical Society 16. Configuration management theory, practice, and application CERN Document Server Quigley, Jon M 2015-01-01 Configuration Management: Theory, Practice, and Application details a comprehensive approach to configuration management from a variety of product development perspectives, including embedded and IT. It provides authoritative advice on how to extend products for a variety of markets due to configuration options. The book also describes the importance of configuration management to other parts of the organization. It supplies an overview of configuration management and its process elements to provide readers with a contextual understanding of the theory, practice, and application of CM. Explaining what a configuration item is and what it implies, the book illustrates the interplay of configuration and data management with all enterprise resources during each phase of a product lifecycle. It also demonstrates the interrelationship of CM to functional resources. Shedding light on current practice, the book describes CM baselines, configuration identification, management baseline changes, and acceptance criteria ... 17. Offshore Vendors’ Software Development Team Configurations DEFF Research Database (Denmark) Chakraborty, Suranjan; Sarker, Saonee; Rai, Sudhanshu 2012-01-01 This research uses configuration theory and data collected from a major IT vendor organization to examine primary configurations of distributed teams in a global off-shoring context. The study indicates that off-shoring vendor organizations typically deploy three different types of configurations... 18. Multi level configuration of ETO products DEFF Research Database (Denmark) Petersen, Thomas Ditlev; Jørgensen, Kaj Asbjørn; Hvolby, Hans-Henrik 2007-01-01 The paper introduces and defines central concepts related to multi level configuration and analyzes which challenges an engineer to order company must deal with to be able to realize a multi level configuration system. It is argued that high flexibility can be achieved and focus can be directed...... in certain business processes if a multi level configuration system is realized.... 19. Configuration mixing for spin-isospin modes International Nuclear Information System (INIS) Ichimura, Munetake 2005-01-01 Development of theories of configuration mixing is reviewed, concentrating on their application to spin-isospin modes, especially to the Gamow-Teller transitions. This talk is divided into three historical stages, the first order configuration mixing as the first stage, the second order configuration mixing as the second stage, and the delta-isobar-hole mixing as the third stage 20. Code organization and configuration management International Nuclear Information System (INIS) Wellisch, J.P.; Ashby, S.; Williams, C.; Osborne, I. 2001-01-01 Industry experts are increasingly focusing on team productivity as the key to success. The base of the team effort is the four-fold structure of software in terms of logical organisation, physical organisation, managerial organisation, and dynamical structure. The authors describe the ideas put into action within the CMS software for organising software into sub-systems and packages, and to establish configuration management in a multi-project environment. The authors use a structure that allows to maximise the independence of software development in individual areas, and at the same time emphasises the overwhelming importance of the interdependencies between the packages and components in the system. The authors comment on release procedures, and describe the inter-relationship between release, development, integration, and testing 1. Knowledge Engineering for Embedded Configuration DEFF Research Database (Denmark) Oddsson, Gudmundur Valur 2008-01-01 into the system the knowledge needed to achieve them. In order to understand the system, one draws simplified functional streams and identifies archetypes from the product assortment, and then one maps the two together into a system breakdown model. The system model indicates how many encapsulation models (EMs......This thesis presents a way to simplify setup of complex product systems with the help of embedded configuration. To achieve this, one has to focus on what subsystems need to communicate between themselves. The required internal knowledge is then structured at three abstraction levels......, and predefined relation types are suggested. The models are stringent and thought out so they can be implemented in software. They should allow both import and export of product knowledge from the knowledge-based system. The purpose of this work is to simplify the installation process of product systems... 2. Study of High Lift Configurations Science.gov (United States) Edward, Jack R.; Hassan, Hassan A. 2000-01-01 This project focus on the implementation of the Warren-Hassan transition / turbulence model (Journal of Aircraft, Vol. 35, No. 5) into the NASA code CFL3D and its testing for multi-element airfoils in landing configuration at different angles of attack. The Warren-Hassan transition model solves an evolution equation for a kinetic energy characteristic of non-turbulent fluctuations. This is combined with an empirical estimate of the frequency of the most amplified first-mode disturbance to yield an expression for an eddy viscosity characteristic of non-turbulent fluctuations. This is combined with the k - zeta model for fully turbulent flow to yield a unified approach capable of predicting both transition onset and extent. Blending of the non-turbulent and turbulent components of the model is accomplished by an intermittency function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). 3. Shapes of nuclear configurations in a cranked harmonic oscillator model International Nuclear Information System (INIS) Troudet, T.; Arvieu, R. 1980-05-01 The shapes of nuclear configurations are calculated using Slater determinants built with cranked harmonic oscillator single particle states. The nuclear forces role is played by a volume conservation condition (of the potential or of the density) in a first part. In a second part, we have used the finite range, density dependent interaction of Cogny. A very simple classification of configurations emerges in the first part, the relevant parameter being the equatorial eccentricity of the nuclear density. A critical equatorial eccentricity is obtained which governs the accession to the case for which the nucleus is oblate and symmetric around its axis of rotation. Nuclear configurations calculated in the second part observe remarkably well these behaviors 4. Reactor Configuration Development for ARIES-CS International Nuclear Information System (INIS) Ku LP 2005-01-01 New compact, quasi-axially symmetric stellarator configurations have been developed as part of the ARIES-CS reactor studies. These new configurations have good plasma confinement and transport properties, including low losses of α particles and good integrity of flux surfaces at high β. We summarize the recent progress by showcasing two attractive classes of configurations--configurations with judiciously chosen rotational transforms to avoid undesirable effects of low order resonances on the flux surface integrity and configurations with very small aspect ratios (∼2.5) that have excellent quasi-axisymmetry and low field ripples 5. Exercise in Configurable Products using Creo parametric DEFF Research Database (Denmark) Christensen, Georg Kronborg 2017-01-01 Family tables is a long know method with ProEngineer/Creo parametric to make families of products – like families of bolts and roller bearings. Configurable Products expand these possibilities in two major ways: First it makes configurable assemblies possible where one topologically different com...... been available as: configurable assemblies in earlier versions of Creo) An example of a practical application of configurable products is shown below where an outdoor Play/Exercise system is transferred from AutoCAD 2D to a 3D configurable product in Creo 3.0.... 6. The Periodic Table as a Mnemonic Device for Writing Electronic Configurations. Science.gov (United States) Mabrouk, Suzanne T. 2003-01-01 Presents an interactive method for using the periodic table as an effective mnemonic for writing electronic configurations. Discusses the intrinsic relevance of configurations to chemistry by building upon past analogies. Addresses pertinent background information, describes the hands-on method, and demonstrates its use. Transforms the traditional… 7. Symbolic Configuration for Interactive Container Ship Stowage Planning DEFF Research Database (Denmark) Kroer, Christian; Svendsen, Martin Kjær; Jensen, Rune Møller 2014-01-01 Low-cost containerized shipping requires high-quality stowage plans. Scalable stowage planning optimization algorithms have been developed recently. All of these algorithms, however, produce monolithic solutions that are hard for stowage coordinators to modify, which is necessary in practice owin... 8. Supply chain configuration concepts, solutions, and applications CERN Document Server Chandra, Charu 2016-01-01 This book discusses the models and tools available for solving configuration problems, emphasizes the value of model integration to obtain comprehensive and robust configuration decisions, proposes solutions for supply chain configuration in the presence of stochastic and dynamic factors, and illustrates application of the techniques discussed in applied studies. It is divided into four parts, which are devoted to defining the supply chain configuration problem and identifying key issues, describing solutions to various problems identified, proposing technologies for enabling supply chain confirmations, and discussing applied supply chain configuration problems. Its distinguishing features are: an explicit focus on the configuration problem an in-depth coverage of configuration models an emphasis on model integration and application of information modeling techniques in decision-making New to this edition is Part II: Technologies, which introduces readers to various technologies being utilized for supply chai... 9. Spectral distributions of mixed configurations of identical nucleons in the seniority scheme II. Configuration-seniority scheme International Nuclear Information System (INIS) Quesne, C.; Spitz, S. 1978-01-01 Configuration-seniority spectral distributions as well as fixed seniority and fixed total seniority and parity distributions are studied in detail for mixed configurations of identitical nucleons. The decomposition of any (1+2) -body Hamiltonian into irreducible tensors with respect to the unitary and symplectic groups in each subshell is obtained. Group theoretical methods based on the Wigner-Eckart theorem for the higher unitary groups are used to get analytical expressions for the partial widths of configuration-seniority distributions. During this derivation, various isoscalar factors for the chain SU (2Ω) is contained inSp (2Ω) are determined. Numerical calculations of centroid energies, partial widths, and mixing parameters are performed in the Sn and Pb nuclei with a surface delta and a gaussian interactions. Average ordinary and total seniority breaking is studied. Total seniority space truncations in the ground state region are discussed in the Pb nuclei in connections with various approximation schemes 10. Optimizing the Configuration of Sensor Networks to Detect Intruders. Energy Technology Data Exchange (ETDEWEB) Brown, Nathanael J. K. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jones, Katherine A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Nozick, Linda Karen [Cornell Univ., Ithaca, NY (United States); Xu, Ningxiong [Cornell Univ., Ithaca, NY (United States) 2015-03-01 This paper focuses on optimizing the selection and configuration of detection technologies to protect a target of interest. The ability of an intruder to simply reach the target is assumed to be sufficient to consider the security system a failure. To address this problem, we develop a game theoretic model of the strategic interactions between the system owner and a knowledgeable intruder. A decomposition-based exact method is used to solve the resultant model. 11. Metrics for measuring distances in configuration spaces International Nuclear Information System (INIS) Sadeghi, Ali; Ghasemi, S. Alireza; Schaefer, Bastian; Mohr, Stephan; Goedecker, Stefan; Lill, Markus A. 2013-01-01 In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices 12. In-memory interconnect protocol configuration registers Energy Technology Data Exchange (ETDEWEB) Cheng, Kevin Y.; Roberts, David A. 2017-09-19 Systems, apparatuses, and methods for moving the interconnect protocol configuration registers into the main memory space of a node. The region of memory used for storing the interconnect protocol configuration registers may also be made cacheable to reduce the latency of accesses to the interconnect protocol configuration registers. Interconnect protocol configuration registers which are used during a startup routine may be prefetched into the host's cache to make the startup routine more efficient. The interconnect protocol configuration registers for various interconnect protocols may include one or more of device capability tables, memory-side statistics (e.g., to support two-level memory data mapping decisions), advanced memory and interconnect features such as repair resources and routing tables, prefetching hints, error correcting code (ECC) bits, lists of device capabilities, set and store base address, capability, device ID, status, configuration, capabilities, and other settings. 13. Contrast configuration influences grouping in apparent motion. Science.gov (United States) Ma-Wyatt, Anna; Clifford, Colin W G; Wenderoth, Peter 2005-01-01 We investigated whether the same principles that influence grouping in static displays also influence grouping in apparent motion. Using the Ternus display, we found that the proportion of group motion reports was influenced by changes in contrast configuration. Subjects made judgments of completion of these same configurations in a static display. Generally, contrast configurations that induced a high proportion of group motion responses were judged as more 'complete' in static displays. Using a stereo display, we then tested whether stereo information and T-junction information were critical for this increase in group motion. Perceived grouping was consistently higher for same contrast polarity configurations than for opposite contrast polarity configurations, regardless of the presence of stereo information or explicit T-junctions. Thus, while grouping in static and moving displays showed a similar dependence on contrast configuration, motion grouping showed little dependence on stereo or T-junction information. 14. In-memory interconnect protocol configuration registers Science.gov (United States) Cheng, Kevin Y.; Roberts, David A. 2017-09-19 Systems, apparatuses, and methods for moving the interconnect protocol configuration registers into the main memory space of a node. The region of memory used for storing the interconnect protocol configuration registers may also be made cacheable to reduce the latency of accesses to the interconnect protocol configuration registers. Interconnect protocol configuration registers which are used during a startup routine may be prefetched into the host's cache to make the startup routine more efficient. The interconnect protocol configuration registers for various interconnect protocols may include one or more of device capability tables, memory-side statistics (e.g., to support two-level memory data mapping decisions), advanced memory and interconnect features such as repair resources and routing tables, prefetching hints, error correcting code (ECC) bits, lists of device capabilities, set and store base address, capability, device ID, status, configuration, capabilities, and other settings. 15. A configurable CDS for the production laboratory CERN Document Server Meek, Irish 2003-01-01 Various aspects of a configurable chromatography data system (CDS) for the production laboratory are discussed. The Atlas CDS can be configured extensively to fit the production laboratory work flow and meet the needs of analysts. The CDS can also be configured to automatically create a sample sequence with the required number of injections and download methods to the dedicated instrument. The Atlas Quick Start wizard offers uses quick way of generating a sequence from a predefined template and starting a run. (Edited abstract). 16. Visualization of the CMS python configuration system International Nuclear Information System (INIS) Erdmann, M; Fischer, R; Klimkovich, T; Mueller, G; Steggemann, J; Hegner, B; Hinzmann, A 2010-01-01 The job configuration system of the CMS experiment is based on the Python programming language. Software modules and their order of execution are both represented by Python objects. In order to investigate and verify configuration parameters and dependencies naturally appearing in modular software, CMS employs a graphical tool. This tool visualizes the configuration objects, their dependencies, and the information flow. Furthermore it can be used for documentation purposes. The underlying software concepts as well as the visualization are presented. 17. Visualization of the CMS python configuration system Energy Technology Data Exchange (ETDEWEB) Erdmann, M; Fischer, R; Klimkovich, T; Mueller, G; Steggemann, J [RWTH Aachen University, Physikalisches Institut 3A, 52062 Aachen (Germany); Hegner, B [CERN, CH-1211 Geneva 23 (Switzerland); Hinzmann, A, E-mail: [email protected] 2010-04-01 The job configuration system of the CMS experiment is based on the Python programming language. Software modules and their order of execution are both represented by Python objects. In order to investigate and verify configuration parameters and dependencies naturally appearing in modular software, CMS employs a graphical tool. This tool visualizes the configuration objects, their dependencies, and the information flow. Furthermore it can be used for documentation purposes. The underlying software concepts as well as the visualization are presented. 18. Elemental representation and configural mappings: combining elemental and configural theories of associative learning. Science.gov (United States) McLaren, I P L; Forrest, C L; McLaren, R P 2012-09-01 In this article, we present our first attempt at combining an elemental theory designed to model representation development in an associative system (based on McLaren, Kaye, & Mackintosh, 1989) with a configural theory that models associative learning and memory (McLaren, 1993). After considering the possible advantages of such a combination (and some possible pitfalls), we offer a hybrid model that allows both components to produce the phenomena that they are capable of without introducing unwanted interactions. We then successfully apply the model to a range of phenomena, including latent inhibition, perceptual learning, the Espinet effect, and first- and second-order retrospective revaluation. In some cases, we present new data for comparison with our model's predictions. In all cases, the model replicates the pattern observed in our experimental results. We conclude that this line of development is a promising one for arriving at general theories of associative learning and memory. 19. International Space Station Configuration Analysis and Integration Science.gov (United States) Anchondo, Rebekah 2016-01-01 Ambitious engineering projects, such as NASA's International Space Station (ISS), require dependable modeling, analysis, visualization, and robotics to ensure that complex mission strategies are carried out cost effectively, sustainably, and safely. Learn how Booz Allen Hamilton's Modeling, Analysis, Visualization, and Robotics Integration Center (MAVRIC) team performs engineering analysis of the ISS Configuration based primarily on the use of 3D CAD models. To support mission planning and execution, the team tracks the configuration of ISS and maintains configuration requirements to ensure operational goals are met. The MAVRIC team performs multi-disciplinary integration and trade studies to ensure future configurations meet stakeholder needs. 20. Pair creation by dynamic field configurations International Nuclear Information System (INIS) Aoyama, H. 1982-01-01 This thesis deals with the dynamics of the classical configuration of a quantum field unstable due to pair creation. The effective action method is developed first to treat such problems for a simple two-field model. Physical quantities such as pair creation probabilities are related to a complex function called the effective configuration, which is defined to minimize the effective action. Unitarity of the S-matrix is verified at the lowest order of the weak-field approximation. At the same order, the real valued vacuum expectation value of the quantum field, named the real configuration, is constructed in terms of the effective configuration. An integro-differential equation for the real configuration is given and is used to show that the real configuration is causal, while the effective configuration is not. Two practical applications of the effective action method are discussed. The first deals with pair creation in an anisotropic universe, and the real geometry is given in terms of the effective geometry in the samll anisotropy limit. The second deals with expanding vacuum bubbles. Corresponding to three possible situations, three kinds of field equations of each of the effective configuration and the real configuration are obtained. The behavior of the bubble is also studied by a semi-classical method, and one of the three situations is suggested to be plausible 1. The Ragnarok Architectural Software Configuration Management Model DEFF Research Database (Denmark) Christensen, Henrik Bærbak 1999-01-01 The architecture is the fundamental framework for designing and implementing large scale software, and the ability to trace and control its evolution is essential. However, many traditional software configuration management tools view 'software' merely as a set of files, not as an architecture....... This introduces an unfortunate impedance mismatch between the design domain (architecture level) and configuration management domain (file level.) This paper presents a software configuration management model that allows tight version control and configuration management of the architecture of a software system... 2. Configuration management: Phase II implementation guidance Energy Technology Data Exchange (ETDEWEB) 1994-03-01 Configuration management (CM) is essential to maintaining an acceptable level of risk to the public, workers, environment, or mission success. It is a set of activities and techniques used to maintain consistency among physical and functional configuration, applicable requirements, and key documents. This document provides guidance for continuing the implementation of CM in a phased and graded manner. It describes a cost-effective approach to documented consistency with requirements, with early emphasis on items most important to safety and environmental protection. It is intended to help responsible line managers and configuration management staff personnel in meeting the Energy Systems configuration management policy standard. 3. Comparison between four dissimilar solar panel configurations Science.gov (United States) Suleiman, K.; Ali, U. A.; Yusuf, Ibrahim; Koko, A. D.; Bala, S. I. 2017-12-01 Several studies on photovoltaic systems focused on how it operates and energy required in operating it. Little attention is paid on its configurations, modeling of mean time to system failure, availability, cost benefit and comparisons of parallel and series-parallel designs. In this research work, four system configurations were studied. Configuration I consists of two sub-components arranged in parallel with 24 V each, configuration II consists of four sub-components arranged logically in parallel with 12 V each, configuration III consists of four sub-components arranged in series-parallel with 8 V each, and configuration IV has six sub-components with 6 V each arranged in series-parallel. Comparative analysis was made using Chapman Kolmogorov's method. The derivation for explicit expression of mean time to system failure, steady state availability and cost benefit analysis were performed, based on the comparison. Ranking method was used to determine the optimal configuration of the systems. The results of analytical and numerical solutions of system availability and mean time to system failure were determined and it was found that configuration I is the optimal configuration. 4. TWRS authorization basis configuration control summary International Nuclear Information System (INIS) Mendoza, D.P. 1997-01-01 This document was developed to define the Authorization Basis management functional requirements for configuration control, to evaluate the management control systems currently in place, and identify any additional controls that may be required until the TWRS [Tank Waste Remediation System] Configuration Management system is fully in place 5. Deformed configurations, band structures and spectroscopic ... 2014-03-20 Mar 20, 2014 ... The deformed configurations and rotational band structures in =50 Ge and Se nuclei are studied by deformed Hartree–Fock with quadrupole constraint and angular momentum projection. Apart from the `almost' spherical HF solution, a well-deformed configuration occurs at low excitation. A deformed ... 6. Improving the quotation process with product configuration DEFF Research Database (Denmark) Hvam, Lars; Christensen, Simon Pape 2006-01-01 How can product configuration support the process of engineering highly complex industrial products? This article describes how an IT-based product configuration system was developed to support the process of mak-ing budget quotations. The article is based on a research project carried out... 7. Configuration of Web services as parametric design NARCIS (Netherlands) Ten Teije, Annette; Van Harmelen, Frank; Wielinga, Bob 2004-01-01 The configuration of Web services is particularly hard given the heterogeneous, unreliable and open nature of the Web. Furthermore, such composite Web services are likely to be complex services, that will require adaptation for each specific use. Current approaches to Web service configuration are 8. Upgrades to the ISIS moderator configuration International Nuclear Information System (INIS) Taylor, A.D. 1989-01-01 The current ISIS moderator configuration, was designed in 1980 to provide a flexible set of beams for a hypothetical instrument suite. The use of fluid moderators at three different temperatures offering six faces to the instruments, has proved to be effective. In this paper we discuss an upgrade of these moderators in the light of the current and projected instrument configuration. (author) 9. Overview of Java application configuration frameworks OpenAIRE Denisov, Victor 2013-01-01 This paper reviews three major application configuration frameworks for Java-based applications: java.util.Properties, Apache Commons Configuration and Preferences API. Basic functionality of each framework is illustrated with code examples. Pros and cons of each framework are described in moderate detail. Suggestions are made about typical use cases for each framework. 10. Synthesis and configurational analysis of phosphonate cavitands NARCIS (Netherlands) Jacopozzi, Paola; Dalcanale, Enrico; Spera, Silvia; Chrisstoffels, L.A.J.; Reinhoudt, David; Lippmann, Tino; Mann, Gerhard 1998-01-01 Synthesis, separation and configurational analysis of phosphonated and partially phosphonated cavitands derived from resorcinarenes are described. The configuration of all diastereomers has been elucidated by their 1H, 31P NMR spectra and 13C relaxation times. In all cases the course of the bridging 11. Microsoft System Center Configuration Manager advanced deployment CERN Document Server Coupland, Martyn 2014-01-01 If you are an experienced Configuration Manager administrator looking to advance your career or get more from your current environment, then this book is ideal for you. Prior experience of deploying and managing a Configuration Manager site would be helpful in following the examples throughout this book. 12. Generation of Astron-Spherator configuration International Nuclear Information System (INIS) Narihara, Kazumichi; Hasegawa, Mitsuru; Tomita, Yukihiro; Tsuzuki, Tetsuya; Sato, Kuninori; Mohri, Akihiro. 1983-01-01 It was experimentally demonstrated that Astron-Spherator configuration is formed by injecting a pulsed relativistic electron beam in a toroidal device SPAC-VI with external toroidal and vertical magnetic fields. A plasma is confined in the extended magnetic region produced by a slender core of current carrying energetic electrons. This configuration continued for 40 ms without fatal instabilities. (author) 13. Exotic configurations for gauge theory strings International Nuclear Information System (INIS) Yajnik, U.A. 1987-01-01 This paper discusses a class of string configurations occuring in nonabelian gauge theories, which are such that a component of the charged scalar field responsible for the string has a nonvanishing expectation value in the core of the string. A systematic procedure is given for setting up the ansatz for such configurations. (orig.) 14. SRP [Salt Repository Project] configuration management plan International Nuclear Information System (INIS) 1987-01-01 This configuration management plan describes the organization, policies, and procedures that will be used on the Salt Repository Project (SRP) to implement the configuration management disciplines and controls. Configuration management is a part of baseline management. Baseline management is defined in the SRP Baseline Procedures Notebook and also includes cost and schedule baselines. Configuration management is a discipline applying technical and administrative direction and surveillance to identify and document the functional and physical characteristics of an item, to control changes to those characteristics, to record and report change processing and implementation status, and to audit the results. Configuration management is designed as a project management tool to determine and control baselines, and ensure and document all components of a project interface both physically and functionally. The purpose is to ensure that the product acquired satisfies the project's technical and operational requirements, and that the technical requirements are clearly defined and controlled throughout the development and acquisition process. 5 figs 15. Configuration Management Plan for K Basins International Nuclear Information System (INIS) Weir, W.R.; Laney, T. 1995-01-01 This plan describes a configuration management program for K Basins that establishes the systems, processes, and responsibilities necessary for implementation. The K Basins configuration management plan provides the methodology to establish, upgrade, reconstitute, and maintain the technical consistency among the requirements, physical configuration, and documentation. The technical consistency afforded by this plan ensures accurate technical information necessary to achieve the mission objectives that provide for the safe, economic, and environmentally sound management of K Basins and the stored material. The configuration management program architecture presented in this plan is based on the functional model established in the DOE Standard, DOE-STD-1073-93, open-quotes Guide for Operational Configuration Management Programclose quotes 16. Evolution of the Configuration Database Design International Nuclear Information System (INIS) Salnikov, A. 2006-01-01 The BABAR experiment at SLAC successfully collects physics data since 1999. One of the major parts of its on-line system is the configuration database which provides other parts of the system with the configuration data necessary for data taking. Originally the configuration database was implemented in the Objectivity/DB ODBMS. Recently BABAR performed a successful migration of its event store from Objectivity/DB to ROOT and this prompted a complete phase-out of the Objectivity/DB in all other BABAR databases. It required the complete redesign of the configuration database to hide any implementation details and to support multiple storage technologies. In this paper we describe the process of the migration of the configuration database, its new design, implementation strategy and details 17. Communicating knowledge: Making embedded configuration work DEFF Research Database (Denmark) Oddsson, Gudmundur Valur; Hvam, Lars 2007-01-01 A lot of systems are assembled from near-independent mechatronic subsystems that have to be configured to match each other. An example of such systems are e.g. home entertainment systems, where TV, DVD and Receiver are matched to form an overall system, and compilation of pumps and controllers...... to form fresh water supply systems. Sometimes an external knowledge system keeps track of how each subsystem has to be configured, but the actual configuration is often done manually. Installing and maintaining those kinds of systems can be a tedious task and often requires repetitive labour. The idea...... is to “split-up” the product knowledge and encapsulate it into each subsystem. Then, when the subsystems are assembled, the configuration of each subsystem can either be done automatically or with minimum input. The concept could be called: embedded configuration. This article will try to connect three aspects... 18. Onset of pseudo-thermal equilibrium within configurations and super-configurations International Nuclear Information System (INIS) Busquet, Michel 2006-01-01 Level populations within a configuration and configuration populations within super-configuration or within one ion are shown to follow a Boltzmann law at some effective temperature different from the actual electron temperature (as it would be when Griem criterion is valid). Origin of this pseudo-thermal equilibrium is discussed and basis of a model are presented 19. Onset of pseudo-thermal equilibrium within configurations and super-configurations Energy Technology Data Exchange (ETDEWEB) Busquet, Michel [ARTEP Inc., 2922 Excelsior Springs Court, Elicott City, MD 21042 (United States)]. E-mail: [email protected] 2006-05-15 Level populations within a configuration and configuration populations within super-configuration or within one ion are shown to follow a Boltzmann law at some effective temperature different from the actual electron temperature (as it would be when Griem criterion is valid). Origin of this pseudo-thermal equilibrium is discussed and basis of a model are presented. 20. Improving motorcycle conspicuity through innovative headlight configurations. Science.gov (United States) Ranchet, Maud; Cavallo, Viola; Dang, Nguyen-Thong; Vienne, Fabrice 2016-09-01 1. FAST Plasma Scenarios and Equilibrium Configurations International Nuclear Information System (INIS) Calabro, G.; Crisanti, F.; Ramogida, G.; Cardinali, A.; Cucchiaro, A.; Maddaluno, G.; Pizzuto, A.; Pericoli Ridolfini, V.; Tuccillo, A.A.; Zonca, F.; Albanese, R.; Granucci, G.; Nowak, S. 2008-01-01 In this paper we present the Fusion Advanced Studies Torus (FAST) plasma scenarios and equilibrium configurations, designed to reproduce the ITER ones (with scaled plasma current) and suitable to fulfil plasma conditions for integrated studies of burning plasma physics, Plasma Wall interaction, ITER relevant operation problems and Steady State scenarios. The attention is focused on FAST flexibility in terms of both performance and physics that can be investigated: operations are foreseen at a wide range of parameters from high performance H-Mode (toroidal field, B T , up to 8.5 T; plasma current, I P , up to 8 MA) to advanced tokamak (AT) operation (I P =3 MA) as well as full non inductive current scenario (I P =2 MA). The coupled heating power is provided with 30MW delivered by an Ion Cyclotron Resonance Heating (ICRH) system (30-90MHz), 6 MW by a Lower Hybrid (LH) system (3.7 or 5 GHz) for the long pulse AT scenario, 4 MW by an Electron Cyclotron Resonant Heating (ECRH) system (170 GHz-B T =6T) for MHD and electron heating localized control and, eventually, with 10 MW by a Negative Ion Beam (NNBI), which the ports are designed to accommodate. In the reference H-mode scenario FAST preserves (with respect to ITER) fast ions induced as well as turbulence fluctuation spectra, thus, addressing the cross-scale couplings issue of micro- to meso-scale physics. The noninductive scenario at I P =2MA is obtained with 60-70 % of bootstrap and the remaining by LHCD. Predictive simulations of the H-mode scenarios described above have been performed by means of JETTO code, using a semi-empirical mixed Bohm/gyro-Bohm transport model. Plasma position and Shape Control studies are also presented for the reference scenario 2. MAP, MAC, and vortex-rings configurations in the Weinberg-Salam model Science.gov (United States) Teh, Rosy; Ng, Ban-Loong; Wong, Khai-Ming 2015-11-01 We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)×U(1) Weinberg-Salam model of electromagnetic and weak interactions. When the ϕ-winding number n = 1, and 2, the configurations are monopole-antimonopole pair (MAP) and monopole-antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the z-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number n = 3. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of 4 πn / e. In the MAP configurations, the monopole-antimonopole pair is bounded by the Z0 field flux string and there is an electromagnetic current loop encircling it. The monopole and antimonopole possess magnetic charges ± 4πn/e sin2θW respectively. In the MAC configurations there is no string connecting the monopole and the adjacent antimonopole and they possess magnetic charges ± 4 πn/e respectively. The MAC configurations possess infinite total energy and zero magnetic dipole moment whereas the MAP configurations which are actually sphalerons possess finite total energy and magnetic dipole moment. The configurations were investigated for varying values of Higgs self-coupling constant 0 ≤ λ ≤ 40 at Weinberg angle θW = π/4. 3. National Ignition Facility Configuration Management Plan International Nuclear Information System (INIS) Cabral, S G; Moore, T L 2002-01-01 This Configuration Management Plan (CMP) describes the technical and administrative management process for controlling the National Ignition Facility (NIF) Project configuration. The complexity of the NIF Project (i.e., participation by multiple national laboratories and subcontractors involved in the development, fabrication, installation, and testing of NIF hardware and software, as well as construction and testing of Project facilities) requires implementation of the comprehensive configuration management program defined in this plan. A logical schematic illustrating how the plan functions is provided in Figure 1. A summary of the process is provided in Section 4.0, Configuration Change Control. Detailed procedures that make up the overall process are referenced. This CMP is consistent with guidance for managing a project's configuration provided in Department of Energy (DOE) Order 430.1, Guide PMG 10, ''Project Execution and Engineering Management Planning''. Configuration management is a formal discipline comprised of the following four elements: (1) Identification--defines the functional and physical characteristics of a Project and uniquely identifies the defining requirements. This includes selection of components of the end product(s) subject to control and selection of the documents that define the project and components. (2) Change management--provides a systematic method for managing changes to the project and its physical and functional configuration to ensure that all changes are properly identified, assessed, reviewed, approved, implemented, tested, and documented. (3) Data management--ensures that necessary information on the project and its end product(s) is systematically recorded and disseminated for decision-making and other uses. Identifies, stores and controls, tracks status, retrieves, and distributes documents. (4) Assessments and validation--ensures that the planned configuration requirements match actual physical configurations and 4. Integration, Configuration and Coordination: from Project to Reality, at CERN CERN Document Server Barberan Marin, Maria; Bernardini, Marzia; Birtwistle, Thomas; Chemli, Samy; Corso, Jean-Pierre; Coupard, Julie; Foraz, Katy; Grillot, Serge; Muttoni, Yvon; Perrot, Anne-Laure 2016-01-01 The rigorous process in place at CERN to approve and follow-up the implementation of any modification of the LHC machine and its Injectors is presented in this paper. Our methodology implies the support of three teams, in charge of the configuration management, the scheduling and safety coordination, and the 3D integration studies. At each stage of the project the support of the three teams evolves, to provide the adequate support in the preparation phase and during the technical stops and long shutdowns. The formal roles and the processes used to govern the interaction of the Integration, Configuration and Coordination teams, and their relation to the project teams during the preparation and implementation phases, for activities to be performed in LHC and its injector chain are described and discussed. 5. Improved superposition schemes for approximate multi-caloron configurations International Nuclear Information System (INIS) Gerhold, P.; Ilgenfritz, E.-M.; Mueller-Preussker, M. 2007-01-01 Two improved superposition schemes for the construction of approximate multi-caloron-anti-caloron configurations, using exact single (anti-)caloron gauge fields as underlying building blocks, are introduced in this paper. The first improvement deals with possible monopole-Dirac string interactions between different calorons with non-trivial holonomy. The second one, based on the ADHM formalism, improves the (anti-)selfduality in the case of small caloron separations. It conforms with Shuryak's well-known ratio-ansatz when applied to instantons. Both superposition techniques provide a higher degree of (anti-)selfduality than the widely used sum-ansatz, which simply adds the (anti)caloron vector potentials in an appropriate gauge. Furthermore, the improved configurations (when discretized onto a lattice) are characterized by a higher stability when they are exposed to lattice cooling techniques 6. A new approach to configurable primary data collection. Science.gov (United States) Stanek, J; Babkin, E; Zubov, M 2016-09-01 The formats, semantics and operational rules of data processing tasks in genomics (and health in general) are highly divergent and can rapidly change. In such an environment, the problem of consistent transformation and loading of heterogeneous input data to various target repositories becomes a critical success factor. The objective of the project was to design a new conceptual approach to configurable data transformation, de-identification, and submission of health and genomic data sets. Main motivation was to facilitate automated or human-driven data uploading, as well as consolidation of heterogeneous sources in large genomic or health projects. Modern methods of on-demand specialization of generic software components were applied. For specification of input-output data and required data collection activities, we propose a simple data model of flat tables as well as a domain-oriented graphical interface and portable representation of transformations in XML. Using such methods, the prototype of the Configurable Data Collection System (CDCS) was implemented in Java programming language with Swing graphical interfaces. The core logic of transformations was implemented as a library of reusable plugins. The solution is implemented as a software prototype for a configurable service-oriented system for semi-automatic data collection, transformation, sanitization and safe uploading to heterogeneous data repositories-CDCS. To address the dynamic nature of data schemas and data collection processes, the CDCS prototype facilitates interactive, user-driven configuration of the data collection process and extends basic functionality with a wide range of third-party plugins. Notably, our solution also allows for the reduction of manual data entry for data originally missing in the output data sets. First experiments and feedback from domain experts confirm the prototype is flexible, configurable and extensible; runs well on data owner's systems; and is not dependent on 7. Configurations of Leadership Practices in Hospital Units DEFF Research Database (Denmark) Meier, Ninna 2015-01-01 configurations of leadership practices varied in four different clinical settings, thus contributing with contextual accounts of leadership as practice, and suggested “configurations of practice” as a way to carve out similarities and differences in leadership practices across settings....... and interviews with ten interdisciplinary clinical managers. Findings: – Comparing leadership as configurations of practices across four different clinical settings, the author shows how flexible and often shared leadership practices were embedded in and central to the core clinical work in all units studied... 8. Atom localization with double-cascade configuration International Nuclear Information System (INIS) Gordeev, Maksim Yu; Rozhdestvensky, Yuri V; Efremova, Ekaterina A 2016-01-01 We investigate the one-dimensional (1D) and two-dimensional (2D) atom localization of a four-level system in a double-cascade configuration. We demonstrate the possibility of 1D localization in the field of a standing wave, 2D localization in the field of two standing waves and 2D localization only in the field of running waves by using different configurations of driven waves on transitions. In addition, for each configuration we reached a high-precision atom localization in one of the states at scales much smaller than the wavelength of the incident optical radiation. (paper) 9. Simulation of steam explosion in stratified melt-coolant configuration International Nuclear Information System (INIS) Leskovar, Matjaž; Centrih, Vasilij; Uršič, Mitja 2016-01-01 Highlights: • Strong steam explosions may develop spontaneously in stratified configurations. • Considerable melt-coolant premixed layer formed in subcooled water with hot melts. • Analysis with MC3D code provided insight into stratified steam explosion phenomenon. • Up to 25% of poured melt was mixed with water and available for steam explosion. • Better instrumented experiments needed to determine dominant mixing process. - Abstract: A steam explosion is an energetic fuel coolant interaction process, which may occur during a severe reactor accident when the molten core comes into contact with the coolant water. In nuclear reactor safety analyses steam explosions are primarily considered in melt jet-coolant pool configurations where sufficiently deep coolant pool conditions provide complete jet breakup and efficient premixture formation. Stratified melt-coolant configurations, i.e. a molten melt layer below a coolant layer, were up to now believed as being unable to generate strong explosive interactions. Based on the hypothesis that there are no interfacial instabilities in a stratified configuration it was assumed that the amount of melt in the premixture is insufficient to produce strong explosions. However, the recently performed experiments in the PULiMS and SES (KTH, Sweden) facilities with oxidic corium simulants revealed that strong steam explosions may develop spontaneously also in stratified melt-coolant configurations, where with high temperature melts and subcooled water conditions a considerable melt-coolant premixed layer is formed. In the article, the performed study of steam explosions in a stratified melt-coolant configuration in PULiMS like conditions is presented. The goal of this analytical work is to supplement the experimental activities within the PULiMS research program by addressing the key questions, especially regarding the explosivity of the formed premixed layer and the mechanisms responsible for the melt-water mixing. To 10. External magnetic field configurations for EXTRAP International Nuclear Information System (INIS) Bonnevier, B. 1982-08-01 The strongly inhomogeneous magnetic field for stabilization of a pinch in an Extrap configuration can be created in various ways. Some possibilities both for the linear case and for the toroidal case are discussed. (author) 11. Space shuttle configuration accounting functional design specification Science.gov (United States) 1974-01-01 An analysis is presented of the requirements for an on-line automated system which must be capable of tracking the status of requirements and engineering changes and of providing accurate and timely records. The functional design specification provides the definition, description, and character length of the required data elements and the interrelationship of data elements to adequately track, display, and report the status of active configuration changes. As changes to the space shuttle program levels II and III configuration are proposed, evaluated, and dispositioned, it is the function of the configuration management office to maintain records regarding changes to the baseline and to track and report the status of those changes. The configuration accounting system will consist of a combination of computers, computer terminals, software, and procedures, all of which are designed to store, retrieve, display, and process information required to track proposed and proved engineering changes to maintain baseline documentation of the space shuttle program levels II and III. 12. Configuration Management for Wendelstein 7-X International Nuclear Information System (INIS) Brakel, R.; Eeten, P.v.; Hartmann, D.A.; Henkelmann, K.; Knauer, J.; Mueller, K.; Okkenga-Wolf, A.; Wenzel, U. 2009-01-01 A complex system like the large superconducting Wendelstein 7-X stellarator necessitates a dedicated organizational structure which assures permanent consistency between the requirements of its system specification and the performance attributes of all its components throughout its life time. This includes well-defined processes and centrally coordinated information structures. For this purposes the department Configuration Management (CM) has recently been established at W7-X. The detailed tasks of CM for W7-X are oriented along common CM standards and comprise configuration identification, change management, configuration status accounting and configuration verification. While the assembly of W7-X is proceeding some components are still under procurement or even under design. Thus design changes and non-conformances may have a direct impact on the assembly process. Highest priority has therefore been assigned to efficient control of change and non-conformance processes which might delay the assembly schedule. 13. Molecular Electronic Terms and Molecular Orbital Configurations. Science.gov (United States) Mazo, R. M. 1990-01-01 Discussed are the molecular electronic terms which can arise from a given electronic configuration. Considered are simple cases, molecular states, direct products, closed shells, and open shells. Two examples are provided. (CW) 14. Deformed configurations, band structures and spectroscopic ... 2014-03-20 Mar 20, 2014 ... Our study gives insight into possible deformed structures at spherical shell closure. ... Considerable experimental and theoretical efforts ... True deformation effects can be seen only by considering configuration mixing. 15. Microsoft Windows 2000 Router Configuration Guide National Research Council Canada - National Science Library Richburg, Florence 2001-01-01 The purpose of this guide is to provide technical guidance to network administrators of small to medium size networks in the configuration and integration of Microsoft Windows 2000 Server Router features... 16. Status Configurations, Military Service and Higher Education. Science.gov (United States) Wang, Lin; Elder, Glen H; Spence, Naomi J 2012-12-01 The U.S. Armed Forces offer educational and training benefits as incentives for service. This study investigates the influence of status configurations on military enlistment and their link to greater educational opportunity. Three statuses (socioeconomic status of origin, cognitive ability and academic performance) have particular relevance for life course options. We hypothesize that young men with inconsistent statuses are more likely to enlist than men with consistent status profiles, and that military service improves access to college for certain configurations. Analyses of the National Longitudinal Study of Adolescent Health (Add Health) show (1. that several status configurations markedly increased the likelihood of military enlistment and (2. within status configurations, recruits were generally more likely to enroll in higher education than nonveterans, with associate degrees being more likely. 17. Optimal sensor configuration for complex systems DEFF Research Database (Denmark) 1998-01-01 . The procedure for sensor configuration is based on the simultaneous perturbation stochastic approximation (SPSA) algorithm. SPSA avoids the need for detailed modeling of the sensor response by simply relying on the observed responses obtained by limited experimentation with test sensor configurations. We......The paper considers the problem of sensor configuration for complex systems with the aim of maximizing the useful information about certain quantities of interest. Our approach involves: 1) definition of an appropriate optimality criterion or performance measure; and 2) description of an efficient...... and practical algorithm for achieving the optimality objective. The criterion for optimal sensor configuration is based on maximizing the overall sensor response while minimizing the correlation among the sensor outputs, so as to minimize the redundant information being provided by the multiple sensors... 18. Optimal sensor configuration for complex systems DEFF Research Database (Denmark) 1998-01-01 configuration is based on maximizing the overall sensor response while minimizing the correlation among the sensor outputs. The procedure for sensor configuration is based on simultaneous perturbation stochastic approximation (SPSA). SPSA avoids the need for detailed modeling of the sensor response by simply......Considers the problem of sensor configuration for complex systems. Our approach involves definition of an appropriate optimality criterion or performance measure, and description of an efficient and practical algorithm for achieving the optimality objective. The criterion for optimal sensor...... relying on observed responses as obtained by limited experimentation with test sensor configurations. We illustrate the approach with the optimal placement of acoustic sensors for signal detection in structures. This includes both a computer simulation study for an aluminum plate, and real... 19. Theorem on axially symmetric gravitational vacuum configurations Energy Technology Data Exchange (ETDEWEB) Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare 1977-01-24 A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested. 20. Status Configurations, Military Service and Higher Education Science.gov (United States) Wang, Lin; Elder, Glen H.; Spence, Naomi J. 2012-01-01 The U.S. Armed Forces offer educational and training benefits as incentives for service. This study investigates the influence of status configurations on military enlistment and their link to greater educational opportunity. Three statuses (socioeconomic status of origin, cognitive ability and academic performance) have particular relevance for life course options. We hypothesize that young men with inconsistent statuses are more likely to enlist than men with consistent status profiles, and that military service improves access to college for certain configurations. Analyses of the National Longitudinal Study of Adolescent Health (Add Health) show (1. that several status configurations markedly increased the likelihood of military enlistment and (2. within status configurations, recruits were generally more likely to enroll in higher education than nonveterans, with associate degrees being more likely. PMID:24511161 1. Configurable Web Warehouses construction through BPM Systems Directory of Open Access Journals (Sweden) 2016-08-01 Full Text Available The process of building Data Warehouses (DW is well known with well defined stages but at the same time, mostly carried out manually by IT people in conjunction with business people. Web Warehouses (WW are DW whose data sources are taken from the web. We define a flexible WW, which can be configured accordingly to different domains, through the selection of the web sources and the definition of data processing characteristics. A Business Process Management (BPM System allows modeling and executing Business Processes (BPs providing support for the automation of processes. To support the process of building flexible WW we propose a two BPs level: a configuration process to support the selection of web sources and the definition of schemas and mappings, and a feeding process which takes the defined configuration and loads the data into the WW. In this paper we present a proof of concept of both processes, with focus on the configuration process and the defined data. 2. Molecular dynamics simulation of equilibrium configurations of plasmas containing multi-species dusts International Nuclear Information System (INIS) Liu, Yanhong; Chew, Lock Yue 2007-01-01 Equilibrium configurations of dusty plasmas with grains of different sizes, which interact through a screened Coulomb force field and confined by a two-dimensional quadratic potential, are studied using molecular dynamics simulation. The system configuration depends on the sizes, masses and charges of the grain species as well as the screening strength of the background plasma. The consideration of the grain size has established a different equilibrium configuration relative to that of point grains. In the new configurations, grains of different species separate into different shells, with the grains of larger mass and charge located away from the system center, forming a shell that surrounds the grains of smaller mass and charge at the system center. This configuration occurs beyond a critical grain radius, and its structure and size are determined by the competing effects between the inter-grain electrostatic repulsive force, the screening effect of the plasma and the mass-dependent confinement force of the quadratic potential 3. Vortex configuration in the presence of local magnetic field and locally applied stress International Nuclear Information System (INIS) Wissberg, Shai; Kremen, Anna; Shperber, Yishai; Kalisky, Beena 2017-01-01 Highlights: • We discuss different ways to determine vortex configuration using a scanning SQUID. • We determined the vortex configuration by approaching the sample during cooling. • We observed an accumulation of vortices when contact was made with the sample. • We show how we can manipulate local vortex configuration using contact. - Abstract: Vortex configuration is determined by the repulsive interaction, which becomes dominant with increasing vortex density, by the pinning potential, and by other considerations such as the local magnetic fields, currents flowing in the sample, or as we showed recently, by local stress applied on the sample. In this work we describe different ways to control vortex configuration using scanning SQUID microscopy. 4. Vortex configuration in the presence of local magnetic field and locally applied stress Energy Technology Data Exchange (ETDEWEB) Wissberg, Shai; Kremen, Anna; Shperber, Yishai; Kalisky, Beena, E-mail: [email protected] 2017-02-15 Highlights: • We discuss different ways to determine vortex configuration using a scanning SQUID. • We determined the vortex configuration by approaching the sample during cooling. • We observed an accumulation of vortices when contact was made with the sample. • We show how we can manipulate local vortex configuration using contact. - Abstract: Vortex configuration is determined by the repulsive interaction, which becomes dominant with increasing vortex density, by the pinning potential, and by other considerations such as the local magnetic fields, currents flowing in the sample, or as we showed recently, by local stress applied on the sample. In this work we describe different ways to control vortex configuration using scanning SQUID microscopy. 5. Discharge breakdown in the EXTRAP configuration International Nuclear Information System (INIS) Drake, J.R. 1982-02-01 The breakdown of a discharge in a linear EXTRAP configuration has been studied experimentally. In this configuration the breakdown occurs along the zero B-field line, which is the axis of the linear octupole magnetic field, between the anode and cathode which constitute the ends of the linear device. Breakdown could be described by a modified Townsend criterion which included additional electron losses due to the presence of the B-field transverse to the discharge. (author) 6. An intelligent sales assistant for configurable products OpenAIRE Molina, Martin 2001-01-01 Some of the recent proposals of web-based applications are oriented to provide advanced search services through virtual shops. Within this context, this paper proposes an advanced type of software application that simulates how a sales assistant dialogues with a consumer to dynamically configure a product according to particular needs. The paper presents the general knowl- edge model that uses artificial intelligence and knowledge-based techniques to simulate the configuration process. Finall... 7. Particle transort in field-reversed configurations Energy Technology Data Exchange (ETDEWEB) Tuszewski, M.; Linford, R.K.; Lipson, J.; Sgro, A.G. 1981-01-01 A field reversed configuration (FRC) is a compact toroid that contains no toroidal field. These plasmas are observed to be grossly stable for about 10-100 ..mu..sec. The lifetimes appear limited by an n = 2 rotational instability which may be caused by particle loss. Particle transport is therefore an important issue for these configurations. We investigate particle loss with a steady-state, 1-D model which approximates the experimental observation of elongated FRC equilibrium with about constant separatrix radius. 8. Benzofuranoid and bicyclooctanoid neolignans:absolute configuration International Nuclear Information System (INIS) Alvarenga, M.A. de; Giesbrecht, A.M.; Gottlieb, O.R.; Yoshida, M. 1977-01-01 The naturally occuring benzofuranoid and bicyclo (3,2,1) octanoid neolignans have their relative configurations established by 1 H and 13 C NMR, inclusively with aid of the solvent shift technique. Interconversion of the benzofuranoid type compounds, as well as for a benzofuranoid to a bicyclooctanoid derivate, make ORD correlations, ultimately with (2S, 3S) - and (2R,3R)-2,3- dihydrobenzofurans, possible, and led to the absolute configurations of both series of neolignans [pt 9. Observed benefits from product configuration systems DEFF Research Database (Denmark) Hvam, Lars; Haug, Anders; Mortensen, Niels Henrik 2013-01-01 This article presents a study of the benefits obtained from applying product configuration systems based on a case study in four industry companies. The impacts are described according to main objectives in literature for imple-menting product configuration systems: lead time in the specification...... affected by the use of product configu-ration systems e.g. increased sales, decrease in the number of SKU's, improved ability to introduce new products, and cost reductions.......This article presents a study of the benefits obtained from applying product configuration systems based on a case study in four industry companies. The impacts are described according to main objectives in literature for imple-menting product configuration systems: lead time in the specification...... processes, on-time delivery of the specifica-tions, and resource consumption for making specifications, quality of specifications, optimization of products and services, and other observations. The purpose of the study is partly to identify specific impacts observed from implementing product configuration... 10. Dynamic airspace configuration by genetic algorithm Directory of Open Access Journals (Sweden) Marina Sergeeva 2017-06-01 Full Text Available With the continuous air traffic growth and limits of resources, there is a need for reducing the congestion of the airspace systems. Nowadays, several projects are launched, aimed at modernizing the global air transportation system and air traffic management. In recent years, special interest has been paid to the solution of the dynamic airspace configuration problem. Airspace sector configurations need to be dynamically adjusted to provide maximum efficiency and flexibility in response to changing weather and traffic conditions. The main objective of this work is to automatically adapt the airspace configurations according to the evolution of traffic. In order to reach this objective, the airspace is considered to be divided into predefined 3D airspace blocks which have to be grouped or ungrouped depending on the traffic situation. The airspace structure is represented as a graph and each airspace configuration is created using a graph partitioning technique. We optimize airspace configurations using a genetic algorithm. The developed algorithm generates a sequence of sector configurations for one day of operation with the minimized controller workload. The overall methodology is implemented and successfully tested with air traffic data taken for one day and for several different airspace control areas of Europe. 11. Intellectual Model-Based Configuration Management Conception Directory of Open Access Journals (Sweden) Bartusevics Arturs 2014-07-01 Full Text Available Software configuration management is one of the most important disciplines within the software development project, which helps control the software evolution process and allows including into the end project only tested and validated changes. To achieve this, software management completes certain tasks. Concrete tools are used for technical implementation of tasks, such as version control systems, servers of continuous integration, compilers, etc. A correct configuration management process usually requires several tools, which mutually exchange information by generating various kinds of transfers. When it comes to introducing the configuration management process, often there are situations when tool installation is started, yet at that given moment there is no general picture of the total process. The article offers a model-based configuration management concept, which foresees the development of an abstract model for the configuration management process that later is transformed to lower abstraction level models and tools are indicated to support the technical process. A solution of this kind allows a more rational introduction and configuration of tools 12. The configuration of residential area in urban structure of the palace in Siak Sri Indrapura - Riau Science.gov (United States) 2018-05-01 This article is part of major research in describing the configuration of waterfront residential area in urban space structure of the palace and related to the Malay Kingdom in the waterside of the Strait of Malacca. This research aimed to identify the configuration of riverfront residential area in Siak Sri Indrapura City based on physical and non-physical aspects. The method used in this research was qualitative rationalistic referring to the components of urban design theory. The results of the research showed that the spatial configuration in Siak Sri Indrapura City is linear and related to the past events and socio-cultural and socio-economic interaction of the society. 13. MCSA Windows Server 2012 R2 installation and configuration study guide exam 70-410 CERN Document Server Panek, William 2015-01-01 Master Windows Server installation and configuration withhands-on practice and interactive study aids for the MCSA: WindowsServer 2012 R2 exam 70-410 MCSA: Windows Server 2012 R2 Installation and ConfigurationStudy Guide: Exam 70-410 provides complete preparationfor exam 70-410: Installing and Configuring Windows Server 2012 R2.With comprehensive coverage of all exam topics and plenty ofhands-on practice, this self-paced guide is the ideal resource forthose preparing for the MCSA on Windows Server 2012 R2. Real-worldscenarios demonstrate how the lessons are applied in everydaysettings. Reader 14. Feedback control of plasma configuration in JT-60 International Nuclear Information System (INIS) Ninomiya, Hiromasa; Kikuchi, Mitsuru; Yoshino, Ryuji; Hosogane, Nobuyuki; Kimura, Toyoaki; Kurihara, Kenichi; Takahashi, Minoru; Hayashi, Kazuo. 1986-08-01 Plasma current, plasma position (center of the outermost magnetic surface), decay index n index and width of the divertor throat are feedback controlled by using 5 kinds of poloidal field coils in JT-60. 5 control commands are calculated in a feedback control computer in each 1 msec. These feedback control functions are checked in ohmically heated plasma. The control characteristics of the plasma are well understood by the simplified control analysis and are consistent with the precise matrix transfer function analysis in the frequency domain and the simulation analysis which include the effects of eddy currents, delay time elements and mutual interactions between controllers. The usefulness of these analyses is experimentally confirmed. Each controlled variable is well feedback controlled to the command and the experimentally realized equilibrium configuration is checked by the well calibrated magnetic probes. Fast boundary identification code is used for the identification of the equilibrium and results are consistent with the precalculated plasma equilibria. By using this feedback control system of the plasma configuration and the equilibrium identification method, we have obtained the stable limiter and divertor configuration. The maximum parameters obtained during OH(I) experimental period are plasma current I p = 1.8 MA, the effective safety factor q eff e = 5.7 x 10 19 m -3 (Murakami parameter of 4.5) and the pulse length of 5 ∼ 10 sec. (author) 15. Local random configuration-tree theory for string repetition and facilitated dynamics of glass Science.gov (United States) Lam, Chi-Hang 2018-02-01 We derive a microscopic theory of glassy dynamics based on the transport of voids by micro-string motions, each of which involves particles arranged in a line hopping simultaneously displacing one another. Disorder is modeled by a random energy landscape quenched in the configuration space of distinguishable particles, but transient in the physical space as expected for glassy fluids. We study the evolution of local regions with m coupled voids. At a low temperature, energetically accessible local particle configurations can be organized into a random tree with nodes and edges denoting configurations and micro-string propagations respectively. Such trees defined in the configuration space naturally describe systems defined in two- or three-dimensional physical space. A micro-string propagation initiated by a void can facilitate similar motions by other voids via perturbing the random energy landscape, realizing path interactions between voids or equivalently string interactions. We obtain explicit expressions of the particle diffusion coefficient and a particle return probability. Under our approximation, as temperature decreases, random trees of energetically accessible configurations exhibit a sequence of percolation transitions in the configuration space, with local regions containing fewer coupled voids entering the non-percolating immobile phase first. Dynamics is dominated by coupled voids of an optimal group size, which increases as temperature decreases. Comparison with a distinguishable-particle lattice model (DPLM) of glass shows very good quantitative agreements using only two adjustable parameters related to typical energy fluctuations and the interaction range of the micro-strings. 16. Configuration affects parallel stent grafting results. Science.gov (United States) Tanious, Adam; Wooster, Mathew; Armstrong, Paul A; Zwiebel, Bruce; Grundy, Shane; Back, Martin R; Shames, Murray L 2018-05-01 A number of adjunctive "off-the-shelf" procedures have been described to treat complex aortic diseases. Our goal was to evaluate parallel stent graft configurations and to determine an optimal formula for these procedures. This is a retrospective review of all patients at a single medical center treated with parallel stent grafts from January 2010 to September 2015. Outcomes were evaluated on the basis of parallel graft orientation, type, and main body device. Primary end points included parallel stent graft compromise and overall endovascular aneurysm repair (EVAR) compromise. There were 78 patients treated with a total of 144 parallel stents for a variety of pathologic processes. There was a significant correlation between main body oversizing and snorkel compromise (P = .0195) and overall procedural complication (P = .0019) but not with endoleak rates. Patients were organized into the following oversizing groups for further analysis: 0% to 10%, 10% to 20%, and >20%. Those oversized into the 0% to 10% group had the highest rate of overall EVAR complication (73%; P = .0003). There were no significant correlations between any one particular configuration and overall procedural complication. There was also no significant correlation between total number of parallel stents employed and overall complication. Composite EVAR configuration had no significant correlation with individual snorkel compromise, endoleak, or overall EVAR or procedural complication. The configuration most prone to individual snorkel compromise and overall EVAR complication was a four-stent configuration with two stents in an antegrade position and two stents in a retrograde position (60% complication rate). The configuration most prone to endoleak was one or two stents in retrograde position (33% endoleak rate), followed by three stents in an all-antegrade position (25%). There was a significant correlation between individual stent configuration and stent compromise (P = .0385), with 31 17. Configuring Airspace Sectors with Approximate Dynamic Programming Science.gov (United States) Bloem, Michael; Gupta, Pramod 2010-01-01 In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time. 18. Comparison of hollow cathode discharge plasma configurations International Nuclear Information System (INIS) Farnell, Casey C; Farnell, Cody C; Williams, John D 2011-01-01 Hollow cathodes used in plasma contactor and electric propulsion devices provide electrons for sustaining plasma discharges and enabling plasma bridge neutralization. Life tests show erosion on hollow cathodes exposed to the plasma environment produced in the region downstream of these devices. To explain the observed erosion, plasma flow field measurements are presented for hollow cathode generated plasmas using both directly immersed probes and remotely located plasma diagnostics. Measurements on two cathode discharge configurations are presented: (1) an open, no magnetic field configuration and (2) a setup simulating the discharge chamber environment of an ion thruster. In the open cathode configuration, large amplitude plasma potential oscillations, ranging from 20 to 85 V within a 34 V discharge, were observed using a fast response emissive probe. These oscillations were observed over a dc potential profile that included a well-defined potential hill structure. A remotely located electrostatic analyzer (ESA) was used to measure the energy of ions produced within the plasma, and energies were detected that met, and in some cases exceeded, the peak oscillatory plasma potentials detected by the emissive probe. In the ion thruster discharge chamber configuration, plasma potentials from the emissive probe again agreed with ion energies recorded by the remotely located ESA; however, much lower ion energies were detected compared with the open configuration. A simplified ion-transit model that uses temporal and spatial plasma property measurements is presented and used to predict far-field plasma streaming properties. Comparisons between the model and remote measurements are presented. 19. Configuration Fuzzing for Software Vulnerability Detection. Science.gov (United States) Dai, Huning; Murphy, Christian; Kaiser, Gail 2010-02-15 Many software security vulnerabilities only reveal themselves under certain conditions, i.e., particular configurations of the software together with its particular runtime environment. One approach to detecting these vulnerabilities is fuzz testing, which feeds a range of randomly modified inputs to a software application while monitoring it for failures. However, typical fuzz testing makes no guarantees regarding the syntactic and semantic validity of the input, or of how much of the input space will be explored. To address these problems, in this paper we present a new testing methodology called configuration fuzzing. Configuration fuzzing is a technique whereby the configuration of the running application is randomly modified at certain execution points, in order to check for vulnerabilities that only arise in certain conditions. As the application runs in the deployment environment, this testing technique continuously fuzzes the configuration and checks "security invariants" that, if violated, indicate a vulnerability; however, the fuzzing is performed in a duplicated copy of the original process, so that it does not affect the state of the running application. In addition to discussing the approach and describing a prototype framework for implementation, we also present the results of a case study to demonstrate the approach's efficiency. 20. Evaluating the fermionic determinant of dynamical configurations International Nuclear Information System (INIS) Hasenfratz, Anna; Alexandru, Andrei 2002-01-01 We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of the ratios of fermionic determinants is essential for a recently proposed updating method of smeared link dynamical fermions. This update creates a sequence of configurations by changing a subset of the gauge links by a pure gauge heat bath or over-relaxation step. The acceptance of the proposed configuration depends on the ratio of the fermionic determinants on the new and original configurations. We study this ratio as a function of the number of links that are changed in the heat bath update. We find that even when every link of a given direction and parity of a 10 fm 4 configuration is updated, the average of the determinant ratio is still close to one and with the improved stochastic estimator the proposed change is accepted with about 20% probability. This improvement suggests that the new updating technique can be efficient even on large lattices and could provide an updating method for dynamical overlap actions 1. System of ispFlash configuration International Nuclear Information System (INIS) Bourrion, Olivier 2003-01-01 The aim of this module is to allow the use of FPGA components instead of EPLD components which for an equivalent or even inferior capacity are more expensive. For instance, the idea is to replace CPLD components having 512 macro-cells by one FPGA spartan II of Xilinx. However, due to the configuration's volatility, one configuration means is needed to put under voltage. A solution appears to be the using of a high capacity Flash memory coupled to a CPLD of small size to comply with the FPGA configuration protocol; also, one has to provide an in situ configuration means for this memory. Obviously, a product having an equivalent functionality already exists, since Xilinx and ALTERA supply PROMs of serial configuration. Unfortunately, they are expensive and a dealer is implied while the FLASH, the small CPLD and the FPGA spartan II are currently available. In conclusion, by using this assembly, which requires a small supplementary surface and a delay of upmost 240 ms (for the largest FPGA 1 Mbit), one obtains a solution cheaper and more performing than an EPLD of high capacity 2. Prediction of Protein Configurational Entropy (Popcoen). Science.gov (United States) Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel 2018-03-13 A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ . 3. Fiber optic configurations for local area networks Science.gov (United States) Nassehi, M. M.; Tobagi, F. A.; Marhic, M. E. 1985-01-01 A number of fiber optic configurations for a new class of demand assignment multiple-access local area networks requiring a physical ordering among stations are proposed. In such networks, the data transmission and linear-ordering functions may be distinguished and be provided by separate data and control subnetworks. The configurations proposed for the data subnetwork are based on the linear, star, and tree topologies. To provide the linear-ordering function, the control subnetwork must always have a linear unidirectional bus structure. Due to the reciprocity and excess loss of optical couplers, the number of stations that can be accommodated on a linear fiber optic bus is severely limited. Two techniques are proposed to overcome this limitation. For each of the data and control subnetwork configurations, the maximum number of stations as a function of the power margin, for both reciprocal and nonreciprocal couplers, is computed. 4. Configurational entropy in brane-world models Energy Technology Data Exchange (ETDEWEB) Correa, R.A.C. [CCNH, Universidade Federal do ABC, Santo Andre, SP (Brazil); Rocha, Roldao da [CMCC, Universidade Federal do ABC, Santo Andre, SP (Brazil); International School for Advanced Studies (SISSA), Trieste (Italy) 2015-11-15 In this work we investigate the entropic information on thick brane-world scenarios and its consequences. The brane-world entropic information is studied for the sine-Gordon model and hence the brane-world entropic information measure is shown to be an accurate way for providing the most suitable range for the bulk AdS curvature, in particular from the informational content of physical solutions. Besides, the brane-world configurational entropy is employed to demonstrate a high organisational degree in the structure of the configuration of the system, for large values of a parameter of the sine-Gordon model but the one related to the AdS curvature. The Gleiser and Stamatopoulos procedure is finally applied in order to achieve a precise correlation between the energy of the system and the brane-world configurational entropy. (orig.) 5. Configurational entropy in brane-world models Energy Technology Data Exchange (ETDEWEB) Correa, R. A. C., E-mail: [email protected] [CCNH, Universidade Federal do ABC, 09210-580, Santo André, SP (Brazil); Rocha, Roldão da, E-mail: [email protected] [CMCC, Universidade Federal do ABC, 09210-580, Santo André, SP (Brazil); International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste (Italy) 2015-11-02 In this work we investigate the entropic information on thick brane-world scenarios and its consequences. The brane-world entropic information is studied for the sine-Gordon model and hence the brane-world entropic information measure is shown to be an accurate way for providing the most suitable range for the bulk AdS curvature, in particular from the informational content of physical solutions. Besides, the brane-world configurational entropy is employed to demonstrate a high organisational degree in the structure of the configuration of the system, for large values of a parameter of the sine-Gordon model but the one related to the AdS curvature. The Gleiser and Stamatopoulos procedure is finally applied in order to achieve a precise correlation between the energy of the system and the brane-world configurational entropy. 6. Configurational entropy in brane-world models International Nuclear Information System (INIS) Correa, R. A. C.; Rocha, Roldão da 2015-01-01 In this work we investigate the entropic information on thick brane-world scenarios and its consequences. The brane-world entropic information is studied for the sine-Gordon model and hence the brane-world entropic information measure is shown to be an accurate way for providing the most suitable range for the bulk AdS curvature, in particular from the informational content of physical solutions. Besides, the brane-world configurational entropy is employed to demonstrate a high organisational degree in the structure of the configuration of the system, for large values of a parameter of the sine-Gordon model but the one related to the AdS curvature. The Gleiser and Stamatopoulos procedure is finally applied in order to achieve a precise correlation between the energy of the system and the brane-world configurational entropy 7. Modelling Configuration Knowledge in Heterogeneous Product Families DEFF Research Database (Denmark) Queva, Matthieu Stéphane Benoit; Männistö, Tomi; Ricci, Laurent 2011-01-01 Product configuration systems play an important role in the development of Mass Customisation. The configuration of complex product families may nowadays involve multiple design disciplines, e.g. hardware, software and services. In this paper, we present a conceptual approach for modelling...... the variability in such heterogeneous product families. Our approach is based on a framework that aims to cater for the different stakeholders involved in the modelling and management of the product family. The modelling approach is centred around the concepts of views, types and constraints and is illustrated...... by a motivation example. Furthermore, as a proof of concept, a prototype has been implemented for configuring a non-trivial heterogeneous product family.... 8. Dependability Analysis Methods For Configurable Software International Nuclear Information System (INIS) Dahll, Gustav; Pulkkinen, Urho 1996-01-01 Configurable software systems are systems which are built up by standard software components in the same way as a hardware system is built up by standard hardware components. Such systems are often used in the control of NPPs, also in safety related applications. A reliability analysis of such systems is therefore necessary. This report discusses what configurable software is, and what is particular with respect to reliability assessment of such software. Two very commonly used techniques in traditional reliability analysis, viz. failure mode, effect and criticality analysis (FMECA) and fault tree analysis are investigated. A real example is used to illustrate the discussed methods. Various aspects relevant to the assessment of the software reliability in such systems are discussed. Finally some models for quantitative software reliability assessment applicable on configurable software systems are described. (author) 9. Modeling the planar configuration of extraordinary magnetoresistance International Nuclear Information System (INIS) El-Ahmar, S; Pozniak, A A 2015-01-01 Recently the planar version of the extraordinary magnetoresistance (EMR) magnetic field sensor has been constructed and verified in practice. Planar configuration of the EMR device gives many technological advantages, it is simpler than the classic and allows one to build the sensor using electric materials of the new type (such as graphene or topological insulators) much easier. In this work the planar configuration of the EMR sensor is investigated by performing computational simulations using the finite element method (FEM). The computational comparison of the planar and classic configurations of EMR is presented using three-dimensional models. Various variants of the geometry of EMR sensor components are pondered and compared in the planar and classic version. Size of the metal overlap is considered for sensor optimization as well as various semiconductor-metal contact resistance dependences of the EMR signal. Based on computational simulations, a method for optimal placement of electric terminals in a planar EMR device is proposed. (paper) 10. Model-Driven Configuration of SELinux Policies Science.gov (United States) Agreiter, Berthold; Breu, Ruth The need for access control in computer systems is inherent. However, the complexity to configure such systems is constantly increasing which affects the overall security of a system negatively. We think that it is important to define security requirements on a non-technical level while taking the application domain into respect in order to have a clear and separated view on security configuration (i.e. unblurred by technical details). On the other hand, security functionality has to be tightly integrated with the system and its development process in order to provide comprehensive means of enforcement. In this paper, we propose a systematic approach based on model-driven security configuration to leverage existing operating system security mechanisms (SELinux) for realising access control. We use UML models and develop a UML profile to satisfy these needs. Our goal is to exploit a comprehensive protection mechanism while rendering its security policy manageable by a domain specialist. 11. Applying Product Configuration Systems in Engineering Companies DEFF Research Database (Denmark) This Ph.D. thesis looks into the application of configuration systems in engineering companies, and how configuration systems can be used to support business processes in engineering companies. Often the motivation stated by researchers and practitioners is, that a configuration project...... and sustain competitive advantage” (Teece, Pisano, & Shuen, 1997, pp.509) This question has puzzled academics and preoccupied managers for the last century. Yet, it seems there is still no consensus regarding the meaning of strategy, and how strategy works. Type in the word “strategy” on Amazon.co.uk and 76......,133 books apply. Type it in on Google scholar and 8,580,000 homepages apply3. Obviously, strategy is an important subject. However, the subject also seems to be difficult to perceive. Although this thesis is not about strategy, or strategizing, I would like to pursue the definition of strategy one step... 12. Siroco, a configurable robot control system International Nuclear Information System (INIS) Tejedor, B.G.; Maraggi, G.J.B. 1988-01-01 The SIROCO (Configurable Robot Control System) is an electronic system designed to work in applications where mechanized remote control equipment and robots are necessary especially in Nuclear Power Plants. The structure of the system (hardware and software) determines the following user characteristics: a) Reduction in the time spent in NDT and in radiation doses absorbed, due to remote control operation; b) possibility for full automation in NDT, c) the system can simultaneously control up to six axes and can generate movements in remote areas; and d) possibility for equipment unification, due to SIROCO being a configurable system. (author) 13. Mastering System Center 2012 Configuration Manager CERN Document Server Rachui, Steve; Martinez, Santos; Daalmans, Peter 2012-01-01 Expert coverage of Microsoft's highly anticipated network software deployment tool The latest version of System Center Configuration Manager (SCCM) is a dramatic update of its predecessor Configuration Manager 2007, and this book offers intermediate-to-advanced coverage of how the new SCCM boasts a simplified hierarchy, role-based security, a new console, flexible application deployment, and mobile management. You'll explore planning and installation, migrating from SCCM 2007, deploying software and operating systems, security, monitoring and troubleshooting, and automating and customizing SCC 14. TWRS configuration management requirement source document International Nuclear Information System (INIS) Vann, J.M. 1997-01-01 The TWRS Configuration Management (CM) Requirement Source document prescribes CM as a basic product life-cycle function by which work and activities are conducted or accomplished. This document serves as the requirements basis for the TWRS CM program. The objective of the TWRS CM program is to establish consistency among requirements, physical/functional configuration, information, and documentation for TWRS and TWRS products, and to maintain this consistency throughout the life-cycle of TWRS and the product, particularly as changes are being made 15. Design review of the INTOR mechanical configuration International Nuclear Information System (INIS) Brown, T.G. 1981-01-01 The INTOR conceptual design has been carried out by design teams working in the home countries with periodic workshop sessions in Vienna to review the ongoing work and to make decisions on the evolving design. The decisions taken at each workshop session were then incorporated into each national design activity, so that the four national design contributions would progressively converge toward a single design with increasingly greater detail. This paper defines the final INTOR configuration that has evolved during the conceptual design phase, defining the major system design alternatives that were considered and the rationale for selecting the final system configuration 16. Automated firewall analytics design, configuration and optimization CERN Document Server Al-Shaer, Ehab 2014-01-01 This book provides a comprehensive and in-depth study of automated firewall policy analysis for designing, configuring and managing distributed firewalls in large-scale enterpriser networks. It presents methodologies, techniques and tools for researchers as well as professionals to understand the challenges and improve the state-of-the-art of managing firewalls systematically in both research and application domains. Chapters explore set-theory, managing firewall configuration globally and consistently, access control list with encryption, and authentication such as IPSec policies. The author 17. Design configuration of GCFR core assemblies International Nuclear Information System (INIS) LaBar, M.P.; Lee, G.E.; Meyer, R.J. 1980-05-01 The current design configurations of the core assemblies for the gas-cooled fast reactor (GCFR) demonstration plant reactor core conceptual design are described. Primary emphasis is placed upon the design innovations that have been incorporated in the design of the core assemblies since the establishment of the initial design of an upflow GCFR core. A major feature of the design configurations is that they are prototypical of core assemblies for use in commercial plants; a larger number of the same assemblies would be used in a commercial plant 18. Runtime accelerator configuration tools at Jefferson Laboratory International Nuclear Information System (INIS) Tiefenback, M.G.; Doolittle, L.; Benesch, J.F. 1997-01-01 RF and magnet system configuration and monitoring tools are being implemented at Jefferson Lab to improve system reliability and reduce operating costs. They are prototype components of the Momentum Management System being developed. The RF is of special interest because it affects the momentum and momentum spread of the beam, and because of the immediate financial benefit of managing the klystron DC supply power. The authors describe present and planned monitoring of accelerating system parameters, use of these data, RF system performance calculations, and procedures for magnet configuration for handling beam of any of five beam energies to any of three targets 19. Configuration Management Issues at Research Reactors International Nuclear Information System (INIS) Morris, Charles R. 2013-01-01 Configuration Management (from IAEA TECDOC 1651): • The Main Functions of the configuration management process are to: • maintain design requirements of structures, systems and components; • track current as-built drawings, documents, and design basis library; • confirm design change packages demonstrate compliance to design basis in calculations, procurement, safety reviews, update of affected documents, and SSC data; • confirm work orders demonstrate compliance to mandated preventive maintenance; • surveillance, parts replacement and design change installation requirements; • demonstrate procurement of spare parts qualified to meet design basis for proper make, model and quality-level for the SSC location and form, fit and function 20. System configuration on Web with mashup. OpenAIRE 清水, 宏泰; SHIMIZU, Hiroyasu 2014-01-01 Mashup become trend for create Web service due to popularizing cloud service. Mashup is method for create Web service from several Web services and API. Mashup has a few problems. One of the problem is deference of data format and label. Semantic Web can solve it. This paper propose method of building a system on Web with mashup using semantic Web. Mashup system configuration can express as URL. So, editing URL for mashup is editing system configuration. And any device can use this system on ... 1. Position paper - primary ventilation system configuration International Nuclear Information System (INIS) Dalpiaz, E.L. 1994-06-01 The purpose of this paper is to develop and document a position on the configuration of the primary ventilation system. This configuration will be used on the waste storage tanks currently being designed for the Multi-Function Waste Tank Facility. The primary ventilation system provides a single treatment train and exhaust fan for each waste storage tank. The ventilation systems from each of two tanks are grouped with an additional treatment train and exhaust fan that function as backup to either of the two systems 2. Calculation of Configurational Entropy in Complex Landscapes Directory of Open Access Journals (Sweden) Samuel A Cushman 2018-04-01 Full Text Available Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1 the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2 the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3 given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4 for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5 demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6 I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7 I show that the 3. New superconducting coil configuration for energy storage International Nuclear Information System (INIS) Tokorabet, M.; Mailfert, A.; Colteu, A. 1998-01-01 Energy storage using superconducting coils involves the problem of electromagnetic field pollution outside the considered system. Different configurations are widely studied: the torus, the alone solenoid and multiple parallel solenoids enclosed in one container. A new configuration which minimizes the external pollution is studied in this paper. The theoretical system is composed of two spherical distributions of the current which are concentric. The analytical study uses solution of Laplace equations. Parametric study covers energy, flux density and geometrical data. The second study concerns the numerical approach of this design using coaxial solenoids. A comparison between this new system and the known systems is presented as a conclusion. (orig.) 4. Redetermination and absolute configuration of atalaphylline Directory of Open Access Journals (Sweden) Hoong-Kun Fun 2010-02-01 Full Text Available The title acridone alkaloid [systematic name: 1,3,5-trihydroxy-2,4-bis(3-methylbut-2-enylacridin-9(10H-one], C23H25NO4, has previously been reported as crystallizing in the chiral orthorhombic space group P212121 [Chantrapromma et al. (2010. Acta Cryst. E66, o81–o82] but the absolute configuration could not be determined from data collected with Mo radiation. The absolute configuration has now been determined by refinement of the Flack parameter with data collected using Cu radiation. All features of the molecule and its crystal packing are similar to those previously described. 5. Helical post stellarator. Part 1: Vacuum configuration International Nuclear Information System (INIS) Moroz, P.E. 1997-08-01 Results on a novel type of stellarator configuration, the Helical Post Stellarator (HPS), are presented. This configuration is different significantly from all previously known stellarators due to its unique geometrical characteristics and unique physical properties. Among those are: the magnetic field has only one toroidal period (M = 1), the plasma has an extremely low aspect ratio, A ∼ 1, and the variation of the magnetic field, B, along field lines features a helical ripple on the inside of the torus. Among the main advantages of a HPS for a fusion program are extremely compact, modular, and simple design compatible with significant rotational transform, large plasma volume, and improved particle transport characteristics 6. Design issues for optimum solar cell configuration Science.gov (United States) Kumar, Atul; Thakur, Ajay D. 2018-05-01 A computer based simulation of solar cell structure is performed to study the optimization of pn junction configuration for photovoltaic action. The fundamental aspects of photovoltaic action viz, absorption, separation collection, and their dependence on material properties and deatails of device structures is discussed. Using SCAPS 1D we have simulated the ideal pn junction and shown the effect of band offset and carrier densities on solar cell performance. The optimum configuration can be achieved by optimizing transport of carriers in pn junction under effect of field dependent recombination (tunneling) and density dependent recombination (SRH, Auger) mechanisms. 7. The Broader Spectrum of Magnetic Configurations for Fusion Energy Technology Data Exchange (ETDEWEB) Prager, S C [Princeton Plasma Physics Laboratory, Princeton, NJ (United States); Ryutov, D D [Lawrence Livermore National Laboratory, Livermore, CA (United States) 2012-09-15 Over the decades, a large array of magnetic configurations has been studied, producing a huge amount of fusion plasma science. As configurations are developed, information and techniques learned through one configuration influence the development of other configurations. In this way, configurations evolve unexpectedly in response to new information. Configurations that were at a pause can become unstuck by new discoveries, and configurations that appeared promising for fusion energy can become unattractive as new limits are uncovered. The plasma science of fusion energy is sufficiently complex that, as we approach ever closer to practical fusion power, the need for potential contributions of broad research of multiple magnetic configurations remains strong. (author) 8. Wavefunction and energy of the 1s22sns configuration in a beryllium atom International Nuclear Information System (INIS) Huang Shizhong; Ma Kun; Yu Jiaming; Liu Fen 2008-01-01 A new set of trial functions for 1s 2 2sns configurations in a beryllium atom is suggested. A Mathematica program based on the variational method is developed to calculate the wavefunctions and energies of 1s 2 2sns (n = 3–6) configurations in a beryllium atom. Non-relativistic energy, polarization correction and relativistic correction which include mass correction, one-and two-body Darwin corrections, spin-spin contact interaction and orbit-orbit interaction, are calculated respectively. The results are in good agreement with experimental data. (atomic and molecular physics) 9. Asymmetrical Polyhedral Configuration of Giant Vesicles Induced by Orderly Array of Encapsulated Colloidal Particles. Science.gov (United States) Natsume, Yuno; Toyota, Taro 2016-01-01 Giant vesicles (GVs) encapsulating colloidal particles by a specific volume fraction show a characteristic configuration under a hypertonic condition. Several flat faces were formed in GV membrane with orderly array of inner particles. GV shape changed from the spherical to the asymmetrical polyhedral configuration. This shape deformation was derived by entropic interaction between inner particles and GV membrane. Because a part of inner particles became to form an ordered phase in the region neighboring the GV membrane, free volume for the other part of particles increased. Giant vesicles encapsulating colloidal particles were useful for the model of "crowding effect" which is the entropic interaction in the cell. 10. Selecting Actuator Configuration for a Benson Boiler DEFF Research Database (Denmark) Kragelund, Martin Nygaard; Leth, John-Josef; Wisniewski, Rafal 2009-01-01 with particular focus on a boiler in a power plant operated by DONG Energy - a Danish energy supplier. The problem has been reformulated using mathematic notions from economics. The selection of actuator configuration has been limited to the fuel system which in the considered plant consists of three different... 11. Length scale for configurational entropy in microemulsions NARCIS (Netherlands) Reiss, H.; Kegel, W.K.; Groenewold, J. 1996-01-01 In this paper we study the length scale that must be used in evaluating the mixing entropy in a microemulsion. The central idea involves the choice of a length scale in configuration space that is consistent with the physical definition of entropy in phase space. We show that this scale may be 12. Quality in Supply in Project Configured Networks DEFF Research Database (Denmark) Koch, Christian; Larsen, Casper Schultz 2006-01-01 The paper argues that in the AEC-industry the material and knowledge supply chains are increasingly intertwined and moreover characterised by configuration by project. In such a setting creating value for the customers and the enterprises becomes dependent of the ability to organise and coordinate... 13. Spent Nuclear Fuel Project Configuration Management Plan International Nuclear Information System (INIS) Reilly, M.A. 1995-01-01 This document is a rewrite of the draft ''C'' that was agreed to ''in principle'' by SNF Project level 2 managers on EDT 609835, dated March 1995 (not released). The implementation process philosphy was changed in keeping with the ongoing reengineering of the WHC Controlled Manuals to achieve configuration management within the SNF Project 14. Offshore Vendors' Software Development Team Configuration DEFF Research Database (Denmark) Chakraborty, Suranjan; Sarker, Saonee; Rai, Sudhanshu 2011-01-01 were compared on their inherent process-related and resource-related flexibilities. The thick-at-client configuration emerged as the one that offers superior flexibility (in all dimensions).However, additional analysis also revealed contingencies apart from flexibility that may influence... 15. Sandia software guidelines, Volume 4: Configuration management Energy Technology Data Exchange (ETDEWEB) 1992-06-01 This volume is one in a series of Sandia Software Guidelines for use in producing quality software within Sandia National Laboratories. This volume is based on the IEEE standard and guide for software configuration management. The basic concepts and detailed guidance on implementation of these concepts are discussed for several software project types. Example planning documents for both projects and organizations are included. 16. Apple Configurator 2 (version 2.3) OpenAIRE Lara Lasner-Frater 2018-01-01 Apple Configurator 2 (AC2) is a free mass-deployment utility that allows you to update multiple iPads, iPhones, iPod Touch devices, and Apple TVs at the same time, including apps, website links, iBooks, and software updates. 17. XVCL: XML-based Variant Configuration Language DEFF Research Database (Denmark) Jarzabek, Stan; Basset, Paul; Zhang, Hongyu 2003-01-01 XVCL (XML-based Variant Configuration Language) is a meta-programming technique and tool that provides effective reuse mechanisms. XVCL is an open source software developed at the National University of Singapore. Being a modern and versatile version of Bassett's frames, a technology that has... 18. DICOM supported sofware configuration by XML files International Nuclear Information System (INIS) LucenaG, Bioing Fabian M; Valdez D, Andres E; Gomez, Maria E; Nasisi, Oscar H 2007-01-01 A method for the configuration of informatics systems that provide support to DICOM standards using XML files is proposed. The difference with other proposals is base on that this system does not code the information of a DICOM objects file, but codes the standard itself in an XML file. The development itself is the format for the XML files mentioned, in order that they can support what DICOM normalizes for multiple languages. In this way, the same configuration file (or files) can be use in different systems. Jointly the XML configuration file generated, we wrote also a set of CSS and XSL files. So the same file can be visualized in a standard browser, as a query system of DICOM standard, emerging use, that did not was a main objective but brings a great utility and versatility. We exposed also some uses examples of the configuration file mainly in relation with the load of DICOM information objects. Finally, at the conclusions we show the utility that the system has already provided when the edition of DICOM standard changes from 2006 to 2007 19. Status Configurations, Military Service and Higher Education Science.gov (United States) Wang, Lin; Elder, Glen H., Jr.; Spence, Naomi J. 2012-01-01 The U.S. Armed Forces offer educational and training benefits as incentives for service. This study investigates the influence of status configurations on military enlistment and their link to greater educational opportunity. Three statuses (socioeconomic status of origin, cognitive ability and academic performance) have particular relevance for… 20. Configurable multi-perspective business process models NARCIS (Netherlands) La Rosa, M.; Dumas, M.; Hofstede, ter A.H.M.; Mendling, J. 2011-01-01 A configurable process model provides a consolidated view of a family of business processes. It promotes the reuse of proven practices by providing analysts with a generic modeling artifact from which to derive individual process models. Unfortunately, the scope of existing notations for 1. Holistic processing of face configurations and components. Science.gov (United States) Hayward, William G; Crookes, Kate; Chu, Ming Hon; Favelle, Simone K; Rhodes, Gillian 2016-10-01 Although many researchers agree that faces are processed holistically, we know relatively little about what information holistic processing captures from a face. Most studies that assess the nature of holistic processing do so with changes to the face affecting many different aspects of face information (e.g., different identities). Does holistic processing affect every aspect of a face? We used the composite task, a common means of examining the strength of holistic processing, with participants making same-different judgments about configuration changes or component changes to 1 portion of a face. Configuration changes involved changes in spatial position of the eyes, whereas component changes involved lightening or darkening the eyebrows. Composites were either aligned or misaligned, and were presented either upright or inverted. Both configuration judgments and component judgments showed evidence of holistic processing, and in both cases it was strongest for upright face composites. These results suggest that holistic processing captures a broad range of information about the face, including both configuration-based and component-based information. (PsycINFO Database Record (c) 2016 APA, all rights reserved). 2. Configuration mixing of mean-field states International Nuclear Information System (INIS) Bender, M; Heenen, P-H 2005-01-01 Starting from self-consistent mean-field models, we discuss how to include correlations from fluctuations in collective degrees of freedom through symmetry restoration and configuration mixing, which give access to ground-state correlations and collective excitations. As an example for the method, we discuss the spectroscopy of neutron-deficient Pb isotopes 3. Self Configurable Intelligent Distributed Antenna System DEFF Research Database (Denmark) Kumar, Ambuj; Mihovska, Albena Dimitrova; Prasad, Ramjee 2016-01-01 with their respective base stations, spectrum pooling and management at antenna end is not efficient. The situation worsens in Heterogeneous and Dense-net conditions in an Area of Interest (AoI). In this paper, we propose a DAS based intelligent architecture referred to as Self Configurable Intelligent Distributed... 4. Static Equilibrium Configurations of Charged Metallic Bodies ... African Journals Online (AJOL) In this paper we developed a simple numerical scheme to determine the static equilibrium configuration of charged metallic bodies by minimizing the potential energy function. The method developed has some advantages; it combines the general theory and the physical meanings nested in the mathematical model and this ... 5. Studies of a flexible heliac configuration International Nuclear Information System (INIS) Hender, T.C.; Cantrell, J.L.; Harris, J.H. 1987-07-01 This paper documents a detailed study of the Flexible Heliac configuration. The remarkable flexibility of this device - which allows variation of the rotational transform, shear, and magnetic well depth over a relatively wide range - is described. Engineering considerations of error fields, finite cross-section conductors, and plasma coil clearances are also discussed 6. Sibling Gender Configuration and Family Processes NARCIS (Netherlands) van der Pol, Lotte D.; Mesman, Judi; Groeneveld, Marleen G.; Endendijk, Joyce J.; van Berkel, Sheila R.; Hallers-Haalboom, Elizabeth T.; Bakermans-Kranenburg, Marian J. 2016-01-01 The current study focuses on the effects of sibling gender configuration on family processes during early childhood. In a sample of 369 two-parent families with two children (youngest 12 months, oldest about 2 years older), both siblings’ noncompliant and oppositional behaviors and fathers’ and 7. Private Cloud Configuration with MetaConfig DEFF Research Database (Denmark) Nielsen, Thomas; Iversen, Christian; Bonnet, Philippe 2011-01-01 With the advent of private clouds, the challenge of configuring a mix of physical and virtual machines is no longer reserved to a few system administrator gurus. How to assign virtual machines onto physical machines to leverage the available resources? How to maintain the virtual machine... 8. Motion-insensitive rapid configuration relaxometry. Science.gov (United States) Nguyen, Damien; Bieri, Oliver 2017-08-01 Triple echo steady state (TESS) uses the lowest steady state configuration modes for rapid relaxometry. Due to its unbalanced gradient scheme, however, TESS is inherently motion-sensitive. The purpose of this work is to merge TESS with a balanced acquisition scheme for motion-insensitive rapid configuration relaxometry, termed MIRACLE. The lowest order steady state free precession (SSFP) configurations are retrieved by Fourier transformation of the frequency response of N frequency-shifted balanced SSFP (bSSFP) scans and subsequently processed for relaxometry, as proposed with TESS. Accuracy of MIRACLE is evaluated from simulations, phantom studies as well as in vivo brain and cartilage imaging at 3T. Simulations and phantom results revealed no conceptual flaw, and artifact-free configuration imaging was achieved in vivo. Overall, relaxometry results were accurate in phantoms and in good agreement for cartilage and for T2 in the brain, but apparent low T1 values were observed for brain white matter; reflecting asymmetries in the bSSFP profile. Rapid T1 and T2 mapping with MIRACLE offers analogous properties as TESS while successfully mitigating its motion-sensitivity. As a result of the Fourier transformation, relaxometry becomes sensitive to the voxel frequency distribution, which may contain useful physiologic information, such as structural brain integrity. © 2016 International Society for Magnetic Resonance in Medicine. Magn Reson Med 78:518-526, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine. 9. Dynamics and configurations of galaxy triplets International Nuclear Information System (INIS) Anosova, J.P.; Orlov, V.V.; Chernin, A.D.; Ivanov, A.V.; Kiseleva, L.G. 1990-01-01 The purpose is to infer the probable dynamical states of galaxy triplets by the observed data on their configurations. Two methods are proposed for describing the distributions of the triplet configuration parameters characterizing a tendency to alignment and hierarchy: (1) obtaining a representative sample of configurations and determining its statistical parameters (moments and percentages); and (2) dividing the region of possible configurations of triple systems (Agekian and Anosova, 1967) into a set of segments and finding the probabilities for the configurations to find themselves in each of them. Both these methods allow representation of the data by numerical simulations as well as observations. The effect of projection was studied. It rather overestimates the alignment and hierarchy of the triple systems. Among the parameters of interest there are found some parameters that are least sensitive to projection effects. The samples consist of simulated galaxy triplets (with hidden mass) as well as of 46 probably physical triple galaxies (Karachentseva et al., 1979). The observed triples as well as numerical models show a tendency to alignment. The triple galaxies do not show any tendency to hierarchy (formation of the temporary binaries), but this tendency may be present for simulated triplets without significant dark matter. The significant hidden mass (of order ten times the total mass of a triplet) decreases the probability of forming a binary and so weakens the hierarchy. Small galaxy groups consisting of 3 to 7 members are probably the most prevalent types of galaxy aggregate (Gorbatsky, 1987). Galaxy triplets are the simplest groups, but dynamically nontrivial ones 10. Experimental and theoretical study of the hyperfine structure in the lower configurations in 45Sc II International Nuclear Information System (INIS) Villemoes, P.; van Leeuwen, R.; Arnesen, A.; Heijkenskjoeld, F.; Kastberg, A.; Larsson, M.O.; Kotochigova, S.A. 1992-01-01 We have measured the hyperfine structure (hfs) of 12 levels in the configurations 3d4s, 3d 2 , and 3d4p in singly ionized scandium by collinear fast-ion-beam--laser spectroscopy. The hfs of the four levels in the configuration 3d4s has to our knowledge not been measured before. From these levels the ions were excited to levels in the 3d4p configuration by the frequency-doubled output of a ring dye laser with an intracavity mounted LiIO 3 crystal. Levels in the 3d 2 configuration were excited to levels in the 3d4p configuration with visible laser light. The resulting magnetic dipole (A) and electric quadrupole (B) hfs constants are analyzed in Sandars-Beck effective-operator formalism. The multiconfiguration Dirac-Fock method has been used to calculate the hfs constants for levels in the configurations 3d4s, 3d5s, 3d6s, 3d 2 , and 3d4p. Within the framework of the configuration-interaction method, an approach is presented for the calculation of the core polarization, which uses a virtual basis set localized inside the core. For all levels, this approach gives better results compared to previously published calculations 11. Characterization of the equilibrium configuration for modulated beams in a plasma wakefield accelerator CERN Document Server Martorelli, Roberto 2016-01-01 We analyze the equilibrium configuration for a modulated beam with sharp boundaries exposed to the fields self-generated by the interaction with a plasma. Through a semi-analytical approach we show the presence of multiple equilibrium configurations and we determine the one more suitable for wakefield excitation. Once pointed out the absence of confinement for the front of the beam and the consequently divergence driven by the emittance, we study the evolution of the equilibrium configuration while propagating in the plasma, discarding all the others time-dependencies. We show the onset of a rigid backward drift of the equilibrium configuration and we provide an explanation in the increasing length of the first bunch. 12. Software control and system configuration management: A systems-wide approach Science.gov (United States) Petersen, K. L.; Flores, C., Jr. 1984-01-01 A comprehensive software control and system configuration management process for flight-crucial digital control systems of advanced aircraft has been developed and refined to insure efficient flight system development and safe flight operations. Because of the highly complex interactions among the hardware, software, and system elements of state-of-the-art digital flight control system designs, a systems-wide approach to configuration control and management has been used. Specific procedures are implemented to govern discrepancy reporting and reconciliation, software and hardware change control, systems verification and validation testing, and formal documentation requirements. An active and knowledgeable configuration control board reviews and approves all flight system configuration modifications and revalidation tests. This flexible process has proved effective during the development and flight testing of several research aircraft and remotely piloted research vehicles with digital flight control systems that ranged from relatively simple to highly complex, integrated mechanizations. 13. Fuel control device for various gas turbine configurations Energy Technology Data Exchange (ETDEWEB) Stearns, C F; Tutherly, H W 1980-09-29 The hydromechanic fuel control device can be adapted for various engine configurations as for example turbofan-, turbopro-, and turboshaft engines by providing those elements which are common for all engine configurations in the main housing and a detachable block for each individual configuration with all control elements and flow channels necessary for the respective configuration. 14. Developing a Frame of Reference for understanding configuration systems DEFF Research Database (Denmark) 2008-01-01 This paper uses the theory of technical systems to develop a frame of reference of product configuration systems. Following a definition of the configuration task, product model and product configuration system the theory of technical systems are presented. Configuration systems are then related... 15. Interaction region International Nuclear Information System (INIS) Anon. 1982-01-01 The Interaction Region Group addressed the basic questions of how to collide the SLC beams, how to maximize and monitor the luminosity, and how to minimize the detector backgrounds at the interaction region. In practice, five subgroups evolved to study these questions. The final focus group provided three alternative designs to acheive the 1 to 2 micron beam spot size required by the SLC, as well as studying other problems including: eta, eta' matching from the collider arcs, the implementation of soft bends near the interaction region, beam emittance growth, and magnet tolerances in the final focus. The beam position monitor group proposed two devices, a strip line monitor, and a beamstrahlung monitor, to bring the beams into collision. The luminosity monitor group reviewed the possible QED processes that would be insensitive to weak interaction (Z 0 ) effects. The beam dumping group proposed locations for kicker and septum magnets in the final focus that would achieve a high dumping efficiency and would meet the desired beam tolerances at the Moller scattering target in the beam dump line. Working with the Polarization Group, the Moller experiment was designed into the beam dump beam line. A beam dump was proposed that would maintain radiation backgrounds (penetrating muons) at acceptible levels. The detector backgrounds group proposed soft-bend and masking configurations to shield the detector from synchrotron radiation from the hard/soft bends and from the final focus quadrupoles and evaluated the effectiveness of these designs for the three final focus optics designs. Backgrounds were also estimated from: large angle synchrotron radiation, local and distant beam-gas interactions, 2-photon interactions, and from neutrons and backscattered photons from the beamstrahlung dump 16. Sustainable supply chain design: a configurational approach. Science.gov (United States) Masoumik, S Maryam; Abdul-Rashid, Salwa Hanim; Olugu, Ezutah Udoncy; Raja Ghazilla, Raja Ariffin 2014-01-01 Designing the right supply chain that meets the requirements of sustainable development is a significant challenge. Although there are a considerable number of studies on issues relating to sustainable supply chain design (SSCD) in terms of designing the practices, processes, and structures, they have rarely demonstrated how these components can be aligned to form an effective sustainable supply chain (SSC). Considering this gap in the literature, this study adopts the configurational approach to develop a conceptual framework that could configure the components of a SSC. In this respect, a process-oriented approach is utilized to classify and harmonize the design components. A natural-resource-based view (NRBV) is adopted to determine the central theme to align the design components around. The proposed framework presents three types of SSC, namely, efficient SSC, innovative SSC, and reputed SSC. The study culminates with recommendations concerning the direction for future research. 17. Configuration management in nuclear power plants CERN Document Server 2003-01-01 Configuration management (CM) is the process of identifying and documenting the characteristics of a facility's structures, systems and components of a facility, and of ensuring that changes to these characteristics are properly developed, assessed, approved, issued, implemented, verified, recorded and incorporated into the facility documentation. The need for a CM system is a result of the long term operation of any nuclear power plant. The main challenges are caused particularly by ageing plant technology, plant modifications, the application of new safety and operational requirements, and in general by human factors arising from migration of plant personnel and possible human failures. The IAEA Incident Reporting System (IRS) shows that on average 25% of recorded events could be caused by configuration errors or deficiencies. CM processes correctly applied ensure that the construction, operation, maintenance and testing of a physical facility are in accordance with design requirements as expressed in the d... 18. Maximum Profit Configurations of Commercial Engines Directory of Open Access Journals (Sweden) Yiran Chen 2011-06-01 Full Text Available An investigation of commercial engines with finite capacity low- and high-price economic subsystems and a generalized commodity transfer law [n ∝ Δ (P m] in commodity flow processes, in which effects of the price elasticities of supply and demand are introduced, is presented in this paper. Optimal cycle configurations of commercial engines for maximum profit are obtained by applying optimal control theory. In some special cases, the eventual state—market equilibrium—is solely determined by the initial conditions and the inherent characteristics of two subsystems; while the different ways of transfer affect the model in respects of the specific forms of the paths of prices and the instantaneous commodity flow, i.e., the optimal configuration. 19. Fingerprinting Mobile Devices Using Personalized Configurations Directory of Open Access Journals (Sweden) Kurtz Andreas 2016-01-01 Full Text Available Recently, Apple removed access to various device hardware identifiers that were frequently misused by iOS third-party apps to track users. We are, therefore, now studying the extent to which users of smartphones can still be uniquely identified simply through their personalized device configurations. Using Apple’s iOS as an example, we show how a device fingerprint can be computed using 29 different configuration features. These features can be queried from arbitrary thirdparty apps via the official SDK. Experimental evaluations based on almost 13,000 fingerprints from approximately 8,000 different real-world devices show that (1 all fingerprints are unique and distinguishable; and (2 utilizing a supervised learning approach allows returning users or their devices to be recognized with a total accuracy of 97% over time 20. Isabelle dipole and quadrupole coil configurations International Nuclear Information System (INIS) Dahl, P.F.; Hahn, H. 1980-01-01 The coil configurations of the ISABELLE dipole and quadrupole magnets have been reviewed and a number of improvements were suggested for incorporation into the final design. The coil designs are basically single layer multiple block approximations to cosine current distributions, wound from a high aspect ratio non-keystoned braided conductor. The blocks are separated by knife-edge wedges to maximize the quench propagation velocity. The current density variation is obtained by an appropriate distribution of the spacer turns and, to a lesser degree, by the wedge locations. The use of inert turns is necessary to minimize the peak field enhancement both in the ends and in the two dimensional section. Schemes for deriving turns distributions yielding harmonic coefficients satisfying the stringent ISABELLE tolerances on field uniformity, while allowing for simplicity in winding and taking into account quench propagation considerations, will be discussed, as well as our approach to the coil end configuration 1. Symmetric configurations highlighted by collective quantum coherence Energy Technology Data Exchange (ETDEWEB) Obster, Dennis [Radboud University, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto (Japan); Sasakura, Naoki [Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto (Japan) 2017-11-15 Recent developments in quantum gravity have shown the Lorentzian treatment to be a fruitful approach towards the emergence of macroscopic space-times. In this paper, we discuss another related aspect of the Lorentzian treatment: we argue that collective quantum coherence may provide a simple mechanism for highlighting symmetric configurations over generic non-symmetric ones. After presenting the general framework of the mechanism, we show the phenomenon in some concrete simple examples in the randomly connected tensor network, which is tightly related to a certain model of quantum gravity, i.e., the canonical tensor model. We find large peaks at configurations invariant under Lie-group symmetries as well as a preference for charge quantization, even in the Abelian case. In future study, this simple mechanism may provide a way to analyze the emergence of macroscopic space-times with global symmetries as well as various other symmetries existing in nature, which are usually postulated. (orig.) 2. Sustainable Supply Chain Design: A Configurational Approach Science.gov (United States) Masoumik, S. Maryam; Raja Ghazilla, Raja Ariffin 2014-01-01 Designing the right supply chain that meets the requirements of sustainable development is a significant challenge. Although there are a considerable number of studies on issues relating to sustainable supply chain design (SSCD) in terms of designing the practices, processes, and structures, they have rarely demonstrated how these components can be aligned to form an effective sustainable supply chain (SSC). Considering this gap in the literature, this study adopts the configurational approach to develop a conceptual framework that could configure the components of a SSC. In this respect, a process-oriented approach is utilized to classify and harmonize the design components. A natural-resource-based view (NRBV) is adopted to determine the central theme to align the design components around. The proposed framework presents three types of SSC, namely, efficient SSC, innovative SSC, and reputed SSC. The study culminates with recommendations concerning the direction for future research. PMID:24523652 3. Instanton Field Configurations and Black Holes CERN Document Server Konopleva, N P 2005-01-01 The role of vacuum relativization in QCD and nucleus theory is discussed. It is shown that relativistic vacuum must be described by vacuum Einstein equations. Black Holes have to make their appearance in QCD because of Schwarzschildean solution of these equations. Instanton configurations of any fields do not change vacuum Einstein equations and their solutions, because their energy-momentum tensors are zero. But they make it possible to determine a space-time topology, which cannot be defined by differential Einstein equations. Therefore, Black Holes number in space-time is possibly connected with instanton configurations of fields and other matter. Instantons do not fall into Black Holes and are the very matter which surrounds them. 4. Automated software configuration in the MONSOON system Science.gov (United States) Daly, Philip N.; Buchholz, Nick C.; Moore, Peter C. 2004-09-01 MONSOON is the next generation OUV-IR controller project being developed at NOAO. The design is flexible, emphasizing code re-use, maintainability and scalability as key factors. The software needs to support widely divergent detector systems ranging from multi-chip mosaics (for LSST, QUOTA, ODI and NEWFIRM) down to large single or multi-detector laboratory development systems. In order for this flexibility to be effective and safe, the software must be able to configure itself to the requirements of the attached detector system at startup. The basic building block of all MONSOON systems is the PAN-DHE pair which make up a single data acquisition node. In this paper we discuss the software solutions used in the automatic PAN configuration system. 5. The International Thermonuclear Experimental Reactor configuration evolution International Nuclear Information System (INIS) Lousteau, D.C.; Nelson, B.E.; Lee, V.D.; Thomson, S.L.; Miller, J.M.; Lindquist, W.B. 1989-01-01 The International Thermonuclear Experimental Reactor (ITER) conceptual design activities consist of two phases: a definition phase, completed in September 1988, and a design phase, now in progress. The definition phase was successful in identifying a consistent set of technical characteristics and the broad definition of the required reactor configuration and hardware. Scheduled for completion in November 1990, the design phase is producing a more detailed definition of the required components, a first cost estimate, and a description of site requirements. A major activity in the ITER design phase is the period of joint work conducted at the Max Planck Institute for Plasma Physics, Garching, Federal Republic of Germany, from June through October 1989. An official report of the findings and conclusions of this activity will be submitted to and published by the International Atomic Energy Agency (IAEA). This paper highlights the evolution of the reactor mechanical configuration since the conclusion of the definition phase. 8 figs., 2 tabs 6. TCV divertor upgrade for alternative magnetic configurations Directory of Open Access Journals (Sweden) H. Reimerdes 2017-08-01 Full Text Available The Swiss Plasma Center (SPC is planning a divertor upgrade for the TCV tokamak. The upgrade aims at extending the research of conventional and alternative divertor configurations to operational scenarios and divertor regimes of greater relevance for a fusion reactor. The main elements of the upgrade are the installation of an in-vessel structure to form a divertor chamber of variable closure and enhanced diagnostic capabilities, an increase of the pumping capability of the divertor chamber and the addition of new divertor poloidal field coils. The project follows a staged approach and is carried out in parallel with an upgrade of the TCV heating system. First calculations using the EMC3-Eirene code indicate that realistic baffles together with the planned heating upgrade will allow for a significantly higher compression of neutral particles in the divertor, which is a prerequisite to test the power dissipation potential of various divertor configurations. 7. Enhancing operability and reliability through configuration management International Nuclear Information System (INIS) Hancock, L.R. 1993-01-01 This paper describes the evolution of plant design control techniques from the early 1970's to today's operating environment that demands accurate, up-to-date design data. This evolution of design control is responsible for the increasingly troublesome scenario of design data being very difficult to locate and when found, its credibility is questioned. The design information could be suspect because there are discrepancies between two or more source documents or there is a difference between the design documents and the physical configuration of the plant. This paper discusses the impact these design control problems are having on plant operations and presents common sense solutions for improving configuration management techniques to ultimately enhance operability and reliability 8. Formal Verification Method for Configuration of Integrated Modular Avionics System Using MARTE Directory of Open Access Journals (Sweden) Lisong Wang 2018-01-01 Full Text Available The configuration information of Integrated Modular Avionics (IMA system includes almost all details of whole system architecture, which is used to configure the hardware interfaces, operating system, and interactions among applications to make an IMA system work correctly and reliably. It is very important to ensure the correctness and integrity of the configuration in the IMA system design phase. In this paper, we focus on modelling and verification of configuration information of IMA/ARINC653 system based on MARTE (Modelling and Analysis for Real-time and Embedded Systems. Firstly, we define semantic mapping from key concepts of configuration (such as modules, partitions, memory, process, and communications to components of MARTE element and propose a method for model transformation between XML-formatted configuration information and MARTE models. Then we present a formal verification framework for ARINC653 system configuration based on theorem proof techniques, including construction of corresponding REAL theorems according to the semantics of those key components of configuration information and formal verification of theorems for the properties of IMA, such as time constraints, spatial isolation, and health monitoring. After that, a special issue of schedulability analysis of ARINC653 system is studied. We design a hierarchical scheduling strategy with consideration of characters of the ARINC653 system, and a scheduling analyzer MAST-2 is used to implement hierarchical schedule analysis. Lastly, we design a prototype tool, called Configuration Checker for ARINC653 (CC653, and two case studies show that the methods proposed in this paper are feasible and efficient. 9. A Two-Bladed Teetering Hub configuration for the DTU 10 MW RWT: loads considerations DEFF Research Database (Denmark) Bergami, Leonardo; Aagaard Madsen, Helge; Rasmussen, Flemming 2014-01-01 study on an alternative downwind two-bladed rotor configuration. The study is based on a model representative of next generation multi-MW wind turbines: the DTU 10-MW Reference Wind Turbine (RWT). As a first design iteration, the aerodynamic characteristics of the original rotor are maintained......As the size of wind turbine rotors continuously grows, the need for innovative solutions that would yield to lighter rotor configurations becomes more urgent. Traditional wind turbine designs have favored the classic three-bladed upwind rotor configuration. This work presents instead a concept...... in load variations, and hence in fatigue damage, affects the turbine blades, shaft and tower, and originates from the aerodynamic unbalance on the rotor, as well as from aeroelastic interaction with the tower frequency. To mitigate the load amplification caused by the interaction between the tower... 10. Configuration dependent deformation in 183Au International Nuclear Information System (INIS) Joshi, P.; Kumar, A.; Govil, I.M.; Mukherjee, G.; Singh, R.P.; Muralithar, S.; Bhowmik, R.K. 1998-01-01 The lifetime measurements in 183 Au nucleus were carried in order to probe the deformation properties of the band built on the i 3/2 and h 9/2 configurations. The nucleus of 183 Au was populated using a reaction 28 Si( 159 Tb,4n) 183 Au at a beam energy of 140 MeV. Lifetime measurements were carried out using Recoil Distance Measurements (RDM) method 11. Ultrasonic imaging with a fixed instrument configuration Energy Technology Data Exchange (ETDEWEB) Witten, A.; Tuggle, J.; Waag, R.C. 1988-07-04 Diffraction tomography is a technique based on an inversion of the wave equation which has been proposed for high-resolution ultrasonic imaging. While this approach has been considered for diagnostic medical applications, it has, until recently, been limited by practical limitations on the speed of data acquisition associated with instrument motions. This letter presents the results of an experimental study directed towards demonstrating tomography utilizing a fixed instrument configuration. 12. Magnetic Configuration Control of ITER Plasmas International Nuclear Information System (INIS) Albanese, R.; Artaserse, G.; Mattei, M.; Ambrosino, G.; Crisanti, F.; Tommasi, G. de; Fresa, R.; Portone, A.; Sartori, F.; Villone, F. 2006-01-01 The aim of this paper is to review the capability of the ITER Poloidal Field (PF) system of controlling the broad range of plasma configurations presently forecasted during ITER operation. The attention is focused on the axi-symmetric aspects of plasma magnetic configuration control since they pose the greatest challenges in terms of control power and they have the largest impact on machine capital cost. The paper is broadly divided in two main sections devoted, respectively, to open loop (feed-forward) and closed loop (feedback) control. In the first part of the study the PF system is assessed with respect to the initiation, ramp-up, sustained burn, ramp-down phases of the main plasma inductive scenario. The limiter-to-divertor configuration transition phase is considered in detail with the aim of assessing the PF capability to form an X-point at the lowest possible current and, therefore, to relax the thermal load on the limiter surfaces. Moreover, during the sustained burn it is important to control plasmas with a broad range of current density profiles. In the second part of the study the plasma vertical feedback control requirements are assessed in details, in particular for the high elongation configurations achievable during the early limiter-to-X point transition phase. Non-rigid plasma displacement models are used to assess the control system voltage and current requirements of different radial field control circuits obtained, for example, by connecting the outermost PF coils, some CS coils, coils sub-sections etc. At last, the main 3D effects of the vessel ports are modeled and their impact of vertical stabilization evaluated. (author) 13. Optical configurations for the Virgo interferometer International Nuclear Information System (INIS) Hello, P. 1993-01-01 We present, in this paper, the potential optical configurations for the VIRGO interferometer, as well as for other similar antennas (LIGO...), and the implications for its sensitivity for the detection of gravitational waves (GW's). The dual recycling arrangement may particularly relax the severe optical specifications required in a power recycling interferometer. Finally, a new idea to improve the symmetry of the interferometer is presented. (author). 11 refs., 2 figs 14. Configuration management with chef-solo CERN Document Server Rahman, Naveed ur 2014-01-01 This is a step-by-step guide, full of hands-on examples of real-world deployment tasks. Each topic is explained and placed in context, while also pointing out the key details of the concepts used. This book is aimed at system administrators and system engineers who have an understanding of configuration management tools and infrastructure. For novice administrators, it contains easy-to-use application recipes to get started immediately. 15. Configuration spaces geometry, topology and representation theory CERN Document Server Cohen, Frederick; Concini, Corrado; Feichtner, Eva; Gaiffi, Giovanni; Salvetti, Mario 2016-01-01 This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology. 16. Numerical Investigation of a Generic Scramjet Configuration OpenAIRE Karl, Sebastian 2011-01-01 A Supersonic Combustion Ramjet (scramjet) is, at least in theory, an efficient air-breathing propulsion system for sustained hypersonic flight at Mach numbers above approximately M=5. Important design issues for such hypersonic propulsion systems, are the lack of ground based facilities capable of testing a full-sized engine at cruise flight conditions and the absence of general scaling laws for the extrapolation of wind tunnel data to flight configurations. Therefore, there is a strong need ... 17. Configurating computer-controlled bar system OpenAIRE Šuštaršič, Nejc 2010-01-01 The principal goal of my diploma thesis is creating an application for configurating computer-controlled beverages dispensing systems. In the preamble of my thesis I present the theoretical platform for point of sale systems and beverages dispensing systems, which are required for the understanding of the target problematics. As with many other fields, computer tehnologies entered the field of managing bars and restaurants quite some time ago. Basic components of every bar or restaurant a... 18. Development of configuration risk management tool International Nuclear Information System (INIS) Masuda, Takahiro; Doi, Eiji 2003-01-01 Tokyo Electric Power Company (referred to as TEPCO hereinafter), and other Japanese utilities as well, have been trying to improve the capacity factor of their Nuclear Power Plants (NPPs) through modernization of Operation and Maintenance strategy. TEPCO intends to apply risk information to O and M field with maintaining or even improving both safety and production efficiency. Under these situations, TEPCO with some BWR utilities started to develop a Configuration Risk Management (CRM) tool that can estimate risk in various plant conditions due to configuration changes during outage. Moreover, we also intend to apply CRM to on-line maintenance (OLM) in the near future. This tool can calculate the Core Damage Frequency (CDF) according to given plant condition, such as SSCs availability, decay heat level and the inventory of coolant in both outage state and full-power operation. From deterministic viewpoint, whether certain configuration meet the related requirements of Technical Specifications. User-friendly interface is one of the important features of this tool because this enables the site engineers with little experience in PSA to quantify and utilize the risk information by this tool. (author) 19. The Database Driven ATLAS Trigger Configuration System CERN Document Server Martyniuk, Alex; The ATLAS collaboration 2015-01-01 This contribution describes the trigger selection configuration system of the ATLAS low- and high-level trigger (HLT) and the upgrades it received in preparation for LHC Run 2. The ATLAS trigger configuration system is responsible for applying the physics selection parameters for the online data taking at both trigger levels and the proper connection of the trigger lines across those levels. Here the low-level trigger consists of the already existing central trigger (CT) and the new Level-1 Topological trigger (L1Topo), which has been added for Run 2. In detail the tasks of the configuration system during the online data taking are Application of the selection criteria, e.g. energy cuts, minimum multiplicities, trigger object correlation, at the three trigger components L1Topo, CT, and HLT On-the-fly, e.g. rate-dependent, generation and application of prescale factors to the CT and HLT to adjust the trigger rates to the data taking conditions, such as falling luminosity or rate spikes in the detector readout ... 20. Loop Quantization and Symmetry: Configuration Spaces Science.gov (United States) Fleischhack, Christian 2018-06-01 Given two sets S 1, S 2 and unital C -algebras A_1, A_2 of functions thereon, we show that a map {σ : {S}_1 \\longrightarrow {S}_2} can be lifted to a continuous map \\barσ : spec A_1 \\longrightarrow spec A_2 iff σ^\\ast A_2 := σ^\\ast f \| f \\in A_2 \\subseteq A_1. Moreover, \\bar σ is unique if existing, and injective iff σ^\\ast A_2 is dense. Then, we apply these results to loop quantum gravity and loop quantum cosmology. For all usual technical conventions, we decide whether the cosmological quantum configuration space is embedded into the gravitational one; indeed, both are spectra of some C *-algebras, say, A_cosm and A_grav, respectively. Typically, there is no embedding, but one can always get an embedding by the defining A_cosm := C^\\ast(σ^\\ast A_grav), where {σ} denotes the embedding between the classical configuration spaces. Finally, we explicitly determine {C^\\ast(σ^\\ast A_grav) in the homogeneous isotropic case for A_grav generated by the matrix functions of parallel transports along analytic paths. The cosmological quantum configuration space so equals the disjoint union of R and the Bohr compactification of R, appropriately glued together. 1. A low emittance configuration for spear International Nuclear Information System (INIS) Blumberg, L.N.; Cerino, J.; Harris, J.; Hettel, R.; Hofmann, A.; Liu, R.Z.; Stego, R.; Wiedemann, H.; Winick, H. 1985-01-01 The quality of synchrotron radiation beams from SPEAR, in particular the brilliance of undulator radiation, can be improved significantly by reducing the emittance of the stored electron beam. A reduction of the horizontal emittance by a factor of 3.5 to a value of 130 nanometer-radians (nm-r) at 3 GeV has been achieved by using stronger focussing, mainly in the horizontal plane. The low emittance configuration also reduces the dispersion and vertical beta functions in the straight sections, making them more suitable for wigglers. The higher betatron tunes lead to a larger phase advance between the two kickers, which has to be corrected during injection by shunting current from some quadrupoles. The configuration was optimized within SPEAR hardware limitations and tested for dynamic aperture with the tracking program PATRICIA. After implementation of this scheme, beam was successfully injected and accumulated. The measured emittance of the stored beam was in agreement with calculations. Presently the configuration is being made operational 2. Study on Resource Configuration on Cloud Manufacturing Directory of Open Access Journals (Sweden) Yanlong Cao 2015-01-01 Full Text Available The purpose of manufacturing is to realize the requirement of customer. In manufacturing process of cloud system, there exist a lot of resource services which have similar functional characteristics to realize the requirement. It makes the manufacturing process more diverse. To develop the quality and reduce cost, a resource configuration model on cloud-manufacturing platform is put forward in this paper. According to the generalized six-point location principle, a growth design from the requirement of customers to entities with geometric constraints is proposed. By the requirement growing up to product, a configuration process is used to match the entities with the instances which the resources in the database could supply. Different from most existing studies, this paper studies the tolerance design with multiple candidate resource suppliers on cloud manufacturing to make the market play a two-level game considering the benefit of customers and the profit of resources to give an optimal result. A numerical case study is used to illustrate the proposed model and configuration process. The performance and advantage of the proposed method are discussed at the end. 3. Permutation-invariant distance between atomic configurations Science.gov (United States) Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel 2015-09-01 We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity. 4. Permutation-invariant distance between atomic configurations International Nuclear Information System (INIS) Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel 2015-01-01 We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity 5. System engineering and configuration management in ITER International Nuclear Information System (INIS) Chiocchio, S.; Martin, E.; Barabaschi, P.; Bartels, Hans Werner; How, J.; Spears, W. 2007-01-01 The construction of ITER will represent a major challenge for the fusion community at large, because of the intrinsic complexity of the tokamak design, the large number of different systems which are all essential for its operation, the worldwide distribution of the design activities and the unusual procurement scheme based on a combination of in-kind and directly funded deliverables. A key requirement for the success of such a large project is that a systematic approach to ensure the consistency of the design with the required performance is adopted. Also, effective project management methods, tools and working practices must be deployed to facilitate the communication and collaboration among the institutions and industries involved in the project. The authors have been involved in the definition and practical implementation of the design integration and configuration control structure inside ITER and in the system engineering process during the selection and optimization of the machine configuration. In parallel, they have assessed design, drawing and documentation management software to be used for the construction phase. Here, they describe the experience gained in recent years, explain the drivers behind the selection of the documents and drawings management systems, and illustrate the scope and issues of the configuration management activities to ensure the congruence of the design, to control and track the design changes and to manage the interfaces among the ITER systems 6. The self-description data configuration model Energy Technology Data Exchange (ETDEWEB) Abadie, Lana, E-mail: [email protected] [ITER Organization, Route de vinon sur Verdon, 13115 St Paul Lez Durance (France); Di Maio, Franck; Klotz, Wolf-Dieter; Mahajan, Kirti; Stepanov, Denis; Utzel, Nadine; Wallander, Anders [ITER Organization, Route de vinon sur Verdon, 13115 St Paul Lez Durance (France) 2012-12-15 Highlights: Black-Right-Pointing-Pointer We use the relational model to represent the configuration data for ITER. Black-Right-Pointing-Pointer We explain the different modeled views namely physical, functional and control. Black-Right-Pointing-Pointer We explain how this information is used to generate configuration files. Black-Right-Pointing-Pointer We explain that this information is validated. - Abstract: ITER will consist of roughly 160 plant systems I and C delivered in kind which need to be integrated into the ITER control infrastructure. To make the integration of all these plant systems I and C, a smooth operation, the CODAC (Controls, Data Access and Communications) group release every year the core software environment which consists of many applications. In this paper we would like to describe what configuration data and how it is modeled in the version 2. The model is based on three views, the physical one which lists the components with their signals, the functional view which describes the control functions and variables required to implement them and the control view which links the two previous views. We use Hibernate as an ORM (Object Relational Mapping) framework with a PostgreSQL database and Spring as a framework to handle transactions. 7. Configuration management plan for the GENII software International Nuclear Information System (INIS) Rittmann, P.D. 1994-01-01 The GENII program calculates doses from radionuclides released into the environment for a variety of possible exposure scenarios. The user prepares an input data file with the necessary modelling assumptions and parameters. The program reads the user's input file, computes the necessary doses and stores these results in an output file. The output file also contains a listing of the user's input and gives the title lines from the data libraries which are accessed in the course of the calculations. The purpose of this document is to provide users of the GENII software with the configuration controls which are planned for use by WHC in accordance with WHC-CM-3-10. The controls are solely for WHC employees. Non-WHC individuals are not excluded, but no promise is made or implied that they will be informed of errors or revisions to the software. The configuration controls cover the GENII software, the GENII user's guide, the list of GENII users at WHC, and the backup copies. Revisions to the software must be approved prior to distribution in accordance with this configuration management plan 8. Performance expectations in the new configuration International Nuclear Information System (INIS) Lallia, P.P.; Rebut, P.-H. 1989-01-01 The pumped divertor to be installed in JET should allow a control of the particles and of the impurities. The new hardware required into the vacuum vessel leads to a reduction of the plasma cross section. While a plasma current of 6 MA should still be possible, this will affect the confinement of the plasma. The JET performances in the New Configuration are estimated from the critical electron temperature gradient model by using a 1-D transport code. It has been shown in the past that this model gives a rather satisfactory description of the JET discharges. However it does not address the particle transport and density profiles have to be imposed. By comparison with numerical simulations of the present JET configuration, it is shown that the reduction in plasma size should be more than balanced by the lower impurity concentration expected to result from the divertor. In terms of thermonuclear Q th , a doubling is found relatively to the expectations in the present configuration (≅ .9 against .45). On the other hand Q th should be lowered to .3 if the impurity control is inefficient. In this case as presently observed in JET it is expected that no steady state will be achieved. (author) 9. REDUNDANT ARRAY CONFIGURATIONS FOR 21 cm COSMOLOGY Energy Technology Data Exchange (ETDEWEB) Dillon, Joshua S.; Parsons, Aaron R., E-mail: [email protected] [Department of Astronomy, UC Berkeley, Berkeley, CA (United States) 2016-08-01 Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of systematics. Next-generation telescopes are now being designed and built to meet these challenges, drawing lessons from first-generation experiments that showed the benefits of densely packed, highly redundant arrays—in which the same mode on the sky is sampled by many antenna pairs—for achieving high sensitivity, precise calibration, and robust foreground mitigation. In this work, we focus on the Hydrogen Epoch of Reionization Array (HERA) as an interferometer with a dense, redundant core designed following these lessons to be optimized for 21 cm cosmology. We show how modestly supplementing or modifying a compact design like HERA’s can still deliver high sensitivity while enhancing strategies for calibration and foreground mitigation. In particular, we compare the imaging capability of several array configurations, both instantaneously (to address instrumental and ionospheric effects) and with rotation synthesis (for foreground removal). We also examine the effects that configuration has on calibratability using instantaneous redundancy. We find that improved imaging with sub-aperture sampling via “off-grid” antennas and increased angular resolution via far-flung “outrigger” antennas is possible with a redundantly calibratable array configuration. 10. Configuration and Data Management Process and the System Safety Professional Science.gov (United States) Shivers, Charles Herbert; Parker, Nelson C. (Technical Monitor) 2001-01-01 This article presents a discussion of the configuration management (CM) and the Data Management (DM) functions and provides a perspective of the importance of configuration and data management processes to the success of system safety activities. The article addresses the basic requirements of configuration and data management generally based on NASA configuration and data management policies and practices, although the concepts are likely to represent processes of any public or private organization's well-designed configuration and data management program. 11. Driving spin transition at interface: Role of adsorption configurations Science.gov (United States) Zhang, Yachao 2018-01-01 A clear insight into the electrical manipulation of molecular spins at interface is crucial to the design of molecule-based spintronic devices. Here we report on the electrically driven spin transition in manganocene physisorbed on a metallic surface in two different adsorption configurations predicted by ab initio techniques, including a Hubbard-U correction at the manganese site and accounting for the long-range van der Waals interactions. We show that the application of an electric field at the interface induces a high-spin to low-spin transition in the flat-lying manganocene, while it could hardly alter the high-spin ground state of the standing-up molecule. This phenomenon cannot be explained by either the molecule-metal charge transfer or the local electron correlation effects. We demonstrate a linear dependence of the intra-molecular spin-state splitting on the energy difference between crystal-field splitting and on-site Coulomb repulsion. After considering the molecule-surface binding energy shifts upon spin transition, we reproduce the obtained spin-state energetics. We find that the configuration-dependent responses of the spin-transition originate from the binding energy shifts instead of the variation of the local ligand field. Through these analyses, we obtain an intuitive understanding of the effects of molecule-surface contact on spin-crossover under electrical bias. 12. High-Fidelity Multidisciplinary Design Optimization of Aircraft Configurations Science.gov (United States) Martins, Joaquim R. R. A.; Kenway, Gaetan K. W.; Burdette, David; Jonsson, Eirikur; Kennedy, Graeme J. 2017-01-01 To evaluate new airframe technologies we need design tools based on high-fidelity models that consider multidisciplinary interactions early in the design process. The overarching goal of this NRA is to develop tools that enable high-fidelity multidisciplinary design optimization of aircraft configurations, and to apply these tools to the design of high aspect ratio flexible wings. We develop a geometry engine that is capable of quickly generating conventional and unconventional aircraft configurations including the internal structure. This geometry engine features adjoint derivative computation for efficient gradient-based optimization. We also added overset capability to a computational fluid dynamics solver, complete with an adjoint implementation and semiautomatic mesh generation. We also developed an approach to constraining buffet and started the development of an approach for constraining utter. On the applications side, we developed a new common high-fidelity model for aeroelastic studies of high aspect ratio wings. We performed optimal design trade-o s between fuel burn and aircraft weight for metal, conventional composite, and carbon nanotube composite wings. We also assessed a continuous morphing trailing edge technology applied to high aspect ratio wings. This research resulted in the publication of 26 manuscripts so far, and the developed methodologies were used in two other NRAs. 1 13. Evaluation of Sensor Configurations for Robotic Surgical Instruments Directory of Open Access Journals (Sweden) Jesús M. Gómez-de-Gabriel 2015-10-01 Full Text Available Designing surgical instruments for robotic-assisted minimally-invasive surgery (RAMIS is challenging due to constraints on the number and type of sensors imposed by considerations such as space or the need for sterilization. A new method for evaluating the usability of virtual teleoperated surgical instruments based on virtual sensors is presented. This method uses virtual prototyping of the surgical instrument with a dual physical interaction, which allows testing of different sensor configurations in a real environment. Moreover, the proposed approach has been applied to the evaluation of prototypes of a two-finger grasper for lump detection by remote pinching. In this example, the usability of a set of five different sensor configurations, with a different number of force sensors, is evaluated in terms of quantitative and qualitative measures in clinical experiments with 23 volunteers. As a result, the smallest number of force sensors needed in the surgical instrument that ensures the usability of the device can be determined. The details of the experimental setup are also included. 14. Evaluation of Sensor Configurations for Robotic Surgical Instruments. Science.gov (United States) Gómez-de-Gabriel, Jesús M; Harwin, William 2015-10-27 Designing surgical instruments for robotic-assisted minimally-invasive surgery (RAMIS) is challenging due to constraints on the number and type of sensors imposed by considerations such as space or the need for sterilization. A new method for evaluating the usability of virtual teleoperated surgical instruments based on virtual sensors is presented. This method uses virtual prototyping of the surgical instrument with a dual physical interaction, which allows testing of different sensor configurations in a real environment. Moreover, the proposed approach has been applied to the evaluation of prototypes of a two-finger grasper for lump detection by remote pinching. In this example, the usability of a set of five different sensor configurations, with a different number of force sensors, is evaluated in terms of quantitative and qualitative measures in clinical experiments with 23 volunteers. As a result, the smallest number of force sensors needed in the surgical instrument that ensures the usability of the device can be determined. The details of the experimental setup are also included. 15. Driving reconnection in sheared magnetic configurations with forced fluctuations Science.gov (United States) Pongkitiwanichakul, Peera; Makwana, Kirit D.; Ruffolo, David 2018-02-01 We investigate reconnection of magnetic field lines in sheared magnetic field configurations due to fluctuations driven by random forcing by means of numerical simulations. The simulations are performed with an incompressible, pseudo-spectral magnetohydrodynamics code in 2D where we take thick, resistively decaying, current-sheet like sheared magnetic configurations which do not reconnect spontaneously. We describe and test the forcing that is introduced in the momentum equation to drive fluctuations. It is found that the forcing does not change the rate of decay; however, it adds and removes energy faster in the presence of the magnetic shear structure compared to when it has decayed away. We observe that such a forcing can induce magnetic reconnection due to field line wandering leading to the formation of magnetic islands and O-points. These reconnecting field lines spread out as the current sheet decays with time. A semi-empirical formula is derived which reasonably explains the formation and spread of O-points. We find that reconnection spreads faster with stronger forcing and longer correlation time of forcing, while the wavenumber of forcing does not have a significant effect. When the field line wandering becomes large enough, the neighboring current sheets with opposite polarity start interacting, and then the magnetic field is rapidly annihilated. This work is useful to understand how forced fluctuations can drive reconnection in large scale current structures in space and astrophysical plasmas that are not susceptible to reconnection. 16. Evaluation of Sensor Configurations for Robotic Surgical Instruments Science.gov (United States) Gómez-de-Gabriel, Jesús M.; Harwin, William 2015-01-01 Designing surgical instruments for robotic-assisted minimally-invasive surgery (RAMIS) is challenging due to constraints on the number and type of sensors imposed by considerations such as space or the need for sterilization. A new method for evaluating the usability of virtual teleoperated surgical instruments based on virtual sensors is presented. This method uses virtual prototyping of the surgical instrument with a dual physical interaction, which allows testing of different sensor configurations in a real environment. Moreover, the proposed approach has been applied to the evaluation of prototypes of a two-finger grasper for lump detection by remote pinching. In this example, the usability of a set of five different sensor configurations, with a different number of force sensors, is evaluated in terms of quantitative and qualitative measures in clinical experiments with 23 volunteers. As a result, the smallest number of force sensors needed in the surgical instrument that ensures the usability of the device can be determined. The details of the experimental setup are also included. PMID:26516863 17. Techno-economic analysis of biofuel production considering logistic configurations. Science.gov (United States) Li, Qi; Hu, Guiping 2016-04-01 In the study, a techno-economic analysis method considering logistic configurations is proposed. The economic feasibility of a low temperature biomass gasification pathway and an integrated pathway with fast pyrolysis and bio-oil gasification are evaluated and compared with the proposed method in Iowa. The results show that both pathways are profitable, biomass gasification pathway could achieve an Internal Rate of Return (IRR) of 10.00% by building a single biorefinery and integrated bio-oil gasification pathway could achieve an IRR of 3.32% by applying decentralized supply chain structure. A Monte-Carlo simulation considering interactions among parameters is also proposed and conducted, which indicates that both pathways are at high risk currently. Copyright © 2016 Elsevier Ltd. All rights reserved. 18. Design of materials configurations for enhanced phononic and electronic properties Science.gov (United States) Daraio, Chiara The discovery of novel nonlinear dynamic and electronic phenomena is presented for the specific cases of granular materials and carbon nanotubes. This research was conducted for designing and constructing optimized macro-, micro- and nano-scale structural configurations of materials, and for studying their phononic and electronic behavior. Variation of composite arrangements of granular elements with different elastic properties in a linear chain-of-sphere, Y-junction or 3-D configurations led to a variety of novel phononic phenomena and interesting physical properties, which can be potentially useful for security, communications, mechanical and biomedical engineering applications. Mechanical and electronic properties of carbon nanotubes with different atomic arrangements and microstructures were also investigated. Electronic properties of Y-junction configured carbon nanotubes exhibit an exciting transistor switch behavior which is not seen in linear configuration nanotubes. Strongly nonlinear materials were designed and fabricated using novel and innovative concepts. Due to their unique strongly nonlinear and anisotropic nature, novel wave phenomena have been discovered. Specifically, violations of Snell's law were detected and a new mechanism of wave interaction with interfaces between NTPCs (Nonlinear Tunable Phononic Crystals) was established. Polymer-based systems were tested for the first time, and the tunability of the solitary waves speed was demonstrated. New materials with transformed signal propagation speed in the manageable range of 10-100 m/s and signal amplitude typical for audible speech have been developed. The enhancing of the mitigation of solitary and shock waves in 1-D chains were demonstrated and a new protective medium was designed for practical applications. 1-D, 2-D and 3-D strongly nonlinear system have been investigated providing a broad impact on the whole area of strongly nonlinear wave dynamics and creating experimental basis for new 19. Risk-based configuration control system: Analysis and approaches International Nuclear Information System (INIS) Samanta, P.K.; Kim, I.S.; Lofgren, E.V.; Vesely, W.E. 1990-01-01 This paper presents an analysis of risks associated with component outage configurations during power operation of a nuclear power plant and discusses approaches and strategies for developing a risk-based configuration control system. A configuration, as used here, is a set of component states. The objective of risk-based configuration control is to detect and control plant configurations using a risk-perspective. The configuration contributions to core-melt frequency and core-melt probability are studied for two plants. Large core-melt frequency can be caused by configurations and there are a number of such configurations that are not currently controlled by technical specifications. However, the expected frequency of occurrence of the impacting configurations is small and the actual core-melt probability contributions are also generally small. Effective strategies and criteria for controlling configuration risks are presented. Such control strategies take into consideration the risks associated with configurations, the nature and characteristics of the configuration risks, and also the practical considerations such as adequate repair times and/or options to transfer to low risk configurations. Alternative types of criteria are discussed that are not overly restrictive to result in unnecessary plant shutdown, but rather motivates effective test and maintenance practices that control risk-significant configurations to allow continued operation with an adequate margin to meet challenges to safety 20. Risk-based configuration control system: Analysis and approaches International Nuclear Information System (INIS) Samanta, P.K.; Vesely, W.E.; Kim, I.S.; Lofgren, E.V. 1989-01-01 This paper presents an analysis of risks associated with component outage configurations during power operation of a nuclear power plant and discusses approaches and strategies for developing a risk-based configuration control system. A configuration, as used here, is a set of component states. The objective of risk-based configuration control is to detect and control plant configurations using a risk-perspective. The configuration contributions to core-melt frequency and core-melt probability are studied for two plants. Large core-melt frequency can be caused by configurations and there are a number of such configurations that are not currently controlled by technical specifications. However, the expected frequency of occurrence of the impacting configurations is small and the actual core-melt probability contributions are also generally small. Effective strategies and criteria for controlling configuration risks are presented. Such control strategies take into consideration the risks associated with configurations, the nature and characteristics of the configuration risks, and also the practical considerations such as adequate repair times and/or options to transfer to low risk configurations. Alternative types of criteria are discussed that are not overly restrictive to result in unnecessary plant shutdown, but rather motivates effective tests and maintenance practices that control; risk-significant configurations to allow continued operation with an adequate margin to meet challenges to safety. 3 refs., 7 figs., 2 tabs 1. Risk-based configuration control system: Analysis and approaches International Nuclear Information System (INIS) Samanta, P.K.; Kim, I.S.; Vesely, W.E.; Lofgren, E.V. 1989-01-01 This paper presents an evaluation of the configuration risks associated with the operation of a nuclear power plant and the approaches to control these risks using risk-based configuration control considerations. In that context, the actual and maximum potential configuration risks at a plant are analyzed and the alternative types criteria for a risk-based configuration control systems are described. The risk-based configuration calculations which are studied here focus on the core-melt frequency impacts from given plant configurations. By calculating the core-melt frequency for given configurations, the configurations which cause large core-melt frequency increases can be identified and controlled. The duration time in which the configuration can exist can then be limited or the core-melt frequency level associated with the configuration can be reduced by various actions. Furthermore, maintenances and tests can be scheduled to avoid the configurations which cause large core-melt frequency increases. Present technical specifications do not control many of these configurations which can cause large core-melt frequency increases but instead focus on many risk-unimportant allowed outage times. Hence, risk-based configuration management can be effectively used to reduce core-melt frequency associated risks at a plant and at the same time can provide flexibility in plant operation. The alternative strategies for controlling the core-melt frequency and other risk contributions include: (1) controlling the increased risk level which is associated with the configuration; (2) controlling the individual configuration risk which is associated with a given duration of a configuration; (3) controlling the time period configuration risk from configurations which occur in a time period 2. ATLAS software configuration and build tool optimisation Science.gov (United States) Rybkin, Grigory; Atlas Collaboration 2014-06-01 ATLAS software code base is over 6 million lines organised in about 2000 packages. It makes use of some 100 external software packages, is developed by more than 400 developers and used by more than 2500 physicists from over 200 universities and laboratories in 6 continents. To meet the challenge of configuration and building of this software, the Configuration Management Tool (CMT) is used. CMT expects each package to describe its build targets, build and environment setup parameters, dependencies on other packages in a text file called requirements, and each project (group of packages) to describe its policies and dependencies on other projects in a text project file. Based on the effective set of configuration parameters read from the requirements files of dependent packages and project files, CMT commands build the packages, generate the environment for their use, or query the packages. The main focus was on build time performance that was optimised within several approaches: reduction of the number of reads of requirements files that are now read once per package by a CMT build command that generates cached requirements files for subsequent CMT build commands; introduction of more fine-grained build parallelism at package task level, i.e., dependent applications and libraries are compiled in parallel; code optimisation of CMT commands used for build; introduction of package level build parallelism, i. e., parallelise the build of independent packages. By default, CMT launches NUMBER-OF-PROCESSORS build commands in parallel. The other focus was on CMT commands optimisation in general that made them approximately 2 times faster. CMT can generate a cached requirements file for the environment setup command, which is especially useful for deployment on distributed file systems like AFS or CERN VMFS. The use of parallelism, caching and code optimisation significantly-by several times-reduced software build time, environment setup time, increased the efficiency of 3. EMMA: a new paradigm in configurable software International Nuclear Information System (INIS) Nogiec, J. M.; Trombly-Freytag, K. 2017-01-01 EMMA is a framework designed to create a family of configurable software systems, with emphasis on extensibility and flexibility. It is based on a loosely coupled, event driven architecture. The EMMA framework has been built upon the premise of composing software systems from independent components. It opens up opportunities for reuse of components and their functionality and composing them together in many different ways. As a result, it provides the developer of test and measurement applications with a lightweight alternative to microservices, while sharing their various advantages, including composability, loose coupling, encapsulation, and reuse. 4. EMMA: a new paradigm in configurable software Science.gov (United States) Nogiec, J. M.; Trombly-Freytag, K. 2017-10-01 EMMA is a framework designed to create a family of configurable software systems, with emphasis on extensibility and flexibility. It is based on a loosely coupled, event driven architecture. The EMMA framework has been built upon the premise of composing software systems from independent components. It opens up opportunities for reuse of components and their functionality and composing them together in many different ways. It provides the developer of test and measurement applications with a lightweight alternative to microservices, while sharing their various advantages, including composability, loose coupling, encapsulation, and reuse. 5. Lidar configurations for wind turbine control DEFF Research Database (Denmark) Mirzaei, Mahmood; Mann, Jakob 2016-01-01 Lidar sensors have proved to be very beneficial in the wind energy industry. They can be used for yaw correction, feed-forward pitch control and load verification. However, the current lidars are expensive. One way to reduce the price is to use lidars with few measurement points. Finding the best...... by the lidar is compared against the effective wind speed on a wind turbine rotor both theoretically and through simulations. The study provides some results to choose the best configuration of the lidar with few measurement points.... 6. Discrete Morse functions for graph configuration spaces International Nuclear Information System (INIS) Sawicki, A 2012-01-01 We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear. (paper) 7. Improving motorcycle conspicuity through innovative headlight configurations OpenAIRE RANCHET, Maud; CAVALLO, Viola; DANG, Nguyen-Thong; VIENNE, Fabrice 2016-01-01 L'article décrit une expérimentation qui évalue différentes configurations de feux avant de moto susceptibles d'améliorer la détectabilité des motocycles dans des environnements comportant des distracteurs visuels (constitués par les feux de circulation diurne des voitures). Most motorcycle crashes involve another vehicle that violated the motorcycle's right-of-way at an inter-section. Two kinds of perceptual failures of other road users are often the cause of such accidents:motorcycle-det... 8. Optimal configuration for programmable Moessbauer experiments Energy Technology Data Exchange (ETDEWEB) Pasquevich, Gustavo A; Veiga, Alejandro L; Zelis, Pedro Mendoza; Sanchez, Francisco H, E-mail: [email protected] [Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (Argentina) 2010-03-01 Based on channel independency of recently developed Moessbauer instrumentation an approximation to optimal configuration of experiments is presented. The analysis relies on the presumption that all the available channels of the spectrum are not equally efficient for a given experimental application. A quantification of this concept is presented and a method for different channel layout comparison is proposed. The optimization of recorded spectra is important in dynamic experiments where efficiency in data taking imposes feasibility limits as well as in static applications as a way of reducing experimental time. 9. Kinetic Stability of the Field Reversed Configuration International Nuclear Information System (INIS) E.V. Belova; R.C. Davidson; H. Ji; and M. Yamada 2002-01-01 New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). The FRC is an innovative confinement approach that offers a unique fusion reactor potential because of its compact and simple geometry, translation properties, and high plasma beta. One of the most important issues is FRC stability with respect to low-n (toroidal mode number) MHD modes. There is a clear discrepancy between the predictions of standard MHD theory that many modes should be unstable on the MHD time scale, and the observed macroscopic resilience of FRCs in experiments 10. Configuration Management for eXtreme Programming DEFF Research Database (Denmark) Asklund, U.; Bendix, Lars Gotfred; Ekman, T. 2003-01-01 Extreme programming (XP) is a software development method that prescribes the use of 12 different practices. Four of these practices (collective code ownership, continuous integration, small releases and refactoring) can indeed be given good support by the use of simple configuration management (CM......) techniques. We report on our experience in providing many groups of novice developers with CM education, processes and tools to support the four CM-related XP practices in their projects. True to the spirit of XP both education and processes are very lightweight and we found that it was sufficient to focus... 11. Metasurface Cloaks for Large Cylindrical Cluster Configurations DEFF Research Database (Denmark) Arslanagic, Samel; Yakovlev, A.B. 2014-01-01 Here, we investigate the performance of metasurfaces used for cloaking of cluster configurations formed by different arrangements of multiple dielectric cylinders and excited by an electric line source. While a suitably designed metasurface can be used to effectively cloak isolated electrically...... small cylinders, we demonstrate that even electrically large clusters of such particles can be cloaked by covering its constituent cylinders with the metasurface cloaks. This holds for densely packed cylinders due to significantly reduced coupling by the presence of the cloaks. The results may... 12. Instant Apple Configurator how-to CERN Document Server Edge, Charles 2013-01-01 Filled with practical, step-by-step instructions and clear explanations for the most important and useful tasks. Get the job done and learn as you go. A how-To book with practical recipes accompanied with rich screenshots for easy comprehension.This book follows the Packt How-to approach, offering an informative yet practical guide that is easy to understand. The book takes a meticulous approach to providing quick and simple recipe-based solutions for security and deployment of iOS devices.""Instant Apple iOS Configurator Utility How-to"" book is ideal for anyone with a working knowledge in iO 13. Resistive instabilities in general toroidal plasma configurations International Nuclear Information System (INIS) Glasser, A.H.; Greene, J.M.; Johnson, J.L. 1975-01-01 Previous work by Johnson and Greene on resistive instabilities is extended to finite-pressure configurations. The Mercier criterion for the stability of the ideal magnetohydrodynamic interchange mode is rederived, the generalization of the earlier stability criterion for the resistive interchange mode is obtained, and a relation between the two is noted. Conditions for tearing mode instability are recovered with the growth rate scaling with the resistivity in a more complicated manner than eta 3 / 5 . Nyquist techniques are used to show that favorable average curvature can convert the tearing mode into an overstable mode and can often stabilize it 14. Remote Sampler Demonstration Isolok Configuration Test International Nuclear Information System (INIS) Kelly, Steve E. 2016-01-01 The accuracy and precision of a new Isolok sampler configuration was evaluated using a recirculation flow loop. The evaluation was performed using two slurry simulants of Hanford high-level tank waste. Through testing, the capability of the Isolok sampler was evaluated. Sample concentrations were compared to reference samples that were simultaneously collected by a two-stage Vezin sampler. The capability of the Isolok sampler to collect samples that accurately reflect the contents in the test loop improved – biases between the Isolok and Vezin samples were greatly reduce for fast settling particles. 15. Business cases for product configuration systems DEFF Research Database (Denmark) Shafiee, Sara; Kristjansdottir, Katrin; Hvam, Lars In the recent years, product configuration systems (PCSs) have received greater attention from industries providing customized products as a response to increased demand to fulfil diverse customers’ needs for customized products. Before developing a PCS, a well-established business case has...... to be made in order to secure the success and delivery of the project as it will increase the commitment from the business side. This paper presents a framework for supporting the development of business cases for PCSs and discusses the experiences from multiple case studies benefiting from the suggested... 16. Configuration management in nuclear power plants International Nuclear Information System (INIS) 2003-01-01 Configuration management (CM) is the process of identifying and documenting the characteristics of a facility's structures, systems and components of a facility, and of ensuring that changes to these characteristics are properly developed, assessed, approved, issued, implemented, verified, recorded and incorporated into the facility documentation. The need for a CM system is a result of the long term operation of any nuclear power plant. The main challenges are caused particularly by ageing plant technology, plant modifications, the application of new safety and operational requirements, and in general by human factors arising from migration of plant personnel and possible human failures. The IAEA Incident Reporting System (IRS) shows that on average 25% of recorded events could be caused by configuration errors or deficiencies. CM processes correctly applied ensure that the construction, operation, maintenance and testing of a physical facility are in accordance with design requirements as expressed in the design documentation. An important objective of a configuration management program is to ensure that accurate information consistent with the physical and operational characteristics of the power plant is available in a timely manner for making safe, knowledgeable, and cost effective decisions with confidence. Currently, the nuclear industry and governmental organizations are showing an increasing interest in the implementation of this process as an effective way of limiting configuration errors and related risks. In this report the necessary attributes of a good operational CM are identified. It is recognized and emphasized that a CM is one aspect of the overall management system. Nevertheless, this is an important part of managerial activity focused on the compliance of knowledge of the plant personnel, plant documentation and records with the state of the plant technology. The concepts developed in this report present a basic approach to CM, taking into 17. Magnetocrystalline and configurational anisotropies in Fe nanostructures International Nuclear Information System (INIS) Vavassori, P.; Bisero, D.; Carace, F.; Liberati, M.; Di Bona, A.; Gazzadi, G.C.; Valeri, S. 2005-01-01 Arrays of single-crystal Fe micron and submicron squares and disks, have been fabricated using a focused ion beam apparatus from a film epitaxially grown on MgO. The hysteresis loops of the patterned areas differ from those of the continuous film as a consequence of the different reversal determined by the lateral confinement of the Fe film. By means of modulated field magneto-optical anisometry measurements we studied the symmetry and the strength of the overall anisotropy. For the smaller square elements we observed a higher-order term in the overall anisotropy with eightfold symmetry arising from the configurational contribution 18. Remote Sampler Demonstration Isolok Configuration Test Energy Technology Data Exchange (ETDEWEB) Kelly, Steve E. [Washington River Protection Solutions, LLC, Richland, WA (United States) 2016-06-08 The accuracy and precision of a new Isolok sampler configuration was evaluated using a recirculation flow loop. The evaluation was performed using two slurry simulants of Hanford high-level tank waste. Through testing, the capability of the Isolok sampler was evaluated. Sample concentrations were compared to reference samples that were simultaneously collected by a two-stage Vezin sampler. The capability of the Isolok sampler to collect samples that accurately reflect the contents in the test loop improved – biases between the Isolok and Vezin samples were greatly reduce for fast settling particles. 19. MHD-stability of the Scyllac configuration International Nuclear Information System (INIS) Berge, G.; Freidberg, J.P. 1975-01-01 The results of a stability analysis for a diffuse high-β, l=1 helical configuration are presented. It is shown that there exists a gross m=1 mode whose properties are quite similar to those predicted by the sharp-boundary model. In addition, two new classes of m=1 modes are found, one localized on the inside of the plasma, the other one outside. For any monotonic pressure profile, these modes are unstable although their growth rates are very small. A further study suggests that small changes in the profile may stabilize these modes. (author) 20. Complexity of Configurators Relative to Integrations and Field of Application DEFF Research Database (Denmark) Kristjansdottir, Katrin; Shafiee, Sara; Battistello, Loris . Moreover, configurators are commonly integrated to various IT systems within companies. The complexity of configurators is an important factor when it comes to performance, development and maintenance of the systems. A direct comparison of the complexity based on the different application...... integrations to other IT systems. The research method adopted in the paper is based on a survey followed with interviews where the unit of analysis is based on operating configurators within a company.......Configurators are applied widely to automate the specification processes at companies. 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http://www.owen-lu.com/robot-arm-desc	Introduction This tutorial deals with the theory and implementation of the control of a 6 degree of freedom robot arm. The main idea is to use a C# form to obtain inputs from the user and send those inputs to MATLAB to perform trajectory calculations. The commands are then sent in regular intervals through Bluetooth to Arduino which then sends individual axis commands to a PWM driver via I2C. Components As it turns out, in this system most of the components could be bought from an electronics store. The main components are listed below. 1. Arduino Pro Mini (Microcontroller) 2. PCA9685 (16-Channel PWM Driver) 3. HC-06 (Bluetooh Module) 4. Variable DC step-down (~6V at 6A) 5. UF5404 (High current diodes) 6. 6x hobby servos (High torque metal geared) 7. Robot Arm Chassis/Claw Note: The main issue that must be dealt with is the potential high current draw at 6V. Most 6V supplies cannot supply such large peak current draws and therefore voltage regulators will be used to drop a 12V DC source to 6V. In my case, I was able to obtain two 3A variable voltage regulators and connect the outputs together using diodes to isolate the supplies from each other. The idea is that if the current draw is too large, the other regulator will share the load. 6A total was chosen since each servo was budgeted approximately 1A (this is a rule of thumb). The reason why the variable voltage aspect is important is due to possibility that the two diodes in OR configuration (diode OR gate) will have different voltage drops. Schematic Below is the schematic of the hardware connections between the Arduino, HC-06, voltage regulators and PCA8685 driver. The connections between the different components can be done directly as each of the boards have necessary protection circuitry and logic level shifts. Note that the servos are not shown Communication This section detail the implementation of how communication is done from C# to Arduino via Bluetooth and C# to MATLAB. C# to Arduino (Bluetooth) In order to use Bluetooth communication, you must first pair your HC-06 or other Bluetooth device to your computer. The computer will show it has a COM port device which is the exact same way an Arduino will show up. The relevant default settings for the HC-06 are shown below: 1. Baud Rate: 9600 (8N1) 2. PIN: 1234 3. Name: HC-06 8-N-1 is a common notation that specifies the format of the data coming in and going out. This means that 8 bits with No parity and 1 stop bit are being sent in discrete packets. A baud rate of 9600 is indicative of how fast the transfer occurs 9600 meaning 9600 bits per second. This creates a problem, as 8 bits necessarily implies that only a number between 0-255 can be sent in one packet. However, if we are controlling angles of servos, then only numbers between 0-180 representing the rotation in degrees is necessary. Implementation The idea is that a start byte indicating that a command is beginning is sent first to the Arduino. The Arduino then listens for the information until it sees another start byte in which case it realizes another command is being sent. In our case, there are 6 servos, meaning 6 numbers from 0-180 are sent in each command. The data sent to Arduino is summarized in a list below. 1. Start byte (255) 2. Axis command 0 (0-180) 3. Axis command 1 (0-180) 4. Axis command 2 (0-180) 5. Axis command 3 (0-180) 6. Axis command 4 (0-180) 7. Axis command 5 (0-180) Assuming that you know the basics of C# using the Toolbox for Forms, just add a "SerialPort" to the form and configure it to 9600 8N1. Note that if you used AT commands with the HC-06 you can change the baud rate. In my case I used 19200 baud rate. The settings for reference are given below. Then the knitty gritty around displaying the COM ports and selecting them is needed, the code in the form of a Visual Studio solution will be provided at the end of the tutorial :). The portion of the code to look for is when the transmission begins in the serial port. In theory, you can send the bytes in any order, and u can also send any number of bytes during one command. The snippet is given below so you know what to look for. Following the C# Master Code, the Arduino Slave code for receiving commands is also given. The main idea is that the commands from C# are stored in the Arduino after these key executions are complete. C# Master Code byte[] TxBytes = new byte[7]; // create vector of new bytes // send all bytes TxBytes[0] = Convert.ToByte(255); TxBytes[1] = Convert.ToByte(vScrollBar1.Value); TxBytes[2] = Convert.ToByte(vScrollBar2.Value); TxBytes[3] = Convert.ToByte(vScrollBar3.Value); TxBytes[4] = Convert.ToByte(vScrollBar4.Value); TxBytes[5] = Convert.ToByte(vScrollBar5.Value); TxBytes[6] = Convert.ToByte(vScrollBar6.Value); if (serCOM.IsOpen == true) { // write all the bytes for (int i = 0; i < 7; i++) { serCOM.Write(TxBytes, i, 1); } } } Arduino Slave Code void loop() { // receive command from the serial if(Serial.available() >= 7) // wait for sufficient data { byte inByte = Serial.read(); // get incoming byte if( inByte == 255 ) // if it is a start byte read all the data { for(int i = 0; i < 6; i++) { } } } } Note that once the Arduino is hooked up to the HC-06, transmission of data can already happen. As long as the baud rate of the HC-06 and the Arduino are the same the communication will work. It is a good idea to just test the HC-06 and Arduino communication at this point. Trajectory Generation The whole point of offloading calculations to MATLAB is that there are many easy to use functions that make MATLAB programming a lot easier than writing functions from scratch and working with different types of arrays or lists. That being said, it is of course possible to implement these calculations without MATLAB if you either don't have it or just don't want to use it. The idea behind trajectory generation is that you know a path that you wish to move along as well as the speed that you wish to move along it. The question is, what are commands that need to be sent in order for the point of interest, often called an "end-effector" such as a claw or milling bit move along that path at a specified velocity profile. In this case, we will do a simple line between two points, at a constant velocity. My tutorial here on trajectory generation covers lines and general curves. Note that in these tutorials, a method in which velocity ramps upwards is used. This is necessary in precision systems, however servo commands are very low resolution and velocity "ramping" has no real benefit. Assuming that the trajectory is now planned (it should come out as a vector of X,Y components) we now work on deriving the relationships. The general approach is to linearize the system in two variables and then invert the system explicitly and incrementally to derive the path. Suppose we have a robot with 3 linkages, and 3 motors placed at the origin, $$x_1,x_2$$. The equations describing $$x_1,x_2$$ are given below. Let us suppose that $$x_2$$ is the end effector for now in order to avoid a redundant degree of freedom. $$x_1 = (L_1 cos(\theta_1),L_1 sin(\theta_1))$$ $$x_2 = (L_2 cos(\theta_1 + \theta_2),L_2 sin(\theta_1 + \theta_2)) + x_1$$ Now linearize $$x_2$$ $$\Delta x_2 \approx \frac{dx_2}{d\theta_1} \Delta \theta_1 + \frac{dx_2}{d\theta_2} \Delta \theta_2$$ Where $$\Delta x_2 = x_{2,n} - x_{2,n-1}$$ $$x_{2,0} = x_2(\theta_{1,0} ,\theta_{2,0})$$ Finally we can write the matrix equation to be solved for each increment $$\begin{bmatrix} u_x & v_x \\ u_y & v_y \end{bmatrix} \begin{bmatrix} \Delta \theta_1 \\ \Delta \theta_2 \end{bmatrix} = \begin{bmatrix} \Delta x_{2,x} \\ \Delta x_{2,y} \end{bmatrix}$$ The critical MATLAB code to generate a path between $$x_0$$ and $$x_1$$ at some velocity is shown below. Matlab Code x = @(t1,t2) [ L2cos(t1+t2)+L1cos(t1); L2sin(t1+t2)+L1sin(t1)]; % Suppose the plot was a line from x0 to 10,10 split into 100 pieces x0 = x(th1,th2); x1 = [px,py]'; T = norm(x1-x0)/vel; % time to complete motion N = round(T/(1/50)); % Divide time by the update time posx = [linspace(x0(1),x1(1),N)' linspace(x0(2),x1(2),N)']; inposx = diff(posx); n = length(inposx); % store all angles over time tVector = zeros(n+1,2); tVector(1,:) = [th1,th2]; for i=1:n % solve for the incremental angle A = [ dth1(tVector(i,1),tVector(i,2)) dth2(tVector(i,1),tVector(i,2))]; incth = linsolve(A,inposx(i,:)'); % Add incremental angle to get absolute angle tVector(i+1,:) = tVector(i,:) + incth'; end C# Code for MATLAB First I recommend that you look at MATLAB's documentation on calling functions from C#, you can copy paste the code and it will work provided you've added "Matlab Application Type Library" via the References tab. I found that one line was buggy which was the line specifying the directory, basically an extra single quote is added to the address shown below. matlab.Execute(@"cd 'C:\Users\Owen\Documents\MATLAB\ROBOT ARM'"); The critical C# code that gets an array from MATLAB and stores it to a C# variable is shown below. object result = null; //// Call the MATLAB function myfunc matlab.Feval("gentraj", 1, out result, Convert.ToDouble(txtServo2.Text), Convert.ToDouble(txtServo3.Text), Convert.ToDouble(px), Convert.ToDouble(py), Convert.ToDouble(txtSpeed.Text)); // Convert.ToDouble(txtSpeed.Text) var res = (result as object[]).Select(x => (double[,])x).ToArray(); object t_angArray = res.GetValue(0); angArray = (double[,])t_angArray; Conclusion Now that you have had a basic run through of the methods used, hopefully you can examine the code and figure out what is going on. Below is the source code for each of the components. It is assumed that you have installed the PCA9685 library. Adafruit has very good documentation and instructions online on how you can get the driver working. C# Visual Studio SLN Arduino Code MATLAB Functions	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5312061309814453, "perplexity": 1821.9506655343002}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986664662.15/warc/CC-MAIN-20191016041344-20191016064844-00084.warc.gz"}
http://www.maa.org/programs/faculty-and-departments/course-communities/spherical-coordinates	# Spherical Coordinates The authors point out the problem with using angles $\phi$ and $\theta$ in spherical coordinates in the opposite way that they are used in other sciences, especially physics and engineering. They explain why this poses a larger problem for students than is generally acknowledged. Then they propose to switch the use of these angles, which could relatively easily be accomplished by adjusting current calculus textbooks. Identifier: http://www.math.oregonstate.edu/bridge/papers/CMJspherical.pdf Rating: Creator(s): Tevian Dray and Corinne A. Manogue Cataloger: Tevian Dray Publisher: College Mathematics Journal Rights: Mathematical Association of America	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6616109013557434, "perplexity": 983.9750513237065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396106.25/warc/CC-MAIN-20160624154956-00134-ip-10-164-35-72.ec2.internal.warc.gz"}
https://timpani.wordpress.com/	## test LaTeX $i\hbar\frac{\partial}{\partial t}\left\|\Psi(t)\right>=H\left\|\Psi(t)\right>$ $\eta_{k,i}(x) \equiv \frac{\displaystyle{\prod_{{\scriptstyle j=0}\atop{\scriptstyle j\ne 1}}^{3}(x-x_{k+j})}}{\displaystyle{\prod_{{\scriptstyle j=0}\atop{\scriptstyle j\ne 1}}^{3}(x_{k+i}-x_{k+j})}}$ $\left< A \| B \right>$ ping o~ ## Hello world! Welcome to WordPress.com. This is your first post. Edit or delete it and start blogging!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 3, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16091135144233704, "perplexity": 25730.943059239715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510867.6/warc/CC-MAIN-20181016201314-20181016222814-00333.warc.gz"}
https://www.studentclan.com/2018/02/27/elementary-number-theory-and-its-application-6th-edition-by-kenneth-h-rosen-exercises-1-1-14/	# Elementary Number Theory and Its Application, 6th Edition by Kenneth H. Rosen Exercises 1.1.14 14. Show that $[2x] + [2y] >= [x] + [y] + [x + y]$ whenever x and y are real numbers. Solution: We have to show that $[2x]+[2y]>=[x]+[y]+[x+y]$ Where $x,y$ are real numbers We write $x,y$ as $x=n+\epsilon$ $y=m+\delta$ Where $n,m$ are integers and $\epsilon,\delta$ are non-negative real numbers less than 1. There are two possibilities for the right hand side. $n+m+(n+m)=2n+2m$ Or $n+m+(n+m+1)=2n+2m+1$ If $\epsilon+\delta>=1$ There are two possibilities for the left hand side. $\lceil2x\rceil=\begin{cases} 2n & \epsilon<1/2\\ 2n+1 & otherwise \end{cases}$ And $\lceil2y\rceil=\begin{cases} 2m &\delta<1/2\\ 2m+1 & otherwise \end{cases}$ We are trying to prove that the right hand side is always less than or equal to the left hand side. We construct a proof by contradiction and assume that right hand side is greater than left hand side. So the right hand side must be $2n+2m+1$ and the left hand side must be $2n+2m$ But then, $\epsilon+\delta>=1$ So at least one of them must be equal to or greater than $1/2$ So the left hand side cannot equal $2n+2m$ Hence we arrive at a contradiction and end the proof. ## 17 Replies to “Elementary Number Theory and Its Application, 6th Edition by Kenneth H. Rosen Exercises 1.1.14” 1. Hi my friend! I want to say that this post is amazing, nice written and include approximately all important infos. I would like to see more posts like this. 2. Having read this I thought it was rather informative. I appreciate you taking the time and energy to put this article together. I once again find myself spending a significant amount of time both reading and leaving comments. But so what, it was still worth it! 3. An impressive share! I have just forwarded this onto a co-worker who has been doing a little research on this. And he actually ordered me dinner simply because I found it for him… lol. So let me reword this…. Thanks for the meal!! But yeah, thanks for spending some time to discuss this topic here on your web site. 4. I’m not that much of a online reader to be honest but your blogs really nice, keep it up! I’ll go ahead and bookmark your site to come back down the road. Cheers 5. Thanks for finally writing about >Elementary Number Theory and Its Application, 6th Edition by Kenneth H. Rosen Exercises 1.1.14 – Student Clan <Liked it! 6. Hello Dear, are you actually visiting this website on a regular basis, if so after that you will absolutely take pleasant knowledge. 7. Wow that was unusual. I just wrote an extremely long comment but after I clicked submit my comment didn’t appear. Grrrr… well I’m not writing all that over again. Anyways, just wanted to say superb blog! 8. I regard something truly special in this web site . 9. Wow, fantastic blog layout! How long have you been blogging for? you made blogging look easy. The overall look of your website is excellent, let alone the content! 10. Having read this I believed it was rather enlightening. I appreciate you taking the time and energy to put this information together. I once again find myself spending a significant amount of time both reading and commenting. But so what, it was still worth it! 11. Hello i am kavin, its my first time to commenting anyplace, when i read this paragraph i thought i could also create comment due to this sensible post. 12. But wanna tell that this is very useful , Thanks for taking your time to write this. 13. Thank you very much for the content. I wish you continued success. 14. Everything is very open with a clear description of the challenges.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 18, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7555528879165649, "perplexity": 755.2437509464928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323583408.93/warc/CC-MAIN-20211016013436-20211016043436-00357.warc.gz"}
http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/statug_ttest_details14.htm	# The TTEST Procedure #### Two-Independent-Sample Design Define the following notation: ##### Normal Difference (DIST=NORMAL TEST=DIFF) Observations at the first class level are assumed to be distributed as , and observations at the second class level are assumed to be distributed as , where , , , and are unknown. The within-class-level mean estimates ( and ), standard deviation estimates ( and ), standard errors ( and ), and confidence limits for means and standard deviations are computed in the same way as for the one-sample design in the section Normal Data (DIST=NORMAL). The mean difference is estimated by Under the assumption of equal variances (), the pooled estimate of the common standard deviation is The pooled standard error (the estimated standard deviation of assuming equal variances) is The pooled 100(1 – )% confidence interval for the mean difference is The t value for the pooled test is computed as The p-value of the test is computed as Under the assumption of unequal variances (the Behrens-Fisher problem), the unpooled standard error is computed as Satterthwaite’s (1946) approximation for the degrees of freedom, extended to accommodate weights, is computed as The unpooled Satterthwaite 100(1 – )% confidence interval for the mean difference is The t value for the unpooled Satterthwaite test is computed as The p-value of the unpooled Satterthwaite test is computed as When the COCHRAN option is specified in the PROC TTEST statement, the Cochran and Cox (1950) approximation of the p-value of the statistic is the value of p such that where and are the critical values of the t distribution corresponding to a significance level of p and sample sizes of and , respectively. The number of degrees of freedom is undefined when . In general, the Cochran and Cox test tends to be conservative (Lee and Gurland 1975). The 100(1 – )% CI= EQUAL and CI= UMPU confidence intervals for the common population standard deviation assuming equal variances are computed as discussed in the section Normal Data (DIST=NORMAL) for the one-sample design, except replacing by and by . The folded form of the F statistic, , tests the hypothesis that the variances are equal (Steel and Torrie 1980), where A test of is a two-tailed F test because you do not specify which variance you expect to be larger. The p-value (Steel and Torrie 1980) is equal-tailed and is computed as where , , , and are the degrees of freedom that correspond to , , , and , respectively. Note that the p-value is similar to the probability of a greater value under the null hypothesis that , The test is not very robust to violations of the assumption that the data are normally distributed, and thus it is not recommended without confidence in the normality assumption. ##### Lognormal Ratio (DIST=LOGNORMAL TEST=RATIO) The DIST= LOGNORMAL analysis is handled by log-transforming the data and null value, performing a DIST= NORMAL analysis, and then transforming the results back to the original scale. See the section Normal Data (DIST=NORMAL) for the one-sample design for details on how the DIST= NORMAL computations for means and standard deviations are transformed into the DIST= LOGNORMAL results for geometric means and CVs. As mentioned in the section Coefficient of Variation, the assumption of equal CVs on the lognormal scale is analogous to the assumption of equal variances on the normal scale. ##### Normal Ratio (DIST=NORMAL TEST=RATIO) The distributional assumptions, equality of variances test, and within-class-level mean estimates ( and ), standard deviation estimates ( and ), standard errors ( and ), and confidence limits for means and standard deviations are the same as in the section Normal Difference (DIST=NORMAL TEST=DIFF) for the two-independent-sample design. The mean ratio is estimated by No estimates or confidence intervals for the ratio of standard deviations are computed. Under the assumption of equal variances (), the pooled confidence interval for the mean ratio is the Fieller (1954) confidence interval, extended to accommodate weights. Let where is the pooled standard deviation defined in the section Normal Difference (DIST=NORMAL TEST=DIFF) for the two-independent-sample design. If (which occurs when is too close to zero), then the pooled two-sided 100(1 – )% Fieller confidence interval for does not exist. If , then the interval is For the one-sided intervals, let which differ from and only in the use of in place of . If , then the pooled one-sided 100(1 – )% Fieller confidence intervals for do not exist. If , then the intervals are The pooled t test assuming equal variances is the Sasabuchi (1988a, 1988b) test. The hypothesis is rewritten as , and the pooled t test in the section Normal Difference (DIST=NORMAL TEST=DIFF) for the two-independent-sample design is conducted on the original values () and transformed values of with a null difference of 0. The t value for the Sasabuchi pooled test is computed as The p-value of the test is computed as Under the assumption of unequal variances, the unpooled Satterthwaite-based confidence interval for the mean ratio is computed according to the method in Dilba, Schaarschmidt, and Hothorn (2007, the section "Two-sample Problem" on page 20), extended to accommodate weights. The degrees of freedom for the confidence interval are based on the same approximation as in Tamhane and Logan (2004) for the unpooled t test but with the null mean ratio replaced by the maximum likelihood estimate : Let where and are the within-class-level standard deviations defined in the section Normal Difference (DIST=NORMAL TEST=DIFF) for the two-independent-sample design. If (which occurs when is too close to zero), then the unpooled Satterthwaite-based two-sided 100(1 – )% confidence interval for does not exist. If , then the interval is The t test assuming unequal variances is the test derived in Tamhane and Logan (2004). The hypothesis is rewritten as , and the Satterthwaite t test in the section Normal Difference (DIST=NORMAL TEST=DIFF) for the two-independent-sample design is conducted on the original values () and transformed values of with a null difference of 0. The degrees of freedom are computed as The t value for the Satterthwaite-based unpooled test is computed as The p-value of the test is computed as	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9872717261314392, "perplexity": 1556.077990717742}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159570.46/warc/CC-MAIN-20180923173457-20180923193857-00129.warc.gz"}
https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Heat_and_Thermodynamics_(Tatum)/11%3A_Heat_Engines/11.07%3A_A_Useful_Exercise	$$\require{cancel}$$ # 11.7: A Useful Exercise It would probably not be a useful exercise to try to memorise the details of the several heat engine cycles described in this chapter. What probably would be a useful exercise is as follows. Note that in each cycle there are four stages, which, in principle at least (if not always in practice) are well defined and separated one from the next. These stages are described by one or another of an isotherm, an adiabat, an isochor or an isobar. It would probably be a good idea to ask oneself, for each stage in each engine, the values of ∆Q, ∆W and ∆U, noting, of course, that in each case, ∆U = ∆Q + ∆W. In each case take care to note whether heat is added to or lost from the engine , whether the engine does work or whether work is done on it, and whether the internal energy increases or decreases. By doing this, one could then easily determine how much heat is supplied to the engine, and how much net work it does during the cycle, and hence determine the efficiency of the engine. The following may serve as useful guidelines. In these guidelines it is assumed that any work done is reversible, and that (except for the steam engine or Rankine cycle) the working substance may be treated as if it were an ideal gas. Along an isotherm, the internal energy of an ideal gas is unchanged. That is to say, ∆U = 0. The work done (per mole of working substance) will be an expression of the form RT ln(V2/V1), and the heat lost or gained will then be determined by ∆Q + ∆W = 0. Along an adiabat, no heat is gained or lost, so that ∆Q = 0. The expression for the work done per mole will be of the form $$\frac{R\left(T_{1}-T_{2}\right)}{\gamma-1}=\frac{P_{1} V_{1}-P_{2} V_{2}}{\gamma-1}$$ where V is the molar volume. Just be sure to understand whether work is done on or by the engine. The change in the internal energy (be sure to understand whether it is an increase or a decrease) is then given by ∆U = ∆W. Along an isochor, no work is done. That is, ∆W = 0. The heat lost or gained per mole will be of an expression of the form CV(T2T1), where CV is the molar heat capacity at constant volume. The change in the internal energy (be sure to understand whether it is an increase or a decrease) is then given by ∆U = ∆Q. Along an isobar, none of Q, W or U are unchanged. The work done per mole (by or on the engine?) will be an expression of the form ∆W = P(V2V1) = R(T2T1). The heat added to or lost from the engine will be an expression of the form CP(T2 T1), where CP is the molar heat capacity at constant pressure. The change in the internal energy (be sure to understand whether it is an increase or a decrease) is then given by ∆U = ∆Q + ∆W. It might also be a good idea to try to draw each cycle in the T : S plane (with the intensive variable T on the vertical axes). Indeed I particularly urge you to do this for the Carnot cycle, which will look particularly simple. Note that, while the area inside the cycle in the P : V plane is equal to the net work done on the engine during the cycle, the area inside the cycle in the T : S plane is equal to the net heat supplied to the engine during the cycle.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.825253963470459, "perplexity": 368.44491610130376}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362919.65/warc/CC-MAIN-20211203212721-20211204002721-00283.warc.gz"}
https://proofwiki.org/wiki/Definition:P-Integrable_Function	# Definition:Integrable Function/p-Integrable ## Definition Let $\struct {X, \Sigma, \mu}$ be a measure space. Let $f \in \MM_{\overline \R}, f: X \to \overline \R$ be a measurable function. Let $p \ge 1$ be a real number. Then $f$ is said to be $p$-integrable in respect to $\mu$ if and only if: $\displaystyle \int \size f^p \rd \mu < +\infty$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8736310601234436, "perplexity": 100.03487456832816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657176116.96/warc/CC-MAIN-20200715230447-20200716020447-00490.warc.gz"}
http://mathhelpforum.com/advanced-algebra/54935-abelian.html	# Math Help - Abelian 1. ## Abelian Prove that a group of order 4 is Abelian. To prove that a group is Abelian, I need to show that it has an identity, inverses, is associative, and is closed under the operation. I can definitely do this for specific groups, but I am not sure how to do this for a generality. Can someone please help me get started? 2. Couple of thoughts: all groups of order 4 are either cyclic groups or klein groups. If an element of the group has order 4 then the group is cyclic, or if all the elements are self-inverse then the group is klein. This might help you start thinking about proving that all groups of order 4 are abelian (where gh=hg). 3. Originally Posted by bluejay Prove that a group of order 4 is Abelian. To prove that a group is Abelian, I need to show that it has an identity, inverses, is associative, and is closed under the operation. I can definitely do this for specific groups, but I am not sure how to do this for a generality. Can someone please help me get started? Let the elements be $\{e,a,b,c\}$. Now the orders of $a,b,c$ must be larger than $1$ and divide $4$ - the order of the group. If any of them are $4$ then the group is cyclic and therefore abelian. Thus, it is safe to assume that $a,b,c$ all have order $2$. Therefore, $a^2=b^2=c^2 = e$. Consider $ab$. It cannot be the case that $ab=b,ab=a$ for that would imply $a=e$ or $b=e$. It also cannot be the case that $ab=e$ for that would mean $b$ is inverse of $a$ - however this is impossible since $a$ is its own inverse and inverses are unique. Thus, it collows that $ab=c$. Using a similar argument we can show $ba=c$. And by symmetry of these elements we have $ac=b,ca=b,bc=a,cb=a$. This shows the group is abelian.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8191367387771606, "perplexity": 89.16261403409946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507444465.10/warc/CC-MAIN-20141017005724-00132-ip-10-16-133-185.ec2.internal.warc.gz"}
https://quantumcomputing.stackexchange.com/questions/21612/does-rm-tr-pi-z-rho-pi-z-le-p-imply-cal-e-rho-and-cal-e-pi-z-r	# Does ${\rm tr}(\Pi_z\rho\Pi_z)\le p$ imply $\cal E(\rho)$ and $\cal E(\Pi_{-z}\rho\Pi_{-z})$ are close in trace distance? Suppose I have a quantum operation $$\mathcal{E}$$ and a state $$\rho$$ such that: $$\operatorname{tr}(\Pi_z \rho \Pi_z) \le p$$ for some probability $$p$$ and some projection $$\Pi_z$$ onto some subspace of the Hilbert space. Let $$\Pi_{-z} = \mathbb{1} - \Pi_z$$. I would like to prove (or disprove) that $$\mathcal{E}(\rho)$$ and $$\mathcal{E}(\Pi_{-z} \rho \Pi_{-z})$$ are close to each other, i.e. finding a bound for: $$\|\| \mathcal{E}(\rho) - \mathcal{E}(\Pi_{-z} \rho \Pi_{-z}) \|\|_1$$ The first thing it comes natural to do is to apply contractivity of quantum channels: $$\|\| \mathcal{E}(\rho) - \mathcal{E}(\Pi_{-z} \rho \Pi_{-z}) \|\|_1 \le \|\| \rho - \Pi_{-z} \rho \Pi_{-z} \|\|_1$$ But now I can't go ahead. Can you help me? Using the triangle inequality, we have $$\|\|\rho-\Pi_{-z}\rho\Pi_{-z}\|\|_1\leq \|\|\rho\|\|_1+\|\|\Pi_{-z}\rho\Pi_{-z}\|\|_1=1+\mathrm{Tr}(\Pi_{-z}\rho\Pi_{-z})$$ (the final equality holds because $$\rho$$ and $$\Pi_{-z}\rho\Pi_{-z}$$ are positive semidefinite). Then we can use $$\Pi_{z}^2=\Pi_{z}$$ and cyclicity of the trace to find $$\mathrm{Tr}(\Pi_{-z}\rho\Pi_{-z})=\mathrm{Tr}(\rho+\Pi_{z}\rho\Pi_{z}-\Pi_{z}\rho-\rho\Pi_{z})=\mathrm{Tr}(\rho-\Pi_{z}\rho\Pi_{z})=1-p.$$ Overall we thus have $$\|\|\mathcal{E}(\rho)-\mathcal{E}(\Pi_{-z}\rho\Pi_{-z})\|\|_1\leq 2-p.$$ • isn't the first one $2 - p$? Oct 20 at 14:03 • The second equality is not correct. Consider $\rho = \begin{pmatrix} \alpha & \beta \\ \beta^* & 1-\alpha \end{pmatrix}$ and $\Pi_z = \|0\rangle \langle 0\|$. Then the LHS gives $\sqrt{\alpha^2 + \|\beta\|^2}$ but the RHS gives $\alpha$, These are clearly not the same when $beta \neq 0$. Oct 21 at 18:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9876989126205444, "perplexity": 130.35798538085746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362571.17/warc/CC-MAIN-20211203000401-20211203030401-00442.warc.gz"}
https://www.physicsforums.com/threads/matrices-and-norms.205009/	# Matrices and norms 1. Dec 17, 2007 ### mathboy I'm trying to understand one step in the following proof to the following problem: http://img402.imageshack.us/img402/264/82127528zq9.jpg [Broken] Last edited by a moderator: May 3, 2017 2. Dec 17, 2007 ### Kreizhn I'm not sure if this will help you explicitly, but there's a little identity that might contribute to your solution We know that $$\displaystyle\left( \sum_i a_i \right) ^2 \geq 0$$ by non-negativity of a square, with equality holding iff the summand is identically 0. Furthermore, we can expand this to $$\displaystyle\left( \sum_i a_i \right) ^2 = \sum_i a_i^2 + 2 \sum_{i<j} a_i a_j$$ Thus $$\sum_i a_i^2 + 2 \sum_{i<j} a_i a_j \geq 0$$ Also, this can probably be generalized but off the top of my head I'm not too sure how, but $$(x-y)^2 \geq 0$$ $$\Rightarrow x^2+y^2-2xy \geq 0$$ $$\Rightarrow 2xy \leq x^2+y^2$$ 3. Dec 17, 2007 ### mathboy Thanks, but I already knew all that. So far I have [si [sj(A_ij)y_j]^2]^(1/2) <= [si [sjN y_j]^2]^(1/2) = nN [[sj(y_j)]^2]^(1/2) but leaves me wondering what to do with [sj(y_j)]^2 4. Dec 17, 2007 ### Kreizhn Then the only thing left that I can think of using is the identity above that I gave, namely $$\displaystyle\left( \sum_i a_i \right) ^2 = \sum_i a_i^2 + 2 \sum_{i<j} a_i a_j$$ Then as long as you can make a non-negativity argument about $$\sum_{i<j} a_i a_j$$ You'll be good to go 5. Dec 17, 2007 ### mathboy Still can't get it. I'm just trying to understand one step in the following proof to the following problem: http://img402.imageshack.us/img402/264/82127528zq9.jpg [Broken] Last edited by a moderator: May 3, 2017 6. Dec 17, 2007 ### Kreizhn In all honesty, I'm wondering if there just isn't a typo. It seems like the exponents should all be nested one parentheses earlier, though I might be missing something 7. Dec 17, 2007 ### mathboy It's an online solution by a professor (whom I don't know personally) to Spivak's "Calculus on Manifolds". If it is a typo, what is the proper way to finish it off? I've checked that there is no mistake before the inequality sign. I'm thinking that his n should be mn I think I've corrected the professor's solution, and I think his M is supposed to be N[mn]^(1/2) Last edited: Dec 17, 2007 8. Dec 17, 2007 ### morphism I think this is correct. He probably made the same mistake I did and treated both summations as if they run up to n, and not that one runs up to n and the other to m. Similar Discussions: Matrices and norms	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8868545889854431, "perplexity": 1026.946145942001}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824931.84/warc/CC-MAIN-20171022003552-20171022023552-00865.warc.gz"}
http://savannah.gnu.org/bugs/?36233	## GNU TeXmacs - Bugs: bug #36233, incorrect output from a for loop... You are not allowed to post comments on this tracker with your current authentification level. ## bug #36233: incorrect output from a for loop in maxima session Submitted by: Kamaraju Kusumanchi Submitted on: Wed 18 Apr 2012 01:33:45 AM UTC Category: Plugins Priority: 3 - Low Item Group: Error Status: In Progress Privacy: Public Assigned to: Andrey Grozin Originator Name: Open/Closed: Open Release: 1.0.7.15 Release: None Fixed Release: None Fixed Release: Keywords: Mon 25 Nov 2013 02:27:02 PM UTC, comment #6: I cannot reproduce this bug. However, printing 1000 numbers is extremely slow... Joris van der Hoeven <vdhoeven> Thu 15 Nov 2012 03:30:25 PM UTC, comment #5: > And it also seems that this behaviour is relatively new. I tested the bug, and I reproduced it on older versions of TeXmacs (one year ago). So, it may be not so new. Francois Poulain <fpoulain> Sat 13 Oct 2012 05:43:32 AM UTC, comment #4: Another example of the same bug: at the maxima prompt in TeXmacs, say 1;2; The bytes sent by maxima to TeXmacs are (I use p_out from the pnambic plugin) [02]latex:$\displaystyle \mbox{\tt\red(\mathrm{\%o1}) \black}1$[05][0a] [02]latex:$\displaystyle \mbox{\tt\red(\mathrm{\%o2}) \black}2$[05][0a] [02]channel:prompt[05] [02]latex:\red (\mathrm{\%i}3) \black[05][05] However, in the TeXmacs window I only see (%o1) 1 The line (%o2) 2 is completely missing. What's even more strange, the next prompt is (%i1), in spite of the fact that maxima has sent the code instructing TeXmacs to write (%i3) ! It seems that when output pieces are sent to TeXmacs too quickly, it handles the first of them (or first few of them), and just ignors the rest. And it also seems that this behaviour is relatively new. Andrey Grozin <grozin> Fri 21 Sep 2012 11:46:34 AM UTC, comment #3: This is a bug in TeXmacs. maxima produces the correct output and sends it to stdout (very quickly). TeXmacs receives it via a pipe; it seems that when it cannot handle input via this pipe, it simply throes it away. I modified tm_maxima to say exec maxima ... \| tee /path/to/out where out is a fifo, and said cat out \| p_out where p_out is from the pnambic plugin. Then I started maxima-5.28.0 (sbcl) from TeXmacs-1.0.7.16, and defined f(n):=for i:1 thru n do display(i); f(10) produces the expected result. f(100) produces the expected result in the window which traces the fifo out, this proves that all the right bytes are sent to TeXmacs via the pipe. However, TeXmacs displays only the beginning of the output. The length varies (and seems to depend on the current load level of the computer). Sometimes, lines up to i=52 are displayed; sometimes, up to i=11; etc. Never up to the end, i=100. Sorry, I cannot fix this. Somebody who knows TeXmacs internals is needed here. Andrey Grozin <grozin> Sun 09 Sep 2012 06:53:12 PM UTC, comment #2: Sorry, my fault. The "Need info" was meant for Andrey Grozin, the maintainer of the plugin, asking for his input on the matter. But I guess it's supposed to mean that the submitter has to provide more info. I'm setting it back to none. Cannot confirm myself though. Miguel de Benito <mdbenito> Sun 09 Sep 2012 04:27:10 PM UTC, comment #1: Why is the status set to "Need Info"? What more information do you need? raju Kamaraju Kusumanchi <kamaraju> Wed 18 Apr 2012 01:33:45 AM UTC, original submission: Using texmacs 1.0.7.15, maxima 5.27.0, GCL 2.6.7 on a Debian Wheezy, kernel 3.0.0-1-686-pae, 32 bit machine To reproduce the bug 1) start texmacs 2) Insert -> Session -> Maxima Inside the maxima session, enter for i : 0 thru 1000 do display( i ); The output is displayed only for a few values of i. The exact number of displayed values varies from run to run (suggesting that this is a memory related issue) but never 1000. A native maxima session (without using texmacs), displays the values of i all the way up to 1000. This bug is originally reported at http://bugs.debian.org/cgi-bin/bugreport.cgi?bug=434768 by Miguel Aguado. thanks -- Kamaraju S Kusumanchi http://malayamaarutham.blogspot.com/ Kamaraju Kusumanchi <kamaraju> No files currently attached Depends on the following items: None found Items that depend on this one: None found Carbon-Copy List • -unavailable- added by vdhoeven (Posted a comment) • -unavailable- added by grozin (Posted a comment) • -unavailable- added by mdbenito (Updated the item) • -unavailable- added by kamaraju (Submitted the item) • Do you think this task is very important? This task has 0 encouragements so far. Only logged-in users can vote. Please enter the title of George Orwell's famous dystopian book (it's a date): Date Changed By Updated Field Previous Value => Replaced By Wed 27 Nov 2013 10:03:58 PM UTCvdhoevenStatusNoneIn Progress Mon 25 Nov 2013 02:27:02 PM UTCvdhoevenPriority7 - High3 - Low Assigned tovdhoevengrozin Sat 27 Oct 2012 10:49:04 AM UTCagraefCarbon-Copy-Added agraef Fri 21 Sep 2012 08:49:38 PM UTCmdbenitoAssigned togrozinvdhoeven Sun 09 Sep 2012 06:53:12 PM UTCmdbenitoStatusNeed InfoNone Sun 09 Sep 2012 06:43:53 AM UTCmdbenitoPriority5 - Normal7 - High Item GroupNoneError StatusNoneNeed Info Assigned toNonegrozin	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6487178802490234, "perplexity": 12442.255226878708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824756.90/warc/CC-MAIN-20160723071024-00222-ip-10-185-27-174.ec2.internal.warc.gz"}
http://blog.hotwhopper.com/2015/07/scary-movie.html	Scroll To Top ## Tuesday, July 28, 2015 ### Scary Movie Sou \| 11:43 PM Here's something to entertain. I don't live in the USA so am completely impartial on this score. Not quite. What I mean is, I have no say in the matter. However I'll make a pact ... ...if you do live in the USA, ple..e..e..ase don't vote for any of the GOP's not a scientists (or any "not a scientist" for that matter), and I promise I won't vote for any Australian denier politician. More here. 1. This may be good for Hillary, given that even in the USA the majority accept the science and will see the GOP leadership as fools in this matter. However, I am not sure if such a video helps to convince more people that climate change is a problem. It could make the issue even more of a political one and thus not something you think about with your brain, but decide upon with your gut. 1. We have seen the effects of reasoned arguments in the USA. Michael Mann is attacked, slandered, gets death threats; the same probably applies for Jim Hansen and many other climate scientists. Ridicule is as good or better an approach. 2. At a certain point you have to decide that these people are unpersuadable; they just have to be defeated! Ridicule is as good a strategy as any, and God only knows - the Pope sure does! - they deserve it. This is hardly the only issue on which GOP recalcitrants bloody-mindedly refuse to abandon their comprehensive fantasy world - if you 'debate' them they think you think they have a point, and that they will beat you (because privileged, reactionary bastards usually 'win', sadly...) 2. I cannot understand US politics. So many views and so much talk, but do they get out and vote much on the day? 1. No all that bad but not al lthat great https://en.wikipedia.org/wiki/Voter_turnout_in_the_United_States_presidential_elections They are in the same ballpark as most Canadian elections but AIUI they vote for everything from dogcatcher to sherrif to judge to president in one single election (I don't think I'm joking about the dogcatcher) in one massive ballot so there probably is more reason to turn out. On the other hand, voting rates might be higher but over the last few election cycles, there have been very determined efforts to disenfranchise (mainly black Democratic) voters or to make voting so difficult in some areas (black/latino?) Democratic voters so participation rates might be five or ten percent higher without the deliberate obstructions but I'm just guessing. While there probably is an undercurrent of racism here, well of course there is, the main reason for hitting these communities is that it is easier to disenfranchise poor Blacks and Latinos than wealthy white enclaves who also might vote Democrat. Voting is not compulsory and I think the prospective voter must make sure to register to vote in most or all states. 2. Voters must register ahead of time to really count in almost all jurisdictions in the US. In some, they can cast a provisional ballot with same-day registration, but provisional ballots are only opened if the result is very close. Racism is more than just an undercurrent; it pervades everything. At the national level, the GOP is explicitly racist (though they try to be careful about language, it's obvious), Democrats less so. At the local level, all bets are off -- the Democrats after all used to be the southern racist party, until the in the 1960s, the northern branch of the party decided it was untenable. The GOP saw the opportunity and ran with it. That leads to a situation where blacks almost never vote for the GOP. So the GOP is generally in favor of disenfranchising them. 3. And don't forget the gerrymandering - distortion of voting precinct boundaries to favor one party or the other, regardless of whether the included neighborhoods are close together or not. Every ten years, after the census, the party in power in each state legislature gets to redrawn the district lines, supposedly to equalize population amongst districts, but really to influence what party gets elected. A cute trick in Michigan in 2011 was when the Republican legislature reorganized 3 districts in such a way the two sitting U.S. Representatives, both Democrats, ended up living in the same district. Rather than run against each other in the primary, one of them ran for Senate instead, and was elected. And yes, Democrats do the same thing. There's been a fair amount of litigation about redistricting since 2010. 4. Gerrymandering - https://en.m.wikipedia.org/wiki/Gerrymandering 5. Gerrymandering runs wild in my district. In order to water down my vote, they've split my district into two and linked us to the rest of the districts by redrawing the lines over an uninhabitable military bombing range. That's right, most of the land in my district is a bombing range. 3. Does the US Republican Party require standardized test scores for selecting their political candidates? WAIS-R less than 70, S.A.T <= 620? I mean the cut-off must be fairly stringent. You don't get that level of stupid easily. I can say that none of our major Con politicians deny the reality of climate change here in Canada. They just lie instead and proceed to show by their actions either they don't believe in climate change or else believe that the END TIMES are upon us and so they really don't have to worry about anything more than a year or two from now. My guess is that the Rapture is due on August 22 2017 at roughly 18:30 Eastern Daylight Savings Time (20:00 in Newfoundland. 1. Their stupidity is bought and paid for by the Koch Brothers and other fossil fuel interests. Sadly today in American politics "Money talks and bullshit walks" (per Ozzie Meyers of Abscam infamy) 2. Well, for climate change I suppose so, but a lot of rabid (I use the word advisedly) Republicans seem stark raving mad / totally impervious to reason on all kinds of topics. I mean, seriously the Governor of Texas mobilized the Texas Guard (whatever that is) as a precaution again an invasion and coup by the American Army this spring. 3. Connedspiracy and superstition, fear-mongering and knee-jerk reactionism rule their daze. It's far more then just bible-thumping stupidity, Republicans ooze fright from their very pores. Don't ask one to open its mouth, unless you want to be entertained by a moron. I can't imagine living that way. It's probably why they've all clumped together in herds (so called "Red States" and neighborhoods). Safety in numbers is also a breeding ground for contempt for the rest of the world and how they might live / think. 4. I would divide them into engaged and not engaged politically. So the engaged are the ones that vote in the Republican primaries and probably a majority share what I would call irrational political views. While the not engaged are normal people but are practically apolitical and they don't vote. 4. Parody can be effective - this may have some impact considering that it seems to represent a Clinton campaign theme. --- The current situation in the US is quite odd. The Republican party is being dragged around by the hyperconservative no-government Tea Party (an 'astro-turf' group manufactured by big tobacco, the Koch brothers, and lobbyists), which acts on the margins of voting numbers to swing far above their weight. For those in countries with parliamentary systems, it's quite similar to the effect of tiny parties brought in to edge out a majority - they can demand far more than their representation should justify by making the difference between winning or losing. Add to that the fact that every national level election is now a national referendum, with outside groups pumping in money wherever a race is close, rather than reflecting the views of the local constituency, and we've ended up with a bi-polar government. There are no longer conservative Democrats from the South, or liberal Republicans from the North-East or the coasts, because with national attention and national money there is no variety in the candidate positions. And thus we no longer have political cross-over to support compromise - all votes become all or nothing along party lines. I wish I saw any potential resolution to this partisanship. But sadly I don't. 5. Proof positive that idiots abound everywhere, ESPECIALLY within the government, politics, media and industry. Anyone expecting to find intelligence or informed 'leadership' from these sources should have their own heads examined. 1. Do not underestimate them. You do not get to the top if you are stupid. They only act as if because that gets them votes. 2. No, they are mostly not stupid, but they are so ideologically driven that often they appear stupid. They are also incredibly out of touch with people who have to live in the real world. One of the things contributing to the complete lack of collegiality in Washington (which did exist before about 1990) is that members of Congress spend so little time there. With just a two year term, they are always running for office, so they go home every weekend (almost) to stay in touch with the people who contribute money and the ones (like the TeaPartiers) who will actually get out and vote in the primary. Ordinary people generally not welcome. And since they don't spend time getting to know each other in Washington, they can continue to look at each other as enemies instead of colleagues. No cooperation with the enemy! 3. Chomsky and Orwell agree - to be truly Evil and/or Stupid requires a philosophy. Or ideology. These people are stupid - in fact, they're as stupid as people ever get; their world-view is actually too maladapted to successfully survive in even the medium term. They're just not necessarily thick (though some, being Dunning -Krugerites of the first water actually are, but because they don't - in fact, can't - know it their confident bluster takes in far too many.) It's an irony: a lot of stupid and dangerous people are the first to bewail 'political correctness', and yet, in the West, the truly dominant political correctness is that you're really not allowed to tell such people that that's what they are! 4. I agree with Victor, the people at the top are not necessarily stupid. And some of them are very cunning and very ruthless. They get where they are by appealing to a particular demographic to build up a power-base. So you can say many of the people they represent ARE stupid. 5. The beasts of Bentonville are especially cunning and ruthless. The stupid reason Trump has soared is because so many GOP voters actually blame Reaganomics for why they're life is now rough and insecure. They wrongly think the Donald will be different. I wouldn't doubt, more likely than not, he's part of Sam's Quail Hunting Club just like everyone from Richard Nixon onwards. Under Wal~Mart's policy of demanding that its suppliers supply goods to them at ridiculously low prices, the only way the suppliers can possibly accomplish this is to shut down production in the United States and ship it to sweatshop factories overseas. Which has caused the exodus of multi-millions of U.S. manufacturing jobs. Wal-Mart pays its workers below subsistence wages & benefits and destroys communities. Wal~Mart buys political hopefuls early in their careers and their assured that there's more to come if you follow the instructions. The Walton's DNA needs to be tested, especially the Robson side of the clan. 6. Also, rated "D" for the grades they got in science classes! 1. But Donald Trump is as close as the red states will ever get to voting for Boss Hogg of Hazard County fame. Trump can afford the biggest clown shoes, but yes, none of the stupid party should ever be allowed to have the launch code. It is simply mind boggling that the only country to ever bomb civilians with nuclear weapons (the Japanese were surrendering) tries to say who can or cannot have nukes. 7. I suspect Ben Franklin set up an unworkable US federal government system deliberately. With the president, the legislature and the judiciary pulling in different directions it becomes impossible for anyone to effectively wield power. 1. Franklin was only part of the discussion for the US Constitution, being 81 and of poor health. And a number of his ideas, such as a unicameral legislature, didn't pass. He certainly doesn't deserve majority credit for it. 8. Yeah sure, vote for a third party. It worked so well back in 2000 when Ralf Nader attracted votes from the left allowing GW to win by a hanging chad. If Gore had won this would be a very different planet today. 1. I also remember reading that certain environmental groups in Florida were upset with Gore because he wouldn't take a firm position against expansion of Homestead Air Force base in the Everglades, then either didn't vote or voted for a third party. Apparently the Florida race was so close that Gore would have won the state if all those dissatisfied people had voted for him. I saw that happen in the Michigan governors race some years ago - Detroit Democrats not turning out to vote because the mayor (and main motivator) was miffed at the sitting Democratic governor. Result? New Republican governor elected who hung around for three terms and managed to cut taxes and spend the state into a deficit. Maybe the Republicans have an advantage in that their voters follow blindly. 2. How would this planet be any different? They are two sides of the same coin, it's not left vs right, it's top vs bottom with no tolerance. The Brezinski Strategy and the Wolfowitz Doctrine of global domination are pretty much identical. 3. Bert from ElthamJuly 31, 2015 at 2:56 PM The conservative Supreme Court decided Florida's vote. A count done after the event showed that Gore won Florida. He should have been the elected President. Instead the conservatives installed a moron puppet Bush. The rest is a sordid history of idiocy only exceeded by the moronicity and greed of the GOP flunkies that do the bidding of the military industrial owners. They are still doing their bidding now! Bert 4. It appears to be just like the myth that Perot caused Poppy Bush to lose to Bubba Clinton. Where is the evidence that Nader was indeed a spoiler? I don't mind backpedaling if I'm wrong... I've really missed you folks, been so busy it reminds me of the time ruthless Sam Walton burned us out building stores and doing the grand opening work. Just now it's for different greedy Khazillionaires... SpaghettiO has been a blessing for me so far. If Hillary wins I'm probably toast. 9. Well, well, well........ "GOP presidential hopeful Jeb Bush says human activity is contributing to climate change and the country has an obligation to work to stop it. “I think it’s appropriate to recognize this and invest in the proper research to find solutions over the long haul but not be alarmists about it,” Bush said in an interview published Thursday with Bloomberg BNA. “We should not say the end is near, not deindustrialize the country, not create barriers for higher growth, not just totally obliterate family budgets, which some on the left advocate by saying we should raise the price of energy so high that renewables then become viable,” he added. http://thehill.com/policy/energy-environment/249771-jeb-bush-humans-contribute-to-climate-change 1. Dubya2 has already had a private chat with the people from the coal industry. There's a fair chance we are going to something rather like Groundhog day: the presidency bought for a Bush by the fossil fuel industry, and the Bush tearing up not Kyoto but the Paris agreement this time around. Don't forget that Dubya1 said similar things about climate, but did nothing because he felt it was more important to have a strong economy than a viable planet to live on. Oh, and then he trashed the economy anyhow. There's nothing like a fossil fuel industry funded Dubya to really wreck things. But a lot of people now are unable to remember how much better the world was before Dubya1. 2. "Alarmists", "deindustrialise","obliterate","left", and on the other side "higher growth", "family budgets" and an implied "the poors". Apply thesaurus, shuffle around a little, day to day, and there's the essential Jeb Bush climate snippet for the duration, I predict. Others may well steal the template. The problem with "I'm not a scientist" is the introduction - "I'm not". People don't want someone who's not something. They want people who are things and will say so firmly. "I am ...!" - that's what they want to hear. See how that works? I do and it horrifies me but there it is. 3. I'm more concerned about the arms makers he's been courted by. Also, the biggest source of emissions by far is the world's defense and war machines. Jeb has all the dastardly dudes who invaded Iraq the first time, invaded the second time and sold Saddam anthrax & various munitions. Sold all kinds of shyt to Iran and plenty of others. With Mena connection drug money$. Jeb Bush made$10m in speeches since 2007 - 10 to a Korean metals company called Poongsan that makes cluster bombs & US coins. Have you noticed that a new planet has been found that can support life and is habitable, the same week Humpty Trumpet soared to a double digit lead? Instead of commenting as "Anonymous", please comment using "Name/URL" and your name, initials or pseudonym or whatever. You can leave the "URL" box blank. This isn't mandatory. You can also sign in using your Google ID, Wordpress ID etc as indicated. NOTE: Some Wordpress users are having trouble signing in. If that's you, try signing in using Name/URL or OpenID. Details here.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17713017761707306, "perplexity": 3536.1929946132946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607802.75/warc/CC-MAIN-20170524055048-20170524075048-00279.warc.gz"}
https://dmoj.ca/problem/gfssoc2s4	GFSSOC '15 Fall S4 - Mostly Talking View as PDF Points: 15 (partial) Time limit: 1.0s Java 8 2.5s Memory limit: 128M Authors: Problem type The Waterloo campus is a huge utopia of information held in buildings. There are unidirectional pathways which connect buildings to each other, and one cannot travel unless they are on one of these paths. There may be multiple paths connecting two buildings. A common problem for your boss Calvin (who is at Waterloo) these days is that every time he sets foot outside there are annoying people who ask him questions about algorithms. In fact, in each pathway , there are classmates who are there to bother Calvin, for one minute each. Calvin, being a nice guy, must help each and every one of them. There is only one way to get out of talking to annoying classmates — a girlfriend! Luckily for Calvin, Cindy agreed to walk with him today, but only for one pathway (she's busy too!). Cindy is not willing to travel through the main pathways, which are too mainstream for her, but instead knows secret pathways that cannot be used unless she is there. Cindy therefore, has her own pathway set, consisting of different paths. Being the girlfriend, Cindy requires attention — for each pathway in her set, she needs to be attended to for minutes. Calvin wants to get from the computer science building (building ) to another computer science building (building ), and can choose to call Cindy to accompany him for any one pathway. Knowing this information, you would like to help your boss minimize the amount of time spent outside, with or without calling Cindy to walk with Calvin on one of the paths. Input Specification Line 1: 2 integers space separated: Next lines: 3 integers space separated — , meaning that there is a unidirectional pathway from building to building , with coders to talk to. Line : one integer, Next lines: 3 integers space separated — , meaning that there is a unidirectional pathway from building to building , which Cindy and Calvin can take together for minutes. Note: It is not guaranteed that Cindy's paths are unique from the normal paths. Output Specification One integer — the minimum time Calvin needs to travel from building to building , or -1 if it is impossible to do so. It is guaranteed that the minimum time will always be less than or equal to . Sample Input 4 3 1 2 5 2 3 5 3 4 5 2 1 3 7 2 4 3 Sample Output 8 Explanation of Output for Sample Input There are many ways Calvin could've arrived at building from building . The fastest way is to get Calvin from in 5 minutes, and then call Cindy over to take Calvin through her secret passage from for a total of 8 minutes. Another possible (but slower) way is to call Cindy right away to have her walk with Calvin from in 7 minutes, and then go from for a total of 12 minutes.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4255516231060028, "perplexity": 1827.6717153070208}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499954.21/warc/CC-MAIN-20230202003408-20230202033408-00761.warc.gz"}
https://www.ncbi.nlm.nih.gov/pubmed/8670908?dopt=Abstract	Format Choose Destination EMBO J. 1996 Aug 1;15(15):4040-9. # Reduced replication of 3TC-resistant HIV-1 variants in primary cells due to a processivity defect of the reverse transcriptase enzyme. ### Author information 1 Department of Human Retrovirology, University of Amsterdam, Academic Medical Center, Utrecht, Netherlands. ### Abstract Human immunodeficiency virus type 1 (HIV-1) variants with resistance mutations in the reverse transcriptase (RT) gene appear during drug therapy with the nucleoside analogue 2',3'-dideoxy-3'-thiacytidine (3TC). These resistance mutations alter the methionine (Met) residue of the conserved YMDD motif, which is part of the catalytic core of the RT enzyme. Isoleucine (Ile) variants are initially observed, followed by the appearance and eventual outgrowth of viruses encoding valine (Val). Similar replication kinetics were measured for wild-type and 3TC-resistant HIV-1 viruses in tissue culture infections of a T cell line, but we measured reduced polymerase activity for the two mutant RT enzymes compared with the wild-type enzyme (Ile = 43% and Val = 67%). Gel analysis of the reverse transcription products revealed that both 3TC-resistant RT mutants produce significantly shorter cDNA molecules than the wild-type enzyme [Met (wt)>Val>Ile], indicating that 3TC-resistant RT polymerases are less processive enzymes. Interestingly, these enzyme defects were more pronounced under limiting dNTP concentrations and we therefore assayed virus replication in primary cells that contain relatively low dNTP levels. Under these conditions, we measured significantly reduced replication kinetics for the 3TC-resistant HIV-1 variants [Met (wt)>Val>Ile]. If the level of virus replication can be similarly reduced in 3TC-treated patients that develop drug-resistant HIV-1 variants, this may be of considerable clinical benefit. PMID: 8670908 PMCID: PMC452124 [Indexed for MEDLINE] Free PMC Article	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8256356120109558, "perplexity": 23057.422132223383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540545146.75/warc/CC-MAIN-20191212181310-20191212205310-00247.warc.gz"}
https://cs.stackexchange.com/questions/88577/what-does-the-big-o-complexity-of-a-function-mean	# What does the "big O complexity" of a function mean? What do people mean when they refer to the "big O complexity" of a function? What is the big O complexity of $9n^2 + 10n$, for example? First of all, when people talk about big O complexity, they refer to the complexity of an algorithm, usually its running time. A somewhat better term is big O asymptotics. Big O makes sense to functions beyond the running time of an algorithm, indeed beyond any kind of complexity measure of an algorithm. Big O notation actually first appeared in the context of number theory, where it is used to simplify many statements. Now back to your question. There really isn't any such thing as the big O complexity of a function. Let us take as an example your function. It has many big O estimates, such as: • $9n^2 + 10n = O(9n^2 + 10n)$. • $9n^2 + 10n = O(n^2)$. • $9n^2 + 10n = O(n^3)$. The first two estimates are better than the third one, since they are tight: not only do we have $9n^2 + 10n = O(9n^2 + 10n)$, but in fact $9n^2 + 10n = \Omega(9n^2 + 10n)$, whereas it is not true that $9n^2 + 10n = \Omega(n^3)$. Comparing the first two estimates, the second one is better since it is simpler. What does simple mean? Although this is an informal notion, everybody will agree that functions of the form $a^n n^k \log^\ell n$ are simple. If we fix this class of simple functions, then the unique simple function $f(n)$ such that $9n^2 + 10n = O(f(n))$ and moreover this is a tight bound is $f(n) = n^2$ (i.e., $a=1$, $k=2$, $\ell=0$). This could be termed "the" big O asymptotics of $9n^2 + 10n$, but a much better term would be the big $\Theta$ asymptotics of $9n^2 + 10n$, since the statement $9n^2 + 10n = \Theta(n^2)$ encompasses the property that this a tight upper bound. This discussion suggests that when you are given an explicit function, you shouldn't be looking for big O and big $\Omega$ estimates – instead, you should aim higher, at a simple big $\Theta$ estimate. The true role of big O and big $\Omega$ is in other situations. One situation is when analyzing the running time of an algorithm. The exact running time could depend on the input in a complicated way. For example, when running binary search on an array of length $n$, the algorithm could terminate after one step, two steps, or more – but always within $O(\log n)$ steps. We cannot describe the running time using big $\Theta$, since the best lower bound $\Omega(1)$ and the best upper bound $O(\log n)$ do not match. The same cannot be said about your example. Another situation in which it makes sense to use big O and big Omega is when it is hard to find the exact asymptotics of a function. Take as an example the central binomial coefficient $\binom{2n}{n}$. Since $\sum_{m=0}^{2n} \binom{2n}{m} = 4^n$ and since $$\binom{2n}{0} < \binom{2n}{1} < \cdots < \binom{2n}{n-1} < \binom{2n}{n} > \binom{2n}{n+1} > \cdots > \binom{2n}{2n-1} > \binom{2n}{2n},$$ we can obtain the following upper and lower bounds: $$\frac{4^n}{2n+1} \leq \binom{2n}{n} \leq 4^n.$$ This shows that $\binom{2n}{n} = O(4^n)$ and $\binom{2n}{n} = \Omega(4^n/n)$, where in both cases we are using simple functions as our estimators. The true rate of growth is $\binom{2n}{n} = \Theta(4^n/\sqrt{n})$, but this is harder to establish. In more complicated cases, it could be hard to find the exact rate of growth, or perhaps we are content with only an upper bound or only a lower bound, and then it makes sense to use big O or big $\Omega$. One could also come up with contrived examples, which rarely happen in practice, in which there is no simple big $\Theta$ estimate for a given function. For example, consider the function $$f(n) = \begin{cases} n & \text{ if n is even}, \\ n^2 & \text{ if n is odd}. \end{cases}$$ The best simple lower bound one could give is $f(n) = \Omega(n)$, and the best simple upper bound is $f(n) = O(n^2)$, but the two don't match. Finally, while in analyzing algorithms we usually don't care about multiplicative constants, since they depend on details which our analysis abstracts away on purpose, in other situations it makes sense to ask for information beyond big Theta. For example, we can get an asymptotic estimate of the form $$\binom{2n}{n} \sim \frac{4^n}{\sqrt{\pi n}}.$$ Or we could ask for an asymptotic series, such as $$\binom{2n}{n} = \frac{4^n}{\sqrt{\pi n}} - \frac{4^n}{8\sqrt{\pi} n^{3/2}} + O\left(\frac{4^n}{n^{5/2}}\right).$$ At this point in your training, however, it's probably better to concentrate at the more elementary stuff, which is of more widespread use in computer science.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7545127272605896, "perplexity": 149.08401327301405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571989.67/warc/CC-MAIN-20220813232744-20220814022744-00794.warc.gz"}
https://rprogramminghelp.xyz/dgamma-r-example-2-23454	Home » R Studio Assignment Help » Dgamma R Example # Dgamma R Example Dgamma R Example The R analogues of the gamma-ray emission are the G-ray, G-band, and Y-band, visit site The G-band corresponds to the emission of the $Z$-ray. The $Y$-band corresponds the emission of $Z$ below the line of sight (LOS) (see also @D12 [@D12a]). The $GZ$ analogues of each of the two classes of gamma-ray emitters are shown in Fig. $fig:GZ$ (a) and (b), respectively. Web Site gray-scale Do My Coding Homework show the range of values of $E_\gamma$ and $E_Z$ as a function of the distance. The red points represent the $Z\rightarrow 2s$ transition; the red shaded green points correspond to the $Z+2s$ and $Z+T$ transitions. The $Z+Z$ transition corresponds to the $2s$ excitation energy of $\gamma$-rays. The $GZ+2Z$, $GZ-2Z$, and $GZ\rightrightarrow 2Z$ transitions correspond to the excitation energies $E_i$ of the $2S$ and $2Z$ transitions respectively. The red shaded black points represent the values of $GZ$, $Z$, and the $2Z\rightleftharpoons 2Z$ transition, respectively. ————————- ———- ————————- ——————– $x$ $\protect\Delta\phi$ $E_X$ $\alpha$ ${\boldsymbol\Gamma}_\phi$ $z$ $\Gamma_F$ $[\Gam_{F_1}$\] $0.1\%$ [$\Gam_F$]{} -0.1 0. ## Dragon Text Game R Programming 08 -1.05 1.57 [$^{\rm 1}$]{}$1.1^{+0.2}_{-0.3}$; [$^{1}$] ————————– ———- ———— ————————- The red dashed curves correspond to $\Delta\phi=0$ and $\alpha=2$; the red solid linked here correspond to $E_2$ and $-2E_2$. (a) The T$_2$ emission of the $\gamma-$emission of $Z+3S$; (b) The $Z$ emission of $2Z+2S$; and (c) The $2Z-2S$ emission of $\gammo$-emission of the $4S$ emission. The black dashed curves correspond respectively to $\Delta \phi=0, 0.00016$ and $0$; the black solid curves correspond respectively with $\alpha=1$. The red shading green curves correspond to the $\alpha=0.1$. This example illustrates the $Z-2s$ transition in a two-dimensional electron gas by the $GZ \rightarrow 2S$ and 2Z transition in a three-dimensional electron-gas by the $ZZ-2\rightarrow 3S$ transitions. These examples illustrate the importance of the data-driven detection of the X-ray emission in the AGN [@D13] and the high $z$ state of the XRB [@D14b]. ## Dragon Text Game R Programming The R-style class is a general class that has many properties that make it useful, by analogy. It is used throughout the R-class in a number of ways to cover different problems. Let’s walk through the R-Style examples that we’ll use. In this example, the R-styles are simple and important site to understand. In the example, we’ll use the R style to call a function named “r-mode”. Let x be an object with x-style. The R-style object is called a x-style object. And the R-key is called a keyof x-style object that is used to specify x keyof x-styles R style object. Another way Here’s a more complex example, which uses a keyof R-style and a keyof the R style object, to create a keyclass key. And the keyof the key read review the R style are named a key and a R style object. The R style object is called Rstyle object.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5060784220695496, "perplexity": 531.4175977613928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00731.warc.gz"}
https://www.shaalaa.com/concept-notes/arithmetic-progression-ap_1825	# Arithmetic Progression (A.P.) #### notes A sequence a_1, a_2, a_3,…, an,… is called arithmetic sequence or arithmetic progression if a_(n + 1) = a_n + d, n ∈ N, where a_1 is called the first term and the constant term d is called the common difference of the A.P. The n^(th) term (general term) of the A.P. is a^n = a + (n – 1) d. The sum to n term of A.P is S_n= n/2[2a+(n-1)d] We can also write, S_n = n/2[a+l] We can verify the following simple properties of an A.P. : (1) If a constant is added to each term of an A.P., the resulting sequence is also an A.P. (2) If a constant is subtracted from each term of an A.P., the resulting sequence is also an A.P. (4) If each term of an A.P. is multiplied by a constant, then the resulting sequence is also an A.P. (5) If each term of an A.P. is divided by a non-zero constant then the resulting sequence is also an A.P. Arithmetic mean: Given two numbers a and b. We can insert a number A between them so that a, A, b is an A.P. Such a number A is called the arithmetic mean (A.M.) of the numbers a and b. Note that, in this case, we have A – a = b – A, i.e., A =(a+b)/2 We may also interpret the A.M. between two numbers a and b as their average (a+b)/2. For example, the A.M. of two numbers 4 and 16 is 10. We have, thus constructed an A.P. 4, 10, 16 by inserting a number 10 between 4 and 16. The Arithmetic mean is d = (b - a)/(n + 1) If you would like to contribute notes or other learning material, please submit them using the button below. ### Shaalaa.com Arithmetic Progression [00:04:26] S 0%	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.971157968044281, "perplexity": 719.4653580719805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038492417.61/warc/CC-MAIN-20210418133614-20210418163614-00196.warc.gz"}
https://www.physicsforums.com/threads/hrmm-derivative-problems-concept.8052/	# Hrmm derivative problems (concept?) 1. Oct 30, 2003 ### VikingStorm I've been trying to do these concept-based questions, (but I think my concept isn't that sound). "Suppose f'(2)=4, g'(2)=3, f(2)=-1 and g(2)=1. Find the derivative at 2 of each of the following functions a. s(x)=f(x)+g(x) b. p(x)=f(x)g(x) c. q(x)=f(x)/g(x)" I began doing this, without reading the find the derivative part. What order would I exactly solve it in? Or does it work straight in by plugging in the derivatives? (too simple, so must not be it) "If f(x)=x, find f'(137)" This is a pure concept question I'm sure... "Explain what is wrong with the equation (x^2-1)/(x-1)=x+1, and why lim(x^2)/(x-1)=lim(x+1) both x->1" The top factors out and supposedly cancels, though I'm not sure why I can't do that. 2. Oct 30, 2003 ### Soroban Hello, VikingStorm! "Suppose f'(2)=4, g'(2)=3, f(2)=-1 and g(2)=1. Find the derivative at 2 of each of the following functions a. s(x) = f(x) + g(x) b. p(x) = f(x)g(x) c. q(x) = f(x)/g(x)" Yes , you're right ... After finding the derivative, just plug in the given values. (a) s'(x) = f '(x) + g'(x) Hence: s'(2) = f'(2) + g'(2) = 4 + 3 = 7 (b) p'(x) = f(x)g'(x) + g(x)f '(x) Hence: p'(2) = f(2)g'(2) + g(2)f '(2) = (-1)(3) + (1)(4) = 1 (c) q'(x) = [g(x)f '(x) - f(x)g'(x)]/[g(x)]^2 Hence: q'(2) = [(1)(4) - (-1)(3)][1^2] = 7 3. Nov 2, 2003 ### phoenixthoth for the first one, note that f'(x)=1 for all x, so f'(137)=1. another way to look at is is that for y=x, y=x is a tangent line at all points. the slope of the tangent line is 1 everywhere, so since f'(x) is the slope of the tangent line at (x,f(x)), f'(137)=1. for the second question, the main thing is what is meant by the equality sign. suppose A(x) and B(x) are two algebraic expressions defined for some set such as the set of real numbers. then we say that A(x)=B(x) if and only if A(x) equals B(x) for all real numbers x. such equations like A(x)=B(x) that are true "everywhere" are called identities. (x^2-1)/(x-1)=x+1 is not* an identity because the equation isn't always true: it fails when x=1. if you let A(x)=(x^2-1)/(x-1) and B(x)=x+1, note that A(x)=B(x) for all real numbers except x=1. when you take the limit as x approaches 1, x is never allowed to actually equal 1, so limA(x)=limB(x).	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8860485553741455, "perplexity": 2219.6417076535963}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542244.4/warc/CC-MAIN-20161202170902-00078-ip-10-31-129-80.ec2.internal.warc.gz"}
https://community.wolfram.com/groups/-/m/t/1379392	GROUPS: # [WWS18] Water Basin Delineation Posted 7 months ago 615 Views \| 0 Replies \| 6 Total Likes \| # Summary Detailed digital information about water is of great important not only for urban design and development, but also for geopolitical strategic plans. A large portion of world population is now living in water stress regions. There are alarming patterns between the water crisis and political/civil unrest in parts of the world (e.g., Yemen, Syria, even Iran). Therefore, having digital model of water sources is essential. My main goal here is to extract the hydrographic basin (also called, the drainage basin) out of digital elevation models (DEM). Detailed watershed segmentation of a geographical region is obtained using built-in morphological functions of Wolfram language that I applied on the DEM of the region. The watershed lines dividing neighboring basins, together with their elevation values, are extracted. We treated the centroid of sub-basins as vertexes of a graph where connections between neighboring vertexes depend on the land surface characteristics and boundary lines. We assumed that a valid connection between two vertexes (say, two sub-basins) can be made only if the two vertexes have minimum elevation at the boundary compared to all neighboring vertexes. Our results show a great match with the the watershed segmentation obtained manually by appropriate choice of markers (say, using a seasoned geographer knowledge). # DEM of Lake Urmia (Orumiyeh, Persian: ارومیه) The region that I choose for my analysis is lake Urmia on the north west of Iran. It is a UNESCO biosphere reserve which is now dangerously shrinking due to water mismanagement and also drought. We set the region a box between two points with altitudes and longitudes {35.5,44} and {39,48}. We extract the DEM using GeoElevationData function. region = {{35.5, 44}, {39, 48}}; data = N[QuantityMagnitude@ GeoElevationData[region, UnitSystem -> "Metric"]]; reliefmap = ReliefPlot[data, DataReversed -> True, PlotLegends -> BarLegend[Automatic, LegendLabel -> "elevation(m)"]] # Watershed segmentation We covert the DEM data into an image. mimg = ImageAdjust[Image[data]]; From now on, we shall treat our DEM as an image with colors corresponds to elevations. We find watershed segmentation (i.e., a detailed sub-basin structure) using Immersion method, mainly because the labeling of segments correspond to the relative value for a sub-basin's minimum elevation. wsc = WatershedComponents[mimg, Method -> "Immersion"]; bnds = ColorNegate@Image[wsc, "Bit"]; Next, we label the boundary between two adjacent sub-basins by the indexes of corresponding sub-basins. To do so, we use black-and-white image of watersheds where the boundaries (say, lines) have value one (white lines). Then, we assign two indexes to the line separating two sub-basins. These indexes are the indexes of adjacent sub-basins separated by the line. We shall do index assignment of lines in two steps: 1. Shift the sub-basin with higher index into the lines (using Erosion). bindex = Erosion[Replace[wsc, 0 -> Max[wsc] + 1, {2}], 1]; 2. Shift the sub-basin with lower index into the lines (using Dilation) tindex = Dilation[wsc, 1]; The first step has one subtlety: to shift the higher index into the lines, first we need to set the boundary value higher than any value in the image; otherwise the Erosion function will extend the boundaries only. doubleIndexArray = Replace[Transpose[{bindex, tindex}, {3, 1, 2}], {n_, n_} -> {0, 0}, {2}]; doubleIndexPairs = Prepend[DeleteCases[ DeleteDuplicates[Flatten[doubleIndexArray, 1]], {0, 0}], {0, 0}] After labeling the boundaries by two indexes, we find the minimum elevation along the boundaries separating two sub-basins. Now we have the information of adjacent sub-basins and the minimum elevation along the boundaries. bndSegs = Replace[doubleIndexArray, Dispatch@MapIndexed[#1 -> First[#2] - 1 &, doubleIndexPairs], {2}]; MinATborders = ComponentMeasurements[{mimg, bndSegs}, "Min"][[All, 2]]] # Graph made out of centroids of sub-basins From now on, we shall treat a sub-basin as a vertex. For the sake of representation, the location of the vertex is set as the centroids of sub-basins. The most important question is how the vertexes are connected together and what are the corresponding clusters made out of connected vertexes. In other word, the clusters represent larger basins that form a unique hydro-graphical ecosystem with a unique water graph. g0=Graph[Apply[UndirectedEdge,Rest@doubleIndexPairs,{1}]]; g1=WeaklyConnectedGraphComponents[g0][[1]]; sortBasin[x_]:=Keys[x]->SortBy[Values[x],Association[MinATborders][Sort[{#,Keys[x]}]]&]; sortedBasins=sortBasin[#]&/@basinConnect ## Algorithm to make connections between sub-basins (how/where to connect vertexes and form edges) 1. Built a set for each sub-basin whose elements are the adjacent sub-basins. 2. Sort them by the minimum value of the boundary separating them. 3. Make a connection between two adjacent sub-basin by choosing the first element of the sorted list in step#2 4. Check for possible cycles in the graph (i.e., loops). If any, replace the original connection by the making the connection with the second element in the list of sorted sub-basins obtained in step#2. 5. Repeat step#5 until there is no more change in the graph Here is the graph that we obtain following above steps: # Comparison of our result with a basin structure obtained by pre-determined markers Let us assume that we are a seasoned geographer with a good knowledge of large basins (e.g., where the rivers are running and what branches of a river are independent and where they merge) and how they are connected on a map. Then, one shall obtain the following basins for our selected region: Now, let us overlay our graph on the top of map and compare different results # Concluding remarks Detailed watershed segmentation of a geographical region is obtained using built-in morphological functions of Wolfram language that we applied on the raw Digital Elevation Model (DEM) of the region. The watershed lines dividing neighboring basins, together with their elevation values, are extracted from DEM. We treated the centroid of sub-basins as vertexes of a graph where connections between neighboring vertexes depend on the land surface characteristics and boundary lines. We assumed that a valid connection between two vertexes (say, two sub-basins) can be made only if the two vertexes have minimum elevation at the boundary compared to all neighboring vertexes. Our results show a great match with the the watershed segmentation obtained manually by appropriate choice of markers (say, using a seasoned geographer knowledge). # Future works With the detailed dynamic relationships of hydrographic basins in force, we will be able to develop models describing the water flow (or water level) among basins using the precipitation data. Next, the water usage for irrigation and urban uses can be added into the model. Using these information, one will be able to develop an elaborate model for water management of a large hydrographic basin. Our approach can be improved further by treating a few loops (cycles) that appear in the graph. In this regard, one can remove the connection between two vertexes where the initial one has higher elevation and replace it with the second vertex in the list of neighboring basins sorted by the minimum boundary elevation.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44100847840309143, "perplexity": 2474.4990472567115}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247489282.7/warc/CC-MAIN-20190219000551-20190219022551-00019.warc.gz"}
http://www.aimsciences.org/article/doi/10.3934/dcdsb.2015.20.2751	# American Institute of Mathematical Sciences October 2015, 20(8): 2751-2759. doi: 10.3934/dcdsb.2015.20.2751 ## Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system 1 Department of Mathematics, Southeast University, Nanjing 211189, China, China Received November 2014 Revised February 2015 Published August 2015 We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equation \begin{eqnarray} \left\{\begin{array}{lll} n_t + u \cdot \nabla n = \Delta n - \chi\nabla\cdot(n \nabla c),&{} x\in\Omega,\ t>0,\\ c_t + u \cdot \nabla c = \Delta c - nc, &{} x \in \Omega,\ t>0,\\ u_t + \kappa(u\cdot\nabla)u = \Delta u + \nabla P + n\nabla\phi ,&{} x\in\Omega,\ t>0,\\ \nabla\cdot u=0, &{}x\in\Omega,\ t>0, \end{array}\right. \end{eqnarray} in a bounded domain $\Omega\subset\mathbb{R}^2$. It is known that if $\chi>0$, $\kappa\in\mathbb{R}$ and $\phi\in C^2(\bar{\Omega})$, for sufficiently smooth initial data, the model possesses a unique global classical solution which satisfies $(n, c, u)\rightarrow(\bar{n}_0, 0, 0)$ as $t\rightarrow\infty$ uniformly with respect to $x\in\Omega$, where $\bar{n}_0:=\frac{1}{\|\Omega\|}\int_{\Omega}n(x, 0)dx$. In the present paper, we prove this solution converges to $(\bar{n}_0, 0, 0)$ exponentially in time. Citation: Qingshan Zhang, Yuxiang Li. Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2751-2759. doi: 10.3934/dcdsb.2015.20.2751 ##### References: [1] M. Chae, K. Kang and J. Lee, Existence of smooth solutions to coupled chemotaxis-fluid equations,, Discrete Contin. Dyn. Syst., 33 (2013), 2271. doi: 10.3934/dcds.2013.33.2271. Google Scholar [2] M. Chae, K. Kang and J. 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Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4165-4188. doi: 10.3934/dcdsb.2020092 2019 Impact Factor: 1.27 ## Metrics • PDF downloads (108) • HTML views (0) • Cited by (47) ## Other articlesby authors • on AIMS • on Google Scholar [Back to Top]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7760463356971741, "perplexity": 8067.462681658511}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400189928.2/warc/CC-MAIN-20200919013135-20200919043135-00751.warc.gz"}
https://www.physicsforums.com/threads/rf-value.52112/	# Rf value?#@$%^& 1. Nov 9, 2004 ### xLaser rf value!?#@$%^& Hey guys, Before doing a lab tomorrow, we need to find out what Rf values are, i can't seem to find a defintion about it online so some help would be great. Basically we are doin this BIO but the teacher wont tell us exactly about the lab but it is about chlorophylls and pigments. thx alot. m!ke 2. Nov 9, 2004 ### UrbanXrisis There is no such thing as a table of Rf values. Chromatographic retention times are sensitively and unpredictably dependent on the conditions; if you run chromatography on the same sample three consecutive times (using the "same conditions") you will get different retention values (Rf or whatever) for the same substance each time! That's not to say that the values will be wildly different; in sensitive techniques such as gas chromatography you get almost the same values for the same substance on consecutive runs. But with TLC the only way to unambiguously identify something is to run an authentic sample on the same plate as the substance to be identified. Not "another plate, right afterwards." The same plate. That's why you will never find a table of Rf values. Or of GC retention times, for that matter. 3. Nov 9, 2004 ### UrbanXrisis Oh, for the definition: The retention factor, or Rf, is defined as the distance traveled by the compound divided by the distance traveled by the solvent. 4. Nov 9, 2004 ### xLaser ah ok i c, the last part about the definition was all i needed, thx alot dude, i'll update u on what happens tomorrow. =)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7423123121261597, "perplexity": 1707.490940725601}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542323.80/warc/CC-MAIN-20161202170902-00064-ip-10-31-129-80.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/projectile-doubt.170461/	# Projectile doubt. 1. May 16, 2007 ### perfectz Projectile doubt....... CHOOSE THE CORRECT ANSWER AND EXPLAIN. What is the nature of proportionality between the muzzle angle and the horizontal distance traveled by a projectile? a) Directly proportional. b) Inversely proportional. c) None of the above. ( who says learning physics is boring?:tongue2: ) Last edited: May 16, 2007 2. May 16, 2007 ### Staff: Mentor Well, what do you think? 3. May 17, 2007 ### husky88 Well think about this. The bigger the angle, the higher the projectile goes. The higher it goes, the longer time it takes to reach the ground. The longer it takes to reach the ground,... You don't even need formulas for this. 4. May 17, 2007 ### Staff: Mentor True. Also true. Not sure what you can immediately deduce from this. You might want to reconsider that. 5. May 18, 2007 ### husky88 Well, what I thought was the longer it takes to reach the ground, the more time it has to travel horizontally, therefore the more horizontal distance it travels. Skipping over, you get: The bigger the angle, the more horizontal distance it travels. So they are directly proportional. 6. May 18, 2007 ### Weimin So what about the angle of 90 degrees? :-) 7. May 18, 2007 ### husky88 Hmm. It does say it is a muzzle angle, so if the angle is 90, then you end up in shooting yourself and then you wouldn't care about the answer anyway. :) Yeah, I guess my non-formula logic doesn't apply for a 90 angle. Then the answer would be C. 8. May 18, 2007 ### husky88 I just realized that if you throw it too high, then Vx will decrease. So yeah, all my posts don't make sense. Except for the one with the 90 degree angle. :) Could you say it is proportional to sin(2angle), then? Last edited: May 18, 2007 9. May 18, 2007 ### cristo Staff Emeritus What makes you think that? 10. May 18, 2007 ### perfectz Am I right? i too came to Husky's answer before posting the topic. But i had doubts whether it was right or wrong. let the angle be 'A'. Let the velocity be 'V' therefore horizontal component = V cos A vertical component = V sin A therefore horizontal displacement = V cos A t(time of flight) units vertical displacement = V sin A * t units At maximum height, V sin A = 0. ----------------> l consider formula V = U-gt ----------------> ll therefore substituting l in ll 0 = V sin A - gt t = (V sin A)/g total time of flight = 2t =2((V sin A)/g) range is nothing but the horizontal displacement V cos A * t so range = (2(V sin A)/g} * V cos A therefore range is directly proportional to Sin2A Am I right guys? 11. May 18, 2007 ### perfectz dont just visit people 12. May 18, 2007 ### Astronuc Staff Emeritus Last edited: May 18, 2007 13. May 18, 2007 ### perfectz ya hooooooooooooooooooooo Thanks guys. Physics Forums Rok and you guys are cool the site u gave me is just beyond cool dude How much does wind affect the range of a projectile body? And how much does the shape and weight of the body affect the range? Last edited: May 18, 2007 Similar Discussions: Projectile doubt.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8942339420318604, "perplexity": 4979.498477961074}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948521188.19/warc/CC-MAIN-20171213030444-20171213050444-00068.warc.gz"}
https://www.physicsforums.com/threads/got-an-astrophysics-astrodynamics-question.892851/	# Got an astrophysics/ astrodynamics question... 1. Nov 10, 2016 ### Oracle1 How would a solar system need to be set up to provide a life bearing world, standard 1 g, with the surface area of Jupiter with a standard day / night 24 hour cycle? 2. Nov 10, 2016 ### phinds I think that would work if the Earth were the size of Jupiter and made of styrofoam. Since it's mass, not diameter, that determines orbit, the Earth would have the same orbital period and with the mass the same as Earth, but being made of styrofoam (approximately) it would have the surface area of Jupiter. Of course, it's hard to figure how you could have a planet made of styrofoam or any equivalently weighted matter. 3. Nov 10, 2016 ### Oracle1 What about outside celestial influences creating a constant counter gravitational effect? All the mass but the desired gravity. 4. Nov 10, 2016 ### phinds OOPS. I forgot to state that of course the gravity on the surface of the styrofoam planet would be way less than on Earth because same mass but much greater diameter 5. Nov 10, 2016 ### Oracle1 Thanks! But darn it, I'm going to have to figure something out! I need this planet to have standard mass and gravity. (though the thought of a Styrofoam planet is amusing.) I don't really want to Sci Fi this. I'm going to be bending just about every other rule into a pretzel for this story. My thinking is: if space is infinite with the possibility of infinite variety, then there must be some version of a solar system that could support a planet like this. I just wanted... NEEDED really, some help figuring out how to set it up. 6. Nov 10, 2016 ### phinds Learn the math of planetary orbits and figure out if one is possible, but a surface the size of Jupiter but gravity same as Earth is going to mean a styrofoam (or equivalent) planet. Period. 7. Nov 10, 2016 ### Oracle1 Well, That seems to put that idea to rest. Thanks for the feedback phinds.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9426472783088684, "perplexity": 1510.3096019288078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593142.83/warc/CC-MAIN-20180722080925-20180722100925-00052.warc.gz"}
http://www.lofoya.com/Solved/1012/in-a-mixture-60-litres-the-ratio-of-milk-and-water-2-1-if-the	# Easy Ratios & Proportion Solved QuestionAptitude Discussion Q. In a mixture 60 litres, the ratio of milk and water $2:1$. If the this ratio is to be $1:2$, then the quantity of water to be further added is: ✖ A. 20 litres ✖ B. 30 litres ✖ C. 40 litres ✔ D. 60 litres Solution: Option(D) is correct Quantity of milk = $60\times \dfrac{2}{3}=40\text{ litres}$ Quantity of water in it =$(60−40)$ litres =$20$ litres. New ratio =1:2 Let, the quantity of water to be added further be $x$ litres. Then milk : water = $\dfrac{40}{20+x}$ Now, \begin{align} \dfrac{40}{20+x}&=\dfrac{1}{2}\\ 20+x&=80\\ \Rightarrow x&=60 \end{align} Edit: For an alternative solution, check comment by Sravan Reddy. ## (2) Comment(s) Purnima Bamola () Initially m:w=2:1 in 60 l so, m=40 l and w=20 l finally m:w=1:2 milk will be same in both ratios so, 1=40 milk 2=80 water left water=80-20=60 l so, 60 l water should be added Sravan Reddy () Without writing equations: Initially its 2:1 of 60 litres. So, 40 litres and 20 litres Now for 1:2 ratio. Water should be $40*2=80$ litres. So, 60 litres should be added	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9460960626602173, "perplexity": 9800.623393782585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542657.90/warc/CC-MAIN-20161202170902-00187-ip-10-31-129-80.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/414775/query-on-brahmagupta-fibonacci-identity	Query on Brahmagupta-Fibonacci Identity According to Brahmagupta-Fibonacci Identity, for $p=q\cdot r$ we can prove if any two of the integers $p,q,r$ are of the form $a^2+n\cdot b^2,$ the third must of the same form This is probably a generalization of this problem or this Now, I want to determine the $n$ such that if $M=r\cdot s=a^2+n\cdot b^2$ where $(r,s)=1, r$ and $s$ must be of the same form for any integer pair $a,b$ Using Program, it seems that $n=1,2,3,7$ satisfy this I think the proof for $2$ will be required here We can safely assume $n$ to be square-free, as its square part(if any) can easily be merged with $b$ Now, if $(a,b)=d$ and $\frac aA=\frac bB=d\implies (A,B)=1$ and $a^2+n\cdot b^2=d^2(A^2+n\cdot B^2)$ As $n$ is square-free, $(A^2,n)=(A,n)=D$(say) and $\frac A{A_1}=\frac nN=D\implies (A_1,N)=1$ Subsequently, $A^2+n\cdot B^2$ becomes $D^2\cdot A_1^2+N\cdot D\cdot B^2=D(D\cdot A^2_1+N\cdot B^2)$ which is not of the form $a^2+n\cdot b^2$ unless $D$ or $N=1$ So, we can focus on $a^2+n\cdot b^2,$ where $(a,n\cdot b)=1$ Some observations can be made: $(1):$ If $p^c$ divides $M=a^2+n\cdot b^2,$ where integer $c\ge1$ and $p$ is prime, $a^2\equiv-n\cdot b^2\pmod {p^c}\iff (a\cdot b^{-1})^2\equiv-n\pmod {p^c}$ $\implies -n$ must be a Quadratic residue of $p^c$ This is a necessary condition for $p^c$ to be of the form $a^2+n\cdot b^2$ So, if $2^c$ (where $c\ge3,$) divides $M,n\equiv-1\pmod 8$ as $x^2\equiv e\pmod {2^c}$ is solvable with exactly $4$ solutions $\iff e\equiv1\pmod 8$ $(2):$ Generalizing the solution of this problem, Let's consider $2^x=a^2+n\cdot b^2$ As $n$ is odd and $(a,b)=1, a\cdot b$ must be odd One value of $x$ is $y,$ i..e, $2^y=a_1^2+nb_1^2$ and if the smallest value of $x$ is $x_\text{min},$ i.e., $2^{x_\text{min}}=a_2^2+n\cdot b_2^2$ $2^{x_\text{min}+y}=(a_1^2+n\cdot b_1^2)(a_2^2+n\cdot b_2^2)=(a_1a_2\pm n\cdot b_1b_2)^2+n(a_1b_2\mp a_2b_1)^2$ Observe that $a_1a_2\pm n\cdot b_1b_2,a_1b_2\mp a_2b_1$ are even and the highest powers of $2$ that divides each will be same $=2^k$(say). So, $2^{x_\text{min}+y-2k}=\left(\frac{a_1a_2\pm n\cdot b_1b_2}{2^k}\right)^2+n\left(\frac{a_1b_2\mp a_2b_1}{2^k}\right)^2$ Following this line, we can be prove $4^k,k\ge 2$ can be represented as $a^2+15b^2$ $2^{3k+2},k\ge 1$ can be represented as $a^2+31b^2$ • Please explain how $p, q, r, a, n, b$ are related. – Hans Engler Jun 8 '13 at 15:28 • @HansEngler, thanks for your observation.Incorporated the missed point. – lab bhattacharjee Jun 8 '13 at 15:33 • Can the answer employ number theory of quadratic number rings, such as results about Euclidean or unique factorization properties, or do you seek a more elementary answer? – Key Ideas Jun 8 '13 at 16:15 • @KeyIdeas, I want to know the pattern of $n$ (if any) via any valid method. – lab bhattacharjee Jun 10 '13 at 15:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8827069401741028, "perplexity": 357.6601878003445}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987835748.66/warc/CC-MAIN-20191023173708-20191023201208-00319.warc.gz"}
https://www.clayford.net/statistics/simulation-to-represent-uncertainty-in-regression-coefficients/?replytocom=1013	# Simulation to Represent Uncertainty in Regression Coefficients Working through Gelman and Hill’s book can be maddening. The exposition is wonderful but recreating their examples leads to new and exciting levels of frustration. Take the height and earnings example in chapter 4. It’s a simple linear regression of earnings on height. You’d think you could download the data from the book web site, use the code in the book, and reproduce the example. They sure lead you to think that. But it doesn’t work that way. For starters, when you load the data it has 2029 records. However the output of the regression in the book shows n = 1192. So subsetting needs to be done. As far as I can tell, the subsetting is not discussed in the book. Now the author has an “earnings” folder on his site under an “examples” directory, which contains a R file called “earnings_setup.R“. (Never mind the book itself doesn’t appear to mention this directory on the web site.) So this seems to be the place where we find out how to subset the data. The key line of code is ok <- !is.na (earn+height+sex+age) & earn>0 & yearbn>25 which creates a logical vector to subset the data. But when you run it and request the dimensions of the data frame you have 1059 records, not 1192! After trial and error I believe the subset to reproduce the results in the book should be ok <- !is.na (earn+height+sex) & earn>0 That gave me 1192. For the record, here’s my full code: heights <- read.dta ("http://www.stat.columbia.edu/~gelman/arm/examples/earnings/heights.dta") attach(heights) male <- 2 - sex # make male 1 (and therefore female = 0) ok <- !is.na (earn+height+sex) & earn>0 heights.clean <- as.data.frame (cbind (earn, height, sex, male)[ok,]) heights.clean$log.earn <- log(heights.clean$earn) OK, so now(!) we can reproduce their example: earn.logmodel.3 <- lm (log.earn ~ height + male + height:male, data=heights.clean) The reason I was interested in this example was for another example in chapter 7 on "using simulation to represent uncertainty in regression coefficients" (p. 142). In other words, instead of using the standard errors and intervals obtained from the predict() function in R, we compute uncertainties by simulation. It seems easy enough using the sim() function from the book's arm package. You do something like the following: library(arm) sim.1 <- sim(earn.logmodel.3, 1000) The sim function takes two arguments: your model and the number of simulations. It returns a vector of simulated residual standard deviations and a matrix of simulated regression coefficients. We can use these to calculate confidence intervals for coefficients that do not have standard errors in the regression output. Their example asks "what can be said about the coefficient of height among men?" If you look up at the model, you can see it contains an interaction term of height and male. To answer the question we can't just look at the standard error of the height coefficient or just the interaction coefficient. There is no simple way to do what they ask using regression output. So the book instructs us to use the output of the sim function to answer this as follows: height.for.men.coef <- sim.1$beta[,2] + sim.1$beta[,4] quantile(height.for.men.coef, c(0.025,0.975)) Except that doesn't work. More frustration. It produces an error that says "Error in sim.1$beta :$ operator not defined for this S4 class" (instead of giving us a 95% interval). With some googling and persistence I was able to determine that the following is how it should be done: height.for.men.coef <- sim.1@coef[,2] + sim.1@coef[,4] quantile(height.for.men.coef, c(0.025,0.975)) 2.5% 97.5% -0.0004378039 0.0507464098 Notice that "@coef" replaces "$beta". And with that I was able to finally reproduce the example I was interested in! Now about this simulation function. While I appreciate functions that save time and make life easy, I do like to know how they work. Fortunately Gelman and Hill provide pseudo-code in the book. It goes like this: 1. Run your regression to compute the vector $\hat{\beta}$ of estimated parameters, the unscaled estimation covariance matrix $V_{\beta}$, and the residual variance $\hat{\sigma^{2}}$ 2. Create n random simulations for the coefficient vector $\beta$ and residual standard deviation. For each simulation draw: 1. Simulate $\sigma = \hat{\sigma}\sqrt{(n - k)/X}$ where X is a random draw from the $\chi^{2}$ distribution with n - k degrees of freedom. 2. Given the random draw of $\sigma$, simulate $\beta$ from a multivariate normal distribution with mean $\hat{\beta}$ and variance matrix $\sigma^{2}V_{\beta}$ Not too bad. Let's use this to manually run our own simulations, so we have an idea of how the sim() function works. (Plus you may not want to use the arm package as it requires loading 9 more packages.) Step 1 is easy enough. That's just running your regression as you normally would. Next we need to extract our estimated parameters, the unscaled covariance matrix and the residual standard deviation. We also need to snag degrees of freedom for our chi-square random draw. Here's how we can get them: # extract coefficents earn.logmodel.3$coef # extract residual standard error from model summary(earn.logmodel.3)$sigma # extract unscaled covariance matrix summary(earn.logmodel.3)$cov.unscaled # extract k and n - k; first two elements in vector summary(earn.logmodel.3)$df Let's use this information to do a single simulation. s.hat <- summary(earn.logmodel.3)$sigma n.minus.k <- summary(earn.logmodel.3)$df[2] library(MASS) # need for mvrnorm function to simulate draws from multivariate normal dist'n # simulate residual standard deviation (s.hat.sim <- s.hatsqrt(n.minus.k/rchisq(1, n.minus.k))) [1] 0.8591814 # use simulated residual standard deviation to simulate regression coefficients mvrnorm(1,earn.logmodel.3$coef, s.hat.sim^2summary(earn.logmodel.3)$cov.unscaled) (Intercept) height male height:male 7.906605029 0.025163124 -0.160828921 0.007904422 That seems to work. How about we try doing 1000 simulations. Here's one way: n <- 1000 sim.2.sigma <- rep(NA,n) sim.2.coef <- matrix(NA,n,4) for (i in 1:n){ sim.2.sigma[i] <- s.hatsqrt(n.minus.k/rchisq(1, n.minus.k)) sim.2.coef[i,] <- mvrnorm(1,earn.logmodel.3$coef,sim.2.sigma[i]^2summary(earn.logmodel.3)$cov.unscaled) } Now let's see how our simulation results compare to what we got using the sim() function: height.for.men.coef.2 <- sim.2.coef[,2] + sim.2.coef[,4] quantile(height.for.men.coef.2, c(0.025,0.975)) 2.5% 97.5% -0.001828216 0.049499381 Looks similar to what we got above. Nice. It's probably better to just use the sim() function for this sort of thing, but at least now we know a little more about what it's doing. ## 5 thoughts on “Simulation to Represent Uncertainty in Regression Coefficients” 1. Tom Cochrane I had similar problems accessing coefficients from simulations even earlier in the book (Ch 4.1 uncertainty in linear fits). Your post, which I got to after a couple of hours of frustration and Googling, gave me the answer I needed – swap an @ for a$. I agree, the book is a mixture of dream and nightmare! Many thanks, Tom 2. Sarah H. You rock! I had the same “\$beta” problem using the sim f(x) and you saved me a lot of time and frustration! Many thanks, Sarah This site uses Akismet to reduce spam. Learn how your comment data is processed.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 10, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7344430088996887, "perplexity": 1430.655056257758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540519149.79/warc/CC-MAIN-20191209145254-20191209173254-00385.warc.gz"}
http://codeforces.com/blog/entry/58754?locale=ru	### Блог пользователя vntshh Автор vntshh, 2 недели назад, , Hi Codeforces! Programming Club, IIT Indore and Euristica 2018 are proud to present our flagship event, Divide By Zero! The contest will take place on Saturday, 7th April at 9:35PM IST. Prizes : Codeforces T-shirts for top 15 participants overall and top 15 participants in India. Thanks to the following people for making the round possible : There are 8 problems, and 2.5 hours to solve them. The points distribution will be updated later. Euristica, sponsored by Arcesium is the inaugral Programming festival of IIT Indore. It comprised of 10 events this year, spanning across various domains like Competitive Programming, Application Development, Cyber Security and Machine Learning. For more information, visit www.euristica.in . Hope you guys enjoy the contest! See you on the leaderboard! UPD: The scoring distribution is 500-1000-1500-2000-2250-2500-3000-3500. UPD 2: Do give your feedback here : https://goo.gl/forms/xbsdMxnkA3XsG4092. Would love to hear your feedback, since that would help us get better! We hope you guys enjoyed the contest and found the problems interesting. UPD 3: You can find the editorial here. Here are the list of winners who won Tshirts. We will contact you guys soon. Congrats! Overall Top 15: Top 15 in India: • • +316 • » 2 недели назад, # \| 0 I think it will be funny, thank you. » 2 недели назад, # \| ← Rev. 2 → +41 First palindrome lucky round of 2018! Sounds good » 2 недели назад, # \| +64 » 2 недели назад, # \| +32 All Divide By Zero rounds: -------------------------------------- 2013 2014 2015 2016 2017 2018 » 2 недели назад, # \| ← Rev. 2 → -54 All number is not able to divide by zero except these number 2013,2014,2015,2016,2017 and 2018.So the divisors of zero are increasing year by year. :D :D :D » 2 недели назад, # \| +24 I hope one day i will get a T-shirt from Codeforces, I think it will be the best gift ever • » » 2 недели назад, # ^ \| 0 suppose the best gift ever will be the invitation from a good company))) • » » » 2 недели назад, # ^ \| ← Rev. 2 → 0 Yeah , it's also a good gift » 2 недели назад, # \| -10 Hope all the problem statements will be short and Contest will be enjoyable. :) :) » 2 недели назад, # \| -56 We have solved A & C & D of last Div.2 Round[#473] in videosWait us for more videos after contesthttps://www.youtube.com/channel/UCmWvb73kIq_oRThWd05Mtfg • » » 2 недели назад, # ^ \| +65 You better create a blog post to invite to your channel instead of irrelevant comment here. • » » » 13 дней назад, # ^ \| -34 It's okay , it's very good idea • » » 13 дней назад, # ^ \| +74 I just visited your channel. You should have mentioned that your videos are in Arabic language. • » » » 13 дней назад, # ^ \| -27 Okay, you are right. » 2 недели назад, # \| -25 Rated？ • » » 13 дней назад, # ^ \| +15 It always is, unless stated otherwise. » 2 недели назад, # \| +116 » 13 дней назад, # \| 0 See you in the leadboard ! So let's paying for a miracle » 13 дней назад, # \| -30 Thanks to organizers of IIT Indore , i hope i will make a great jump in my ratings. » 13 дней назад, # \| +35 I must choose "Divide by Zero or Manchester's derby!". » 13 дней назад, # \| -49 Should I watch IPL or participate in the contest? Help me! • » » 13 дней назад, # ^ \| 0 If you will get any help. Please share with me! • » » 13 дней назад, # ^ \| +8 Participating in a programming contest is better than watching a 'fixed match'. I think. • » » 12 дней назад, # ^ \| -6 I watched IPL and I regret. » 13 дней назад, # \| +17 The problems distribution? » 13 дней назад, # \| ← Rev. 2 → +22 What's wrong about the problem statement? » 13 дней назад, # \| +1 Hack page is not loading for me • » » 12 дней назад, # ^ \| +4 And me.I have just installed a plug-in that has to be an alternative of adobe flash player, but no response.Why it's not as the Educational rounds? I'm talking about the way of displaying the source code for hacking.Please MikeMirzayanov, do something for this. • » » » 12 дней назад, # ^ \| +2 In the usual codeforces round, you cannot copy others' codes to try. It is so easy and less unseccessful hacking attempt. However, in the edu round, there is no award if you have a successful hacking attempt, therefore, you can copy it and try • » » » » 12 дней назад, # ^ \| ← Rev. 2 → 0 OK, not bad. But isn't there another way to display the source code with that property and without depending on adobe flash player?Anyway, Thank you for the explanation. • » » 12 дней назад, # ^ \| 0 I used to face this problem on Google Chrome. Now I use Firefox for hacking, works all the time! » 13 дней назад, # \| 0 why is it so difficult to check the problem statement for the first task? can I get my hacked attempt points back? » 13 дней назад, # \| ← Rev. 2 → -17 Initially the text in the problem did not appear properly and some confusion in problem description (A) also. » 12 дней назад, # \| -16 could someone hack my code » 12 дней назад, # \| +8 Will the round be rated? » 12 дней назад, # \| +19 In my opinion, E and F are too standart, maybe they would be better for educational rounds. » 12 дней назад, # \| -6 Thank you for the round with hacks. It was very interesting! » 12 дней назад, # \| 0 In problem C, I realized c[0] = c[1] is possible after locked.. » 12 дней назад, # \| 0 How to solve D? • » » 12 дней назад, # ^ \| 0 I stored an array of shifts for each level. When type 1 query comes, increase the shift for that level by K. When type 2 query comes, increase the shift for that level by K, and also the shift for the level after by 2k, and after that 4k... to the end of the array (which will be size 63 or something to get max number of elements). When type 3 query comes, find where that node is and go up by dividing by 2. Then you just need to subtract the shifts on each level as you go up. Sample: http://codeforces.com/contest/960/submission/37077181 • » » » 12 дней назад, # ^ \| 0 Okay. Thanks » 12 дней назад, # \| 0 how to solve B? • » » 12 дней назад, # ^ \| +1 If instead of keeping ai and bi, we keep ci= \| ai — bi\|, then our task is to use k1+k2 operations to reduce the cost. So you'll go through the array, find the maximum and decrease the value by 1. If all the elements are 0 it means that you are in an optimal point and the way to go from here is to add 1 and then decrease 1 to the same position up until you don't have any operations left. • » » » 12 дней назад, # ^ \| 0 isn't that tle.... finding max value for n and for(k1+k2) operations • » » » » 12 дней назад, # ^ \| 0 O(10001000) certainly isn't TLE • » » » » » 12 дней назад, # ^ \| 0 thanks man.. i thought i had to be more analytical... i thought about calculating summation(difference) — (k1+k2).....and get a mean from it...then distribute the difference somehow equal to the mean while maintaining k1+k2 operation... it was a bad idea • » » » » » » 12 дней назад, # ^ \| +1 Correct thinking for a long contest, but for contests that last so short, write anything that works(even though it's not optimal). Cheers • » » 12 дней назад, # ^ \| +5 Make a priority queue of the biggest differences between a and b. You can use the greedy approach then : just reduce 1 from the biggest difference that exist (i.e. remove biggest element from pq, reduce it by 1, and add the reduced number to the priority queue)If the priority queue becomes empty while you still have attempts, the minimum result will just be number of remaining attempts modulo 2. • » » » 12 дней назад, # ^ \| 0 Why are we always reducing 1 from the biggest difference ? Why can't we reduce 1 from smaller difference ? • » » » » 12 дней назад, # ^ \| +3 since what counts is the square from the difference, it's always the biggest one that will give the biggest reduction : the reduction of a difference d gives a reduction in total points of :d²-(d-1)²=2d-1 which is an increasing function in d (except for d=0 which is a special case), so it's always better to reduct the biggest difference first. » 12 дней назад, # \| 0 C? • » » 12 дней назад, # ^ \| 0 If you keep a sequence that is all 1's (ie 1 1 1 1 .. 1) the cost is 2^(no of 1's)-1. So you're going to find the largest k so that x>= 2^k -1 and then decrease x by 2^k -1 and add k equal values to your solution. You just have to be careful because the last k values should be larger than the others by at least D. » 12 дней назад, # \| +5 What is the hack for C? • » » 12 дней назад, # ^ \| 0 1000000000 1 is possible • » » » 12 дней назад, # ^ \| +1 Is there any test that it is impossible to create a desired array so the result is "-1"?I saw that there isn't any "-1" in this problem! • » » 12 дней назад, # ^ \| 0 268435356 1 • » » 12 дней назад, # ^ \| 0 1000000000 1 » 12 дней назад, # \| 0 Is there an easier solution for E other than 3 dp's? • » » 12 дней назад, # ^ \| 0 Centroid Decomposition • » » » 12 дней назад, # ^ \| +75 You call Centroid Decomp easier than DP? o.O • » » 12 дней назад, # ^ \| -6 Yep. Just one improvised DFS will do the trick, and I would have done it, if not for the electricity going off... • » » » 12 дней назад, # ^ \| 0 Care to expand please? • » » » 12 дней назад, # ^ \| 0 pls , explain, I am intrigue. » 12 дней назад, # \| 0 how to solve C ? • » » 12 дней назад, # ^ \| 0 the sequence of length n contains 2^n-1 sequences. Hence, the number X can be decomposed into powers of two minus 1. The degrees of the twos in this decomposition are the lengths of the sequences to be used. The degrees of the twos in this decomposition are the lengths of the sequences to be used. Collect on parts. The final sequence will look like:1,1,1,....,1+(d+1),1+(d+1),....,1+(2d+1),1+(2d+1),...where the number of identical terms is equal to the powers of the twos to which we decomposed X.If the number X cannot be completely decomposed into (2^i-1), then at the end of the answer it is necessary to add Another f distinct numbers, each of which will increase from the previous one by d+1. Do not forget to take into account that the length of the answer should not exceed 10000 • » » » 12 дней назад, # ^ \| +6 Answer length never excceeds ~465 by this way. I guess we can forget about the last condition. » 12 дней назад, # \| 0 Why is this simple dfs going TLE?Source • » » 12 дней назад, # ^ \| ← Rev. 3 → 0 Consider case 2 1000001 2 12 1 21 2 3and so on. The simple dfs checks 50000 edges 50000 times, making it . » 12 дней назад, # \| +84 Putting only case where sum of Vi is 0 in E's pretests...Anyway, how to solve G? And is there any technique to deal with counting permutation? • » » 12 дней назад, # ^ \| -9 Surely it is better to put hard cases in the pretests than real tests... would you rather fail and not be able to fix it?? • » » 12 дней назад, # ^ \| +22 Holy shit, I added 2 sum of the values to the answer. RIP good place • » » 12 дней назад, # ^ \| 0 I found some pattern. Which included Pascal triangle and Stirling number of the first kind. I generated the required Stirling number with FFT but got WA :/ I think I should have used NTT or maybe there's a lot simpler solution or something. • » » 12 дней назад, # ^ \| +5 I am very thankful that this did not change my rank! :P » 12 дней назад, # \| 0 Anyone knows Pretest 4 of question D • » » 12 дней назад, # ^ \| +3 I think it is large numbers or something, I got a run time error that I fixed by increasing the size of my array :P • » » » 12 дней назад, # ^ \| +6 3 3 1000000000000000000 1 12345 13 3 1000000000000000000 » 12 дней назад, # \| 0 it really feels good to see my mistake in c after 1 min from the end of the contest » 12 дней назад, # \| +3 Initially the text in the problem did not appear properly, but surprisingly few were able to solve before it appeared properly. » 12 дней назад, # \| 0 Is NTT a must in problem G or it can be done with FFT? Or does it have some simpler solution? • » » 12 дней назад, # ^ \| +1 There is a work around to do FFT under large Modulo. But in this problem it might be risky, as it is time consuming. The idea is -Lets take C = 30000. Now partition each number A(x) as Ca1i + a2i, and B(x) as Cb1i + b2i. Then convolute P = a1 × b1, Q = a1 × b2, R = a2 × b1, S = a2 × b2.You can get the final result as (A × B)i ≡ C2pi + C(qi + ri) + si (mod M). It works because no number while doing fft corsses NC2 and fits into precision. But you can't do fft directly into the main polynomial, then a number can be atmost NM2, and that will overflow. » 12 дней назад, # \| +4 How to solve F? • » » 12 дней назад, # ^ \| 0 If you make a new graph so that the edges are the nodes and the nodes are the edges, you'll have exactly the same problem but you'll have to find the longest path of increasing nodes. This is done by going through the nodes in the order of their values and updating a dp[node]=longest increasing sequence ending in node. • » » » 12 дней назад, # ^ \| 0 ok, but how to "make" the new graph in time? • » » » » 12 дней назад, # ^ \| ← Rev. 2 → +5 You don't really have to make it, you can just imagine it(so that the solution is easier). So for the solution you make dp[node]=the longest sequence of increasing edges so that the last edge goes into node. You then take the edges, sort them by their cost, and then if you have edge (u,v), if dp[u] • » » » » » 11 дней назад, # ^ \| 0 The edges are directed and it seems your solution assumes the edges are undirected.Also, how do you make sure the edges are in the same order as the input? • » » » » 12 дней назад, # ^ \| 0 I don't think there is a way to make it without TL. The edge of a graph having every other vertex connected to vertex 1 has NN edges in it. • » » » 12 дней назад, # ^ \| 0 can't there be (10^10)/4 edges in the new graph? • » » » » 12 дней назад, # ^ \| 0 You don't really have to make it, you can just imagine it(so that the solution is easier). So for the solution you make dp[node]=the longest sequence of increasing edges so that the last edge goes into node. You then take the edges, sort them by their cost, and then if you have edge (u,v), if dp[u] • » » 12 дней назад, # ^ \| 0 It seems like dp and maintaining array of sets(couldn't implement it in time though). • » » 12 дней назад, # ^ \| ← Rev. 3 → +5 Let's loop over the edges in reversed order and assume that the current edge will be the beginning of the path. This way we kinda eliminate the condition about indices being increasing and only have to worry about weights.Define f(node)(w) as the maximum length of a path if we start at node with an edge of weight w. Let's say the current edge goes from A to B and has weight C. Now we have to update the value of f(A)(B) with the maximum value of f(B)(i) + 1 for i > C. Obviously keeping f(node) in the form of a segment tree, in which the indices are the weights of outgoing edges from node, does the job. • » » » 12 дней назад, # ^ \| 0 I did all of this but stopped at the f(node) part because the segment tree of each node can be as large as 100000 (number of weights), is it something like dynamic segment tree or a segment tree with coordinate compression? • » » » » 12 дней назад, # ^ \| +5 Thing is, you have to keep f(node)(w) only if there is an outgoing edge from node with weight w, that means O(M) cells in total. So for each node we can simply sort those weights of outgoing edges and then binary search over them to find the proper indices for querying. https://pastebin.com/ZDqFAcNi • » » » » » 12 дней назад, # ^ \| 0 Thank you » 12 дней назад, # \| ← Rev. 2 → +10 "Вам нужно выбрать путь (возможно, проходящий по одному и тому же ребру или вершине несколько раз)""You need to choose a path (possibly passing through same vertices multiple times)"Почему в условиях на русском (т.е. в переводе) внезапно появляются дополнительные условия? Без переключения на английские условия было непонятно, то ли веса на рёбрах должны неубывать (и рёбра могут повторяться), то ли должны строго возрастать (и рёбра повторяться не могут). Ну то есть, как так получилось?В задаче A, возможно, была та же проблема про уточнение того, что начальная строка может быть пустой (либо это исправили в момент, когда я переключился на английские условия). » 12 дней назад, # \| +76 The point distribution is really unfair. I mean 2500 for F and 3000 for G, when there is a huge difference in difficulty :/ » 12 дней назад, # \| -23 Is it rated? » 12 дней назад, # \| 0 What is the problem with this code?:(37063101 • » » 12 дней назад, # ^ \| +13 That's not how you read the arrays :P • » » » 12 дней назад, # ^ \| +26 Why am I still alive?:(( • » » 12 дней назад, # ^ \| 0 ans should be long long imo • » » » 12 дней назад, # ^ \| ← Rev. 3 → 0 define int num » 12 дней назад, # \| +10 How Tricky!! • » » 12 дней назад, # ^ \| 0 I don't understand that. "At least one 'a' and one 'b' exist" mean that there must at least one 'A' or one 'B' in the string. Then why not handling the case when there's no 'a' or 'b' will fail? • » » » 12 дней назад, # ^ \| 0 most people read it fast, so they didn't care. • » » » » 12 дней назад, # ^ \| +1 I mean, the statement should be "At least one 'a' or one 'b' exist", right? • » » » » » 12 дней назад, # ^ \| 0 Yes, it must be. see the difference!! https://www.englishforums.com/English/LeastLeast/qrvll/post.htm • » » » » » » 12 дней назад, # ^ \| ← Rev. 2 → 0 Who translated this problem??? This is a huge error in the statement!And how could one detect this out? • » » » » » » » 12 дней назад, # ^ \| ← Rev. 2 → 0 I think there is another Opinion in the same link. see, "At least one "A and B" would mean one or more "A and B" as he writes. But at least one OF A and B means A alone, or B alone, or both." • » » » » » » » » 12 дней назад, # ^ \| 0 Sorry, but in the previous reply,"A and B" would mean one or more ("A and B") mean that must be one of A and B in the string. I am very confusionّ! many people have many opinions! But Finally, it should be in the statement in a clear way. • » » » » » » » 12 дней назад, # ^ \| +10 It was me who made a huge error. The "At least one 'a' and one 'b' exist" thing is for the string A and B made, not the string in the input. » 12 дней назад, # \| +46 G : https://www.youtube.com/watch?v=E-i5nrl4SaI + https://www.quora.com/How-can-I-calculate-the-Stirling-numbers-of-the-first-kind. First was one of our icpc practice (and actually a famous DP practice problem, for a lower constraint), and second was pure googling.To be honest, I still don't know what's the "First kind of Stirling number". It's always so fun to get a rating that I don't deserve! • » » 12 дней назад, # ^ \| 0 Did you use FFT or NTT? If FFT, then how did you handle the mod? • » » » 12 дней назад, # ^ \| 0 I used NTT.For handling mods in FFT, look here : http://codeforces.com/blog/entry/48465 • » » » » 12 дней назад, # ^ \| 0 I got WA because I couldn't handle mod in FFT :( • » » 12 дней назад, # ^ \| 0 Can you explaine please, what is the complexity of your F and how it fit in time?37057703Because, I can see you use Divide&Concuer, but at each step use have sort()And you should have: T(n) = 2T(n/2) + O(nlogn) • » » » 12 дней назад, # ^ \| 0 Yeah T(n) = nlg^2n, why not • » » 12 дней назад, # ^ \| +8 Haha, I worked out the formula with one (1) Stirling number using the generating function of Stirling numbers (u generates A or B, z generates N).We want to compute the convolution of sequences \sum_n \left[n, K\right] / n!Unable to parse markup [type=CF_TEX] and K = B - 1 with sum of n equal to N - 1, then multiply it by (N - 1)!; in other words, we want the N - 1-th coefficient of fA - 1(x)fB - 1(x), where .Since , fK is the K-th coefficient of the Taylor series of g with respect to u. We can get it as Hey, the product $f_{A-1}(x) f_{B-1}(x)$ is proportional to fA + B - 2(x)... and we can extract the N - 1-th coefficient by differentiating again: Alternatively, we can use the definition of fA + B - 2 to write it as » 12 дней назад, # \| 0 Can someone point out what's wrong with my code for B? I still can't figure what did I do wrong. • » » 12 дней назад, # ^ \| 0 There is nothing wrong with the code. The idea is just wrong. The right solution is to minimize the max difference, but you just use all your moves to completely remove a difference or two.Instead, find the max difference, remove or add 1 to it, repeat... Sometimes you'll need to add because you must use all the moves. • » » » 12 дней назад, # ^ \| 0 Oh. I guess I never saw it like that. I thought removing maxDiff square would have more impact than minimizing it each time. Thanks for your input. • » » » » 12 дней назад, # ^ \| 0 Array of diffs [1,1] has error = 1^2 + 1^2 = 2. While [0,2] has error = 0^2 + 2^2 = 4 » 12 дней назад, # \| 0 37063254 Can anybody tell me what is wrong with this one?:) • » » 12 дней назад, # ^ \| ← Rev. 3 → +1 since x is int, xx can overflow. It should 1llx*x. Testcase1 0 0 1000000 0 » 12 дней назад, # \| 0 what's the test 18 for E? • » » 12 дней назад, # ^ \| 0 Maybe when sum of all vi's is not zero. So that you will have to consider zero length paths.. not sure though • » » 12 дней назад, # ^ \| 0 they intentionally put the sum of vi = 0 in the first 17 cases so that if you are counting A(u,u) 2 times your code passes pretests but fails system testing... » 12 дней назад, # \| 0 Laughed over people who get WA because of long long in B and made myself the same mistake in C. Stupid karma. • » » 12 дней назад, # ^ \| 0 I submitted that wrong twice. Fuck. » 12 дней назад, # \| +95 You really did intentionally generated pretests in E having zero sum over all vertices to break solution that don't consider zero-length pathes. Welcome to the faggots club :\ • » » 12 дней назад, # ^ \| 0 Nice I had written ans=0 and then added numbers in vertexes earlier in the code, very good descent CF one love » 12 дней назад, # \| -21 @CF :(( » 12 дней назад, # \| +26 My solution of F fails(returns 2) on this test: 3 2 1 2 1 2 3 1 But got accepted! :-? • » » 12 дней назад, # ^ \| 0 What's wrong with it? • » » » 12 дней назад, # ^ \| +5 It says weights of the edges should be in strictly increasing order. • » » 12 дней назад, # ^ \| +10 The same here. Realized it during the contest and resubmitted. Facepalm » 12 дней назад, # \| -13 Problem D was really a very interesting problem. • » » 10 дней назад, # ^ \| +3 Get your code Accepted then, sir. • » » » 10 дней назад, # ^ \| 0 What is the relation between seeing that the problem is interesting and getting it accepted ? • » » » » 10 дней назад, # ^ \| 0 It will make you feel good! » 12 дней назад, # \| +46 Not that I'm complaining, but this solution 37079339 for G passed all tests (3493 ms), while on test "100000 32768 32768" it works 4461ms in "Run On Server" tab. It is strange not to add such a test, given that 2n - 1 is the worst case for logarithmic exponentiation.(if anything, I'd complain about such an ambiguous TL, which allows to pass only some of the solutions) • » » 12 дней назад, # ^ \| +5 I think the major issue is in CF server, which runs in 32bit environment (Thus being very slow on 64bit integer operations) • » » 12 дней назад, # ^ \| 0 Your NTT code is slow. Example, when multipling two small polynomials, you still need a inversion function. O(NlogN) may be found at here: https://discuss.codechef.com/problems/CHEFKNN. • » » 12 дней назад, # ^ \| ← Rev. 2 → 0 And this submit in last 5 sec of contest threw me out of top 15 =( • » » » 12 дней назад, # ^ \| +6 Sorry about that :) I wasn't submitting this till the end of the contest, just because I knew the test for which it is too slow on CF servers. In such case the best tactics is to submit at the very end (=> no hacks), and hope that tests are weak. This is exactly what happened. » 12 дней назад, # \| 0 For the 3rd question I assumed that the elements of the array should be distinct and then for next 1 and half hour I was busy solving the question,also with 3 failed pretest.Later Did I recognised that no-where it was mentioned that the element should be different. Feeling so stupid. » 12 дней назад, # \| +38 Ok contest, the problems were kinda standard-ish, but at least the pretests and tests weren't dumpster fire quality and everything that needed to work (server) worked. Google could learn from this.F was way, way too easy. It's LIS, just with a graph, and it's solved exactly like LIS, just with a graph. I spent about 10 seconds thinking about how to solve it. It would've been better to use something with difficulty between E and G rather than below (this) D.My rating increased! by 2 points » 12 дней назад, # \| ← Rev. 4 → +40 Top 15 Indians:gvaibhav21evil666manBabayashChandnaniteja349jtnydv25ajinkya1p3polingyhitman623GT_18Equinoxsinus_070ShivRamabishekanishant_coder » 12 дней назад, # \| +5 i think problem D E and F have same diffilcultiesnice problem and rapid rating update anyway » 12 дней назад, # \| 0 IN PROBLEM "A" it is written that-> " they have made sure that at this point, at least one 'a' and one 'b' exist in the string." how have they given test case with only bbbbbbbbbb!!! this seems unfair • » » 12 дней назад, # ^ \| +1 You misinterpreted the question. It means that the string has to have at least one a and b to be valid. • » » » 12 дней назад, # ^ \| 0 YES..Thank you.. • » » 12 дней назад, # ^ \| +6 In such a test case, you're suppossed to output NO. » 12 дней назад, # \| ← Rev. 3 → 0 Can anyone tell me what's wrong in my solution 37078196 for D. And why commenting this line gives AC. m=m-(pow(2,t1)); » 12 дней назад, # \| ← Rev. 2 → 0 Got wrong answer in Problem C pretest 1.vector < int > v = {1, 2, 3}; printf("%lld\n",v.size());Output in codeforces ( GNU++11 5.1.0 ) : 55834574851output in my pc ( g++ follows c++11 ) : 3 • » » 12 дней назад, # ^ \| +1 You can't print a variable of data type size using printf and %lld, you should cast it to long long first or use cout • » » 12 дней назад, # ^ \| +9 With printf you need to be very careful about types. If you give the function a parameter of the wrong type, it will print garbage.And here is the problem. The size of the type of v.size() is not standardized. It doesn't have to be a 64 bit integer (although g++ will usually use 64 bit). However Codeforces uses a g++ compiler where v.size() is only 32 bit.Solutions: cast the variable to a long long, or simply use cout << v.size() << '\n'; :-P • » » » 12 дней назад, # ^ \| ← Rev. 2 → +5 Or use %zu to printf a variable of type size_t (which is the return type of vector::size). • » » » 11 дней назад, # ^ \| 0 The size of int, long and long long isn't standardised either. The C standard only requires that they're enough to hold specific ranges. In the same way, size_t only has to be able to represent the return value of sizeof().Different types are differently represented in memory, and you should be very glad implicit type conversions exist in the simplest cases at all (casting a 4-byte int to an 8-byte long long could give you 4 bytes of garbage, but it doesn't). » 12 дней назад, # \| +2 When will we get the Editorial of this contest?TIA. :) » 12 дней назад, # \| 0 During the contest my code for D kept getting TLE. Now it's AC in 2 seconds. The servers are really unreliable; I had to spend a bunch of time optimizing AC code with good complexity. :/ » 12 дней назад, # \| +1 This was an amazing contest! When will the editorials be published? » 12 дней назад, # \| 0 How Solve E? » 12 дней назад, # \| +3 I saw many of my friends AC 4 problems but fst 3 of them! I have too say E and F are too standard ,Why don't put int the Education contest!? » 12 дней назад, # \| +12 where is the editorial?? » 12 дней назад, # \| 0 Hey guys!Before the official editorial comes, here are some of my thoughts on problem A, B, C, D, F: RobeZH Blogspot ArticleI am glad to hear any suggestions or questions! Thanks! » 12 дней назад, # \| ← Rev. 3 → +6 problem F http://codeforces.com/contest/960/submission/37093065 KAN this solution got accepted but fails on this test case 4 5 1 2 3 2 3 4 3 3 5 1 3 5 3 3 6 • » » 12 дней назад, # ^ \| +2 true, the tests were weak, i dont get why they didnt reevaluate the solutions » 12 дней назад, # \| -6 I gotta a native question that hou can I get purple? Desire to improve my ability of coding... • » » 11 дней назад, # ^ \| +4 It is not the right place to ask such question. If you search on google, you will find plenty of posts regarding such question and replies on Codeforces and Quora. If you still think that you need to ask something regarding this, you may create a blog post on codeforces or ask on quora. • » » » 11 дней назад, # ^ \| 0 Okay,I got it.Thanks » 11 дней назад, # \| ← Rev. 2 → -22 The people on codeforces community are racist.They downvote you, just because you are grey. • » » 11 дней назад, # ^ \| 0 I am white. But they didn't leave me either -_- • » » 10 дней назад, # ^ \| 0 colorists	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.521757960319519, "perplexity": 4364.378650438655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937114.2/warc/CC-MAIN-20180420042340-20180420062340-00582.warc.gz"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=128&t=27269&p=83102	## delta u [ENDORSED] isochoric/isometric: $\Delta V = 0$ isothermal: $\Delta T = 0$ isobaric: $\Delta P = 0$ Belle Calforda3f Posts: 67 Joined: Fri Sep 29, 2017 7:07 am ### delta u I just really do not understand delta u: what It means, how to caluculate it, how to know if it equals 0. Can anyone help? thanks Tiffany Cao 1D Posts: 94 Joined: Fri Sep 29, 2017 7:03 am Been upvoted: 1 time ### Re: delta u [ENDORSED] Delta U is the change in internal energy. It is calculated through the formula, DeltaU=q+w. In an isolated system, deltaU=0 and consequently, w=-q. Dang Lam Posts: 55 Joined: Thu Jul 27, 2017 3:01 am ### Re: delta u how do you know if delta u =0 though? is it because there is no change is temperature? since deltaU = 3/2 R deltaT, and since deltaT = 0, deltaU is therefore =0 as well? Nicole 1F Posts: 31 Joined: Fri Sep 29, 2017 7:05 am ### Re: delta u ^Yes, everything you said is correct. ΔU=0 for an isothermal process.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7803003191947937, "perplexity": 7400.791397347379}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141748276.94/warc/CC-MAIN-20201205165649-20201205195649-00685.warc.gz"}
http://mathhelpforum.com/discrete-math/135133-permutations-help.html	1. ## Permutations Help From the digits {1, 2, 3, 4, 5 ,6} How can you form 6 digit numbers that are 600 000 or greater. Also, if you could, succinctly, explain each step. Thanks, a lot. 2. Can the digits be repeated? i.e $\displaystyle 666,666$ ?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7423688173294067, "perplexity": 3446.6213185409374}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946578.68/warc/CC-MAIN-20180424080851-20180424100851-00031.warc.gz"}
https://socratic.org/questions/what-is-the-oxidation-number-of-nitrogen-in-nitrogen-gas-n-2	Chemistry Topics # What is the oxidation number of nitrogen in nitrogen gas N_2? Jul 19, 2016 $\text{Dinitrogen is zerovalent}$ #### Explanation: Oxidation number is the charge left on the central atom, when the bonding electrons are broken with the charge assigned to the most electronegative atom. For homonuclear diatomic molecules, i.e. dinitrogen, dioxygen, dihalogen, of course the atoms have equal electronegativities, and the charge is conceived to be shared. At any rate, the formal oxidation number of $N$ is ZERO. ##### Impact of this question 13185 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5784900784492493, "perplexity": 3308.4188374543937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571147.84/warc/CC-MAIN-20220810040253-20220810070253-00280.warc.gz"}
http://en.wikipedia.org/wiki/Seyfert_galaxy	# Seyfert galaxy The Circinus Galaxy, a Type II Seyfert galaxy Seyfert galaxies are one of the two largest groups of active galaxies, along with quasars. They have quasar-like nuclei (very luminous, distant and bright sources of electromagnetic radiation) with very high surface brightnesses whose spectra reveal strong, high-ionisation emission lines,[1] but unlike quasars, their host galaxies are clearly detectable. Seyfert galaxies account for about 10% of all galaxies[2] and are some of the most intensely studied objects in astronomy, as they are thought to be powered by the same phenomena that occur in quasars, although they are closer and less luminous than quasars. These galaxies have supermassive black holes at their centres which are surrounded by accretion discs of in-falling material. The accretion discs are believed to be the source of the observed ultraviolet radiation. Ultraviolet emission and absorption lines provide the best diagnostics for the composition of the surrounding material.[3] Seen in visible light, most Seyfert galaxies look like normal spiral galaxies, but when studied under other wavelengths, it becomes clear that the luminosity of their cores is of comparable intensity to the luminosity of whole galaxies the size of the Milky Way.[4] Seyfert galaxies are named after Carl Seyfert, who first described this class in 1943.[5] ## Discovery NGC 1068 (Messier 77), one of the first Seyfert galaxies classified Seyfert galaxies were first detected in 1908 by Edward A. Fath and Vesto Slipher, who were using the Lick Observatory to look at the spectra of astronomical objects that were thought to be "spiral nebulae". They noticed that NGC 1068 showed six bright emission lines, which was considered unusual as most objects observed showed an absorption spectrum corresponding to stars. In 1926, Edwin Hubble looked at the emission lines of NGC 1068 and two other such "nebulae" and classified them as extragalactic objects.[6] In 1943, Carl Keenan Seyfert discovered more galaxies similar to NGC 1068 and reported that these galaxies have very bright stellar-like nuclei that produce broad emission lines.[5] A year after, Cygnus A was detected at 160 MHz,[7] and detection was confirmed in 1948 when it was established that it was a discrete source.[8] Its double radio structure became apparent with the use of interferometry.[9] In the next few years, other radio sources such as supernova remnants were discovered. By the end of the 1950s, more important characteristics of Seyfert galaxies were discovered, including the fact that their nuclei are extremely compact (< 100 pc, i.e. "unresolved"), have high mass (≈109±1 solar masses), and the duration of peak nuclear emissions is relatively short (>108 years).[10] In the 1960-1970s, research to further understand the properties of Seyfert galaxies was carried out. A few direct measurements of the actual sizes of Seyfert nuclei were taken, and it was established that the emission lines in NGC 1068 were produced in a region over a thousand light years in diameter.[11] Controversy existed over whether Seyfert redshifts were of cosmological origin.[12] Confirming estimates of the distance to Seyfert galaxies and their age were limited since their nuclei vary in brightness over a time scale of a few years; therefore arguments involving distance to such galaxies and the constant speed of light cannot always be used to determine their age.[12] In the same time period, research had been undertaken in order to survey, identify and catalogue galaxies, including Seyferts. Beginning in 1967, Benjamin Markarian published lists containing a few hundred galaxies distinguished by their very strong ultraviolet emission, with measurements on the position of some of them being improved in 1973 by other researchers.[13] At the time, it was believed that 1% of spiral galaxies are Seyferts.[14] By 1977, it was found that very few Seyfert galaxies are ellipticals, most of them being normal or barred spiral galaxies.[15] During the same time period, efforts have been made to gather spectrophotometric data for Seyfert galaxies. It became obvious that not all spectra from Seyfert galaxies look the same, so they have been subclassified according to the characteristics of their emission spectra. A simple division into types I and II has been devised, with the classes depending on the relative width of their emission lines.[16] It has been later noticed that some Seyfert nuclei show intermediate properties, resulting in their being further subclassified into types 1.2, 1.5, 1.8 and 1.9 (see Classification).[17][18] Early surveys for Seyfert galaxies were biased in counting only the brightest representatives of this group. More recent surveys that count galaxies with low-luminosity and obscured Seyfert nuclei suggest that the Seyfert phenomenon is actually quite common, occurring in 16% ± 5% of galaxies; indeed, several dozen galaxies exhibiting the Seyfert phenomenon exist in the close vicinity (≈27 Mpc) of our own galaxy.[2] ## Characteristics Optical and ultraviolet images of the black hole in the centre of NGC 4151, a Seyfert Galaxy An active galactic nucleus (AGN) is a compact region at the centre of a galaxy that has a higher than normal luminosity over portions of the electromagnetic spectrum. A galaxy having an active nucleus is called an active galaxy. Active galactic nuclei are the most luminous sources of electromagnetic radiation in the Universe, and their evolution puts constraints on cosmological models. Depending on the type, their luminosity varies over a timescale from a few hours to a few years. The two largest subclasses of active galaxies are quasars and Seyfert galaxies, the main difference between the two being the amount of radiation they emit. In a typical Seyfert galaxy, the nuclear source emits at visible wavelengths an amount of radiation comparable to that of the whole galaxy's constituent stars, while in a quasar, the nuclear source is brighter that the constituent stars by at least a factor of 100.[1] Seyfert galaxies have extremely bright nuclei, with luminosities ranging between 108 and 1011 solar luminosities. Only about 5% of them are radio bright; their emissions are moderate in gamma rays and bright in X-rays.[19] Their visible and infrared spectra shows very bright emission lines of hydrogen, helium, nitrogen, and oxygen. These emission lines exhibit strong Doppler broadening, which implies velocities from 500 to 4,000 km/s (310 to 2,490 mi/s), and are believed to originate near an accretion disc surrounding the central black hole.[20] ### Eddington luminosity A lower limit to the mass of the central black hole can be calculated using the Eddington luminosity. This limit arises because light exhibits radiation pressure. Assume a simplified model where a black hole is surrounded by a sphere of luminous gas.[21] Both the attractive gravitational force acting on electron-ion pairs in the sphere and the repulsive force exerted by light follow an inverse-square law. If the gravitational force exerted by the black hole is less than the repulsive force due to radiation pressure, the sphere will be blown away by radiation pressure.[22] The image shows a model of an active galactic nucleus. The central black hole is surrounded by an accretion disc, which is surrounded by a torus. The broad line region and narrow line emission region are shown, as well as jets coming out of the nucleus. The gravitational force of the black hole can be calculated using $F_{grav}=\frac{GM_{BH}m_p}{r^2}$ The outward radiative force is equal to $F_{rad} =\frac{dp}{dt}=\frac{1}{c}\frac{dE}{dt}=\frac{1}{c}\sigma\frac{L}{4\pi r^2}$ $F_{rad}$ must be less than $F_{grav}$, therefore $\frac{1}{c}\sigma\frac{L}{4\pi r^2} < \frac{GM_{BH}m_p}{r^2}$ The luminosity of the black hole must be less than the Eddington luminosity. $L < L_{eddington} = \frac{4\pi c G M_{BH} m_p}{\sigma}$ $= 1.3 \times 10^{38} \frac{M_{BH}}{M_{solar}} \, erg/sec$ $= 30000 \frac{M_{BH}}{M_{solar}} L_{solar}$ In the above derivation, Frad is the outward radiative force, Fgrab is the gravitational force of the black hole, p = momentum, t = time, c = speed of light, E = energy, L = luminosity, r = radius of black hole, G = gravitational constant, MBH = mass of black hole, LEddington is the Eddington luminosity, mp is the proton mass, Msolar is the mass of the Sun and σ is the Stefan–Boltzmann constant. Therefore, given the observed luminosity (which would be less than the Eddington luminosity), an approximate lower limit for the mass of the central black hole at the centre of an active galaxy can be estimated.[19] ### Emissions The emission lines seen on the spectrum of a Seyfert galaxy may come from the surface of the accretion disc itself, or may come from clouds of gas illuminated by the central engine in an ionization cone. The exact geometry of the emitting region is difficult to determine due to poor resolution of the galactic center. However, each part of the accretion disc has a different velocity relative to our line of sight, and the faster the gas is rotating around the black hole, the broader the emission line will be. Similarly, an illuminated disc wind also has a position-dependent velocity. The narrow lines are believed to originate from the outer part of the AGN where velocities are lower, while the broad lines originate closer to the black hole. This is confirmed by the fact that the narrow lines do not vary detectably, which implies that the emitting region is large, contrary to the broad lines which can vary on relatively short timescales. Reverberation mapping is a technique which uses this variability to try to determine the location and morphology of the emitting region. This technique measures the structure and kinematics of the broad line emitting region by observing the changes in the emitted lines as a response to changes in the continuum. The use of reverberation mapping requires the assumption that the continuum originates in a single central source.[23] For 35 AGN, reverberation mapping has been used to calculate the mass of the central black holes and the size of the broad line regions.[24] In the few radio-loud Seyfert galaxies that have been observed, the radio emission is believed to represent synchrotron emission from the jet. The infrared emission is due to radiation in other bands being reprocessed by dust near the nucleus. The highest energy photons are believed to be created by inverse Compton scattering by a high temperature corona near the black hole.[25] ## Classification NGC 1097 is an example of a Seyfert galaxy. A supermassive black hole with a mass of 100 million solar masses lies at the centre of the galaxy. The area around the black hole emits large amounts of radiation from the matter falling into the black hole.[26] Seyferts were first classified as Type I or II, depending on the emission lines shown by their spectra. The spectra of Type I Seyfert galaxies show broad lines that include both allowed lines, like H I, He I or He II and narrower forbidden lines, like O III. They show some narrower allowed lines as well, but even these narrow lines are much broader than the lines shown by normal galaxies. However, the spectra of Type II Seyfert galaxies show only both permitted and forbidden narrow lines. Forbidden lines are spectral lines that occur due to electron transitions not normally allowed by the selection rules of quantum mechanics, but that still have a small probability of spontaneously occurring. The term "forbidden" is slightly misleading, as the electron transitions causing them are not forbidden but highly improbable.[27] In some cases, the spectra show both broad and narrow permitted lines, which is why they are classified as an intermediate type between Type I and Type II, such as Type 1.5 Seyfert. The spectra of some of these galaxies have changed from Type 1.5 to Type II in a matter of a few years. However, the characteristic broad emission line has rarely, if ever, disappeared.[28] The origin of the differences between Type I and Type II Seyfert galaxies is not known yet. There are a few cases where galaxies have been identified as Type II only because the broad components of the spectral lines have been very hard to detect. It is believed by some that all Type II Seyferts are in fact Type I, where the broad components of the lines are impossible to detect because of the angle we are at with respect to the galaxy. Specifically, in Type I Seyfert galaxies, we observe the central compact source more or less directly, therefore sampling the high velocity clouds in the broad line emission region moving around the supermassive black hole thought to be at the centre of the galaxy. By contrast, in Type II Seyfert galaxies, the active nuclei are obscured and only the colder outer regions located further away from the clouds' broad line emission region are seen. This theory is known as the "Unification scheme" of Seyfert galaxies.[29] However, it is not yet clear if this hypothesis can explain all the observed differences between the two types. ### Type I Seyfert galaxies Optical spectrum of the Type I Seyfert galaxy NGC 1275 Type I Seyferts are very bright sources of ultraviolet light and X-rays in addition to the visible light coming from their cores. They have two sets of emission lines on their spectra: narrow lines with widths (measured in velocity units) of several hundred km/s, and broad lines with widths up to 104 km/s.[30] The broad lines originate above the accretion disc of the supermassive black hole thought to power the galaxy, while the narrow lines occur beyond the broad line region of the accretion disc. Both emissions are caused by heavily ionised gas. The broad line emission arises in a region 0.1-1 parsec across. The broad line emission region, RBLR, can be estimated from the time delay corresponding to the time taken by light to travel from the continuum source to the line-emitting gas.[19] ### Type II Seyfert galaxies Type II Seyfert galaxies have the characteristic bright core, as well as appearing bright when viewed at infrared wavelengths.[31] Their spectra contain narrow lines associated with forbidden transitions, and broad lines associated with allowed strong dipole or intercombination transitions.[29] In some Type II Seyfert galaxies, analysis with a technique called spectro-polarimetry (spectroscopy of polarised light component) revealed obscured type I regions. In the case of NCG 1068, nuclear light reflected of a dust cloud was measured, which led scientists to believe in the presence of an obscuring dust torus around a bright continuum and broad emission line nucleus. When the galaxy is viewed from the side, the nucleus is indirectly observed through reflection by gas and dust above and below the torus. This reflection causes the polarisation.[32] ### Type 1.2, 1.5, 1.8 and 1.9 Seyfert galaxies In 1981, Donald Osterbrok introduced the notations Seyfert 1.5, 1.8 and 1.9, where the subclasses are based on the optical appearance of the spectrum, with the numerically larger subclasses having weaker broad-line components relative to the narrow lines. For example, Type 1.9 only shows a broad component in the line, and not in higher order Balmer lines. In Type 1.8, very weak broad lines can be detected in the lines as well as Hα, even if they are very weak compared to the Hα. In Type 1.5, the strength of the Hα and Hβ lines are comparable.[33] ### Other Seyfert-like galaxies In addition to the Seyfert progression from Type I to Type II (including Type 1.2 to Type 1.9), there are other types of galaxies that are very similar to Seyferts or that can be considered as subclasses of them. Very similar to Seyferts are the low-ionisation narrow-line emission radio galaxies (LINER), discovered in 1980. These galaxies have strong emission lines from weakly ionised or neutral atoms, while the emission lines from strongly ionised atoms are relatively weak by comparison. LINERs share a large amount of traits with low luminosity Seyferts. In fact, when seen in visible light, the global characteristics of their host galaxies are indistinguishable. Also, they both show a broad line emission region, but the line emitting region in LINERs has a lower density than in Seyferts.[34] An example of such a galaxy is M104 in the Virgo constellation, also known as the Sombrero galaxy[35] A galaxy that is both a LINER and a Type I Seyfert is NGC 7213, a galaxy that is relatively close compared to other AGNs.[36] Another very interesting subclass are the narrow line Seyfert I galaxies (NLSy1), which have been subject to extensive research in recent years.[37] They have much narrower lines than the broad lines from classic Seyfert I galaxies, steep hard and soft X-ray spectra and strong Fe[II] emission.[38] Their properties suggest that NLSy1 galaxies are young AGNs with high accretion rates, suggesting a relatively small but growing central black hole mass.[39] There are theories suggesting that NLSy1s are galaxies in an early stage of evolution, and links between them and ultraluminous infrared galaxies or Seyfert II galaxies have been proposed.[40] ## Evolution The majority of active galaxies we observe are very distant and show large Doppler shifts. This suggests that active galaxies occurred in the early Universe and, due to cosmic inflation, are receding away from us at very high speeds. Quasars are the furthest active galaxies, some of them being observed at distances 12 billion light years away. Seyfert galaxies are much closer than quasars.[41] Because light has a finite speed, looking across large distances in the Universe is equivalent to looking back in time. Therefore, the observation of active galactic nuclei at large distances and their scarcity in the nearby Universe suggests that they were much more common in the early Universe,[42] implying that active galactic nuclei could be early stages of galactic evolution. This leads to the question about what would be the local (modern-day) counterparts of AGNs found at large redshifts. It has been proposed that NLSy1s could be the small redshift counterparts of quasars found at large redshifts (z>4). The two have many similar properties, for example: high metallicities or similar pattern of emission lines (strong Fe [II], weak O [III]).[43] Some observations suggest that AGN emission from the nucleus is not spherically symmetric and that the nucleus often shows axial symmetry, with radiation escaping in a conical region. Based on this observations, models have been devised to explain the different classes of AGNs as due to their different orientations with respect to the observational line of sight. Such models are called unified models. Unified models explain the difference between Seyfert I and Seyfert II galaxies as being the result of Seyfert II galaxies being surrounded by obscuring toruses which prevent us from seeing the broad line region. Quasars and blazars can be fit quite easily in this model. The main problem of such an unification scheme is trying to explain why some AGN are radio loud while others are radio quiet. It has been suggested that these differences may be due to differences in the spin of the central black hole.[30] ## Examples Seyfert galaxy MRK 1513 The table below lists a few representative Seyfert galaxies from the Markarian catalog.[44] Name Other names Longitude Latitude Right ascension Declination Mark 205 MRK 0205 185.4338322 75.3106237 12h 21m 44.120s +75° 18′ 38.25″ Mark 231 MRK 0231 194.0593100 56.8736767 12h 56m 14.2344s +56° 52′ 25.236″ Mark 266 NGC 5256 204.573720 48.276093 13h 38m 17.69s +48° 16′ 33.9″ Mark 270 NGC 5283 205.2739946 67.6723111 13h 41m 05.759s +67° 40′ 20.32″ Mark 279 MRK 0279 208.2643618 69.3082128 13h 53m 03.447s +69° 18′ 29.57″ Mark 335 MRK 0335 1.5813306 20.2029144 00h 06m 19.519s +20° 12′ 10.49″ Mark 530 NGC 7603 349.7359060 0.2439521 23h 18m 56.617s +00° 14′ 38.23″ Mark 590 NGC 0863 33.6398442 -0.7666930 02h 14m 33.562s −00° 46′ 00.09″ Mark 686 NGC 5695 219.3421784 36.5678087 14h 37m 22.123s +36° 34′ 04.11″ Mark 744 NGC 3786 174.9272970 31.9092853 11h 39m 42.551s +31° 54′ 33.43″ ## References 1. ^ a b Peterson, B. M. (1997). An Introduction to Active Galactic Nuclei. Cambridge University Press. ISBN 978-0-521-47911-0. 2. ^ a b Maiolino, R.; Rieke, G. H (1995). "Low-Luminosity and Obscured Seyfert Nuclei in Nearby Galaxies". The Astrophysical Journal 454: 95–105. Bibcode:1995ApJ...454...95M. doi:10.1086/176468. 3. ^ See "Seyfert Galaxies" as reproduced from Davidsen, A. F. (1993). "Far-Ultraviolet Astronomy on the Astro-1 Space Shuttle Mission". Science 259 (5093): 327–334. Bibcode:1993Sci...259..327D. doi:10.1126/science.259.5093.327. 4. ^ Soper, D. E. "Seyfert Galaxies". University of Oregon. Retrieved 11 October 2013. 5. ^ a b Seyfert, C. K. (1943). "Nuclear Emission in Spiral Nebulae". The Astrophysical Journal 97: 28–40. Bibcode:1943ApJ....97...28S. doi:10.1086/144488. 6. ^ Hubble, E. P. (1926). "Extragalactic nebulae". The Astrophysical Journal 64: 321–369. Bibcode:1926ApJ....64..321H. doi:10.1086/143018. 7. ^ Reber, Grote (1944). "Cosmic Static". The Astrophysical Journal 100: 279–287. Bibcode:1944ApJ...100..279R. doi:10.1086/144668. 8. ^ Bolton, J. G.; Stanley, G. J. (1948). "Observations on the Variable Source of Cosmic Radio Frequency Radiation in the Constellation of Cygnus". Australian Journal of Scientific Research A 1: 58–69. Bibcode:1948AuSRA...1...58B. 9. ^ Hanbury Brown, R.; Jennison, R. C.; Das Gupta, M. K. (1952). "Apparent Angular Sizes of Discrete Radio Sources: Observations at Jodrell Bank, Manchester". Nature 170: 1061 1063. doi:10.1038/1701061a0. 10. ^ Torres-Papaqui, J. P. "TEMA 1. Introduction Active Galactic Nuclei: History and Overview". Universidad de Guanajuato. Retrieved 8 October 201. 11. ^ Walker, M. F. (1968). "Studies of Extragalactic Nebulae. V. Motions in the Seyfert Galaxy NGC 1068". The Astrophysical Journal 151: 71–97. Bibcode:1968ApJ...151...71W. doi:10.1086/149420. 12. ^ a b See "Seyfert Galaxies Currently Known", reproduced from Weedman, D. W. (1977). "Seyfert Galaxies". Annual Reviews of Astronomy and Astrophysics 15: 69–95. Bibcode:1977ARA&A..15...69W. doi:10.1146/annurev.aa.15.090177.000441. 13. ^ Peterson, S. D. (1973). "Optical Positions of the Markarian Galaxies". The Astrophysical Journal 78 (9): 811–827. Bibcode:1973AJ.....78..811P. doi:10.1086/111488. 14. ^ de Vancouleurs, G.; de Vancouleurs, A. (1968). "Photographic, Photometric, and Spectroscopic Observations of Seyfert Galaxies". The Astronomical Journal 73 (9): 858–861. Bibcode:1968AJ.....73..858D. doi:10.1086/110717. 15. ^ Adams, T. F. (1977). "A Survey of the Seyfert Galaxies Based on Large-Scale Image-Tube Plate". The Astrophysical Journal Supplement Series 33: 19–34. Bibcode:1977ApJS...33...19A. doi:10.1086/190416. 16. ^ Weedman, D. W. (1973). "A Photometric Study of Markarian Galaxies". The Astrophysical Journal 183: 29–40. Bibcode:1973ApJ...183...29W. doi:10.1086/152205. 17. ^ Osterbrock, D. E.; Koski, A. T. (1976). "NGC 4151 and Markarian 6: Two intermediate-type Seyfert galaxies". 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Retrieved 30 October 2013.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8993712067604065, "perplexity": 2375.1586553733664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163066152/warc/CC-MAIN-20131204131746-00092-ip-10-33-133-15.ec2.internal.warc.gz"}
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=5111&option_lang=eng	RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 3, Pages 518–541 (Mi tvp5111) Spectral asymptotics of supercritical branching random process E. B. Yarovaya Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Abstract: The paper is concerned with supercritical continuous-time random walks on a multidimensional lattice with finite number of sources of particle generation of the same intensity without any constraint on the variance of jumps. For the evolution operator of the mean population size of particles with nearly critical source intensity, the asymptotic behavior of the Green function and of the eigenvalue is found. The effect of “limit coalescence” of eigenvalues is revealed for such an arrangement of sources that the distances between them go off to infinity. Keywords: branching random walks, convolution-type operators, Green functions, multipoint perturbations, positive eigenvalues. Funding Agency Grant Number Russian Science Foundation 14-21-00162 This research was carried out with the financial support of the Russian Science Foundation (grant 14-21-00162). DOI: https://doi.org/10.4213/tvp5111 Full text: PDF file (676 kB) First page: PDF file References: PDF file HTML file English version: Theory of Probability and its Applications, 2018, 62:3, 413–431 Bibliographic databases: Citation: E. B. Yarovaya, “Spectral asymptotics of supercritical branching random process”, Teor. Veroyatnost. i Primenen., 62:3 (2017), 518–541; Theory Probab. Appl., 62:3 (2018), 413–431 Citation in format AMSBIB \Bibitem{Yar17} \by E.~B.~Yarovaya \paper Spectral asymptotics of supercritical branching random process \jour Teor. Veroyatnost. i Primenen. \yr 2017 \vol 62 \issue 3 \pages 518--541 \mathnet{http://mi.mathnet.ru/tvp5111} \crossref{https://doi.org/10.4213/tvp5111} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3684647} \zmath{https://zbmath.org/?q=an:06918574} \elib{http://elibrary.ru/item.asp?id=29833756} \transl \jour Theory Probab. Appl. \yr 2018 \vol 62 \issue 3 \pages 413--431 \crossref{https://doi.org/10.1137/S0040585X97T98871X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000441079100005} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052735379} • http://mi.mathnet.ru/eng/tvp5111 • https://doi.org/10.4213/tvp5111 • http://mi.mathnet.ru/eng/tvp/v62/i3/p518 SHARE: Citing articles on Google Scholar: Russian citations, English citations Related articles on Google Scholar: Russian articles, English articles This publication is cited in the following articles: 1. Rytova A., Yarovaya E., “Survival Analysis of Particle Populations in Branching Random Walks”, Commun. Stat.-Simul. Comput. 2. E. B. Yarovaya, “Branching random walk with receding sources”, Russian Math. Surveys, 73:3 (2018), 549–551 3. A. I. Rytova, E. B. Yarovaya, “Moments of the numbers of particles in a heavy-tailed branching random walk”, Russian Math. Surveys, 74:6 (2019), 1126–1128 4. I. Khristolyubov, E. B. Yarovaya, “A limit theorem for supercritical random branching walks with branching sources of varying intensity”, Theory Probab. Appl., 64:3 (2019), 365–384 • Number of views: This page: 229 References: 42 First page: 31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19094543159008026, "perplexity": 9845.867289480173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370519111.47/warc/CC-MAIN-20200404011558-20200404041558-00478.warc.gz"}
https://www.iacr.org/cryptodb/data/paper.php?pubkey=11892	## CryptoDB ### Paper: Constructing Optimistic Fair Exchange Protocols from Committed Signatures Authors: Huafei Zhu URL: http://eprint.iacr.org/2003/178 Search ePrint Search Google In PODC 2003, Park et al. \cite{PCSR} first introduce a connection between fair exchange and sequential two-party multi-signature scheme and provide a novel method of constructing fair exchange protocol by distributing the computation of RSA signature. This approach avoids the design of verifiable encryption scheme at the expense of having co-signer store a piece of prime signer's secret key. Dodis and Reyzin \cite{DR} showed that the protocol in \cite{PCSR} is totally breakable in the registration phase, then presented a remedy scheme which is provably secure in the random oracle model, by utilizing Boldyreva non-interactive two-party multi-signature scheme \cite{Bo}. Security in the random oracle model does not imply security in the real world. In this paper, we provide the first two efficient committed signatures which are provably secure in the standard complexity model from strong RSA assumption. Then we construct efficient optimistic fair exchange protocols from those new primitives. ##### BibTeX @misc{eprint-2003-11892, title={Constructing Optimistic Fair Exchange Protocols from Committed Signatures}, booktitle={IACR Eprint archive}, keywords={applications / fair exchange}, url={http://eprint.iacr.org/2003/178}, note={new report [email protected] 12293 received 28 Aug 2003}, author={Huafei Zhu}, year=2003 }	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4204610586166382, "perplexity": 6151.955033664409}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396495.25/warc/CC-MAIN-20200528030851-20200528060851-00215.warc.gz"}
https://researchportal.unamur.be/fr/publications/theoretical-and-computational-chemistry-of-complex-systems-solvat	# Theoretical and Computational Chemistry of Complex Systems: Solvation of DNA and Proteins E. Clementi, G. Corongiu, M. Gratarola, P. Habitz, C. Lupo, P. Otto, D. Vercauteren Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs ## Résumé As is known, atomic and very small molecular systems can be realistically simulated by quantum mechanical models. In complex chemical systems, however, the natural parameters are not only electronic density and energy but also entropy, temperature, and time. To approach this description we use a hierarchy of theoretical models. In model 1, the system is considered as an ensemble of fixed nuclei and electrons—the standard quantum chemical approach. However, our definition of model 1 is broader, since it includes aspects of solid‐state physics. In model 2, the system is considered as an ensemble of atoms (or ions) and atom‐pair potentials are obtained using data from model 1. In model 3, the phase space is scanned either for the generalized coordinates (Monte Carlo) or for both space and momentum coordinates (molecular dynamics). In model 4 (presently not considered) the fluid dynamical equations are solved making use of coefficients and parameters obtained from the previous models. Both theoretical and computational improvements are needed at each level in order to reach a sufficiently realistic simulation for complex systems. We have summarized some recent progress obtained for models 1 and 2 related to new methods for molecular computations and studies on three‐body effects and energy band computations in DNA‐related polymers. We have considered as examples of a complex chemical system the structure of water surrounding DNA (with counterions) and enzymes. Our results from model 3 include the first determination of the position of the Li+, Na+, and K+ counterions in B and Z DNA at room temperature at high relative humidity, and hydration studies on enzymes including variations due to the solvent pH. Copyright © 1982 John Wiley & Sons, Inc. langue originale Anglais 409-433 25 Internat. J. Quantum Chem., Quantum Chem. Symp. 22 16 S https://doi.org/10.1002/qua.560220840 Publié - 1982 ## Empreinte digitale Examiner les sujets de recherche de « Theoretical and Computational Chemistry of Complex Systems: Solvation of DNA and Proteins ». Ensemble, ils forment une empreinte digitale unique.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8636505603790283, "perplexity": 2160.800527060827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103034930.3/warc/CC-MAIN-20220625095705-20220625125705-00250.warc.gz"}
https://tex.stackexchange.com/questions/302675/subfloat-caption-odd-behavior	# \subfloat \caption odd behavior I'm very new to Latex and trying my best to adopt it as my method of choice for paper and my Thesis. I have always managed to solve any problems encountered by browsing through this forum but can't find anything on this error. I have a figure made up of 4 sub-figures in a 2x2 matrix. Somehow my template doesn't allow me to use the subcaption package so I am forced to use the subfig package which seems to work fine if not for the odd error I encountered. My code is as follows: \documentclass[11pt, english, doublespacing,]{MastersDoctoralThesis} \usepackage{graphicx,amsmath,amssymb,rotating,float,cite,multirow,subfig, array,bm,appendix,epsfig,epstopdf,pdfpages,array,caption} \setcounter{secnumdepth}{3} \setcounter{tocdepth}{3} \begin{figure}[!htp] \centering \label{Saliency_Maps} \subfloat[]{\includegraphics[width=0.49\linewidth]{figures/colour_conp.png} \label{Sal:Colour}} \subfloat[]{\includegraphics[width=0.49\linewidth]{figures/intensity_conp.png} \label{Sal:Intensity}} \\ \subfloat[] {\includegraphics[width=0.49\linewidth]{figures/orientation_conp.png} \label{Sal:Orit}} \subfloat[]{\includegraphics[width=0.49\linewidth]{figures/final_sal_map.png} \label{Sal:Final}} \caption{ Conspicuity maps for a sample image showing colour \subref{Sal:Colour}, intensity \subref{Sal:Intensity} and orientation \subref{Sal:Orit} maps which are then combined into the final saliency map \subref{Sal:Final} which will need to be thresholded.} \end{figure} \end{document} The caption is causing all sort of errors such as: Argument of \caption@ydblarg has an extra }. ...inal} which will need to be thresholded.} ...and... Paragraph ended before \caption@ydblarg was complete. ...inal} which will need to be thresholded.} ...among other under full and overfull \hbox errors, which make no sense. Removing the \caption{...} doesn't show any errors, but obviously shows no cation. Also even though there are errors when the \caption{...} is inserted the figures and caption display correctly..... with the exception that the letters under the figures are uppercase while the letters substituted be \subref{...} are lower case. (See image) The errors are only suppressed if I set \setcounter{tocdepth}{3}. Setting it to \setcounter{tocdepth}{2} triggers a whole lot of errors which similarly don't make any sense and there are some odd entries in the "List of Figures" page where the offending image entry should be. Any ideas what could be happening and how I can solve this nagging issue. Alternatives are welcome. Many thanks • Welcome to TeX - LaTeX! Please extend your code snippet to minimal working example (MWE)](meta.tex.stackexchange.com/q/228) including the documentclass and packages needed. – Andrew Swann Apr 5 '16 at 18:34 • Please update your question with the new information. – Andrew Swann Apr 5 '16 at 18:41 • Why can't you use subcaption? it should work just fine. – Johannes_B Apr 8 '16 at 21:04 • I get an error saying "Package subcaption Error: This package can't be used in cooperation(subcaption) with the subfig package. \endinput}{}" and I need to use sibfig as I have some old tex files I'm using in this document that use this and it's laborious to change them all. – PDF417 Apr 9 '16 at 9:58 • For completeness sake, I corrected the capital letters under the sub figures by inserting "\captionsetup[subfigure]{labelfont=rm}" before the \begin{figure}. – PDF417 Apr 9 '16 at 10:00 The cause of your problem is use of \subref{...}. Their use in caption had to be protected: \protect\subref{ ...}. See and test code below: \documentclass{article} \usepackage{graphicx} \usepackage{subfig} \begin{document} \begin{figure}[htp] \centering \subfloat[\label{Sal:Colour}]{\includegraphics[width=0.49\linewidth]{example-image}} \hfill \subfloat[\label{Sal:Intensity}]{\includegraphics[width=0.49\linewidth]{example-image}} \\ \subfloat[\label{Sal:Orit}] {\includegraphics[width=0.49\linewidth]{example-image}} \hfill \subfloat[\label{Sal:Final}]{\includegraphics[width=0.49\linewidth]{example-image}} \caption{ Conspicuity maps for a sample image showing colour \protect\subref{Sal:Colour}, intensity \protect\subref{Sal:Intensity} and orientation \protect\subref{Sal:Orit} maps which are then combined into the final saliency map \protect\subref{Sal:Final} which will need to be thresholded.} \label{Saliency_Maps} \end{figure} \end{document} By the way, label in figure environment had to be always after caption, othervise the referencing will work wrong. • Brilliant, Thanks for your help and comments. The \protect\subre{} was the issue. Noted re: \label after caption. The only difference between mine and yours is that mine still has uppercase letters under each figure and lower case in the caption. Would you have any hints on how to chance the uppercase letter to lower case? Edited the question to include an image of what's happening. – PDF417 Apr 5 '16 at 19:28 • Ah, seem that the goblin "copy-past" was on the work :-). Corrected! – Zarko Apr 5 '16 at 19:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7149399518966675, "perplexity": 2511.2374385349576}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348519531.94/warc/CC-MAIN-20200606190934-20200606220934-00578.warc.gz"}
https://math.stackexchange.com/questions/2110964/triviality-of-vector-bundles-over-lie-groups	# Triviality of vector bundles over Lie groups I was wondering whether the triviality of the tangent bundle of a Lie group is a shared feature with all other vector bundles over Lie groups. Naturally, the first example of a non-trivial vector bundle that comes to mind is the Moebius strip, which is a vector bundle over $S^1$ -a Lie group-, so the answer is no. However, the tangent bundle of a Lie group is also a group, and is hence orientable (unlike the Moebius strip). So, my question is: Are orientable vector bundles over Lie groups trivial? or actually better, does anybody know an example of a non-trivial vector bundle over a Lie group which is itself a Lie group? I thought that a way around this question was to inspect the Euler class of the given bundle, because I thought that I knew the cohomology of Lie groups. I had Borel's theorem in mind: "If $G$ is a compact connected Lie group, then the cohomology ring is an exterior algebra of odd degree" I thought that this implied that even rank bundles would be necessarily trivial. Unfortunately, later I realized this doesn't say that there are no elements of even degree... Also, this would only work for compact groups, and I would like to say something of non-compact groups as well. • As a partial answer, every vector bundle over $\mathrm{SU}(2)$ is trivial. This is because $\mathrm{SU}(2)$ is homeomorphic to the sphere $S^3$ and hence vector bundles of rank $r$ are classified by clutching functions $S^2\to \mathrm{GL}(r)$. But $\pi_2(\mathrm{GL}(2))=1$ (as for any Lie group) so these maps are null-homotopic. – Spenser Jan 23 '17 at 22:50 Here's an indirect way to see that most compact connected Lie groups have nontrivial complex vector bundles over them. The starting point is the observation that if $X$ is a finite CW complex then taking Chern characters gives an isomorphism $$K(X) \otimes \mathbb{Q} \cong H^{2 \bullet}(X, \mathbb{Q})$$ between the rationalized complex K-theory of $X$ and the rational even cohomology of $X$. Now, almost all compact connected Lie groups have nontrivial rational even cohomology: perhaps the simplest example is $S^1 \times S^1$, and the simplest simply connected example is $SU(2) \times SU(2) \cong \text{Spin}(4)$, which has rational cohomology $\mathbb{Q}[x_3, y_3]$ where $x_3, y_3$ are odd, and hence their product $x_3 y_3$ is even. Because the Chern character isomorphism is defined in terms of Chern classes, the conclusion is that not only does there exist a nontrivial complex vector bundle on $SU(2) \times SU(2)$, but there exists one with nontrivial Chern class $c_3$. More explicitly, the classification of complex line bundles over $S^1 \times S^1$ is given by $H^2(S^1 \times S^1, \mathbb{Z}) \cong \mathbb{Z}$, so there are countably many nontrivial complex line bundles over $S^1 \times S^1$. They can all be described as holomorphic line bundles over elliptic curves in terms of divisors and meromorphic functions, if you like.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.952075719833374, "perplexity": 92.18441500254364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524290.60/warc/CC-MAIN-20190715235156-20190716021156-00137.warc.gz"}
https://math.stackexchange.com/questions/145523/links-between-difference-and-differential-equations	# Links between difference and differential equations? Does there exist any correspondence between difference equations and differential equations? In particular, can one cast some classes of ODEs into difference equations or vice versa? • Correspondence in what sense? Could you suggest an example? – Pedro Tamaroff May 15 '12 at 16:19 • Mostly I am interested to know if it is possible to reformulate ones in terms of anothers, but more general possible studied relations would be also interesting. – Alexey Bobrick May 15 '12 at 16:30 • They are a bit, but not totally different. – AD. May 15 '12 at 16:34 • This might generate some interesting answers, I hope. – AD. May 15 '12 at 16:36 • Found a related note in JD Murray, Mathematical Biology I: An Introduction, Chapter 2.: "there is no simple connection between difference equation models and what might appear to be the continuous differential equation analogue, even though a finite difference approximation results in a discrete equation". – np8 Dec 17 '20 at 20:32 Yes, obviously there is some correspondence (numerical solutions of ordinary differential equations are discrete dynamical systems, many proofs in bifurcation theory uses continuous time dynamical systems to analyze discrete original problems, etc). However, the most profound attempt to build a theory that unites difference and differential equations is the time scale calculus. First order example Consider the difference equation $$\begin{equation} x_{n+1} = a x_n,\tag{1} \end{equation}$$ where $$x_0$$ is given, with solution $$\begin{equation} x_n = a^n x_0. \tag{2} \end{equation}$$ Let $$x_n = x(t_n)$$, where $$t_{n+1} = t_n + h$$ and $$t_0 = 0$$, so $$t_n = n h$$. Rewrite the difference equation (1) as $$\frac{x(t_{n}+h)-x(t_n)}{h} = \frac{(a-1)}{h} x(t_n).$$ If $$h$$ is small, this can be approximated by the differential equation $$\begin{equation} x'(t) = \frac{a-1}{h}x(t),\tag{3} \end{equation}$$ with solution $$\begin{equation} x(t) = x(0) \exp \left(\frac{a-1}{h} t\right).\tag{4} \end{equation}$$ Notice that $$\exp\left(\frac{a-1}{h} t\right) = a^{n} + O(n(a-1)^2)$$, so for $$n\ll 1/(a-1)^2$$ we find good agreement with (2). Going in the reverse direction, from the differential equation (3) to the difference equation (1), is called Euler's method. There is a subtlety when approximating a difference equation by a differential equation. For this problem we require that $$\|a-1\| \ll 1$$ since we need $$x_{n+1}- x_n = O(h) \ll 1$$. Otherwise, we should expect (and will find) the approximation of (1) by (3) to be poor. Sometimes it is necessary to reformulate the difference equation so the difference between successive terms is small.$${}^\dagger$$ $${}^\dagger$$ For example, suppose $$a$$ in (1) were large and positive. Let $$y_0=x_0$$ and let $$y_{n+1} = a^{1/p} y_n$$, where $$p$$ is some large integer so $$\|a^{1/p} - 1\|\ll 1$$. Note that $$y_{n p} = x_n$$. The solution to the corresponding differential equation for $$y$$ will be a good approximation to $$y_n$$, and this in turn can be used to approximate $$x_n$$. Second order example Consider the differential equation for the harmonic oscillator $$\begin{equation} x''+x = 0, \hspace{5ex} x(0)=1, \hspace{5ex}x'(0)=0, \tag{5} \end{equation}$$ the solution for which is $$x(t) = \cos t$$. The simplest related difference equation is $$\begin{equation} \frac{1}{h^2}(x_{n+2}-2x_{n+1}+x_n) + x_n = 0, \tag{6} \end{equation}$$ with $$x_0 = x_1 = 1$$. (We show how to get (6) from (5) below.) There are standard techniques for solving simple recurrence relations such as (6) in closed form. We find $$\begin{equation} x_n = \frac{1}{2} \left((1+i h)^{n}+(1 - i h)^{n}\right). \end{equation}$$ Note that $$x_n$$ is real since $$x_n^* = x_n$$. This is the closed form for the solution a computer would find solving (6) iteratively. Recall that $$n=t_n/h$$. For small $$h$$, $$x_n = \cos t_n + \frac{1}{2} h t_n \cos t_n + O(h^2)$$, so the numerical solution to (6) will well approximate $$\cos t_n$$ for $$h t_n \ll 1$$. In the limit $$h\to 0$$, $$x_n \to \cos t_n,$$ as expected. Derivatives and finite differences Morally, a difference equation is a discrete version of a differential equation and a differential equation is a continuous version of a difference equation. The method of numerical integration of ODEs is essentially the rewriting of a differential equation as a difference equation which is then solved iteratively by a computer. This is a big subject with many subtleties. The method can also be applied to nonlinear and partial differential equations. Below we give a brief dictionary between finite difference and differential operators. Define the shift operator $$E$$ such that $$E x_n = x_{n+1}$$. The difference operator $$\Delta = E-1$$ then gives $$\Delta x_n = x_{n+1}-x_n$$. These operators are connected to differentiation by Taylor series. Let $$D x_n = x_n' = d x(t)/d t\|_{t=t_n}$$. Then $$x_{n+1} = E x_n = \sum_{k=0}^\infty \frac{h^k}{k!} D^k x_n = e^{h D}x_n.$$ Thus, as an operator, $$E = e^{h D},$$ and so $$D = \frac{1}{h} \ln E = \frac{1}{h} \ln(1+\Delta) = \frac{1}{h}\sum_{k=1}^\infty (-1)^{k+1} \frac{\Delta^k}{k}.$$ (Think of these operators as acting on polynomials, possibly of very high order.) This formalism gives us a way to convert any ODE into a difference equation and vice-versa. Notice that higher order derivatives can be approximated by $$D^k\approx (\Delta/h)^k$$. Thus, for example, $$x'' = D^2 x \rightarrow \frac{1}{h^2}\Delta^2x_n = \frac{1}{h^2}\Delta(x_{n+1}-x_n) = \frac{1}{h^2} (x_{n+2}-2 x_{n+1} + x_n).$$ When using Euler's method we let $$D \approx \Delta/h$$. We could just as well keep higher order terms in $$\Delta$$ to get recursion relations with three or more terms. It is a sign of the nontrivial nature of the subject that this simple change leads to numerical instabilities. There are many named algorithms that do improve and generalize Euler's method, building on the ideas sketched above. (See, for example, the Runge-Kutta methods, a family of robust algorithms used to numerically solve linear and nonlinear differential equations.) This is in response to Drew N's question about seeing directly that $$D = \frac{1}{h}\sum_{k=1}^\infty (-1)^{k+1} \frac{\Delta^k}{k}$$ is the differential operator. Here we show that $$D t^n = n t^{n-1}$$ for $$n=0,1,\ldots$$, which shows that $$D$$ is the differential operator on polynomials of arbitrarily high degree. (It is straightforward to extend this proof to $$n\in\mathbb{C}$$.) We have \begin{align} D t^n &= \frac{1}{h} \sum_{k=1}^\infty (-1)^{k+1}\frac{1}{k}\Delta^k t^n \\ &= \frac{1}{h} \sum_{k=1}^\infty (-1)^{k+1}\frac{1}{k}(E-1)^k t^n \\ &= \frac{1}{h} \sum_{k=1}^\infty (-1)^{k+1}\frac{1}{k} \sum_{j=0}^k{k\choose j}(-1)^{k-j}E^j t^n & \textrm{binomial theorem} \\ &= \frac{1}{h} \sum_{k,j} (-1)^{j+1}\frac{1}{k}{k\choose j}(t+j h)^n \\ &= \frac{1}{h} \sum_{k,j} (-1)^{j+1}\frac{1}{k}{k\choose j} \sum_{l=0}^n {n\choose l}j^l h^l t^{n-l} & \textrm{binomial theorem} \\ &= \left.\frac{1}{h} \sum_{k,j,l} (-1)^{j+1}\frac{1}{k} {k\choose j}{n\choose l} (x D)^l x^j h^l t^{n-l}\right\|_{x=1} & D = d/dx, (x D)^l = \underbrace{(x D)\cdots (x D)}_{l} \\ &= \left.-\frac{1}{h} \sum_{k,l} \frac{1}{k} {n\choose l} h^l t^{n-l} (x D)^l \sum_{j=0}^k {k\choose j}(-x)^j \right\|_{x=1} \\ &= \left.-\frac{1}{h} \sum_{k,l} \frac{1}{k} {n\choose l} h^l t^{n-l} (x D)^l (1-x)^k \right\|_{x=1} & \textrm{binomial theorem} \\ &= \left.-\frac{1}{h} \sum_{l} {n\choose l} h^l t^{n-l} (x D)^l \sum_{k=1}^\infty \frac{1}{k} (1-x)^k \right\|_{x=1} \\ &= \left.\frac{1}{h} \sum_{l} {n\choose l} h^l t^{n-l} (x D)^l \log x\right\|_{x=1} & \textrm{series for natural logarithm} \\ &= \frac{1}{h} \sum_{l=0}^n {n\choose l} h^l t^{n-l} \delta_{l1} & \textrm{see below} \\ &= \frac{1}{h} {n\choose 1} h t^{n-1} \\ &= n t^{n-1}. \end{align} Note that $$(x D)x^j = j x^j$$ so $$(x D)^l x^j = j^l x^j.$$ Also \begin{align} (x D)^0 \log x\|_{x=1} &= \log 1 = 0 \\ (x D)^1 \log x &= x \frac{1}{x} = 1 \\ (x D)^2 \log x &= (x D)1 = 0 \\ (x D)^3 \log x &= (x D)^2 0 = 0. \end{align} Thus, $$(x D)^l \log x\|_{x=1} = \delta_{l1},$$ where $$\delta_{ij}$$ is the Kronecker delta. • Great work. Very helpful, concise, and clear. Thank you. – wesssg Oct 7 '16 at 5:10 • Why did you apply limit only to left side in formula (3)? I though that h should not appear at right side – LmTinyToon Dec 16 '16 at 10:28 • Using operator formalism you establish $D = (1/h) \sum_{k=1}^\infty (-1)^{k+1} \Delta^{k}/k$, which I believe expands to $1/h\big[ (x_{n+1} - x_n) - (1/2) (x_{n+2} - 2x_{n+1} + x_n) + \dots \big]$. But I just don't intuit why this expression of $D$ must correctly give $Dx_n = x'(t_n)$. One can follow the operator formalism line by line, but is there a way to be convinced this really is $x'(t_n)$ just from the form of this expression alone? – Drew N Dec 16 '18 at 4:05 • I don't understand how $\mathrm{Exp}(n(a-1)) = a^n + O(n(a-1)^2)$ with Taylor series. Can someone please explain that? – user3433489 Sep 5 '20 at 21:50 • @user3433489: We expand in small $a-1$ for fixed $n$. We have \begin{align} e^{n(a-1)} &= (e^{a-1})^n \\ &= (1+(a-1)+(a-1)^2/2+\ldots)^n \\ &= (a+(a-1)^2/2+\ldots)^n \\ &= a^n + n a^{n-1}(a-1)^2/2+\ldots \\ &= a^n + n(a-1)^2/2+\ldots \end{align} In the last step we use that $a^{n-1} = (1+(a-1))^{n-1} = 1+O((n-1)(a-1))$. – user26872 Sep 7 '20 at 16:57 (Adding to user26872's answer as this was not obvious to me so it might help someone else going through his derivation) The identity $$x_{n+1} = Ex_n = \sum\limits_{k=0}^\infty \frac{h^k}{k!}D^k x_n=e^{hD}x_n$$ is true if we consider the following. Let $x_n = x(t_n)$. Let's assume that $x(t)$ is differentiable around some point $t_n$, then it's Taylor series can be defined as $$x(t) = \sum\limits_{k=0}^\infty \frac{x^{(k)}(t_n)}{k!}(t-t_n)^k.$$ If we now perform the same expansion at $t' = t_n+h$ we have $$x(t_n+h) = \sum\limits_{k=0}^\infty \frac{x^{(k)}(t_n)}{k!}h^k = \sum\limits_{k=0}^\infty \frac{h^k D^k}{k!}x(t) = e^{hD} x(t_n)$$ and so $$x_{n+1} = Ex_n \leftrightarrow x(t_n + h) = E x(t_n)$$ thus giving $$E = e^{hD}.$$ One example: You can take the Laplace transform of a discrete function by expressing the target of the Laplace transform as the product of a continuous function and a sequence of shifted delta functions and summing up: $\sum_{k=0}^\infty\int_{0}^\infty f(t)\delta(t - kT)e^{-st}dt$ = $\sum_{k=0}^\infty f(kT)e^{-skT}$, where T is the sampling period. The (unilateral) Z transform is defined as $\sum_{n=0}^{\infty}x[k]z^{-k}$, for a discrete time signal $x[k]$. By substituting $z = e^{sT}$ in the formula for the discretized Laplace transform, the Z transform is obtained, and the s and Z domains are related by $s = \frac{1}{T}\log(Z)$. This is obviously a nonlinear transformation; points left of the imaginary axis in the s plane are mapped to the interior of the unit circle of the Z plane, while points to the right of the imaginary axis are mapped to the exterior. One can use the Bilinear transform, $s = \frac{2(z -1)}{T(z + 1)}$, as a first order approximation to $s = \frac{1}{T}\log(Z)$. So it's possible to (approximately) transform any equation in the s domain into a corresponding equation in the Z domain. This is useful for deriving a difference equation, since it can be shown that the Z transform of a shift, $Z(x[k - n])$, is equal to simply $z^{-n}X(z).$ Due to this property it is often possible to go easily from the Z transform of an expression to a difference equation, simply by inspecting inverse powers of Z and their coefficients in the equation. In short, if the differential equation is amenable to the Laplace transform (i.e. linear time invariant), it can be quite straightforward using this method to get a difference equation representation. First see the correspondence between discrete and continuous dynamical systems. Both are acts of a monoid on some set $$X$$. For discrete dynamical systems the monoid that acts is $$\mathbb{N}$$. For continuous dynamical systems the monoid that acts is $$\mathbb{R}$$. This action comes in the form of a left multiplication $$(.,.):\mathbb{N}\times X \rightarrow X$$ or $$(.,.):\mathbb{R}\times X \rightarrow X$$ and is compatible with the addition structure of $$\mathbb{N}$$ and $$\mathbb{R}$$ respectively. I.e. for all $$n,m \in \mathbb{N}$$ or $$\mathbb{R}$$ and $$x \in X$$ we have $$(0,x) = x$$ and $$(n,(m,x)) = (n + m,x)$$. Now on the story of difference and differential equations. A first order difference equation equals a discrete dynamical system. Note that any difference equation can be converted to a system of first order difference equations (see higher order difference equations). Hence any difference equation equals a discrete dynamical system. Note that the $$\mathbb{N}$$-act is given by $$(n,x) = f^n(x)$$. If the differential condition is sufficiently smooth there exists a unique solution for any point ($$\phi_x^t$$). We use this solution as the $$\mathbb{R}$$-act. I.e. $$(t,x) = \phi_x^t$$. Hence any sufficiently smooth differential equation equals a continuous dynamical system.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 80, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995088577270508, "perplexity": 423.9400771977119}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178351134.11/warc/CC-MAIN-20210225124124-20210225154124-00256.warc.gz"}
http://crypto.stackexchange.com/users/4697/orlp?tab=activity	orlp Reputation 2,905 Top tag Next privilege 3,000 Rep. 7 18 Impact ~60k people reached # 362 Actions Apr 20 accepted State of the art low memory arbitrary-domain PRP? Apr 18 comment State of the art low memory arbitrary-domain PRP? @RickyDemer I think I misunderstood sometimes-recurse shuffle then. Either way, feel free to post your thoughts as an answer :) Apr 18 comment State of the art low memory arbitrary-domain PRP? @RickyDemer I am interested in your claimed algorithm that has a fixed security level of $2^{128}$ (AKA $b = 128$) which gives a PRP on an arbitrary domain of size $n$ (where $n \geq 35$) in $O(1)$ memory. Apr 18 comment State of the art low memory arbitrary-domain PRP? @RickyDemer I don't fully understand your question. $b$ is not really relevant to the question, and you can assume it's some fixed value, e.g. 128 or 256. Unless my math fails me the number of possible permutations of $n$ elements is $n!$, and $35! > 2^{128}$, so a too small domain will only be an issue in the smallest possible cases. Apr 18 comment State of the art low memory arbitrary-domain PRP? @RickyDemer The security level is distinct from the block (domain) size. E.g. AES has a block size of 128, but provided security levels of 128, 192 and 256 bits (although the latter two have later found attacks reducing their security, this is besides the point). Apr 18 comment State of the art low memory arbitrary-domain PRP? @RickyDemer As an example, the core function used in Blake2 is a PRP on domain $\{0, 1\}^{512}$ that uses $2 \cdot 512$ bits of memory. Apr 18 comment State of the art low memory arbitrary-domain PRP? @fgrieu Added the tag. Apr 18 revised State of the art low memory arbitrary-domain PRP? edited tags Apr 18 asked State of the art low memory arbitrary-domain PRP? Jan 24 comment Is there any more information on this RSA backdoor? While this is certainly a smart alternative scheme, I do not believe this answers the question. It does not shed additional light on the scheme mentioned above. Jan 24 comment Is there any more information on this RSA backdoor? @fgrieu There are two different keyspaces here. One assuming an agent with knowledge of $A$, and one without that knowledge. Presumably, if you know $A$ the key space is $256$ bits. Jan 24 comment Is there any more information on this RSA backdoor? I would suggest using two different symbols for the two $k$s, as they do not refer to the same value. Jan 7 awarded Yearling Jun 23 awarded Caucus Jun 23 awarded Constituent May 11 awarded Popular Question May 10 revised Reciprocal block ciphers added 21 characters in body May 10 comment Reciprocal block ciphers @Melab That's just silly. You can make it swap the halves after the last round without any loss to security - any attacker can trivially swap halves of the ciphertext as they please. May 10 answered Reciprocal block ciphers May 10 comment Reciprocal block ciphers When you say reciprocal block cipher, do you mean that $Dk$ and $Ek$ are the same function?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40120217204093933, "perplexity": 1202.9372692578293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860127407.71/warc/CC-MAIN-20160428161527-00156-ip-10-239-7-51.ec2.internal.warc.gz"}
https://motls.blogspot.com/2014/09/gavin-schmidts-analogy-ceasefire.html?m=1	## Tuesday, September 02, 2014 ### Gavin Schmidt's analogy ceasefire ...I agree with him... Shockingly enough, the climate fearmonger Gavin Schmidt of RealClimate.ORG wrote something that I agree with: On arguing by analogy Climate skeptics often like to say that the climate alarmists are analogous to the defenders of Lysenkoism, phlogiston, phrenology, and eugenics, while the climate alarmists themselves love to compare themselves to Galileo Galilei, Isaac Newton, Albert Einstein, Charles Darwin, and maybe even Paul Ehrlich who has predicted that hundreds of millions of Americans would starve to death by the year 2000. Schmidt's main point that I agree with is that these analogies are pretty much worthless for the debate about the substance because these analogies are only relevant for someone who already accepts the basic points about the substance. If one already knows (or at least assumes) that the climate panic is hogwash, he will know that the skeptics' favorite analogies are approximately right while the alarmists' analogies are misleading. If she still believes that the climate is dangerously changing, she will refuse the skeptics' favorite analogies and buy the alarmists' ones. None of these analogies can really settle the starting point, namely the substance of the climate panic or the non-existence of it. All people who are rational know that. (The previous proposition isn't supported by empirical data but it is backed by a logical argument.) If we compare a group of people to some generally accepted big winners (or losers) of the history of science, we are making an assumption that we haven't proven by this analogy itself. And the analogy is only as relevant as its assumptions are valid. In the previous paragraph, I mentioned "people who are rational". It's because many people are not rational and if they hear someone comparing a group (e.g. climate skeptics) to someone who is a loser, they automatically deduce that the group (e.g. climate skeptics) is wrong and bad even though they have actually been given no evidence whatever. The analogies and other demagogic arguments may have a great impact on the reasoning and beliefs of such gullible people. It is not hard to see that most of the devoted believers in the climate change orthodoxy belong among these gullible brainwashed impressionable morons. The previous sentence isn't an analogy; it is a sociological comment about this particular situation. You may check that it's probably right when you open the comments under Schmidt's article. Most of the commenters disagree with Schmidt. They think it's important to compare climate skeptics with unpopular groups. No doubt about it, these critics love to elaborate upon such analogies. While I agree with Schmidt about his main points that these sociological analogies have nothing to say about the substance, I disagree with many other things he believes or writes. Of course, I disagree with the substance of his climate hysteria. But I disagree with some of Schmidt's other sociological claims, too. For example, he insanely believes in the "consensus science": Given the rarity of a consensus-overturning event, the only sensible prior is to assume that [the majority of gullible sheep and multiply counted would-be experts living in a deep and mindless group think is always right]. But this logical implication is completely wrong. Consensus-overturning events may be "rare" if we use a certain measure, but that doesn't imply that the majority is right about controversial questions. In fact, every discovery in science is a consensus-overturning event and almost all of progress in science is composed of these events. So while they may be "rare" in the sense of "percentage of the time" that they occupy on the timeline, they represent almost 100% of the events that the history of science is composed of. To discover something means to find something that others don't know or believe to be non-existent (or to prove the non-existence of something that is believed to exist, like the luminiferous aether). The more important the discovery is, the more likely it is for a significant opposition to emerge. The more important the discovery is, the more visibly it overturns the existing knowledge (or it changes the opinions about more important questions). Otherwise, Schmidt realizes and acknowledges that analogies between two situations are helpful and independent of the assumptions about the scientific substance if they show that a particular method or logic would lead (or would have led or actually has led) to completely wrong or undesirable outcomes in other situations. For example, we may see that the political intimidation of scientists would have distorted lots of other scientific research as well and many discoveries could have become impossible, or impossible to spread. The undesirability of the non-experts' political intervention into the scientific research isn't an analogy. It is a general principle that may be seen theoretically as well as by looking at many examples from the history of science. Of course that the intervening political forces may sometimes happen to be right, too. That's why the existence of such undesirable influences doesn't prove and doesn't disprove the climate change psychopathy. 1. If A argues that the theory of global warming must be true because it is supported by a 97% consensus, and B returns by citing the case of Galileo, B may be putting forward an analogy (I am like Galileo) which is almost certainly a very weak argument, but he may be using Galileo as a counterexample, which could be quite a strong argument. 2. Gavin recently lashed out at someone trying to justify calling skeptics deniers, in this short video clip: http://tinypic.com/r/2lsehp2/5 3. One gauge of rationality is whether someone is alarmed about "climate change" or "global warming." If the first, they are most likely a herd follower, because the real controversy is about global warming, not change, and the terminology change is only a rhetorical device. If the latter, there is at least a chance of rationality. Of course, some may claim to be alarmed about "climate change" but really be worrying about global warming, just because they recognize the value of the change term in convincing the gullible. 4. A pretty nice surprise, indeed! 5. I agree but you may also have other examples where the minority side didn't do as well as Galileo did, like the case of the rejected relationship between AIDS and HIV (Schmidt mentions it as well), not to mention "staged moonlanding" and other conspiracy theories. If you pick those analogies instead of Galileo, the minority side suddenly looks very different and its humiliation looks more understandable. 6. I was intrigued that a question about free will came up from the audience at the end. Anton's response was that the universe does not know what will happen next, due to objective uncertainty, so free will is not excluded. Of course, that is a very different statement than saying free will exists. Plunging in to the deep end, I would say that the main problem with free will is that if it depends on something then it is not free, but if it does not depend on something then we can't say anything about it mathematically or causally. If it operates but we can't say anything about it and it doesn't appear to be causally due to anything, it will look random. So how can we tell free will from randomness? I guess it might take an extraordinarily sensitive experiment which showed a skewed result, but it is hard to imagine what that setup might be. On the whole it seems to me that QM's randomness, along with our subjective experience of free will go together quite nicely. As you say, Libet's experiments are still debated as to what they really imply, and still allow "free won't" (nice paper! - I'm digesting it now). 7. While I support the general notion that consensus itself is not proof, the use of Galileo is itself an inappropriate analogy. The scientific community of the day supported the geo-centric theory, it was the political power of the theocracy that did not. In that sense, given the current theocratic aspirations of the right in American politics, the Galileo analogy (i.e. Church v. Science) is more supportive of the AGW side of the debate. 8. Thanks for the reply. Yes, if one is to be remembered for rejecting the consensus, it is better to be remembered as an Ignaz Semmelweis than as a Peter Duesberg (a prominent cell biologist who rejected the HIV virus theory). 9. Seems to me there is a valid analogy to Lysenkoism that works to discredit warming alarmism, and that is based on the premise that politically/ideologically based science is likely to be flawed. Lysenko tried to show if I remember correctly that acquired traits can be inherited. This was part and parcel of the Marxist ideology that enshrined the proposition that mankind may be fundamentally changed. Global warming alarmist science serves the interests and goals of a group of people who predate any prediction of global warming, and (they say) calls for the same type of measures these people have wanted for a long time. A rational person fears political science and government science even more. Comparing people who don't believe in global warming or that it is caused by man or that it is not a problem to Holocaust deniers is not an analogy. It is merely invective. 10. Ironically it may be that Lysenko was more right than the climate alarmists. An interesting debate is going on among epigeneticists and some of Lamarck and Lysenko's ideas have been exhumed. By contrast the GCMs are stone dead.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5270179510116577, "perplexity": 1347.215166601701}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670162.76/warc/CC-MAIN-20191119172137-20191119200137-00319.warc.gz"}
https://docs.galpy.org/en/v1.7.1/reference/orbit.html	# Orbit (galpy.orbit)¶ See Orbit initialization for a detailed explanation on how to set up Orbit instances. ## Plotting¶ In addition to these methods, any calculable attribute listed below can be plotted versus other attributes using plotATTR, where ATTR is an attribute like R, ll, etc. In this case, the y axis will have ATTR and the overrideable x axis default is time. For example, o.plotR() will plot the orbit’s R vs time. ## Attributes¶ • Orbit.name Name(s) of objects initialized using Orbit.from_name • Orbit.shape Tuple of Orbit dimensions • Orbit.size Total number of elements in the Orbit instance	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3699626624584198, "perplexity": 4919.249424846419}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335286.15/warc/CC-MAIN-20220928212030-20220929002030-00342.warc.gz"}
https://www.acmicpc.net/problem/3428	시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율 1 초 128 MB 63 11 8 33.333% ## 문제 Casting spells is the least understood technique of dealing with real life. Actually, people find it quite hard to distinguish between a real spells like “abrahellehhelleh” (used in the battles and taught at the mage universities) and screams like “rachelhellabracadabra” (used by uneducated witches for shouting at cats). Finally, the research conducted at the Unheard University showed how one can measure the power of a word (be it a real spell or a scream). It appeared that it is connected with the mages’ ability to pronounce words backwards. (Actually, some singers were burned at the stake for exactly the same ability, as it was perceived as demonic possession.) Namely, the power of a word is the length of the maximum subword of the form wwRwwR (where w is an arbitrary sequence of characters and wR is w written backwards). If no such subword exists, then the power of the word is 0. For example, the power of abrahellehhelleh is 12 as it contains hellehhelleh and the power of rachelhellabracadabra is 0. Note that the power of a word is always a multiple of 4. The input contains several test cases. The first line of the input contains a positive integer Z ≤ 40, denoting the number of test cases. Then Z test cases follow, each conforming to the format described in section Input. For each test case, your program has to write an output conforming to the format described in section Output. ## 입력 The input is one line containing a word of length at most 3 · 105, consisting of (large or small) letters of the English alphabet. ## 출력 You should output one integer k being the power of the word. ## 예제 입력 2 abrahellehhelleh 12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3094160556793213, "perplexity": 1639.0071388624606}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948530668.28/warc/CC-MAIN-20171213182224-20171213202224-00582.warc.gz"}
http://mathhelpforum.com/pre-calculus/53416-find-unit-vector.html	# Thread: Find a Unit Vector 1. ## Find a Unit Vector Find a unit vector normal to the plane containing v = 2i + 3j - k and w = -2i - 4j - 3k. 2. $\frac{{v \times w}} {{\left\\| {v \times w} \right\\|}}$ 3. ## plug and chug???? Originally Posted by Plato $\frac{{v \times w}} {{\left\\| {v \times w} \right\\|}}$ Are you saying to plug and chug?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7618592381477356, "perplexity": 3372.1889146054714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218191984.96/warc/CC-MAIN-20170322212951-00277-ip-10-233-31-227.ec2.internal.warc.gz"}
https://tspace.library.utoronto.ca/handle/1807/25632	Search T-Space Advanced Search Home Browse Communities & Collections Issue Date Author Title Subject Sign on to: Receive email updates My Account authorized users Edit Profile Help About T-Space Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/25632 Title: Quantization Techniques in Linearly Precoded Multiuser MIMO System with Limited Feedback Authors: Islam, Muhammad Advisor: Adve, Raviraj Department: Electrical and Computer Engineering Keywords: MIMO Broadcast ChannelLinear PrecodingChannel QuantizationBit Allocation Issue Date: 1-Jan-2011 Abstract: Multi-user wireless systems with multiple antennas can drastically increase the capac- ity while maintaining the quality of service requirements. The best performance of these systems is obtained at the presence of instantaneous channel knowledge. Since uplink-downlink channel reciprocity does not hold in frequency division duplex and broadband time division duplex systems, efficient channel quantization becomes important. This thesis focuses on different quantization techniques in a linearly precoded multi-user wireless system. Our work provides three major contributions. First, we come up with an end-to-end transceiver design, incorporating precoder, receive combining and feedback policy, that works well at low feedback overhead. Second, we provide optimal bit allocation across the gain and shape of a complex vector to reduce the quantization error and investigate its effect in the multiuser wireless system. Third, we design an adaptive differential quantizer that reduces feedback overhead by utilizing temporal correlation of the channels in a time varying scenario. URI: http://hdl.handle.net/1807/25632 Appears in Collections: MasterThe Edward S. Rogers Sr. Department of Electrical & Computer Engineering - Master theses Files in This Item: File Description SizeFormat Islam_Muhammad_Nazmul_201011_MASc_Thesis.pdf866.05 kBAdobe PDF View/Open This item is licensed under a Creative Commons License Items in T-Space are protected by copyright, with all rights reserved, unless otherwise indicated.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2421567291021347, "perplexity": 3285.0623341592695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999654613/warc/CC-MAIN-20140305060734-00070-ip-10-183-142-35.ec2.internal.warc.gz"}
https://docs.decred.org/faq/proof-of-stake/buying-tickets-and-fees/?source=post_page---------------------------	#### 1. Is there a way to see tickets purchased by a local wallet?¶ Use the following command to show all of your tickets1: dcrctl --wallet gettickets true #### 2. Do I pay a transaction fee for the ssgen transaction?¶ No, ssgen transactions do not impose a fee2 (unlike the original ticket purchase transactions which are competing for limited space in each block). They are effectively like proof-of-work coinbase transactions in this regard. #### 3. How do I change the ticket fee?¶ dcrctl --wallet setticketfee <fee> #### 4. How do I manually buy tickets?¶ dcrctl --wallet purchaseticket <fromaccount> <spendlimit> <minconf> Where: Option Explanation fromaccount Usually “default” (unless you have created a different one). spendlimit Maximum number of DCR you want to spend on tickets. minconf This can be set to 0. #### 5. How should I set the ticketfee?¶ The ticketfee (or ticket fee) determines the order in which mempool tickets enter the voting pool. Higher fees encourage proof-of-work miners to put your tickets at the front of the queue. If you set the fee higher than the average your tickets are more likely to be included in the next block. The default txfee is 0.0001 DCR. It would seem then that the best idea is to set your txfee high so you are at the front of the line. But that is not always a good idea. In fact, it is rarely a good idea simply because the mempool queue is very short or zero most of the time. Do not forget that the txfee will eat into your DCR profit as it is charged on every ticket and is non-refundable whether or not it votes. Consider a constant ticket price of 10 DCR. Every block 20 tickets can move into the voting pool from the mempool. That is a value of 200 DCR. Every block generates about 30 DCR and returns 50DCR to the voters. 3 DCR is sent to the Decred Treasury to help fund the project so only 27 ends up in the hands of miners. This means that 77 DCR is freed up each block to go back into tickets, assuming that all returns are reinvested. That is less than half of what the block can handle. The only way more DCR can enter the mempool is by external investment (i.e., buying from an exchange) or from miners who have been saving their DCR waiting for the ticket price to drop. In the case of a ticket price drop, a miner is looking to get into the pool before the price changes again. This happens every 144 blocks (about 12 hours). It does not matter if it is in the first block or the 100th. In 144 blocks 2,880 tickets will be accepted with a value of 28,800 DCR. There is not that sort of volume in the proof-of-stake network at this time. There is one scenario in which you might want to set your fee higher. If the stake cost is about to change in a few blocks, the mempool is not empty and you want to make sure you get the current price, it can help to set your fee a little higher than average to ensure you get in, especially if the next change will mean you miss a ticket. Continue to PoS Solo Mining FAQ ## Sources¶ 1. Decred Forum, Post 9,987 2. Decred Forum, Post 10,219	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4366624057292938, "perplexity": 1528.3132872284743}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314752.21/warc/CC-MAIN-20190819134354-20190819160354-00089.warc.gz"}
https://unistroy.spbstu.ru/en/article/2021.94.5/	# Numerical and Analytical Study on Bending Stiffness of Sandwich Panels at Ambient and Elevated Temperatures Authors: Abstract: This paper presents an investigation on the bending stiffness of sandwich panels at ambient and elevated temperatures. A finite element (FE) model is developed to verify simulations with experimental results, and then a parametric study at different temperatures is carried out. After that, an analytical study to determine the bending stiffness at room temperatures according to the current specification is conducted. Furthermore, the analytical solutions are developed to use at elevated temperatures. The objective of the current research is to compare the numerical and analytical results. It is observed that analytical solutions developed to evaluate the bending stiffness at elevated temperatures are conservative and reliable.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9925394654273987, "perplexity": 4560.015544041133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154878.27/warc/CC-MAIN-20210804142918-20210804172918-00571.warc.gz"}
http://nag.com/numeric/FL/nagdoc_fl24/html/G03/g03dbf.html	G03 Chapter Contents G03 Chapter Introduction NAG Library Manual # NAG Library Routine DocumentG03DBF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. ## 1 Purpose G03DBF computes Mahalanobis squared distances for group or pooled variance-covariance matrices. It is intended for use after G03DAF. ## 2 Specification SUBROUTINE G03DBF ( EQUAL, MODE, NVAR, NG, GMN, LDGMN, GC, NOBS, M, ISX, X, LDX, D, LDD, WK, IFAIL) INTEGER NVAR, NG, LDGMN, NOBS, M, ISX(), LDX, LDD, IFAIL REAL (KIND=nag_wp) GMN(LDGMN,NVAR), GC((NG+1)NVAR(NVAR+1)/2), X(LDX,), D(LDD,NG), WK(2NVAR) CHARACTER(1) EQUAL, MODE ## 3 Description Consider $p$ variables observed on ${n}_{g}$ populations or groups. Let ${\stackrel{-}{x}}_{j}$ be the sample mean and ${S}_{j}$ the within-group variance-covariance matrix for the $j$th group and let ${x}_{k}$ be the $k$th sample point in a dataset. A measure of the distance of the point from the $j$th population or group is given by the Mahalanobis distance, ${D}_{kj}$: $Dkj2=xk-x-jTSj-1xk-x-j.$ If the pooled estimated of the variance-covariance matrix $S$ is used rather than the within-group variance-covariance matrices, then the distance is: $Dkj2=xk-x-jTS-1xk-x-j.$ Instead of using the variance-covariance matrices $S$ and ${S}_{j}$, G03DBF uses the upper triangular matrices $R$ and ${R}_{j}$ supplied by G03DAF such that $S={R}^{\mathrm{T}}R$ and ${S}_{j}={R}_{j}^{\mathrm{T}}{R}_{j}$. ${D}_{kj}^{2}$ can then be calculated as ${z}^{\mathrm{T}}z$ where ${R}_{j}z=\left({x}_{k}-{\stackrel{-}{x}}_{j}\right)$ or $Rz=\left({x}_{k}-{\stackrel{-}{x}}_{j}\right)$ as appropriate. A particular case is when the distance between the group or population means is to be estimated. The Mahalanobis squared distance between the $i$th and $j$th groups is: $Dij2=x-i-x-jTSj-1x-i-x-j$ or $Dij2=x-i-x-jTS-1x-i-x-j.$ Note: ${D}_{jj}^{2}=0$ and that in the case when the pooled variance-covariance matrix is used ${D}_{ij}^{2}={D}_{ji}^{2}$ so in this case only the lower triangular values of ${D}_{ij}^{2}$, $i>j$, are computed. ## 4 References Aitchison J and Dunsmore I R (1975) Statistical Prediction Analysis Cambridge Kendall M G and Stuart A (1976) The Advanced Theory of Statistics (Volume 3) (3rd Edition) Griffin Krzanowski W J (1990) Principles of Multivariate Analysis Oxford University Press ## 5 Parameters 1: EQUAL – CHARACTER(1)Input On entry: indicates whether or not the within-group variance-covariance matrices are assumed to be equal and the pooled variance-covariance matrix used. ${\mathbf{EQUAL}}=\text{'E'}$ The within-group variance-covariance matrices are assumed equal and the matrix $R$ stored in the first $p\left(p+1\right)/2$ elements of GC is used. ${\mathbf{EQUAL}}=\text{'U'}$ The within-group variance-covariance matrices are assumed to be unequal and the matrices ${R}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,{n}_{g}$, stored in the remainder of GC are used. Constraint: ${\mathbf{EQUAL}}=\text{'E'}$ or $\text{'U'}$. 2: MODE – CHARACTER(1)Input On entry: indicates whether distances from sample points are to be calculated or distances between the group means. ${\mathbf{MODE}}=\text{'S'}$ The distances between the sample points given in X and the group means are calculated. ${\mathbf{MODE}}=\text{'M'}$ The distances between the group means will be calculated. Constraint: ${\mathbf{MODE}}=\text{'M'}$ or $\text{'S'}$. 3: NVAR – INTEGERInput On entry: $p$, the number of variables in the variance-covariance matrices as specified to G03DAF. Constraint: ${\mathbf{NVAR}}\ge 1$. 4: NG – INTEGERInput On entry: the number of groups, ${n}_{g}$. Constraint: ${\mathbf{NG}}\ge 2$. 5: GMN(LDGMN,NVAR) – REAL (KIND=nag_wp) arrayInput On entry: the $\mathit{j}$th row of GMN contains the means of the $p$ selected variables for the $\mathit{j}$th group, for $\mathit{j}=1,2,\dots ,{n}_{g}$. These are returned by G03DAF. 6: LDGMN – INTEGERInput On entry: the first dimension of the array GMN as declared in the (sub)program from which G03DBF is called. Constraint: ${\mathbf{LDGMN}}\ge {\mathbf{NG}}$. 7: GC($\left({\mathbf{NG}}+1\right)×{\mathbf{NVAR}}×\left({\mathbf{NVAR}}+1\right)/2$) – REAL (KIND=nag_wp) arrayInput On entry: the first $p\left(p+1\right)/2$ elements of GC should contain the upper triangular matrix $R$ and the next ${n}_{g}$ blocks of $p\left(p+1\right)/2$ elements should contain the upper triangular matrices ${R}_{j}$. All matrices must be stored packed by column. These matrices are returned by G03DAF. If ${\mathbf{EQUAL}}=\text{'E'}$ only the first $p\left(p+1\right)/2$ elements are referenced, if ${\mathbf{EQUAL}}=\text{'U'}$ only the elements $p\left(p+1\right)/2+1$ to $\left({n}_{g}+1\right)p\left(p+1\right)/2$ are referenced. Constraints: • if ${\mathbf{EQUAL}}=\text{'E'}$, $R\ne 0.0$; • if ${\mathbf{EQUAL}}=\text{'U'}$, the diagonal elements of the ${R}_{\mathit{j}}\ne 0.0$, for $\mathit{j}=1,2,\dots ,{\mathbf{NG}}$. 8: NOBS – INTEGERInput On entry: if ${\mathbf{MODE}}=\text{'S'}$, the number of sample points in X for which distances are to be calculated. If ${\mathbf{MODE}}=\text{'M'}$, NOBS is not referenced. Constraint: if ${\mathbf{NOBS}}\ge 1$, ${\mathbf{MODE}}=\text{'S'}$. 9: M – INTEGERInput On entry: if ${\mathbf{MODE}}=\text{'S'}$, the number of variables in the data array X. If ${\mathbf{MODE}}=\text{'M'}$, M is not referenced. Constraint: if ${\mathbf{M}}\ge {\mathbf{NVAR}}$, ${\mathbf{MODE}}=\text{'S'}$. 10: ISX($$) – INTEGER arrayInput Note: the dimension of the array ISX must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}\right)$. On entry: if ${\mathbf{MODE}}=\text{'S'}$, ${\mathbf{ISX}}\left(\mathit{l}\right)$ indicates if the $\mathit{l}$th variable in X is to be included in the distance calculations. If ${\mathbf{ISX}}\left(\mathit{l}\right)>0$ the $\mathit{l}$th variable is included, for $\mathit{l}=1,2,\dots ,{\mathbf{M}}$; otherwise the $\mathit{l}$th variable is not referenced. If ${\mathbf{MODE}}=\text{'M'}$, ISX is not referenced. Constraint: if ${\mathbf{MODE}}=\text{'S'}$, ${\mathbf{ISX}}\left(l\right)>0$ for NVAR values of $l$. 11: X(LDX,$*$) – REAL (KIND=nag_wp) arrayInput Note: the second dimension of the array X must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}\right)$. On entry: if ${\mathbf{MODE}}=\text{'S'}$ the $\mathit{k}$th row of X must contain ${x}_{\mathit{k}}$. That is ${\mathbf{X}}\left(\mathit{k},\mathit{l}\right)$ must contain the $\mathit{k}$th sample value for the $\mathit{l}$th variable, for $\mathit{k}=1,2,\dots ,{\mathbf{NOBS}}$ and $\mathit{l}=1,2,\dots ,{\mathbf{M}}$. Otherwise X is not referenced. 12: LDX – INTEGERInput On entry: the first dimension of the array X as declared in the (sub)program from which G03DBF is called. Constraints: • if ${\mathbf{MODE}}=\text{'S'}$, ${\mathbf{LDX}}\ge {\mathbf{NOBS}}$; • otherwise $1$. 13: D(LDD,NG) – REAL (KIND=nag_wp) arrayOutput On exit: the squared distances. If ${\mathbf{MODE}}=\text{'S'}$, ${\mathbf{D}}\left(\mathit{k},\mathit{j}\right)$ contains the squared distance of the $\mathit{k}$th sample point from the $\mathit{j}$th group mean, ${D}_{\mathit{k}\mathit{j}}^{2}$, for $\mathit{k}=1,2,\dots ,{\mathbf{NOBS}}$ and $\mathit{j}=1,2,\dots ,{n}_{g}$. If ${\mathbf{MODE}}=\text{'M'}$ and ${\mathbf{EQUAL}}=\text{'U'}$, ${\mathbf{D}}\left(\mathit{i},\mathit{j}\right)$ contains the squared distance between the $\mathit{i}$th mean and the $\mathit{j}$th mean, ${D}_{\mathit{i}\mathit{j}}^{2}$, for $\mathit{i}=1,2,\dots ,{n}_{g}$ and $\mathit{j}=1,2,\dots ,\mathit{i}-1,\mathit{i}+1,\dots ,{n}_{g}$. The elements ${\mathbf{D}}\left(\mathit{i},\mathit{i}\right)$ are not referenced, for $\mathit{i}=1,2,\dots ,{n}_{g}$. If ${\mathbf{MODE}}=\text{'M'}$ and ${\mathbf{EQUAL}}=\text{'E'}$, ${\mathbf{D}}\left(\mathit{i},\mathit{j}\right)$ contains the squared distance between the $\mathit{i}$th mean and the $\mathit{j}$th mean, ${D}_{\mathit{i}\mathit{j}}^{2}$, for $\mathit{i}=1,2,\dots ,{n}_{g}$ and $\mathit{j}=1,2,\dots ,\mathit{i}-1$. Since ${D}_{\mathit{i}\mathit{j}}={D}_{\mathit{j}\mathit{i}}$ the elements ${\mathbf{D}}\left(\mathit{i},\mathit{j}\right)$ are not referenced, for $\mathit{i}=1,2,\dots ,{n}_{g}$ and $\mathit{j}=\mathit{i}+1,\dots ,{n}_{g}$. 14: LDD – INTEGERInput On entry: the first dimension of the array D as declared in the (sub)program from which G03DBF is called. Constraints: • if ${\mathbf{MODE}}=\text{'S'}$, ${\mathbf{LDD}}\ge {\mathbf{NOBS}}$; • if ${\mathbf{MODE}}=\text{'M'}$, ${\mathbf{LDD}}\ge {\mathbf{NG}}$. 15: WK($2×{\mathbf{NVAR}}$) – REAL (KIND=nag_wp) arrayWorkspace 16: IFAIL – INTEGERInput/Output On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details. For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit. On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6). ## 6 Error Indicators and Warnings If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF). Errors or warnings detected by the routine: ${\mathbf{IFAIL}}=1$ On entry, ${\mathbf{NVAR}}<1$, or ${\mathbf{NG}}<2$, or ${\mathbf{LDGMN}}<{\mathbf{NG}}$, or ${\mathbf{MODE}}=\text{'S'}$ and ${\mathbf{NOBS}}<1$, or ${\mathbf{MODE}}=\text{'S'}$ and ${\mathbf{M}}<{\mathbf{NVAR}}$, or ${\mathbf{MODE}}=\text{'S'}$ and ${\mathbf{LDX}}<{\mathbf{NOBS}}$, or ${\mathbf{MODE}}=\text{'S'}$ and ${\mathbf{LDD}}<{\mathbf{NOBS}}$, or ${\mathbf{MODE}}=\text{'M'}$ and ${\mathbf{LDD}}<{\mathbf{NG}}$, or ${\mathbf{EQUAL}}\ne \text{'E'}$ or ‘U’, or ${\mathbf{MODE}}\ne \text{'M'}$ or ‘S’. ${\mathbf{IFAIL}}=2$ On entry, ${\mathbf{MODE}}=\text{'S'}$ and the number of variables indicated by ISX is not equal to NVAR, or ${\mathbf{EQUAL}}=\text{'E'}$ and a diagonal element of $R$ is zero, or ${\mathbf{EQUAL}}=\text{'U'}$ and a diagonal element of ${R}_{j}$ for some $j$ is zero. ## 7 Accuracy The accuracy will depend upon the accuracy of the input $R$ or ${R}_{j}$ matrices. If the distances are to be used for discrimination, see also G03DCF. ## 9 Example The data, taken from Aitchison and Dunsmore (1975), is concerned with the diagnosis of three ‘types’ of Cushing's syndrome. The variables are the logarithms of the urinary excretion rates (mg/24hr) of two steroid metabolites. Observations for a total of $21$ patients are input and the group means and $R$ matrices are computed by G03DAF. A further six observations of unknown type are input, and the distances from the group means of the $21$ patients of known type are computed under the assumption that the within-group variance-covariance matrices are not equal. These results are printed and indicate that the first four are close to one of the groups while observations $5$ and $6$ are some distance from any group. ### 9.1 Program Text Program Text (g03dbfe.f90) ### 9.2 Program Data Program Data (g03dbfe.d) ### 9.3 Program Results Program Results (g03dbfe.r)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 174, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9962978363037109, "perplexity": 2426.448375050775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662022.71/warc/CC-MAIN-20160924173742-00084-ip-10-143-35-109.ec2.internal.warc.gz"}
http://ibmaths4u.com/viewtopic.php?f=3&t=346&sid=68d8c7fdea183cf8ca1f298348a06f05	## Complex Numbers Quadratics Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes ### Complex Numbers Quadratics Complex Numbers, Quadratic over complex field - IB Mathematics HL How can we solve the following quadratic equation over the complex field? $z^2-6z+13=0$ Thanks lora Posts: 0 Joined: Wed Apr 10, 2013 7:36 pm	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.909166693687439, "perplexity": 3767.2703471143595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948522343.41/warc/CC-MAIN-20171213084839-20171213104839-00002.warc.gz"}
https://mathematica.stackexchange.com/questions/97059/derivatives-of-vectors	# Derivatives of vectors I have an issue with derivatives of vectors $Assumptions := v ∈ Vectors[3, Reals] (Assuming v is a 3d vector) D[Norm[v]^2, v.{0, 0, 1}] (differentiate with respect to third component) Output: 0 But isn't this supposed to be:$\frac{\partial (v_1^2+v_2^2+v_3^2)}{\partial v_3}=2v_3$• If my answer below answered your question, please accept it so that we can get this question off the unanswered list and so that I can get those meaningless internet points that I so crave! – march Nov 6 '15 at 4:09 • @march Ah! Yep here are your well-deserved points :) Thanks a lot for the help! I simply forgot to click ;) – Otto Nov 7 '15 at 1:56 ## 1 Answer Here's how you should probably do this: vec = Array[v, 3] D[vec.vec, vec.{0, 0, 1}] (* {v[1], v[2], v[3]} ) ( 2 v[3] ) I'll just make a couple of points about D. • It doesn't behave well when given functions like Abs and Norm: D[Norm[{a, b, c}]^2, a] ( 2 Abs[a] Abs'[a] ) Instead, you should typically use more explicit forms of vector norms, which is why I used vec.vec ( v[1]^2 + v[2]^2 + v[3]^2 *) • I would guess that Vectors is mainly useful for doing symbolic tensor math, as shown in the documentation. It's not for what you're trying to do with it. • Meditate on the result of the following evaluation; it will show you why your result was zero and how D interprets its arguments. Clear[v] D[v.{0, 0, 1}, v.{0, 0, 1}] • I upvoted this even though your rep counter was just at 4444, and now I messed up that nice number. Sorry for that, I guess. – Jens Oct 15 '15 at 5:27 • @Jens I wish I could have stayed there forever.$4444 = 66^2 + 88$;$4444 = 4\times1111$with$1+1+1+1 = 4\$. – march Oct 15 '15 at 15:35 • You are correct that Vectors is meant for symbolic tensor manipulations and simplifications. – Stefan R Oct 16 '15 at 17:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6181496977806091, "perplexity": 2958.2874790838196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988753.97/warc/CC-MAIN-20210506114045-20210506144045-00033.warc.gz"}
https://tex.stackexchange.com/questions/330196/numbering-in-list-of-figures-with-images-in-an-itemize-list-on-left-side	# Numbering in list of figures with images in an itemize list on left side According to my prior question: Is it possible to get the images in the list of figures numbered in an itemize list with images on the left side? Right now it looks a bit strange. Here is a solution. \documentclass{article} \usepackage{mwe}% just for the example \usepackage{linegoal} \newcommand{\mycaption}[1]{% \refstepcounter{figure}% \begin{document} \listoffigures \begin{itemize} \item \includegraphics[scale=.15]{example-image} \mycaption{caption} \item \includegraphics[scale=.2]{example-image} \mycaption{an other caption} \end{itemize} \end{document}	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22485041618347168, "perplexity": 3097.7810605398104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986648343.8/warc/CC-MAIN-20191013221144-20191014004144-00298.warc.gz"}
http://mathhelpforum.com/pre-calculus/190090-even-odd-functions.html	# Thread: Even And Odd Functions 1. ## Even And Odd Functions Hey I just took a quiz and got this question wrong: Is the given functions even, odd, or neither? $f(x) = - 4x + \left\| {8x} \right\|$ I answered it was odd because the x coefficient of both terms have a power of 1: $f(x) = - 4{x^1} + \left\| {8{x^1}} \right\|$ Why did I get this answer wrong? Sam 2. ## Re: Even And Odd Functions That is not the correct concept to used to determine if a function is even or odd. Do you know the definition for even and odd functions? 3. ## Re: Even And Odd Functions Originally Posted by ArcherSam Is the given functions even, odd, or neither? $f(x) = - 4x + \left\| {8x} \right\|$ $f(2)=12~\&~f(-2)=20$. If it were an even function then $f(2)=f(-2)~.$ If it were an odd function then $-f(2)=f(-2)~.$ Is it even or odd? 4. ## Re: Even And Odd Functions General rules... a) f(x) is an even function if f(x)=f(-x) b) f(x) is an odd function if f(x)=-f(-x) c) any function f(x) can be written as $f(x)=f_{e}(x)+f_{o}(x)$ where $f_{e}()$ is the 'even part of f()' and $f_{o}()$ is the 'odd part of f()' d) for any function f(x) is... $f_{e}(x)= \frac{f(x)+f(-x)}{2}$ $f_{o}(x)= \frac{f(x)-f(-x)}{2}$ (1) e) given f(x), one computes with (1) its even and odd part. If $f_{o}(x)=0$ then f() is an even function. If $f_{e}(x)=0$, then f() is an odd function. If $f_{e}(x) \ne 0$ and $f_{o}(x) \ne 0$, then f() in neither even nor odd... Kind regards $\chi$ $\sigma$ 5. ## Re: Even And Odd Functions Originally Posted by cheme That is not the correct concept to used to determine if a function is even or odd. Do you know the definition for even and odd functions? Sam, I would slightly edit this (^^) comment... If you have a polynomial with only even exponents (a constant "c" can be written as cx^0, and zero is even, so constant terms are even...), then the function P(x) is even. If you have a polynomial with only odd exponents, then the function P(x) is odd. In your examples, there is an absolute value term, which is not polynomial. 6. ## Re: Even And Odd Functions Hello, Sam! I just took a quiz and got this question wrong: Is the given functions even, odd, or neither? . $f(x) \:=\: - 4x + \|8x\|$ I answered it was odd because the $x$ of both terms have a power of 1: . . $f(x) \:=\:-4{x^1} + \|8x^1\|$ Why did I get this answer wrong? Be careful! That rule about "all odd exponents" or "all even exponents" . . works with polynomials only. . (Edit: as TheChaz already pointed out.) If $x^n$ is "inside" another function, all bets are off! Examples: . $\sqrt{x}\quad e^x\quad\|x\|\quad\ln x$ Look at that function again: . $f(x) \:=\:-4x + \|8x\|$ If $x$ is negative $(x = -a)$, . . we have: . $f(-a) \:=\:-4(-a) + \|8(-a)\| \;=\;4a$ + $8a$ But $-f(a) \:=\:-\left(-4a + \|8a\|\right) \:=\:-\(-4a + 8a) \:=\:4a$ - $8a$ 7. ## Re: Even And Odd Functions Originally Posted by TheChaz Sam, I would slightly edit this (^^) comment... If you have a polynomial with only even exponents (a constant "c" can be written as cx^0, and zero is even, so constant terms are even...), then the function P(x) is even. If you have a polynomial with only odd exponents, then the function P(x) is odd. In your examples, there is an absolute value term, which is not polynomial. As my comment was directed towards the problem at hand, I should have said "the" function and not "a" function. 8. ## Re: Even And Odd Functions @Soroban, cheme, TheChaz Thanks! I was wondering why it worked when my instructor used this method to determine if a function was even or odd. Now I know the using the powers of exponents to determine if a function is even or odd, only works when you have polynomials only. @Plato $\begin{array}{l} f(x) = - 4x + \left\| {8x} \right\|\\ f( - x) = - 4( - x) + \left\| {8( - x)} \right\|\\ f( - x) = 4x + \left\| { - 8x} \right\|\\ f( - x) \ne f(x)\\ - f(x) = - (4x + \left\| {8x} \right\|)\\ - f(x) = - 4x - \left\| {8x} \right\|\\ - f(x) \ne f(x)\\ neither \end{array}$ @chisigma I was trying to understand general rule c, and d. May you solve a problem using rule c and d. 9. ## Re: Even And Odd Functions Originally Posted by ArcherSam @Soroban, cheme, TheChaz Thanks! I was wondering why it worked when my instructor used this method to determine if a function was even or odd. Now I know the using the powers of exponents to determine if a function is even or odd, only works when you have polynomials only... @chisigma I was trying to understand general rule c, and d. May you solve a problem using rule c and d. All right!... is... $f(x)= f_{e}(x) + f_{o}(x) = -4 x + \|8 x\|$ (1) ... so that... $f_{e}(x)= \frac{f(x)+f(-x)}{2}= {-4 x + \|8 x\| +4 x + \|8 x\|}{2} = \|8 x\|$ (2) $f_{o}(x)= \frac{f(x)-f(-x)}{2}= {-4 x + \|8 x\| -4 x - \|8 x\|}{2} = -4 x$ (3) Because neither $f_{e}()$ nor $f_{o}(*)$ is 'identically 0' , then f(x) is 'neither even nor odd'... If You will use this approach in the future, You will be 'very lucky' because it works for any type of fucntion, not only for polynomials... Kind regards $\chi$ $\sigma$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 37, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9180927276611328, "perplexity": 1011.0930566757406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463612537.91/warc/CC-MAIN-20170529184559-20170529204559-00359.warc.gz"}
http://www.ck12.org/algebra/Exponential-Properties-Involving-Products/lesson/Exponential-Properties-Involving-Products-ALG-I/	# Exponential Properties Involving Products ## Add exponents to multiply exponents by other exponents % Progress MEMORY METER This indicates how strong in your memory this concept is Progress % Exponential Properties Involving Products ### Exponential Properties Involving Products In expressions involving exponents, like \begin{align}3^5\end{align} or \begin{align}x^3\end{align}. the number on the bottom is called the base and the number on top is the power or exponent. The whole expression is equal to the base multiplied by itself a number of times equal to the exponent; in other words, the exponent tells us how many copies of the base number to multiply together. #### Writing Expressions in Exponential Form Write in exponential form. a) \begin{align}2 \cdot 2\end{align} \begin{align}2 \cdot 2 = 2^2\end{align} because we have 2 factors of 2 b) \begin{align}(-3)(-3)(-3)\end{align} \begin{align}(-3)(-3)(-3) = (-3)^3\end{align} because we have 3 factors of (-3) c) \begin{align}y \cdot y \cdot y \cdot y \cdot y\end{align} \begin{align}y \cdot y \cdot y \cdot y \cdot y = y^5\end{align} because we have 5 factors of \begin{align}y\end{align} d) \begin{align}(3a)(3a)(3a)(3a)\end{align} \begin{align}(3a)(3a)(3a)(3a)=(3a)^4\end{align} because we have 4 factors of \begin{align}3a\end{align} When the base is a variable, it’s convenient to leave the expression in exponential form; if we didn’t write \begin{align}x^7\end{align}, we’d have to write \begin{align}x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x\end{align} instead. But when the base is a number, we can simplify the expression further than that; for example, \begin{align}2^7\end{align} equals \begin{align}2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2\end{align}, but we can multiply all those 2’s to get 128. Let’s simplify the expressions from Example A. #### Simplifying Expressions Simplify a) \begin{align}2^2\end{align} \begin{align}2^2 = 2 \cdot 2 =4\end{align} b) \begin{align}(-3)^3\end{align} \begin{align}(-3)^3 = (-3)(-3)(-3)=-27\end{align} c) \begin{align}y^5\end{align} \begin{align}y^5\end{align} is already simplified d) \begin{align}(3a)^4\end{align} \begin{align}(3a)^4 = (3a)(3a)(3a)(3a) = 3 \cdot 3 \cdot 3 \cdot 3 \cdot a \cdot a \cdot a \cdot a = 81 a^4\end{align} Be careful when taking powers of negative numbers. Remember these rules: \begin{align}(negative \ number) \cdot (positive \ number) = negative \ number\! \\ (negative \ number) \cdot (negative \ number) = positive \ number \end{align} So even powers of negative numbers are always positive. Since there are an even number of factors, we pair up the negative numbers and all the negatives cancel out. \begin{align}(-2)^6 &= (-2)(-2)(-2)(-2)(-2)(-2)\\ &= \underbrace{ (-2)(-2) }_{+4} \cdot \underbrace{ (-2)(-2) }_{+4} \cdot \underbrace{ (-2)(-2) }_{+4}\\ &= +64\end{align} And odd powers of negative numbers are always negative. Since there are an odd number of factors, we can still pair up negative numbers to get positive numbers, but there will always be one negative factor left over, so the answer is negative: \begin{align}(-2)^5 &= (-2)(-2)(-2)(-2)(-2)\\ &= \underbrace{(-2)(-2)}_{+4} \cdot \underbrace{(-2)(-2)}_{+4} \cdot \underbrace{(-2)}_{-2}\\ &= -32\end{align} #### Use the Product of Powers Property So what happens when we multiply one power of \begin{align}x\end{align} by another? Let’s see what happens when we multiply \begin{align}x\end{align} to the power of 5 by \begin{align}x\end{align} cubed. To illustrate better, we’ll use the full factored form for each: \begin{align}\underbrace{(x \cdot x \cdot x \cdot x \cdot x)}_{x^5} \cdot \underbrace{(x \cdot x \cdot x)}_{x^3} = \underbrace{(x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x)}_{x^8}\end{align} So \begin{align}x^5 \times x^3 = x^8\end{align}. You may already see the pattern to multiplying powers, but let’s confirm it with another example. We’ll multiply \begin{align}x\end{align} squared by \begin{align}x\end{align} to the power of 4: \begin{align}\underbrace{(x \cdot x)}_{x^2} \cdot \underbrace{(x \cdot x \cdot x \cdot x)}_{x^4} = \underbrace{(x \cdot x \cdot x \cdot x \cdot x \cdot x)}_{x^6}\end{align} So \begin{align}x^2 \times x^4 = x^6\end{align}. Look carefully at the powers and how many factors there are in each calculation. \begin{align}5 \ x\end{align}’s times \begin{align}3 \ x\end{align}’s equals \begin{align}(5 + 3) = 8 \ x\end{align}’s. \begin{align}2 \ x\end{align}’s times \begin{align}4 \ x\end{align}’s equals \begin{align}(2 + 4) = 6 \ x\end{align}’s. You should see that when we take the product of two powers of \begin{align}x\end{align}, the number of \begin{align}x\end{align}’s in the answer is the total number of \begin{align}x\end{align}’s in all the terms you are multiplying. In other words, the exponent in the answer is the sum of the exponents in the product. Product Rule for Exponents: \begin{align}x^n \cdot x^m = x^{(n+m)}\end{align} There are some easy mistakes you can make with this rule, however. Let’s see how to avoid them. #### Multiplying Exponents 1. Multiply \begin{align}2^2 \cdot 2^3\end{align}. \begin{align}2^2 \cdot 2^3 = 2^5 = 32\end{align} Note that when you use the product rule you don’t multiply the bases. In other words, you must avoid the common error of writing \begin{align}2^2 \cdot 2^3 = 4^5\end{align}. You can see this is true if you multiply out each expression: 4 times 8 is definitely 32, not 1024. 2. Multiply \begin{align}2^2 \cdot 3^3\end{align}. \begin{align}2^2 \cdot 3^3 = 4 \cdot 27 = 108\end{align} In this case, we can’t actually use the product rule at all, because it only applies to terms that have the same base. In a case like this, where the bases are different, we just have to multiply out the numbers by hand—the answer is not \begin{align}2^5\end{align} or \begin{align}3^5\end{align} or \begin{align}6^5\end{align} or anything simple like that. ### Examples Simplify the following exponents: #### Example 1 \begin{align}(-2)^5\end{align} \begin{align}(-2)^5=(-2)(-2)(-2)(-2)(-2)=-32\end{align} #### Example 2 \begin{align}(10x)^2\end{align} \begin{align}(10x)^2=10^2\cdot x^2=100x^2\end{align} ### Review Write in exponential notation: 1. \begin{align}4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\end{align} 2. \begin{align}3x \cdot 3x \cdot 3x\end{align} 3. \begin{align}(-2a)(-2a)(-2a)(-2a)\end{align} 4. \begin{align}6 \cdot 6 \cdot 6 \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y\end{align} 5. \begin{align}2 \cdot x \cdot y \cdot 2 \cdot 2 \cdot y \cdot x\end{align} Find each number. 1. \begin{align}5^4\end{align} 2. \begin{align}(-2)^6\end{align} 3. \begin{align}(0.1)^5\end{align} 4. \begin{align}(-0.6)^3\end{align} 5. \begin{align}(1.2)^2+5^3\end{align} 6. \begin{align}3^2 \cdot (0.2)^3\end{align} Multiply and simplify: 1. \begin{align}6^3 \cdot 6^6\end{align} 2. \begin{align}2^2 \cdot 2^4 \cdot 2^6\end{align} 3. \begin{align}3^2 \cdot 4^3\end{align} 4. \begin{align}x^2 \cdot x^4\end{align} 5. \begin{align}(-2y^4)(-3y)\end{align} 6. \begin{align}(4a^2)(-3a)(-5a^4)\end{align} ### Notes/Highlights Having trouble? Report an issue. Color Highlighted Text Notes ### Vocabulary Language: English TermDefinition Base When a value is raised to a power, the value is referred to as the base, and the power is called the exponent. In the expression $32^4$, 32 is the base, and 4 is the exponent. Exponent Exponents are used to describe the number of times that a term is multiplied by itself. Power The "power" refers to the value of the exponent. For example, $3^4$ is "three to the fourth power".	{"extraction_info": {"found_math": true, "script_math_tex": 75, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 2, "texerror": 0, "math_score": 1.0000097751617432, "perplexity": 1052.0549062209866}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122726.55/warc/CC-MAIN-20170423031202-00121-ip-10-145-167-34.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/need-help-factoring.223658/	# Need help factoring 1. Mar 22, 2008 ### Bigo75 1. The problem statement, all variables and given/known data x^2-x+1/x+1 -1/2 2. Relevant equations need help factoring this 3. The attempt at a solution A common denominator would be 2(x+1) but that does not change my numerator 2. Mar 22, 2008 ### rocomath 3. Mar 22, 2008 ### Bigo75 I think I got it, common deno is 2(x+1), which gives you 2x^2-3x+1/2(x+1) and that factors into (x-1)(2x-1)/2(x+1) Right? 4. Mar 23, 2008 ### eys_physics Yes it is correct! 5. Mar 24, 2008 ### HallsofIvy Staff Emeritus Assuming your original expression is (x^2-x+1)/(x+1)- 1/2, then it is correct.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9059666991233826, "perplexity": 16367.2844381819}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543577.51/warc/CC-MAIN-20161202170903-00233-ip-10-31-129-80.ec2.internal.warc.gz"}
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=CCRTCN_2000_v12n5_111	A Study on high Quality of Antiwashout Underwater Concrete Title & Authors A Study on high Quality of Antiwashout Underwater Concrete ;;;;; Abstract In case of constructing concrete structure under water, generally concrete mixed with antiwashout admixture, high range water reducer, or AE-water reducing agent etc has been manufactured to ensure the quality of antiwashout underwater concrete because of being difficulty in ascertaining construction situation by the naked eye. The properties of high quality antiwashout underwater concrete that were aimed at affluent fluidity, workability and the compressive strength of 450 kgf/$\small{\textrm{cm}^2}$ at 28 ages using two types of blended cements are following as;(1) Setting time of antiwashout underwater concretes using blended cements was more greatly delayed than that of control concrete, however, was satisfied with criteria value of "Quality standard specification of antiwashout admixture for concrete".(2) As a test results of slump flow, efflux time and box elevation of head, it was found that workability of high quality antiwashout underwater concrete was improved. (3) Heat evolution amount of OPC was 1.5 times as high as that of two types of bended cements in 72 hours. (4) Suspended solids of antiwashout underwater concrete using blended cements was more than that of control concrete, also compressive strength of high quality antiwashout underwater concrete was very low in early age, but was better than that of control concrete as to increasing ages. Keywords heat evolution amount;setting time;suspended solids;efflux time; Language English Cited by References 1. 2. Gypsum and Lime, 1988. 213, pp.43-50 3. コソクリ一ト工學年次論文報告集, 1988. pp.55-58 4. 5. 대한토목학회 학술지, 1991. vol.39. 4, pp.83-97 6. 대한토목학회논문집, 2000. vol.20. 2-A, pp.301-310 7. 대한토목학회, 1995. 8. コソクリ一ト工學年次論文報告潗, 1989. vol.11. 1, pp.155-160 9. CANMET, 1996. pp.59-67 10. コソクリ一ト工學年次論文報告集, 1998. vol.20. 2, pp.319-324 11. コソクリ一ト工學年次報告集, 1991. vol.13. 1, pp.197-202 12.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 1, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.723663866519928, "perplexity": 14630.474613735032}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549429548.55/warc/CC-MAIN-20170727222533-20170728002533-00081.warc.gz"}
http://eprint.iacr.org/2009/526/20100220:123300	## Cryptology ePrint Archive: Report 2009/526 Improved Related-Key Boomerang Attacks on Round-Reduced Threefish-512 Jiazhe Chen and Keting Jia Abstract: Hash function Skein is one of the 14 NIST SHA-3 second round candidates. Threefish is a tweakable block cipher as the core of Skein, defined with a 256-, 512-, and 1024-bit block size. The 512-bit block size is the primary proposal of the authors. Skein had been updated after it entered the second round, the only differences between the original and the new version are the rotation constants. In this paper we construct related-key boomerang distinguishers on round-reduced Threefish-512 based on the new rotation constants using the method of \emph{modular differential}. With these distinguishers, we mount related-key boomerang key recovery attacks on Threefish-512 reduced to 32, 33 and 34 rounds. The attack on 32-round Threefish-512 has time complexity $2^{195}$ with memory of $2^{12}$ bytes. The attacks on Threefish-512 reduced to 33 and 34 rounds has time complexity of $2^{325.56}$ and $2^{483}$ encryptions respectively, and both with negligible memory. The best key recovery attack known before is proposed by Aumasson et al. Their attack, which bases on the old rotation constants, is also a related-key boomerang attack. For 32-round Threefish-512, their attack requires $2^{312}$ encryptions and $2^{71}$ bytes of memory. Category / Keywords: secret-key cryptography / Threefish-512, related-key boomerang attack, modular differential Date: received 1 Nov 2009, last revised 20 Feb 2010 Contact author: jiazhechen at mail sdu edu cn Available format(s): PDF \| BibTeX Citation	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29351192712783813, "perplexity": 8473.171350132323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00053-ip-10-147-4-33.ec2.internal.warc.gz"}
https://luisrguzmanjr.wordpress.com/tag/taniyama-shimura-conjecture/	You are currently browsing the tag archive for the ‘taniyama-shimura conjecture’ tag. Taniyama-Shimura 3: L-Series where it will be crucial in the definition of modularity. For today, we assume our $latex {d}&fg=000000$-dimensional variety $latex {X/\mathbb{Q}}&fg=000000$ has the property that its middle etale cohomology is 2-dimensional. It won’t hurt if you want to just think that $latex {X}&fg=000000$ is an elliptic curve. We will first define the L-series via the Galois representation that we constructed last time. Fix $latex {p}&fg=000000$ a prime not equal to $latex {\ell}&fg=000000$ and of good reduction for $latex {X}&fg=000000$. Let $latex {M=\overline{\mathbb{Q}}^{\ker \rho_X}}&fg=000000$. By definition the representation factors through $latex {{Gal} (M/\mathbb{Q})}&fg=000000$. For $latex {\frak{p}}&fg=000000$ a prime lying over $latex {p}&fg=000000$ the decomposition group $latex {D_{\frak{p}}}&fg=000000$ surjects onto $latex {{Gal} (\overline{\mathbf{F}}_p/\mathbf{F}_p)}&fg=000000$ with kernel $latex {I_{\frak{p}}}&fg=000000$. One of the subtleties we’ll jump over to save time is that $latex {\rho_X}&fg=000000$ acts trivially on $latex {I_{\frak{p}}}&fg=000000$ (it follows from the good reduction assumption), so we can lift the generator of $latex {{Gal} (\overline{\mathbf{F}}_p/\mathbf{F}_p)}&fg=000000$ to get a conjugacy class $latex {{Frob}_p}&fg=000000$ whose image under… View original post 917 more words Taniyama-Shimura 2: Galois Representations where the standard modern approach to defining modularity for other types of varieties. Fix some proper variety $latex {X/\mathbb{Q}}&fg=000000$. Our goal today will seem very strange, but it is to explain how to get a continuous representation of the absolute Galois group of $latex {\mathbb{Q}}&fg=000000$ from this data. I’m going to assume familiarity with etale cohomology, since describing Taniyama-Shimura is already going to take a bit of work. To avoid excessive notation, all cohomology in this post (including the higher direct image functors) are done on the etale site. For those that are intimately familiar with etale cohomology, we’ll do the quick way first. I’ll describe a more hands on approach afterwards. Let $latex {\pi: X\rightarrow \mathrm{Spec} \mathbb{Q}}&fg=000000$ be the structure morphism. Fix an algebraic closure $latex {v: \mathrm{Spec} \overline{\mathbb{Q}}\rightarrow \mathrm{Spec}\mathbb{Q}}&fg=000000$ (i.e. a geometric point of the base). We’ll denote the base change of $latex {X}&fg=000000$ with respect to this morphism $latex {\overline{X}}&fg=000000$. Suppose the dimension of $latex {X}&fg=000000$ is $latex {n}&fg=000000$. Let… View original post 374 more words Great post on understanding the statement of the famous Taniyama-Shimura conjecture that led to the proof of Fermat’s Last Theorem. It’s time to return to plan A. I started this year by saying I’d post on some fundamental ideas in arithmetic geometry. The local system thing is hard to get motivated about, since the way I was going to use it in my research seems irrelevant at the moment. My other option was to blog some stuff about class field theory, since there is a reading group on the topic that I belong to this quarter. The first goal of this new series is to understand the statement of the famous Taniyama-Shimura conjecture that led to the proof of Fermat’s Last Theorem. A lot of people can probably mumble something about the conjecture if they have any experience in algebraic/arithmetic geoemtry or any of the number theory type fields, but most people probably can’t say anything precise about what the conjecture says (I’ll continue to call it a “conjecture” even… View original post 766 more words Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in the proof, by Andrew Wiles, of Fermat’s Last Theorem. More concretely, an elliptic curve is the set of zeros of a cubic polynomial in two variables. Where $ax^{3}+bx^{2}y+cxy^{2}+dy^{3}+ex^{2}+fxy+gy^{2}+hx+iy+j=0$ is the equation of a general cubic polynomial. A famous example being $\displaystyle x^{3}+y^{3}=1$ or in homogeneous form, $\displaystyle X^{3}+Y^{3}=Z^{3}$. This is the first non-trivial case of Fermat’s Last Theorem. A modular elliptic curve is an elliptic curve $E$ that admits a parametrization $X_{0}(N) \rightarrow E$ by a modular curve. This is not the same as a modular curve that happens to be an elliptic curve, and which could be called an elliptic modular curve. The modularity theorem, also known as the Taniyama–Shimura conjecture, asserts that every elliptic curve defined over the rational numbers is a modular form in disguise. In 1985, starting with a fictitious solution to Fermat’s last theorem (the Frey curve), G. Frey showed that he could create an unusual elliptic curve which appeared not to be modular. If the curve were not modular, then this would show that if Fermat’s last theorem were false, then the Taniyama-Shimura conjecture would also be false. Furthermore, if the Taniyama-Shimura conjecture is true, then so is Fermat’s last theorem. However, Frey did not actually prove that his curve was not modular. The conjecture that Frey’s curve was not modular came to be called the “epsilon conjecture,” and was quickly proved by Ribet (Ribet’s theorem) in 1986, establishing a very close link between two mathematical structures (the Taniyama-Shimura conjecture and Fermat’s last theorem) which appeared previously to be completely unrelated By proving the semistable case of the conjecture, Andrew Wiles proved Fermat’s Last Theorem. Some Elliptic curves:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8495806455612183, "perplexity": 276.1361936486536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267865438.16/warc/CC-MAIN-20180623225824-20180624005824-00459.warc.gz"}
https://www.physicsforums.com/threads/help-running-miktex-in-windows-xp.55861/	# Help running MikTex in Windows XP 1. Dec 7, 2004 ### Sirus I have installed the program but cannot seem to execute any of the applications (like texify). Some websites list the following method for running MikTex in XP: "First, I prepare my computer as instructed by http://www.math.auc.dk/~dethlef/Tips/preparation.html [Broken]. I changed all the "user variables" to my favorite directories (say, E:\) except for the variable "DICTDIR". I keep "c:\usr\local\lib" because the installation procedure of ISPELL suggests that we cannot change this. This is a very important step. We need to sychronize the user variables and what we do in the installation steps. Don't worry. If we have done differently in the installation step, we can always come back to change the user variables. Secondly, I download all the first seven files listed in http://www.math.auc.dk/~dethlef/Tips/download.html [Broken]. Thirdly, I install Emacs, AucTeX, Ispell, Ghostscript, Ghostview and MikTeX. I checked at every steps according to the suggestion at http://www.math.auc.dk/~dethlef/Tips/install.html [Broken]. Everything worked when I am done with the installation. The only exception is that I do not see color of different LaTeX commands. For this, I follow the instruction at http://www.eece.unm.edu/pipermail/eece537/2001-November/000034.html [Broken] to modify my .emacs file. Then everything worked great." For those of you who have done it in XP, is it necessary? Thank you, Sirus Last edited by a moderator: May 1, 2017 2. Dec 7, 2004 ### imabug All I did was add the MikTeX binaries folder to my path (Control Panel/System/Advanced/Environment Variables). Open up a command window, run [la]tex mydoc.tex and it goes. All the other stuff you mentioned is helper stuff. Emacs/AucTeX for editing your tex files, ghostscript/ghostview for creating/viewing Postscript files, ispell for spell checking. if you want to use them, install them. otherwise it's not necessary. 3. Dec 8, 2004 ### Sirus Perfect. Thanks.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8572901487350464, "perplexity": 5308.004885985669}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583513441.66/warc/CC-MAIN-20181020205254-20181020230754-00155.warc.gz"}
https://icsecbsemath.com/2017/07/16/class-10-sample-problems-matrices-exercise-12a/	Question 1: State True or False. If False, please state the reason. 1. If $A$ and $B$ are two matrices of order $3 \times 2$ and $2 \times 3$ respectively; then their sum $A + B$ is possible. 2. The Matrices $A_{2 \times 3}$ and $A_{2 \times 3}$ are conformable for subtraction. 3. Transpose of a $2 \times 1$ matrix is a $2\times 1$ matrix. 4. Transpose of a square matrix is a square matrix. 5. A column matrix has many columns and only one row. 1. False: Two matrices can be added together if they are of the same order. Here $A$ is of the Order $3 \times 2$ while $B$ is of the order $2 \times 3$. Hence they cannot be added. 2. True: Two matrices can be subtracted together if they are of the same order. Here both latex A &s=0$and latex B &s=0$ are of the same order. 3. False: The transpose of a matrix is obtained by interchanging rows with columns. Hence the Transpose of a $2 \times 1$ matrix is a $1 \times 2$ matrix. 4. True: Yes Transpose of a square matrix is a square matrix. Here the number of rows is equal to the number of columns. Hence even on transposing, the matrix would remain as a square matrix. 5. False: A Column matrix has one column and many rows. $\\$ Question 2: Given $\begin{bmatrix} x & y+2 \\ 3 & z-1 \end{bmatrix} = \begin{bmatrix} 3 & 1 \\ 3 & 2 \end{bmatrix}$, find $x, \ y \ and \ z$. $\begin{bmatrix} x & y+2 \\ 3 & z-1 \end{bmatrix} = \begin{bmatrix} 3 & 1 \\ 3 & 2 \end{bmatrix}$ $\Rightarrow x = 3$ $y+2 = 1 \ \Rightarrow y = -1$ also $z-1 = 2 \Rightarrow z = 3$ $\\$ Question 3: Solve for $a, \ b \ and \ c$ if; 1. $\begin{bmatrix} -4 & a+5 \\ 3 & 2 \end{bmatrix} = \begin{bmatrix} b+4 & 2 \\ 3 & c-1 \end{bmatrix}$ 2. $\begin{bmatrix} a & a-b \\ b+c & 0 \end{bmatrix} = \begin{bmatrix} 3 & -1 \\ 2 & 0 \end{bmatrix}$ 1) Given $\begin{bmatrix} -4 & a+5 \\ 3 & 2 \end{bmatrix} = \begin{bmatrix} b+4 & 2 \\ 3 & c-1 \end{bmatrix}$; Therefore $-4 = b+ 4 \Rightarrow b = -8$ $a+5 = 2 \Rightarrow a = -3$ $2 = c-1 \Rightarrow c = 3$ 2) $\begin{bmatrix} a & a-b \\ b+c & 0 \end{bmatrix} = \begin{bmatrix} 3 & -1 \\ 2 & 0 \end{bmatrix}$ $a = 3$ $a-b=-1 \Rightarrow b = a-1 = 3-1 = 2$ $b+c = 2 \Rightarrow c = 2-b = 2-2 = 0$ $\\$ Question 4: If $A = \begin{bmatrix} 8 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & -5 \end{bmatrix}$ find 1. $A+B$ 2. $B-A$ 1) $A+B$ $= \begin{bmatrix} 8 & -3 \end{bmatrix} + \begin{bmatrix} 4 & -5 \end{bmatrix}$ $=\begin{bmatrix} 8+4 & -3-5 \end{bmatrix} = \begin{bmatrix} 12 & -8 \end{bmatrix}$ 2) $B-A$ $= \begin{bmatrix} 4 & -5 \end{bmatrix} - \begin{bmatrix} 8 & -3 \end{bmatrix}$ $=\begin{bmatrix} 4-8 & -5-(-3) \end{bmatrix} = \begin{bmatrix} -4 & -2 \end{bmatrix}$ $\\$ Question 5: If $A = \begin{bmatrix} 2 \\ 5 \end{bmatrix}, \ B=\begin{bmatrix} 1 \\ 4 \end{bmatrix} \ and \ C=\begin{bmatrix} 6 \\ -2 \end{bmatrix}$ find: 1. $B+C$ 2. $A-C$ 3. $A+B-C$ 4. $A-B+C$ 1) $B+C$ $= \begin{bmatrix} 1 \\ 4 \end{bmatrix} + \begin{bmatrix} 6 \\ -2 \end{bmatrix}$ $= \begin{bmatrix} 1+6 \\ 4-2 \end{bmatrix}$ $= \begin{bmatrix} 7 \\ 2 \end{bmatrix}$ 2) $A-C$ $= \begin{bmatrix} 2 \\ 5 \end{bmatrix} - \begin{bmatrix} 6 \\ -2 \end{bmatrix}$ $= \begin{bmatrix} 2-6 \\ 5-(-2) \end{bmatrix}$ $= \begin{bmatrix} -4 \\ 7 \end{bmatrix}$ 3) $A+B-C$ $= \begin{bmatrix} 2 \\ 5 \end{bmatrix} + \begin{bmatrix} 1 \\ 4 \end{bmatrix} - \begin{bmatrix} 6 \\ -2 \end{bmatrix}$ $= \begin{bmatrix} 2+1-6 \\ 5+4-(-2) \end{bmatrix}$ $= \begin{bmatrix} -3 \\ 11 \end{bmatrix}$ 4) $A-B+C$ $= \begin{bmatrix} 2 \\ 5 \end{bmatrix} - \begin{bmatrix} 1 \\ 4 \end{bmatrix} + \begin{bmatrix} 6 \\ -2 \end{bmatrix}$ $= \begin{bmatrix} 2-1+6 \\ 5-4+(-2) \end{bmatrix}$ $= \begin{bmatrix} 7 \\ -1 \end{bmatrix}$ $\\$ Question 6: Wherever possible, write each of the following in a single matrix: 1. $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} -1 & -2 \\ 1 & -7 \end{bmatrix}$ 2. $\begin{bmatrix} 2 &3 & 4 \\ 5 & 6 & 7 \end{bmatrix} - \begin{bmatrix} 0 &2 & 3 \\ 6 & -1 & 0 \end{bmatrix}$ 3. $\begin{bmatrix} 0 & 1 & 2 \\ 4 & 6 & 7 \end{bmatrix} + \begin{bmatrix} 3 & 4 \\ 6 & 8 \end{bmatrix}$ 1) $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} -1 & -2 \\ 1 & -7 \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 4 & -3 \end{bmatrix}$ 2) $\begin{bmatrix} 2 &3 & 4 \\ 5 & 6 & 7 \end{bmatrix} - \begin{bmatrix} 0 &2 & 3 \\ 6 & -1 & 0 \end{bmatrix} = \begin{bmatrix} 2 &5 & 7 \\ 11 & 5 & 7 \end{bmatrix}$ 3) Adding this is is not possible as the order of the metrices are not the same. $\\$ Question 7: Find $x$ and $y$ from the following equations: 1. $\begin{bmatrix} 5 & 2 \\ -1 & y-1 \end{bmatrix} - \begin{bmatrix} 1 & x-1 \\ 2 & -3 \end{bmatrix} = \begin{bmatrix} 4 & 7 \\ -3 & 2 \end{bmatrix}$ 2. $\begin{bmatrix} -8 & x \end{bmatrix} + \begin{bmatrix} y & -2 \end{bmatrix} = \begin{bmatrix} -3 & 2 \end{bmatrix}$ 1) $\begin{bmatrix} 5 & 2 \\ -1 & y-1 \end{bmatrix} - \begin{bmatrix} 1 & x-1 \\ 2 & -3 \end{bmatrix} = \begin{bmatrix} 4 & 7 \\ -3 & 2 \end{bmatrix}$ $\begin{bmatrix} 5-1 & 2-(x-1) \\ (-1-2) & y-1-(-3) \end{bmatrix} =\begin{bmatrix} 4 & 7 \\ -3 & 2 \end{bmatrix}$ $= \begin{bmatrix} 4 & 3-x \\ -3 & y+2 \end{bmatrix} =\begin{bmatrix} 4 & 7 \\ -3 & 2 \end{bmatrix}$ Therefore $3-x = 7 \Rightarrow x = -4$ $y+2 = 2 \Rightarrow y = 0$ 2) $\begin{bmatrix} -8 & x \end{bmatrix} + \begin{bmatrix} y & -2 \end{bmatrix} = \begin{bmatrix} -3 & 2 \end{bmatrix}$ Therefore $-8+y=-3 \Rightarrow y = 5$ $x-2=2 \Rightarrow x = 4$ $\\$ Question 8: Given $M = \begin{bmatrix} 5 & -3 \\ -2 & 4 \end{bmatrix}$, find its transpose matrix $M^{t}$. If possible find: 1. $M+M^{t}$ 2. $M^{t}-M$ $M = \begin{bmatrix} 5 & -3 \\ -2 & 4 \end{bmatrix}$ $M^{t} = \begin{bmatrix} 5 & -2 \\ -3 & 4 \end{bmatrix}$ 1) $M+M^{t}$ $= \begin{bmatrix} 5 & -3 \\ -2 & 4 \end{bmatrix} + \begin{bmatrix} 5 & -2 \\ -3 & 4 \end{bmatrix} = \begin{bmatrix} 10 & -5 \\ -5 & 8 \end{bmatrix}$ 2) $M^{t}-M$ $= \begin{bmatrix} 5 & -2 \\ -3 & 4 \end{bmatrix} - \begin{bmatrix} 5 & -3 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$ $\\$ Question 9: Write the additive inverse of matrices A, B and C where $A = \begin{bmatrix} 6 & -5 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 0 \\ 4 & -1 \end{bmatrix}$ and $C = \begin{bmatrix} -2 \\ 4 \end{bmatrix}$. Additive Inverse of $A = \begin{bmatrix} 6 & -5 \end{bmatrix}$ is $= \begin{bmatrix} -6 & 5 \end{bmatrix}$ Additive Inverse of $B = \begin{bmatrix} -2 & 0 \\ 4 & -1 \end{bmatrix}$ is $= \begin{bmatrix} 2 & 0 \\ -4 & 1 \end{bmatrix}$ Additive Inverse of $C = \begin{bmatrix} -2 \\ 4 \end{bmatrix}$ is $= \begin{bmatrix} 7 & -4 \end{bmatrix}$ $\\$ Question 10: Given $A = \begin{bmatrix} 2 & -3 \end{bmatrix}, \ B= \begin{bmatrix} 0 & 2 \end{bmatrix}, \ C= \begin{bmatrix} -1 & 4 \end{bmatrix}$. Find matrix $X$ in each of the following: 1. $X+B=C-A$ 2. $A-X=B+C$ Let $X = \begin{bmatrix} a & b \end{bmatrix}$ 1) $X+B=C-A$ $\begin{bmatrix} a & b \end{bmatrix} +\begin{bmatrix} 0 & 2 \end{bmatrix}=\begin{bmatrix} -1 & 4 \end{bmatrix}-\begin{bmatrix} 2 & -3 \end{bmatrix}$ $\begin{bmatrix} a & b+2 \end{bmatrix} = \begin{bmatrix} -3 & 7 \end{bmatrix}$ Therefore $a = -3 \ and \ b = 5$ Hence $X = \begin{bmatrix} -3 & 5 \end{bmatrix}$ 2) $A-X=B+C$ $\begin{bmatrix} 2 & -3 \end{bmatrix} - \begin{bmatrix} a & b \end{bmatrix} = \begin{bmatrix} 0 & 2 \end{bmatrix} + \begin{bmatrix} -1 & 4 \end{bmatrix}$ $\begin{bmatrix} 2-a & -3-b \end{bmatrix} = \begin{bmatrix} -1 & 6 \end{bmatrix}$ Therefore $a = 3 \ and \ b = -9$ Hence $X = \begin{bmatrix} 3 & -9 \end{bmatrix}$ $\\$ Question 11: Given $A = \begin{bmatrix} -1 & 0 \\ 2 & -4 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & -3 \\ -2 & 0 \end{bmatrix}$. FInd the matrix $X$ in each of the following: 1. $A+X=B$ 2. $A-X=B$ 3. $X-B=A$ Let $X = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ 1) $A+X=B$ $\begin{bmatrix} -1 & 0 \\ 2 & -4 \end{bmatrix}+\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 3 & -3 \\ -2 & 0 \end{bmatrix}$ $\begin{bmatrix} -1+a & b \\ 2+c & -4+d \end{bmatrix} = \begin{bmatrix} 3 & -3 \\ -2 & 0 \end{bmatrix}$ Therefore $a = 4, \ b = -3, \ c = -4 \ and \ d = 4$ Hence $X = \begin{bmatrix} 4 & -3 \\ -4 & 4 \end{bmatrix}$ 2) $A-X=B$ $\begin{bmatrix} -1 & 0 \\ 2 & -4 \end{bmatrix}-\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 3 & -3 \\ -2 & 0 \end{bmatrix}$ $\begin{bmatrix} -1-a & -b \\ 2-c & -4-d \end{bmatrix} = \begin{bmatrix} 3 & -3 \\ -2 & 0 \end{bmatrix}$ Therefore $a = -4, \ b = 3, \ c = 4 \ and \ d = -4$ Hence $X = \begin{bmatrix} -4 & 3 \\ 4 & -4 \end{bmatrix}$ 3) $X-B=A$ $\begin{bmatrix} a & b \\ c & d \end{bmatrix} - \begin{bmatrix} 3 & -3 \\ -2 & 0 \end{bmatrix} =\begin{bmatrix} -1 & 0 \\ 2 & -4 \end{bmatrix}$ $\begin{bmatrix} a-3 & b+3 \\ c+2 & d \end{bmatrix} =\begin{bmatrix} -1 & 0 \\ 2 & -4 \end{bmatrix}$ Therefore $a = 2, \ b = -3, \ c = 0 \ and \ d = -4$ Hence $X = \begin{bmatrix} 2 & -3 \\ 0 & -4 \end{bmatrix}$ $\\$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 147, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9290640354156494, "perplexity": 2163.359126576051}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578582584.59/warc/CC-MAIN-20190422195208-20190422221208-00458.warc.gz"}
https://home.cern/resources/image/experiments/cms-images-gallery	CMS images gallery ID: CERN-PHOTO-201703-062-52 This week, one of the Large Hadron Collider’s experiments gets a “heart transplant”. --- Physicists and engineers are replacing the heart of the CMS experiment - the pixel #detector. This will improve CMS’s ability to make precise measurements on aspects 2017-03-07 Brice, Maximilien: CERN	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9330464601516724, "perplexity": 9287.436274885458}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662522309.14/warc/CC-MAIN-20220518183254-20220518213254-00298.warc.gz"}
https://scikit-optimize.github.io/notebooks/sklearn-gridsearchcv-replacement.html	Top # Scikit-learn hyperparameter search wrapper Iaroslav Shcherbatyi, Tim Head and Gilles Louppe. June 2017. ## Introduction This example assumes basic familiarity with scikit-learn. Search for parameters of machine learning models that result in best cross-validation performance is necessary in almost all practical cases to get a model with best generalization estimate. A standard approach in scikit-learn is using GridSearchCV class, which takes a set of values for every parameter to try, and simply enumerates all combinations of parameter values. The complexity of such search grows exponentially with addition of new parameters. A more scalable approach is using RandomizedSearchCV, which however does not take advantage of the structure of a search space. Scikit-optimize provides a drop in replacement for GridSearchCV, which utilizes Bayesian Optimization where a predictive model reffered to as "surrogate" is used to model the search space and utilized in order to arrive at good parameter values combination as soon as possible. Note: for a manual hyperparameter optimization example, see "Hyperparameter Optimization" notebook. ## Minimal example A minimal example of optimizing hyperparameters of SVC (Support Vector machine Classifier) is given below. from skopt import BayesSearchCV from sklearn.svm import SVC from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75, random_state=0) # log-uniform: understand as search over p = exp(x) by varying x opt = BayesSearchCV( SVC(), { 'C': (1e-6, 1e+6, 'log-uniform'), 'gamma': (1e-6, 1e+1, 'log-uniform'), 'degree': (1, 8), # integer valued parameter 'kernel': ['linear', 'poly', 'rbf'], # categorical parameter }, n_iter=32 ) opt.fit(X_train, y_train) print("val. score: %s" % opt.best_score_) print("test score: %s" % opt.score(X_test, y_test)) /home/ubuntu/miniconda3/envs/testenv/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2010: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified. FutureWarning) val. score: 0.991833704529 test score: 0.993333333333 In practice, one wants to enumerate over multiple predictive model classes, with different search spaces and number of evaluations per class. An example of such search over parameters of Linear SVM, Kernel SVM and decision trees is given below. from skopt import BayesSearchCV from skopt.space import Real, Categorical, Integer from sklearn.svm import SVC, LinearSVC from sklearn.tree import DecisionTreeClassifier from sklearn.pipeline import Pipeline from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75, random_state=0) # used to try different model classes pipe = Pipeline([ ('model', SVC()) ]) # single categorical value of 'model' parameter is used to set the model class lin_search = { 'model': Categorical([LinearSVC()]), 'model__C': Real(1e-6, 1e+6, prior='log-uniform'), } dtc_search = { 'model': Categorical([DecisionTreeClassifier()]), 'model__max_depth': Integer(1,32), 'model__min_samples_split': Real(1e-3, 1.0, prior='log-uniform'), } svc_search = { 'model': Categorical([SVC()]), 'model__C': Real(1e-6, 1e+6, prior='log-uniform'), 'model__gamma': Real(1e-6, 1e+1, prior='log-uniform'), 'model__degree': Integer(1,8), 'model__kernel': Categorical(['linear', 'poly', 'rbf']), } opt = BayesSearchCV( pipe, [(lin_search, 16), (dtc_search, 24), (svc_search, 32)], # (parameter space, # of evaluations) ) opt.fit(X_train, y_train) print("val. score: %s" % opt.best_score_) print("test score: %s" % opt.score(X_test, y_test)) /home/ubuntu/miniconda3/envs/testenv/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2010: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified. FutureWarning) /home/ubuntu/scikit-optimize/skopt/optimizer/optimizer.py:366: UserWarning: The objective has been evaluated at this point before. warnings.warn("The objective has been evaluated " val. score: 0.985152190052 test score: 0.982222222222 ## Iterative search utilizing step function A single call to step function of the BayesSearchCV instance allows to perform partial search for at most n_jobs points in parallel. This allows to use custom stopping criterions and to pickle a parameter search class instance to the file for recovery in case of failures of any sort or in case computations need to be transported to a different machine. An example usage is shown below. from skopt.space import Real, Categorical, Integer from skopt import BayesSearchCV from sklearn.svm import SVC from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75, random_state=0) opt = BayesSearchCV(SVC()) # add instance of a search space 'C': Real(1e-6, 1e+6, prior='log-uniform'), 'gamma': Real(1e-6, 1e+1, prior='log-uniform'), }) for i in range(16): opt.step(X_train, y_train, 'space_1') # save the model or use custom stopping criterion here # model is updated after every step # ... score = opt.score(X_test, y_test) print(i, score) /home/ubuntu/miniconda3/envs/testenv/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2010: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified. 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http://www.tkiee.org/kiee/XmlViewer/f412563	Mobile QR Code #### The Transactions of the Korean Institute of Electrical Engineers ##### ISO Journal TitleTrans. Korean. Inst. Elect. Eng. 1. (Dept. of Energy Policy and Engineering, KEPCO international nuclear graduate school, Korea.) Co-firing, Biomass, Risk Assessment, Risk Metrics, Fluidized Bed Combustion, Pulverized Fuel Combustion ## 1. Introduction Most of the generating capacity in Indonesia is based on fossil fuel technology, in which coal power plants still comprised 67% of the energy mix in 2020. However, as the world's focus on sustainability increases, it becomes increasingly difficult to obtain financing for technologies that are based on the use of fossil fuel. Therefore, a green transformation strategy was developed to increase generating capacity with a focus on renewable energy to support the achievement of a more environmentally friendly supply of electricity. The addition of renewable energy generating capacity can be achieved by adding new renewable energy generating capacity, by replacing non-renewable energy generators with renewable energy plants, or by replacing fossil fuels with renewable energy fuels (1). This research provides the empirical result in the renewable energy mix achieved through co-firing at existing coal power plants in Indonesia. Co-firing is considered as one of the Indonesian breakthrough programs because it can be implemented without significant investment cost and can provide a solution that allows the management of waste and the reduction of the emissions of greenhouse gases. Low-ratio co-firing is a technology that undergoing development for a long while, but its global application remains very slight compared to other technology options. The commercial implementation of co-firing in coal power plants is based on co-firing trials that show technically feasible results and do not interfere with the reliability of the operation of the plants; however, continuous risk analysis and mitigation are required to maintain the optimum operation of this co-firing program. The coal-fired power plants that have the potential for co-firing have a total capacity of up to 18,895 MW. If all of the units in all of the coal power plants operated by co-firing commercially with a percentage of biomass PC (Pulverized Coal) Boilers, 6% Circulating Fluidized Beds (CFBs), and 70% Stocker Boilers, 2.7 GW of renewable energy production capacity can be obtained from co-firing, which would require up to 14 million tons of biomass per year (assuming a Capacity Factor of 70%). This is supported by the combination of integrated policy, establishment of a sustainable biomass supply, business schemes, and well designed biomass supply chain (2). Fig. 1 Energy Mix Projection in Indonesia (1) Determining co-firing coal power plants must consider the range of biomass available near the coal power plants from energy plantation forest areas, oil palm plantations, and the potential of recovered Solid Fuel Waste (SRF) and Refuse Derived Fuel (RDF) so that the distance from the feedstock to the generator is not too long and a reasonable price can be maintained. It will ensure the continuous supply of raw materials that are required for continuous operation of the generator. In addition to mapping the potential sources of biomass, an information system related to the type of boiler is an important factor to ensure the continuity of the operation of the co-firing coal power plants. The different types of boilers that are used in co-firing power plants will determine the types of the raw materials to be used and their characteristics (1). The goal of this research is to identify the potential risks that may hinder the co-firing of biomass in coal-fired power plants and their appropriate management plans. The co-firing technology is expected to help achieving Indonesia's target of replacing 10% of the coal with biomass, both from energy generation and waste by 2025. This target also includes maintaining the continuity of service to stakeholders and providing energy services efficiently so that it can become the basis for formulating strategic plans and avoiding waste. From the research results and experience of using biomass with various coal specifications at several power plants in Indonesia, an optimal risk analysis with mitigation strategies could be carried out. The degree of achievement in co-firing plan is currently evaluated at 67% (1). According to the results of the project feasibility studies (including technical, financial, and environmental feasibilities), we will conduct a risk assessment, beginning with determining the activity goal to be achieved and then identifying and describing what risks may occur, as well as their occurrence and causes, key risk indicators, and their effect on the ability to achieve the predetermined goals. Next, we will identify the cause of the risk to show the factors that lead to the risk. Then, we will measure the potential risk level and the scale of the effects of the risk and determine the existing control measures and their effectiveness. ## 2. Literature review Several literature references have described the technology, benefits, policies, and effects of co-firing biomass on coal-fired power plants. Hughes (3) maintained that blending biomass and coal as a co-firing fuel is a low-cost option for renewable energy only if policy considerations and incentives permit co-firing to be used as a renewable resource, even if the electricity is provided by an existing power plant that is still operating largely as a coal-fired power plant. Opportunities can be obtained if implemented policies support the co-firing activities. Co-burning biomass with coal can be accomplished with very little capital investment. As long as the biomass material used as the co-fired fuel is produced renewably, the co-firing directly offsets the greenhouse gas emissions from unburned coal. Several local and regional environmental benefits can be achieved from co-burning biomass. While these global and local environmental benefits can be achieved at relatively low costs, neither government regulation nor market forces have led to the adoption of the significant co-burning of biomass. Richard et al. (4) demonstrated that wood biomass can be mixed with coal in the range of 5 to 8% for low co-combustion rates before crushing. The preparation of the wood and separate delivery systems should be supplemented by operating the boiler based on the characteristics of coal used at moderate levels, e.g., 10 ~ 15% biomass. A multi-fuel system, such as a fluidized bed, should be used at a suitably high rate, i.e., 25~50%. Further, boilers intended specifically for the combustion of biomass should be used at levels above 50%. Sami et al. (5) emphasized that co-firing residual biomass, rather than crops grown for energy, leads to additional greenhouse gas mitigation by preventing the release of CH4 from the stockpiled biomass. The compositions of coal and biomass fuels differ greatly, and combustion of the combination of biomass fuel and coal can reduce the emissions of NOx and SOx from existing power plants that use pulverized coal. In addition, because biomass is a carbon dioxide neutral fuel, it can reduce carbon dioxide emissions overall. Depending upon the chemical composition of the biomass, co-firing also can reduce the cost of fuel, waste, and the pollution of the soil and water. The following literature explanation technology in coal-fired power plants. These references are helpful in developing biomass co-firing plants. Tillman (6) explained three general techniques that comprise the co-firing technology family, i.e., blending the biomass and coal in the fuel handling system and feeding that blend into the boiler; preparing the biomass fuel separately from the coal and injecting it into the boiler without affecting the conventional coal delivery system; and gasifying the biomass with subsequent combustion of the producer gas in either a boiler or a combined cycle combustion turbine generating plant. Dornburg et al. (7) stated that biomass can become more expensive than the coal if it must be transported long distances. Thus, co-firing at some electric facilities is not feasible. Comparing the cost of the fuel and the quantities of biomass, another major market can be identified, i.e., the market that has smaller scale boilers that pay more for their fuel than a large scale facility. Some unit may fit for using biomass because of their location within a reasonable transportation distance and the high cost of the current fuel, thereby allowing more to be spent to obtain and transport the biomass. A wide variety of biomass conversion options exist that have different performance characteristics. Also, the economic and energetic performance depends on many variables, such as the costs of logistics, scaling effects, and the degree of heat used, etc. Therefore, an analysis of the system is needed to identify its optimal operating characteristics. Hughes (3) reported that co-firing biomass with coal can help reduce the total emissions per unit of energy produced compared to the case coal is used alone. Co-burning biomass with coal has the ability to reduce NOx and SOx emissions from existing power plants that burn pulverized coal. Also, depending on the chemical composition of the biomass, co-burning can reduce the costs of the fuel, minimize waste, and reduce the pollution of the soil and water. Ayhan (8) explained that direct combustion, gasification, and pyrolysis are the technologies for the primary conversion of biomass for the production of electricity. Direct combustion is the process of oxidizing biomass with excess air to produce hot flue gases, which then are used to generate steam in the boiler heat exchange sections. The author indicated that a number of areas require further research and that the technology or computational tools must be developed. Pulverized coal-fired equipment, cyclones, and fluidized beds were found to meet these requirements. The cleaned gasification product gases are delivered directly to a boiler or the combustion section of an industrial or aero-derivative turbine to generate electricity. In indirect gasification cycles, the energy for high temperature steam gasification of the organic fraction of biomass to vapors and gases is provided by an external heat source rather than oxygen. A group of studies have been conducted on risk assessment, risk matrix, and mitigation that may be applied to co-firing technique. Giannakis et al. (9) indicated that risk management is a structured process to manage the risks that occur in achieving certain objectives in the form of a systematic and continuous process. The intention of this process is to identify and measure the level of the risks and determine the best course of action to reduce the likelihood that these risks will occur, minimize their effect, or reduce both, as well as other actions to ensure/create confidence that the desired goals will be achieved. Markowski et al. (10) emphasized that a risk matrix is a tool that describes and ranks process hazards found during one or more comprehensive evaluations (e.g., process hazard analysis, audits, or the investigation of incidents). The risk matrix is a valuable tool for assessing semi-quantitative risk assessment and selecting risk control measures. Huihui et al. (11) stated that managing risks and reducing losses are accomplished by using a set of procedures that include risk identification, estimation, assessment, and transfer in which risk assessment is a key component of the overall risk management framework. In fact, risk is an essential component of all risk management processes because they are methods to categorize and rank risks based upon their relative importance. When identifying risks, the first step is to refer to a predetermined target/context. Then, based on the best information available and considering the results of the context identification, this activity is conducted using various techniques/methodologies, such as brainstorming, interviews, and the analysis of historical data, missing events, observations, surveys, audit results, risk taxonomy, and benchmarking (12). ## 3. Co-firing ### 3.1 Why co-firing? In the electric utility industry, co-firing is often regarded as the most cost-effective method of using biomass. Co-firing was introduced initially as a utility vehicle to support economic development between wood producers and agricultural industries in certain service areas to reduce fossil carbon dioxide (CO2) emissions as part of a voluntary global climate challenge program and to reduce other air emissions, such as nitrogen oxides (NOx) and metals, by creating infrastructural support for fuel supply, transport, and tracking, and provide a way to shift to a greater bio-fuel supply source (6). Co-firing is considered as one of Indonesia's breakthrough programs to increase the renewable energy mix that can be achieved without requiring significant investment costs and also can be a waste management solution. The co-firing program is one of the strategy to accelerate the renewable energy mix to achieve the 23% of renewable energy mix target by 2025. Different from the photovoltaic or wind sources, co-firing can make use of the existing coal-powered plants as well as the grid. Commercial co-firing power plants show technically feasible results and do not interfere with the plant's operational reliability. In addition, the COVID-19 pandemic had a major effect on Indonesia's electricity supply plan, which includes the fields of generation, transmission, distribution, and sales of electric power to Indonesian consumers. The pandemic has made the electricity load lower than normal. Based on the realization of Indonesia's electricity sales in 2020, it is estimated that it will decrease by 0.79% compared to the previous year. As an illustration, electricity sale was 243.06 TWh in 2019, and it increased by 4.57% annually. However, it was still below the electricity sales target at that time, i.e., 248.8 TWh with an annual increase of 7.06% (1). ### 3.2 Co-firing technology Biomass is an attractive renewable fuel to supplement the combustion of coal in utility boilers because when a biofuel replaces a fossil fuel, there is a net reduction in CO2 emissions. Coal co-firing has been shown to be successful with up to 20% biomass mix. The results of extensive applications have shown that co-firing biomass with coal accomplishes the following: (1) increases the efficiency of the boiler; (2) reduces the costs of fuels, and (3) reduces the emissions of NOx and CO2. Every ton of co-fired biomass directly reduces CO2 emissions by more than a ton. Woody biomass contains virtually no sulfur, so SO2 emissions are reduced in direct proportion to the amount of coal that is replaced. However, biomass can contain considerable alkali and alkaline earth elements and chlorine, and when these components are mixed with other components in the gas derived from coal, such as sulfur compounds, a different array of vapor and fine particulate deposition occurs in coal-fired boilers (8). The proportion of coal substituted with biomass must be carried out in stages with a mixture of waste and wood forest waste/products by 1% to 5% of the total coal demand depending on the type of coal power plant system that is being used. There are three types of coal power plant systems, i.e., the Pulverized Coal (PC) type, the Circulating Fluidized Bed (CFB) type, and the Stoker type. The former two types require 1% to 5% biomass, while the latter one uses 100% biomass. There are 52 coal-fired power plants that will be used to implement the co-firing program of Indonesia, assuming a co-firing energy mix of 10%, CF = 70%, and HTE calorific value = 4,200 kCal/kg, waste = 3,200 kCal/kg) (1). Fig. 2 Co-Firing Technology (13,14,30) The co-firing methods that are used to burn a mixture of biomass and coal include direct, indirect, and parallel co-firing (14,15). The direct co-firing method is the simplest, cheapest, and the most commonly used. The biomass is mixed with coal and processed through the same or separate milling equipment and feeders and then mixed with coal into the same boiler for combustion. Generally, there is no investment in the cost of specialized equipment with this method because it uses already available equipment. Because the mixture of biomass and coal is burned together in the boiler, the existing boiler monitoring parameters must be considered because of the difference in the fuel that enters the boiler. Biomass is a renewable fuel that is derived largely from living things in which energy is stored. Generally, biomass has a relatively high volatile content, approximately 60% - 80%, with a low fixed carbon content and lower ash content than coal, so that more reactive than coal (14). The use of biomass also is adjusted based on its availability near the power plant to save the accommodation costs and to maintain an available supply of fuel. The following are illustrated types of biomass that have been used to test co-firing in Indonesia, i.e., Sawdust (SD); Refuse Derived Fuel (RDF); Recovered Solid Fuel (SRF); Rice Husk; Wood Pallets and Chips; and Palm K Shell (16,17,18). Fig. 3 Types of biomass The results of the evaluation of co-firing tests on several coal power plants are summarized in Table 1. Table 1 Typical Characteristics of Biomass Feedstock Compared to Coal (19) Feed stock Moisture content (%) Bulk density (kg/m3) Low heating value (GJNCV/tone) Energy density (GJNCV/m3) Fresh wood 35-58 200 -250 9-12 2-3 Baled straw 15 (air-dried) 140 15 2 Wood chips 20 to 25 (air-dried) 200 15 3 Sawdust 20 to 25 (air-dried) 160 15 2.4 Solid wood 20 (air-dried) 550 15 8 Briquettes 8 650 16 10 Charcoal 2-3 300 27 10 Wood pellets 8 650 17 11 Torrefied wood pellets 2 700 20-21 15 Coal 12 825 20-30 21 The Table 1 shows the types of biomass, from fresh wood to coal, that have different characteristics in water content, specific gravity, calorific value, and energy density, respectively, among which the characteristic closest to coal is Torrefied wood pellets. It can be used as a compact, black solid biofuel for substances such as coal with the same energy content, grindability, and moisture content. It is produced through the carbonization (or slow pyrolysis) of biomass, in which water and volatile organic components evaporate, leaving most of the black carbon behind. Table 2 Fuel Specification Analysis (17) Analysis Parameter Coal (100C) Wood Pellets (100WP) Fuel Mix (5WP95C) Proximate Analysis (% wt) Moisture 16.68 8.96 15.02 Volatile Matter 39.68 72.68 41.06 Fixed Carbon 38.7 15.94 38.62 Ash 4.94 2.42 5.3 Ultimate Analysis (% wt) Carbon 56.6 46.78 56.92 Hydrogen 4.08 5.28 4.16 Oxygen 27.2 36.54 26.81 Sulfur 0.32 0.02 0.27 Hardgrove Grindability Index Ash fusibility temperature - 41 17 45 Deformation temperature (℃) Reducing 1,090 1,150 1,090 Oxidizing 1,150 1,170 1,150 Spherical temperature (℃) Reducing 1,120 1,170 1,120 Oxidizing 1,170 1,200 1,180 Higher heating value (kcal/kg) - 4,536 4,223 4,361 Table 2 shows the results of the analysis of the fuel during the co-firing test. Two different fuels were used during the test, i.e., coal fuel (100C) was used in the first test, while a fuel mixture with a composition of 5% wood pellets and 95% coal (5WP95C) was used in the co-combustion test (17). ### 3.3 Effect of co-firing Most of the technical challenges in co-firing biomass and coal are associated with the quality of the fuels. Biomass differs from coal in a variety of aspects, including its physical qualities and its organic, inorganic, and energy composition. Biomass has less carbon, more oxygen, more silica and potassium, less aluminum and iron, a lower heating value, a higher moisture content, and poorer density and friability compared to coal (8). It also has a higher aspect ratio than coal and is substantially less dense. Also, it is more difficult to shrink it to small sizes. Co-fired biomass can be as large as 1/4 inch in diameter or even larger in some cases. These physical characteristics result in several intriguing combustion difficulties (8). The heating value of biomass is far lower than that of most coals. This is attributable in part to increased moisture level and in part to higher oxygen content. Lower heating values may lead lower flame temperatures, and this is true when the high moisture content causes low heating values. However, the low heating values that are attributable to high concentrations of oxygen are not linked to the low flame temperatures. Despite the fact that the burned heating values of dry biomass and dry coal differ by more than 33%, they have identical adiabatic flame temperatures (8). Fig. 4 Technical Effect of Co-firing on PLTU CFB Fig. 5 Technical Effect of Co-firing on PLTU PC Co-firing technology has several technological problems. First, some attention must be directed to the problem that the alkaline nature of the biomass can cause the combustion chamber to become fouled and corroded. Deposits of ash reduce the heat transfer and also can cause severe corrosion at the high temperatures. Compared to the deposits produced during the combustion of coal, deposits from the combustion of biomass material are denser and more difficult to remove. Second, the maximum particle size of a given biomass that can be fed into and burned in a particular PC boiler via a specific feeding mechanism constitutes a combination of economy and combustion characteristics and requires additional study. Third, the practical performance of the pulverizer should be assessed. Biomass fuels may require a separate pulverizer to achieve high mix ratios and good combustion performance. Because biomass fuel has a lower calorific value than coal, the flow rate of the mixture must be increased to achieve the same heat output as using only coal. This increased fuel flow rate can cause the flame to move away from the mouth of the burner and create flame stability problems. Enlarged fires also are known to cause higher NOx levels (4). When coal is used as fuel in the co-firing test, the temperature of the gas from the furnace is lower than the existing conditions. The rate of the reduction of the temperature of the gas exiting from the furnace depends on the calorific value of the biomass fuel, the fuel's content of volatiles and ash, and the low calorific value of the wood pellets. The volatile content of the wood pellets is higher than that of coal, so the wood pellets burn faster in the furnace, and the high ash content produces more reasonable heat and causes the solid waste to leave the furnace (17). Compared with the existing conditions, the SO2 content in the exhaust gas increased during the co-firing test. Additional research is needed to determine the cause of these conditions and to determine whether the combustion characteristics in the furnace have changed. Generally, because most biomass fuels have low concentrations of sulfur, a reduction in SO2 emissions has been observed in many co-firing applications (20). The co-firing test has no significant effect on the NOx quantity of the exhaust gas. These results indicate that the co-firing test using 5% wood pellets resulted in a 4.40% increase in the specific fuel consumption. To maintain the same energy output, it is necessary to increase the volume of the fuel due to the lower calorific value, such as wood pellets. For example, PLTU can increase volume by average of 30% to generate the same amount of energy (21). From the results of the 5% biomass co-firing tests at several coal-fired power plants, the power plants had reductions in SO2, NOx, and other co-firing particles. However, there are conditions that actually increase these because the sulfur content in coal affects SO2 emissions significantly. The co-firing process can reduce SO2 emissions only by an insignificant amount because the mixing ratio is still small, the coal calorific specification at the location is low, and the biomass supply condition may be contaminated with outside particles. Table 3 Emission Quality Standards for Fossil Fuel (25) Parameters Maximum Rate Coal High Speed Diesel (HSD) Gas (mg/Nm3) (mg/Nm3) (mg/Nm3) Sulfur Dioxide (SO2) 550 650 50 Nitrogen Dioxide (NO2) 550 450 320 Particulate Matter (PM) 100 75 30 Mercury (Hg) 0.03 0 0 According to the standards of emission quality for fossil fuel from the Ministry of Environment and Forestry above, co-firing 5% biomass in coal power plants tends to reduce SO2, NOx, and particulate emissions (25). Fig. 6 Comparison of Emission Products in Coal Power Many factors affect the application of biomass co-firing, including the availability of the fuel, the quality of fuel, whether the fuel complies with the specifications of the existing coal-fired power plant, and purchase price (since the price of raw materials must be lower than the price of the existing fuel). ## 4. Risk Assessment The co-firing biomass business risk analysis is divided into 3 stages, i.e., risk identification, mitigation, and measurement plans. Risk identification is divided into several risk aspects, including business/commercial, operational, social, environmental, and legal risks. Each risk has written sources of the risk and the effects of these sources. The target of the project is to ensure that the implementation of the Co-Firing Coal Power Plant with Biomass program as one of the green booster programs will achieve the green objective strategy's target, which is to generate approximately 1 GW from coal power plants with co-firing capacity by 2025. Project activities are classified according to the taxonomy of risk (risk breakdown structure) and project risk that arises from the development of the company's assets, procurement, and other project activities. ### 4.1 Risk Analysis and Mitigation Risk analysis and mitigation is a structured process for managing the risks to achieve the program's objectives. The process is a systematic and continuous process that is used to identify and measure the level of risk, as well as determine the best course of action to reduce the possibility that a risk will occur as well as minimizing its effect if it does (or both) (12). Risk analysis is a stage in risk management that is designed to identify existing risks and controls and to analyze and evaluate the risks, i.e., measure the level of risk. Then, the best action to be taken is identified and implemented to minimize the occurrence of these risks (22). The identification of risks is a process of identifying/ recognizing and describing the risks that can occur as well as their causes and effects on the ability to achieve the pre-set targets (12,22). The activity stages are divided into three steps: Initiation, Pre-Implementation, and Implementation. Table 4 Risk Analysis for Co-firing PROCESS FLOW RISK IDENTIFICATION RISK LEVEL Initiation Coal power plants that are planned to implement co-firing are not ready yet Moderate Initiation Discontinuous volume of biomass supply Extreme Initiation The quality of the biomass supplied does not meet the specifications Extreme Pre-Implementation The efficiency of co-firing power plants decreases High Pre-Implementation Reliability of co-firing power plants that implement co-firing decreases High Implementation Increase in cost of coal power plants that implement co-firing High Implementation The implementation of co-firing in coal power plants violates the provisions of environmental regulations High Implementation Coal power plants that implement co-firing have difficulty managing Fly Ash Bottom Ash (FABA) High Implementation Decreasing Biomass Quality High ### 4.2 Risk Matrix A risk matrix is useful in determining the level of risk against risk likelihood (determine an acceptable level of risk) and to assess/determine whether a risk requires further handling (mitigation) and its priorities (23). The risk assessment matrix table is used to describe the level of controlled risk after the probability of the occurrence of risk and its potential effect are assessed (24). The risk assessment matrix is a well-known method of conducting semi-quantitative risk analysis. The original risk matrix (ORM) and its variants are used extensively in a variety of contexts. The risk matrix approach is introduced briefly in this section (11). Fig. 7 Risk Matrix for Co-firing There are 9 risks that have been identified based upon the results of risk analysis and their handling related to co-firing activities; two extreme risks, six high risks, and one moderate risk. We select the extreme and high risks for further analysis. #### 4.2.1 Discontinuous volume of biomass supply (Extreme Risk) The causes of this risk, both controlled and uncontrolled, are 1) that the identification data are not sufficiently accurate to describe the existing biomass potential (16,17), 2) unavailability of potential biomass near the coal power plant where the co-firing program is planned to be conducted, 3) limited production volume from biomass producers, 4) few biomass sources or biomass producers near the plant, 5) limited biomass with the quality that meets machine specifications (17), 6) biomass suppliers are still on a small scale/home industry, and 7) the influence of climate change. Risk mitigation measures, both from prevention and recovery, may be used to reduce the risk level as follows. 1) map the potential to maintain a secure supply of the biomass by providing accurate biomass feedstock, in which there are three types of biomass potential, i.e., the potential of energy plantations (HTE), oil palm plantations (PKS), and waste (SRF or RDF) (25); 2) conduct user trials of several alternative types of biomass (e.g., Wood Chips, Palm Kernel Shell, Wood Pellets, Palm Oil, Garbage); 3) assess the potential distribution and transportation of biomass in Central Java, Indonesia, in which this type of production forest has a potential of 370,129 Ha; 4) the potential for the pellet industry with a capacity of 98,555 tons/year, production of 29,503 tons/year, and potential waste of 782 tons/day using data from Final Disposal Sites found in Central Java Province, i.e., based on the data on the average total biomass potential (AVB); 5) the average number of production forests' potential, PKS potential, and waste potential of 9,224,529.87 tons/day (25), and 6) prioritizing co-firing coal power plants in accordance with the clustering of the potential availability of biomass raw materials near existing coal power plants (7). There are several approaches that can be used to estimate the biomass requirements, each of which has advantages and disadvantages. However, it should be noted that the indirect approach is based upon factors developed at the stand level of a forest with a closed canopy, and it cannot be used to make estimates of trees in general. One method that can be used to determine the supply of biomass raw materials is to use a sustainable cycle by calculating the annual need for biomass material and then obtaining the desired number of trees (26,27,28). ##### (1) ${for}est =\dfrac{Cyc\le\times Energy per hectare}{CF\times 8760 hours}\times G en C ap$ Cycle: length of time required to harvest the species of trees used in the forest (years) Energy per hectare: total electrical energy from tree species used for every 1-hectare plant planting (kWh/ha) CF: Generating capacity factor (%) Gen Cap: Generating capacity Table 5 Forest Land Area Requirements to Provide Power Generation (33) Type of Tree Crop Cycle Total Energy 1 MW /year Equivalent MWh Field years kWh /hectare CF=75% (MWh) hectare E. Pelita 5 62,790 6,570.0 523.2 Kaliandra 3 36,104 6,570.0 545.9 Acacia Auri 5 58,604 6,570.0 560.5 Gamal 4 45,209 6,570.0 581.3 Mangium 5 48,837 6,570.0 672.6 A community electricity business scheme should be developed to ensure the supply of biomass by involving the community in feed stock management based upon self-reliance and mutual cooperation, i.e., production forest feed stock, palm kernel shell feed stock, and waste pellet feed stock. A business ecosystem for the management of the biomass supply chain should be developed, long-term biomass sales and purchase agreements should be made to ensure the availability of supply volume, target biomass use adjusted to supply availability, and coal reused to maintain system reliability. #### 4.2.2 The quality of the biomass supplied does not meet the specifications (Extreme Risk) The causes of the above risk, both controlled and uncontrolled, are as follows: The calorific value of the biomass supplied is lower than the calorific value specified; officially, to date there are no mechanisms to test the quality of biomass or to determine whether the properties of the biomass meet specifications (27,28). In addition, biomass suppliers are mixing materials that are outside the specifications and that are not detected by sampling, and the biomass supplied has been mixed with B3 waste. Certain mitigation measures that can be used to reduce the risk level in both prevention and recovery are related to the fact that each type of plant has a different energy value. When choosing species, as well as considering technical matters in the field, one of the considerations is the wood's potential calorific value. In the conversion calculation below, there are several basic variables that must be met, the wood's specific gravity, calorific value, and volume, and the specifications for the generator's heat rate (27,28). ##### (2) $E_{e\le ctric}=\dfrac{V_{wood}\times\rho_{wood}\times wood ca\lor ies\times n_{plants}}{G ene rator heat rate}$ Eelectric: The amount of electrical energy generated as a result of planting a forest area of 1 hectare (kWh/ha) Vwood: Timber harvest volume in cubic meters by planting 1 hectare of trees (m3/ha) ρwood: Density of wood (kg/m3) Wood calories: Calorific value of wood per kilogram (kcal/kg) Generator heat rate : The value of the heat rate of the generator used (kcal/kWh) Table 6 Conversion of Wood Energy into Electrical Energy Per Hectare (33) Type of tree Wood Density Wood Calories Wood Volume Total Mass of Tree Total Energy Generator Heat Rate Total Energy of Electricity kg /m3 kcal /kg m3 /ha ton /ha Gcal /ha kcal /kWh kWh /ha E. Pelita 450 4,000 100 54 180 2,868 62,790 Acacia Auri 400 4,200 100 40 168 2,868 58,604 Mangium 350 4,000 100 35 140 2,868 48,837 Gamal 360 4,000 90 32.4 129 2,868 45,209 Kaliandra 450 4,600 50 22.5 103 2,868 36,104 During the co-firing test of 1,528.58 Tons of 5% sawdust, the average gross electrical energy (Gross) produced was 2,430,410 kWh. For comparison, when 2,420,293 kWh are produced by burning coal, the total fuel consumption is only 1,540.65 Tons of coal. By dividing the total fuel consumption by the total energy produced, the specific fuel consumption (SFC) for co-firing 5% sawdust is 0.629 kg/kWh, while it is 0.637 kg/kWh for 100% coal fuel (16). The results of the co-firing test using 5% wood pellets actually contributed to an increase of 4.40% in specific fuel consumption (SFC). However, to produce 1,189,800 kWh, the total specific fuel consumption (SFC) with 5% co-firing wood pellets is 0.580 kg/kWh compared to using 100% coal. The SFC produced is 0.556 kg/kWh, so when using lower heating value fuels, such as wood pellets, it is necessary to increase the volume of the fuel to maintain the desired energy output. This increase in SFC averages up to 30% in co-firing in coal-fired power plants to produce the same amount of energy (18). It is necessary to determine the quality standards for types of biomass for each type of coal power plant. This is because the different types of boilers in coal power plants influence the type and characteristics of the feedstock that can be used in the co-firing program. CFB and Stoker boilers can use feedstock with wood chips and Palm Shell types mixed with coal, but it is better to use wood pellets and Solid Recovered Fuel (SRF) feedstock for coal power plants with the PC type of boiler (16). For the PC and CFB types of boilers, the substitution of biomass for coal is 5% and for the Stoker type of boiler, the use of biomass is targeted to reach 30% based on the research results pertaining to co-firing coal power plants (16,17,18). Fig. 8 Comparison of Specific Fuel Consumption (SFC) in coal power plants Co-firing 5% biomass can decrease/increase Specific Fuel Consumption (SFC) and Net Plant Heat Rate (NPHR) depending upon the quality of the biomass. Based upon tests conducted by the PT PLN (Persero) Research and Development Center, the changes in SFC and NPHR values depend largely upon the calorific values of the coal and the biomass. The graph above indicates that the SFC value of the average power plant decreased; this value actually increased in only two plants. This is because the calorific value of the biomass is lower than that of coal alone, and, after mixing, the calorific value is lower than when only coal is used. Fig. 9 Comparison of Net Plants Heat Rate (NPHR) in Coal Power Plants If feedstock from an energy plantation forest is used, 8 million tons of biomass/year are required depends on the quality of the biomass supply for 52 co-fired coal power plants in the first stage. From solid waste fuel, 800 tons/year are required assuming that CF is 70%, that the calorific value of wood is 4200 kcal/kg, and that the calorific value of SRF is 3200 kcal/kg (1). Thus, a strict punishment clause must be included for biomass suppliers whose supply does not meet specifications, and a biomass quality testing laboratory must be set up as a transaction point (16,17). The government must issue a Business Permit for Use of Natural Forest Timber Forest Products and a Business Permit for Use of Industrial Forest Timber Products for co-firing and create sufficient biomass storage to maintain the availability of biomass for power generation (8). #### 4.2.3 The efficiency of co-firing power plants decreases (High Risk) The causes of this risk are the biomass's calorific value is lower than that of coal. Table 7 Typical Characteristics of Biomass Feed stock Compared to Coal (19) Plants Capa-city Co- Firing composition Type of Biomass Caloric Value (HHV-Ar Basis) Coal Biomass Fuel Mix MW % kCal /kg kCal /kg kCal /kg A 300 5 Sawdust (SD) 4,212 2,694 4,136 B 300 5 3,865 3,909 3,258 C 300 5 4,199 1,867 4,288 D 330 5 4,296 3,951 4,358 E 360 5 3,905 3,101 4,423 F 400 5 4,047 2,694 4,330 G 500 5 5,395 3,535 5,041 H 660 5 4,237 4,294 4,240 I 300 5 Wood Pellet 4,644 4,486 4,636 J 400 5 4,047 4,487 4,356 K 660 5 4,128 4,280 4,137 L 300 5 Solid Recovered Fuel 4,788 2,901 4,652 M 400 5 Rice Husk 4,459 3,241 4,213 Table 7 shows the results of the tests that the PT PLN (Persero) Research and Development Center conducted at 13 coal-fired power plants in Indonesia that use a fuel mixture of Sawdust (SD), Wood Pellet (WP), Solid Recovered Fuel (SRF), and Rice Husk with a generating capacities of 300 - 660 MW with various average calories of the fuel mix, some of which were lower and some of which were even higher than the calories associated with coal fuel. Of course, with the same type of boiler and nearly the same generating capacity, this result must be analyzed and evaluated to achieve a much higher calorific value after co-firing with biomass. Further, the biomass storage at the coal power plant site is not appropriate. There are non-combustible materials in the biomass that was supplied (8), and the biomass has a high content of alkali and chlorine, which causes the calorific value to decrease rapidly (6). The following mitigations, both prevention and recovery, can be used to reduce the risk level mentioned above: 1) develop a community electricity business scheme to ensure the supply of biomass by involving the community in feedstock management based on self-reliance and mutual cooperation, i.e., production forest feedstock, Palm Kernel Shell (PKS) feedstock, and Waste Pellet feedstock; 2) build a business ecosystem for biomass supply chain management, contract long-term biomass sales and purchase agreements to ensure the availability of the supply volume; 3) cooperate with biomass suppliers near the power plant to prepare adequate biomass storage facilities; 4) encourage the government to establish Indonesian national standards (SNI) for various types of biomass; 5) sort the biomass strictly to obtain the best quality that fits the plant's specifications; 6) measure power plant equipment affected by co-firing (tube boiler and others) before and after the trial period (17); 7) conduct tests to identify the most optimal proportion of biomass to use; 8) change the type of biomass that is used, reject and impose penalties on suppliers who do not conform to specifications, and 9) create sufficient biomass storage to maintain the availability of biomass for the generation of power. #### 4.2.4 Reliability of Co-Firing Power Plants that Implement Co-Firing Decreases (High Risk) Some of the causes of the risk above, both controlled and uncontrolled, include residue from burning biomass that damage generating equipment, changed operation patterns, biomass quality that does not meet the required specifications, and biomass suppliers who commit fraud. The following are mitigation measures, both prevention and recovery, that can reduce the risk level. First, strictly monitor the quality of the biomass. Second, adjust the Standard Operation Procedure to the co-firing operation pattern; direct combustion is the most mature technology in the process of converting biomass into electrical energy, and it is used nearly all over the world. Even so, it has two significant drawbacks, i.e., its high level of emissions and its low efficiency (29). Third, refuse and penalize suppliers for not complying with biomass supply specifications, and revert to using coal to maintain system reliability. Related with the second risk mitigation measure, the fuel feed of the co-firing coal power plant must be adjusted to the boiler specifications at the existing coal power plants. a. Fixed Bed Combustion Underfeed Stoker is a relatively inexpensive technology for small and medium-sized boilers up to 6 MW thermal, suitable for low ash biomass, such as woodchips, pellets, and sawdust, as well as small particles ( < 50 mm). It is simple to operate and control feeding because of the continuous supply into the furnace. Grate Furnaces suits for use with biomass with high water content, non-uniform size, and high ash composition. The homogeneous distribution of biomass in the furnace causes the primary air supply to be distributed evenly, which prevents slagging, greater fly ash production, and a greater need for excess oxygen for combustion that reduces the boiler's efficiency. Additional technology is needed to obtain good performance, particularly with respect to the proportion of NOx and emissions. b. Fluidized Bed Combustion This type of combustion has temperatures in the range of 700 - 1000oC, and the furnace can provide a more homogeneous temperature so that the combustion that occurs is more efficient. However, the specification for the size of the biomass particles is quite strict ( < 80 mm). c. Pulverized Fuel Combustion Biomass is injected pneumatically into the combustion chamber. This system requires fuel that has relatively constant quality. The maximum particle size should not exceed 20 mm, and the moisture content should not exceed 20% by mass. Fuel feeding must be regulated carefully because of the explosive combustion characteristics of the fine particles of fuel. Generally, a mixture of fuel and air is injected tangentially into the inlet to the furnace to form a rotational air flow (vortex flow). Combustion of biomass and coal occurs simultaneously because of their small particle sizes, so load control can be achieved efficiently and load changes can be completed quickly (30). #### 4.2.5 Increase in cost of coal power plants that implement co-firing (High Risk) Some of the causes of this risk, both controlled and uncontrolled, are 1) that the cost of transporting and treating biomass is too high (7); 2) maintenance costs have increased; 3) the unbalanced supply and demand of biomass (8), and 4) the price per calorie of biomass is higher than that of coal (28). Fig. 10 Comparison of the Cost of Production in coal power plants The use of biomass co-firing tends to reduce the cost of production in the range of 0.021 to 0.34 USD Cent/kWh, based upon the Regulation of the Board of Directors of PT PLN (Persero) 001.P/DIR/2020 dated March 5, 2020 in calculating the highest benchmark price of biomass for co-fired power plant co-firing. The highest benchmark price of biomass is one of the references used to determine the Owner Estimate Price in the biomass procurement process (32). Co-firing carried out at several coal-fired power plants using contracted coal and mixing 5% wood pellet biomass can reduce fuel costs if the biomass price is lower than the coal price. However, the price of biomass exceeds the purchase price of coal in some locations, so that the cost of production still exceeds the price of coal. Certain mitigations, both prevention and recovery, that can be performed to reduce the risk level above include 1) negotiating with biomass suppliers to lower the prices of biomass below the prices of coal; 2) limiting the price per calorie of biomass to a maximum of the same as the price per calorie of coal; 3) encouraging the government to issue policies and regulate biomass prices to offer suppliers and users fair economic value; 4) change the type of biomass used, and 5) revert to using coal to maintain the cost of the supply. #### 4.2.6 Implementing co-firing in coal power plants violates the provisions of environmental regulations (High Risk) Some of the causes of the risks discussed above, both controlled and uncontrolled, are that the combustion products do not meet Emission Quality Standards (25); the coal power plant's environmental impact analysis document currently does not accommodate the use of biomass; biomass storage causes environmental pollution (6), and co-firing biomass in a coal power plant is not yet legalized internally or externally (3,13). Some mitigations, both prevention and recovery, that can be used to reduce the risk level above are 1) coordinate with the Ministry of Environment and Forestry to confirm the existence of an environmental permit for co-firing at coal power plants (31); 2) encourage the government to stipulate SNI (Indonesian National Standard) for various types of biomass; 3) submit a revised environmental impact analysis to relevant parties; 4) create a Standard Operation Procedure for storing biomass at the location of the coal power plant; 5) perform exhaust gas treatment to meet Emission Quality Standards (25); 6) stop using biomass until the permit is issued (3); and 7) cooperate with the government to issue regulations immediately on the implementation of co-firing in Indonesia (1). #### 4.2.7 Coal power plants that implement co-firing have difficulty managing Fly Ash Bottom Ash (FABA) (High Risk) Some of the causes of the risk above, both controlled and uncontrolled, include the presence of a mixture of biomass in the coal material that affects the chemical composition and physical properties of the ash that is produced (5), such that FABA cannot be used (21). Certain mitigations, both prevention and recovery, that can be done to reduce the risk level above include 1) standardizing the amount/volume of mixed biomass for each type of coal power plant (volume, size, composition) (4) and 2) looking for other alternative uses that can accept the quality of co-firing ash (21). #### 4.2.8 Decreasing biomass quality (High Risk) Some of the causes of the risk above, both controlled and uncontrolled, are improper placement of biomass, not using the biomass according to the first-in-first-out method, and increased water content or moisture (16,18). Some mitigations, both prevention and recovery, that can be used to reduce the risk level above include 1) covering the biomass with a waterproof material; 2) drying the wood by increasing the temperature of the air, reducing the humidity of the air, and increasing the contact between the dried wood and dry air. Drying in the sun at a relatively low temperature (40 - 60 oC) also minimizes the emission of odorous volatile organic compounds from wood; 3) stirring regularly using a machine, stirrer vehicle, or wheel loader so that the quality of the biomass remains homogeneous, and 4) performing a visual inspection of the biomass, either after it has just arrived or before it is unloaded and used. Visual checks include checking for the possibility that it is mixed with dirt or other materials and treating biomass that may have decreased in quality. ## 5. Co-firing in other economies International experience has shown that co-firing is viable economically when state-funded programs are implemented. In addition to direct management and control, regulatory tools include 1) carbon taxes; 2) feed-in tariffs; 3) direct subsidies, and 4) renewable energy portfolio standards that require a minimum share of renewable energy in electricity generation [ 31]. The current carbon tax has not been enough to solve climate change, but the social value of carbon remains a valid theoretical indicator for measuring greenhouse gas emission reduction policies, plans, and programs. The level of support for co-firing in several European countries starts from 20 to 64 Euro/MWh through the Feed-in Tariff and Green Certificates schemes. An avoidable CO2 value of 30 Euro/t would make co-firing biomass in coal-fired power plants economically viable in Germany. Recently, when evaluating the prospect of co-firing in four European countries, it became apparent that it would be advantageous if a carbon price of 5 Euro/t would make co-firing with biomass prices lower than 2.3 Euro/GJ. A carbon price higher than 50 Euro/t would allow the use of pellets (34). A Renewable Obligation scheme is being used to support co-firing projects in the UK. Renewable Obligation for Electricity utilities in England, Wales, and Scotland began at 2% in 2002, and they had increased to 48.4% in 2019-2020 with certificate issued are tradeable for amount of electricity generated from renewable resources. Having introduced the Renewable Obligation, the share of co-firing in renewable energy generation in the UK has increased. By 2017, when the scheme closed for new capacity and was replaced by a contract-for-difference mechanism, all major coal-fired power plants in the UK were retrofitted to co-firing (35). Although the system was introduced in a technology-neutral way, this no longer has been the case after 2009. Since post-2012 systems discourage co-firing at low biomass proportions, coal-fired power plants have responded by switching to dedicated biomass units. After the UK, South Korea was the second largest market for industrial wood pellets in 2020 (36). Denmark and the Netherlands have taken a different approach. They directly subsidize co-incineration power generation. Since January 2009, Denmark has paid a subsidy of 2 Euro cents/kWh for dedicated and co-firing systems (37). The Netherlands imposes a feed-in tariff premium on the wholesale price of co-firing electricity based on the post-2013 sustainability criteria (38). In 2020, Denmark and the Netherlands were the third and fifth largest markets, respectively, for industrial wood pellets. In 2003, Japan first introduced a standard renewable energy scheme, but it was replaced by feed-in tariffs in 2012. In this program, electricity producers must use renewable energy to generate part of their electricity, and they receive a fixed term contract that specifies their purchase price for electricity. Feed-in tariffs for biomass power plants in Japan range from 13.65 to 33.6 yen/kW, depending upon the type of biomass used. The renewable energy standard helped increase the biomass generation capacity from 1.3 GW in 2004 to 2.3 GW in 2011, and within the framework of feed-in tariffs, biomass power generation reached 3.5 GW (123/166) in 2018 (39). Japan was the fourth largest market for industrial wood pellets in 2020. Strauss (36) pointed out that growth in demand in the next several years will exceed that of any other country. All of the cases mentioned above are in high-income countries. By 2020, few middle-income countries used co-firing. Nonetheless, there is technical potential to burn biomass with coal in their power plants, and this potential only increases co-firing's relative importance. Many rich countries are replacing old coal-fired power plants with plants that produce renewable energy. However, power plants in middle-income countries are younger and have lower budgets. Thus, the spread of biomass co-firing in ASEAN is still limited, although developed countries have validated the technological and economic feasibility of co-burning biomass in coal-fired power plants. Indonesia is a country with a fairly large source of biomass fuel, and it has the opportunity to implement biomass co-firing in a number of coal-fired power plants that have been built over the last 15 years. The urgent need to reduce the levels of greenhouse gas emissions in Indonesia has motivated research and testing of biomass co-firing as a practical technique in existing coal-fired power plants. To create and protect the implementation of co-firing activities in Indonesia, the country also must be equipped with risk analysis and mitigation to optimize opportunities and reduce potential state losses in achieving the renewable energy target of 23% by 2025. ## 5. Conclusion Based the risk analysis result, there are several mitigation activities that must be implemented to keep the implementation of the biomass co-firing program at coal-fired power plants in Indonesia running smoothly and in accordance with the expected targets. Normal or safe operating parameter limits for coal power plants that will carry out co-firing must be adjusted according to the design parameters/reports on the results of the performance of each coal power plant's system or equipment. Operators should refer to the manufacturer's design manual to determine the safe limits for the operation of the coal power plants' equipment when co-firing trials are performed. At each coal-fired power plant where the plan is to implement biomass co-firing, tests must be tested performed initially to ensure that the co-firing can be done safely and will not adversely affect the reliability of the generator. When co-firing is implemented, it is necessary to map the potential and adequacy of the availability of biomass, as well as the utilization of biomass sources that are located as close as possible to the power plant. The characteristics of biomass are different from coal, coal material tends to maintain its calorific value under certain weather conditions, while biomass cannot maintain its calorific value under certain weather conditions so it requires special handling. Obviously, the co-burning of biomass has many advantages. It creates large new domestic businesses, helps develop local economies, creates many jobs, and encourages the development of the forestry sector. The biomass co-firing business has a multiplier effect on local economic growth and environmental recovery, but only a small part of the community is aware of this business opportunity. Finally, government support is needed with respect to policies, knowledge, education, and assistance for the community concerning the need and availability of biomass as co-firing fuel for generators. We still have some limitations in this paper, i.e., we used data from Indonesian coal power cases to identify and assess risk factors. However, the data may not be applicable to a different environment or economic situation. Future research is expected to include a comparison-based study in co-firing to find the variations among different economies. ### Acknowledgements This work was supported by the 2021 Research Fund of the KEPCO International Nuclear Graduate School (KINGS), Republic of Korea. ### References 1 PT PLN (Persero), , Electricity Supply Business Plan, 2021-2030 2 PT PLN (Persero), , Statistic, 2020 3 E. Hughes, , Biomass cofiring: Economics, policy, and opportunities, Biomass and Bioenergy 2000, 19, pp. 457-465 4 L. B. Richard, R. P. Overend, K. R. Craig, , Biomass-fired power generation., Fuel Process Technology 1998; 54, pp. 1-16 5 M Sami, K Annamalai, M Wooldridge, , Co-firing of coal and biomass fuel blends., Prog Energy Combust Sci 2001; 27, pp. 171-214 6 D.A. Tillman, , Biomass cofiring: The technology, the experience, the combustion consequences. Pergamon, Biomass and Bioenergy 2000, 19, pp. 365-384 7 V. Dornburg, A.P.C. Faaij, , Efficiency and economy of wood-fired biomass energy systems in relation to scale regarding heat and power generation using combustion and gasification technologies., Biomass Bioenergy 2001; 21, pp. 91-108 8 Demirbas, , Sustainable cofiring of biomass with coal., Energy Conversion and Management 2003; 44, Vol. , No. , pp. 1465-1479 9 M. Giannakis, T. Papadopoulos, , Supply chain sustainability: A risk management approach., International Journal of Production Economics 2016; 171(Part 4), pp. 455-470 10 A.S. Markowski, M.S. 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Johnson, , Biomass co-firing technology with policies, challenges, and opportunities: A global review., Renew Sustain Energy Rev 2017; 78:1089-101. 36 W. Strauss, 2020, Global pellet markets outlook., Canadian Biomass Magazine 37 S. Knapp, A. G?ldemund, S. Weyand, L. Schebek, , Evaluation of co-firing as a cost effective short-term sustainable CO2 mitigation strategy in Germany., Energ Sustain Soc 2019; 9:32. 38 M. Banja, R. Sikkema, M. J´egard, V. Motola, J.F. Dallemand, , Biomass for energy in the EU - The support framework., Energy Pol 2019; 131:215-28., Vol. , No. , pp. - 39 A. Takanobu, , Sustainable biomass procurement for Japan's bioenergy sector., Renewable Energy Institute, Tokyo. 2018. https://www.ieabioenergy.com/wp-content/uploads/2018/09/4.4-Takanobu-Aikawa.pdf. ## 저자소개 ##### Prida Erni Kesuma She received B.S degree in electrical engineering from Sriwijaya University, Indonesia in 2004. Currently she works for PT PLN (Persero) since 2006. She is a master's degree student of Department of Energy Policy and Engineering, KEPCO International Nuclear Graduate School (KINGS). ##### 윤용범 (Yong-beum Yoon) Dr. Yong-beum Yoon received M.S and Ph.D degrees in Electrical Engineering from Seoul National University in 1896 and 1995. He worked for KEPCO Research Institute from 1986 to 2019. Currently he is a professor at KINGS and his research area include electric power planning and operation. ##### 박수진 (Soo-jin Park) Dr. Soo-jin Park is an associate professor of the Energy Policy and Engineering Department of KINGS. He earned PhD in Development Policy from the KDI School of Public Policy and Management, and master's degree in real estate finance from Cornell university. He also holds KICPA and CIA. His research interest includes economic feasibility assessment and project finance.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6069973111152649, "perplexity": 3954.921451270162}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662510097.3/warc/CC-MAIN-20220516073101-20220516103101-00411.warc.gz"}
http://www.physicsforums.com/printthread.php?t=286458	Physics Forums (http://www.physicsforums.com/index.php) - Astronomy & Astrophysics (http://www.physicsforums.com/forumdisplay.php?f=71) - - Magnetic Reconnection vs Double Layers (http://www.physicsforums.com/showthread.php?t=286458) Suede Jan21-09 03:01 PM Magnetic Reconnection vs Double Layers http://en.wikipedia.org/wiki/Magnetic_reconnection Magnetic reconnection is the process whereby magnetic field lines from different magnetic domains are spliced to one another, changing their patterns of connectivity with respect to the sources. It is a violation of an approximate conservation law in plasma physics, and can concentrate mechanical or magnetic energy in both space and time. Solar flares, the largest explosions in the solar system, may involve the reconnection of large systems of magnetic flux on the Sun, releasing, in minutes, energy that has been stored in the magnetic field over a period of hours to days. Magnetic reconnection in Earth's magnetosphere is one of the mechanisms responsible for the aurora, and it is important to the science of controlled nuclear fusion because it is one mechanism preventing magnetic confinement of the fusion fuel. Magnetic reconnection is something that has supposedly been "tested" and proven in the lab yet for some reason the lab results keep coming out "wrong." Currently when scientists create a "reconnection" event in the lab between two electrically charged plasma sheets the "reconnection" event takes place at twice the speed MHD theory predicts. So far no one has been able to rectify this problem, nor have they been able to produce a "reconnecting" magnetic field without first applying current to the plasma sheets they are observing. The reason being obvious of course, in order to create a magnetic field, one must first induce an electrical current. So far, this is the only known way of producing a magnetic field in a plasma that can be tested. As soon as the current shuts off, so too does the magnetic field. Magnetic reconnection is proposed to account for the sudden bursts of observed kinetic energies that power the aurora's substorms and light up the polar skies. It’s also proposed to account for about a billion other phenomena that I will not get into here. Focusing on the aurora, some very interesting facts come to light. THEMIS, Viking, FAST, UARS and several other satellites have confirmed the existence of parallel electric fields powering the auroras. Electric fields of course must complete a circuit in order to flow. Without charge deficiency in one area of space, there would be no current flow which is a product of charge equalization. Some papers on the findings of parallel electric field aligned currents, otherwise known as "Birkeland currents" after Kristian Birkeland, the man who postulated their existence back in 1901. http://www.iop.org/EJ/abstract/0741-3335/41/3A/004 Quasi-static, magnetic-field-aligned (parallel) potentials have been considered the primary source of charged particle acceleration in the aurora where precipitating electrons create a visible display. This finding has been controversial since, at one time, it was widely believed that parallel potentials could not be supported by a collisionless plasma. We present observations from the fast auroral snapshot (FAST) satellite which strongly support this acceleration mechanism and, moreover, show evidence of a second plasma regime region which supports quasi-static parallel potentials. http://www.agu.org/pubs/crossref/199...13p02329.shtml Electron distribution functions measured on the Dynamics Explorer 1 spacecraft are shown to have the characteristics expected in a region of parallel electric fields. http://www.agu.org/pubs/crossref/1998/97JA02587.shtml Using plasma wave data sampled by the Freja spacecraft from the topside ionosphere during auroral conditions, the possible existence of electric fields with an intense parallel component (a few tens of millivolts per meter) with respect to the Earth's magnetic field is discussed. http://www.agu.org/pubs/crossref/200...JA007540.shtml We present a survey of 64 direct observations of large-amplitude parallel electric fields E∥ in the upward current region of the southern auroral acceleration zone, obtained by the three-axis electric field experiment on Polar. http://www.agu.org/pubs/crossref/200...JA010545.shtml Satellite observations have established that parallel electric fields of both upward and downward current regions of the aurora are supported, at least in part, by strong double layers. http://www.agu.org/pubs/crossref/198...09p09777.shtml It is demonstrated that the simultaneous observations on Viking of upward field-aligned fluxes of energetic ions and electrons of energies in the same range may be due to acceleration in field-aligned electric fields, the ions in an upward directed parallel dc field and the electrons in a downward directed parallel field which is fluctuating but appears as quasi-static for the electrons as long as they are in the acceleration region. http://www.agu.org/pubs/crossref/1998/98JA01236.shtml Magnetic field and particle observations from the Upper Atmosphere Research Satellite particle environment monitor (UARS/PEM) are used to estimate field-aligned currents, electron precipitation energy flux, ionospheric conductivities, and Joule heating rates during the main phase of the November 4, 1993, geomagnetic storm. Given that we know field aligned electrical currents exist in the space plasma surrounding earth, some fundamental properties of conducting plasma can be employed to describe the events many astrophysicists currently ascribe to “magnetic reconnection.” So let’s look at some papers, the models, and how they are related to the observed phenomena. R. E. Ergun et al.: Double layers in the downward current region of the aurora Nonlinear Processes in Geophysics (2003) 10: 45–52 http://hal.archives-ouvertes.fr/docs...10-45-2003.pdf These results suggest that large double layers can account for the parallel electric field in the downward current region and that intense electrostatic turbulence rapidly stabilizes the accelerated electron distributions. These results also demonstrate that parallel electric fields are directly associated with the generation of large-amplitude electron phasespace holes and plasma waves…. We presented direct observations of the parallel electric field in the downward current region of the auroral zone. The observations are consistent with a strong double layer moving along B at the ion acoustic speed in the same direction of the accelerated electrons. The potential drop extends _10 _D along B. Intense electrostatic emissions are spatially separated from the structure on the high-potential side. Electron phase-space holes emerge from the wave turbulence associated with the double layer. The potential structure accelerates electrons to several times their initial thermal velocity which results in a factor of 10 gain from the initial thermal energy. Intense quasielectrostatic wave emissions and electron phase-space holes rapidly modify the accelerated electron distribution. Part of the electron distribution (stagnating electrons) is reflected back into the double layer through interaction with the intense wave turbulence. Thus, the intense wave turbulence may interact with the double layer through this stagnating electron population. Singh, N., and G. Khazanov (2003), Double layers in expanding plasmas and their relevance to the auroral plasma processes, J. Geophys. Res., 108(A4), 8007, doi:10.1029/2002JA009436. http://www.agu.org/pubs/crossref/200...JA009436.shtml When a dense plasma consisting of a cold and a sufficiently warm electron population expands, a rarefaction shock forms [ Bezzerides et al., 1978 ]. In the expansion of the polar wind in the magnetosphere, it has been previously shown that when a sufficiently warm electron population also exists, in addition to the usual cold ionospheric one, a discontinuity forms in the electrostatic potential distribution along the magnetic field lines [ Barakat and Schunk, 1984 ]. Despite the lack of spatial resolution and the assumption of quasi-neutrality in the polar wind models, such discontinuities have been called double layers (DLs). Recently similar discontinuities have been invoked to partly explain the auroral acceleration of electrons and ions in the upward current region [ Ergun et al., 2000 ]. By means of one-dimensional Vlasov simulations of expanding plasmas, for the first time we make here the connection between (1) the rarefaction shocks, (2) the discontinuities in the potential distributions, and (3) DLs. We show that when plasmas expand from opposite directions into a deep density cavity with a potential drop across it and when the plasma on the high-potential side contains hot and cold electron populations, the temporal evolution of the potential and the plasma distribution generates evolving multiple double layers with an extended density cavity between them. One of the DLs is the rarefaction-shock (RFS) and it forms by the reflections of the cold electrons coming from the high-potential side; it supports a part of the potential drop approximately determined by the hot electron temperature. The other DLs evolve from charge separations arising either from reflection of ions coming from the low-potential side or stemming from plasma instabilities; they support the rest of the potential drop. The instabilities forming these additional double layers involve electron-ion (e-i) Buneman or ion-ion (i-i) two-stream interactions. The electron-electron two-stream interactions on the high-potential side of the RFS generate electron-acoustic waves, which evolve into electron phase-space holes. The ion population originating from the low-potential side and trapped by the RFS is energized by the e-i and i-i instabilities and it eventually precipitates into the high-potential plasma along with an electron beam. Applications of these findings to the auroral plasma physics are discussed. Quoting dic.academic’s definition of a double layer Current carrying double layers may arise in plasmas carrying a current. Various instabilities can be responsible for the formation of these layers. One example is the Buneman instability which occurs when the streaming velocity of the electrons (basically the current density divided by the electron density) exceeds the electron thermal velocity of the plasma. Double layers (and other phase space structures) are often formed in the non-linear phase of the instability. One way of viewing the Buneman instability is to describe what happens when the current (in the form of a zero temperature electron beam) has to pass through a region of decreased ion density. In order to prevent charge from accumulating, the current in the system must be the same everywhere (in this 1D model). The electron density also has to be close to the ion density (quasineutrality), so there is also a dip in electron density. The electrons must therefore be accelerated into the density cavity, to maintain the same current density with a lower density of charge carriers. This implies that the density cavity is at a high electrical potential. As a consequence, the ions are accelerated out of the cavity, amplifying the density perturbation. Then there is the situation of a double-double layer, of which one side will most likely be convected away by the plasma, leaving a regular double layer. This is the process in which double layers are produced along planetary magnetic field lines in so-called Birkeland currents. Another known property of charged plasma that can explain the sudden and dramatic bursts of kinetic energy we see in the aurora substorms is something called an “exploding double layer.” Given that we have parallel currents and double layers in the surrounding regions of earths magnetosphere; a simple explanation arises for the sudden substorms: Stability: Double layers in laboratory plasmas may be stable or unstable depending on the parameter regime. [Torven, S. High-voltage double layers in a magnetised plasma column] " (1982) "Journal of Physics D: Applied Physics", Volume 15, Issue 10, pp. 1943-1949] Various types of instabilities may occur, often arising due to the formation of beams of ions and electrons. Unstable double layers are "noisy" in the sense that they produce oscillations across a wide frequency band. A lack of plasma stability may also lead to a dramatic change in configuration often referred to as an explosion (and hence "exploding double layer"). In one example, the region enclosed in the double layer rapidly expands and evolves. [B Song, N D Angelo and R L Merlino Stability of a spherical double layer produced through ionization] " (1992) Journal of "Physics D: Applied Physics", Volume 25, Issue 6, pp. 938-941] An explosion of this type was first discovered in mercury arc rectifiers used in high-power direct-current transmission lines, where the voltage drop across the device was seen to increase by several orders of magnitude. Double layers may also drift, usually in the direction of the emitted electron beam, and in this respect are natural analogues to the smooth--bore magnetron. [ Koenraad Mouthaan and Charles Süsskind, Statistical Theory of Electron Transport in the Smooth-Bore Magnetron] (1966) "Journal of Applied Physics" June 1966, Volume 37, Issue 7, pp. 2598-2606 ] ) (not to be confused with a unit of magnetic moment, the Bohr magneton, which is created by the "classical circular motion" of an electron around a proton). This idea was put forth by Hannes Alfven after the rectifier incident noted above. Double layers and circuits in astrophysics Alfven, Hannes IEEE Transactions on Plasma Science (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 779-793 Continuing on with “magnetic reconnection” as a theory, we find it violates known laws of physics. Fälthammar, does an excellent job describing the problems with “magnetic reconnection” theory as it pertains to real current carrying plasmas here: On the Concept of Moving Magnetic Field Lines Eos, Vol. 88, No. 15, 10 April 2007 Alfvén, who had introduced the concept, became a strong critic of ‘moving’ magnetic field lines [Alfvén, 1976], especially in his later years. He warned against use of the concepts of ‘frozen-in’ and ‘moving’ magnetic field lines for the reasons that are emphasized above. The basic reason for these difficulties with ‘moving’ magnetic field lines is, of course, that motion of magnetic field lines is inherently meaningless. The magnetic field B is a vector field defined as a function of space coordinates and time. At a fixed time, one may trace a field line from any given point in space. But that field line has no identity, and in a time-dependent magnetic field it cannot be identified with any field line at a different time, except by one convention or another. As we have seen, such conventions are fraught with pitfalls and should only be used with utmost care lest they lead to erroneous moving magnetic field lines are “unsafe at any speed.” As does Donald Scott: Real Properties of Electromagnetic Fields and Plasma in the Cosmos IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 35, NO. 4, AUGUST 2007 http://members.cox.net/dascott3/IEEE...tt-Aug2007.pdf Alfvén [1] was explicit in his condemnation of the reconnecting concept: “Of course there can be no magnetic merging energy transfer. The most important criticism of the merging mechanism is that by Heikkila [21], who, with increasing strength, has demonstrated that it is wrong. In spite of all this, we have witnessed, at the same time, an enormously voluminous formalism building up based on this obviously erroneous concept. Hannes Alfvén, a Nobel Laureate, being the founding father of MHD theory that magnetic reconnection is predicated on. This leaves us with two competing models to describe the function of the Aurora and other astrophysical plasmas, one being based on a theory that violates known laws of physics, the other being based on known properties of conducting plasmas. Nereid Jan22-09 09:53 AM Re: Magnetic Reconnection vs Double Layers Quote: Interesting post, Suede. I wonder ... to what extent is the disagreement merely one of appearance? I mean, plasmas behave the way they do (as we learn from experiment and observation), and theories are developed to account for the observed behaviours. It is possible, and to some extent even easy, to develop two theories that are equivalent ... in the sense that there is no experiment or observation which could distinguish between the two, even in principle. In this case, perhaps there are two different ways to look at the bulk properties and behaviours of plasmas that are indistinguishable in terms of any experiment or observation? If so, the choice of which one to use is a matter of practicality, convenience, history, or whatever ... but not of physics. After all, plasmas are composed of particles - charged and uncharged - and so the only 'true' description of their behaviour must be one built on QED, mustn't it? And any physics of plasmas which does not show, explicitly, how it is compatible with QED in the appropriate limit must necessarily be incomplete (at best), mustn't it? for a discussion of this kind of equivalence, in terms of 'expanding universe' vs 'shrinking universe', see here. Suede Jan22-09 01:30 PM Re: Magnetic Reconnection vs Double Layers Quote: Quote by Nereid (Post 2044929) Interesting post, Suede. I wonder ... to what extent is the disagreement merely one of appearance? I mean, plasmas behave the way they do (as we learn from experiment and observation), and theories are developed to account for the observed behaviours. It is possible, and to some extent even easy, to develop two theories that are equivalent ... in the sense that there is no experiment or observation which could distinguish between the two, even in principle. In this case, perhaps there are two different ways to look at the bulk properties and behaviours of plasmas that are indistinguishable in terms of any experiment or observation? If so, the choice of which one to use is a matter of practicality, convenience, history, or whatever ... but not of physics. After all, plasmas are composed of particles - charged and uncharged - and so the only 'true' description of their behaviour must be one built on QED, mustn't it? And any physics of plasmas which does not show, explicitly, how it is compatible with QED in the appropriate limit must necessarily be incomplete (at best), mustn't it? for a discussion of this kind of equivalence, in terms of 'expanding universe' vs 'shrinking universe', see here. my opinion: What I think will happen, is over time 'magnetic reconnection' will evolve from a theory that is incompatible with standard plasma physics to one that is compatible. What they call a "reconnection event" will replace "exploding double layer" but will mean the same thing as an exploding double layer. I don’t think classical plasma physics is too far removed from QED theory. Classical plasma physics starts at the level of the electron and works its way up to macro scale structures. So what you have is a direct unification between classical electrodynamics and the macro scale universe. QED, from what I understand of it, deals mostly in theory below the scale of the electron. If we have, starting at the level of the electron, a working model that can accurately depict and describe macro scale events based on electrical interactions, I think that would put us at a better standing than we are at now. tusenfem Jan23-09 01:01 PM Re: Magnetic Reconnection vs Double Layers It would be nice if you could show in detail that the regions in which reconnection happens can be correctly described by an "exploding double layer". At the moment the observations by e.g. Cluster are so good and in agreement with the theoretical description of reconnection, with the inward motion of "field lines" the energization of particles, the Hall current signature because of the decoupling of the ions from the field. I would look up the observations described by Sergeev et al (and refs therein). Also there is the interesting paper by Treumann et al. about the role of the Hall field. Although I did my PhD on double layers in astrophysics (mentioned in the Wiki page which is greatly rewritten by me with help from my predecessors, in its current and excellent form), I cannot see how a DL can make all the things that are observed near a reconnection region. But please show me with data and a model how it works. tusenfem Jan23-09 01:20 PM Re: Magnetic Reconnection vs Double Layers Quote: Quote by suede So far no one has been able to rectify this problem, nor have they been able to produce a "reconnecting" magnetic field without first applying current to the plasma sheets they are observing. The reason being obvious of course, in order to create a magnetic field, one must first induce an electrical current. Naturally there is a current in the system because reconnection happens in oppositely directed magnetic fields and through Maxwell's equations it is clear that these are two fields are separated by a current sheet, just like in nature in e.g. the Earth's magnetotail. Quote: Quote by suede THEMIS, Viking, FAST, UARS and several other satellites have confirmed the existence of parallel electric fields powering the auroras. Electric fields of course must complete a circuit in order to flow. Without charge deficiency in one area of space, there would be no current flow which is a product of charge equalization. Some papers on the findings of parallel electric field aligned currents, otherwise known as "Birkeland currents" after Kristian Birkeland, the man who postulated their existence back in 1901.… electric fields must complete a circuit to flow? I do hope this is a language problem, because electric fields don't flow. Field aligne electric fields and field aligned currents have absolutely nothing to do with reconnection, so you cannot use that to claim that reconnecting is correct or not. Take a look at my paper here where the motion of the magnetic field is the cause of currents flowing. Something (which you will see I leave to the reader to decide what, reconnection, current disruption,...) sets plasma flows in motion, which is pulled along with the magnetic field (in the tail the frozen in condition is very well satisfied, determined from measurements not assumptions) As there is a barrier this motion needs to be stopped and one of the main ways of stopping is cross tail currents, and these close as field aligned currents. Now these field aligned currents, when they go through a region of low density, they need to be accelerated to maintain the current, which is usually done by a double layer. But from your description above, it sounds like you have no idea what a DL is. And I am insulted! You forget my paper on solitary kinetic Alfvén waves which carry parallel electric field in the auroral zone, and there is the paper by Chust et al which shows strong parallel E-fields measured by Freja and shows that they are real and no artifact. However, all these double layers and parallel electric fields are mainly close to the Earth, most of them in the auroral zone, whereas reconnection happens rather far down the tail (20 Earth radii) or near the nose of the magnetosphere. Suede Jan23-09 01:38 PM Re: Magnetic Reconnection vs Double Layers Quote: Quote by tusenfem (Post 2046544) It would be nice if you could show in detail that the regions in which reconnection happens can be correctly described by an "exploding double layer". At the moment the observations by e.g. Cluster are so good and in agreement with the theoretical description of reconnection, with the inward motion of "field lines" the energization of particles, the Hall current signature because of the decoupling of the ions from the field. I would look up the observations described by Sergeev et al (and refs therein). Also there is the interesting paper by Treumann et al. about the role of the Hall field. Although I did my PhD on double layers in astrophysics (mentioned in the Wiki page which is greatly rewritten by me with help from my predecessors, in its current and excellent form), I cannot see how a DL can make all the things that are observed near a reconnection region. But please show me with data and a model how it works. Just search for 'double layer' 'aurora' 'birkeland current' 'parallel electric field' in any geophysical journal. I turned up a bucket load with just a few simple searches. I'm not sure what kind of data and model you're looking for. Double layers in the downward current region of the aurora http://hal.archives-ouvertes.fr/docs...10-45-2003.pdf Parallel electric fields in the upward current region of the aurora: Numerical solutions Particle Simulation of Auroral Double Layers A double layer is that solution which preserves gross quasineutrality within its volume while permitting momentum balance between incident accelerated particles. The potential of the double layer is limited by the ion kinetic energy but need not match the global potential required for overall charge neutrality. One and two dimensional electrostatic particle simulations verify both double layer solutions and dependence of potentials on the injected energy. The difference between global and local potentials is absorbed in a sheath opposite the injection boundary. Potential formations are strictly dependent on the self-consistent charge distributions they support. Microinstabilities cause changes in particle distributions. Double layer motion is associated with exchange of momentum between particles and these fields. Double layers The basic properties of electrostatic double layers observed in laboratory gaseous discharges are reviewed. Theoretical results from both macroscopic 4-fluid theory and microscopic, Vlasov, theory are described and found to be in fairly good agreement. Recent work on Penrose-stable double layers, as well as double layers with oblique electric and magnetic fields are described. Applications to Birkeland currents in the ionosphere are made. It was found that kilovolt potential which drops along the geomagnetic field can be produced in the topside ionosphere by double layers. Anomalous turbulent resistivity effects are unlikely to produce large parallel potential drops since that would lead to excessive heating of the ambient plasma. Since double layers are laminar structures they will not produce heat until the accelerated particles are stopped in the lower much denser E-layer. Large parallel electric fields in the upward current region of the aurora: Evidence for ambipolar effects Double layers on auroral field lines Time-stationary solutions to the Vlasov-Poisson equation for ion holes and double layers were examined along with particle simulations which pertain to recent observations of small amplitude (e phi)/t sub e approx. 1 electric field structures on auroral field lines. Both the time-stationary analysis and the simulations suggest that double layers evolve from holes in ion phase space when their amplitude reaches (e phi)/t sub e approx. 1. Multiple small amplitude double layers which are seen in long simulation systems and are seen to propagate past spacecraft may account for the acceleration of plasma sheet electrons to produce the discrete aurora. Suede Jan23-09 01:44 PM Re: Magnetic Reconnection vs Double Layers Quote: Quote by tusenfem (Post 2046572) Just some random comments on your first post: Naturally there is a current in the system because reconnection happens in oppositely directed magnetic fields and through Maxwell's equations it is clear that these are two fields are separated by a current sheet, just like in nature in e.g. the Earth's magnetotail. electric fields must complete a circuit to flow? I do hope this is a language problem, because electric fields don't flow. Field aligne electric fields and field aligned currents have absolutely nothing to do with reconnection, so you cannot use that to claim that reconnecting is correct or not. Take a look at my paper here where the motion of the magnetic field is the cause of currents flowing. Something (which you will see I leave to the reader to decide what, reconnection, current disruption,...) sets plasma flows in motion, which is pulled along with the magnetic field (in the tail the frozen in condition is very well satisfied, determined from measurements not assumptions) As there is a barrier this motion needs to be stopped and one of the main ways of stopping is cross tail currents, and these close as field aligned currents. Now these field aligned currents, when they go through a region of low density, they need to be accelerated to maintain the current, which is usually done by a double layer. But from your description above, it sounds like you have no idea what a DL is. And I am insulted! You forget my paper on solitary kinetic Alfvén waves which carry parallel electric field in the auroral zone, and there is the paper by Chust et al which shows strong parallel E-fields measured by Freja and shows that they are real and no artifact. However, all these double layers and parallel electric fields are mainly close to the Earth, most of them in the auroral zone, whereas reconnection happens rather far down the tail (20 Earth radii) or near the nose of the magnetosphere. A double layer can "explode" at any point and we have evidence for their existence throughout the magnetosphere of earth. I do indeed know what a double layer is, in fact I quoted the dictionary definition of one. If you want to believe magnetic field lines are real physical objects that merge and reconnect I suppose that's your business. I personally prefer Alfven's opinion. Suede Jan23-09 02:32 PM Re: Magnetic Reconnection vs Double Layers 24 July 2008 Surprise sequence Strung out like a line of buoys in the ocean, THEMIS tracked the true sequence of events. The outermost satellites registered a reconnection, an aurora appeared near Earth, then the inner probes saw a current disruption. This sequence was a surprise, as researchers expected the aurora to occur last. I'll tell you why it's a "suprise". Magentic reconnection isn't real and the models are wrong. That's a pretty huge suprise btw. That's like predicting: egg first splaters, then hammer falls. Sundance Jan24-09 06:39 AM Re: Magnetic Reconnection vs Double Layers Hello Suede Search Plasma Z-pinch Tokamaks reversed field pinch and arXiv tokamak http://arxiv.org/find/all/1/all:+Tokamak/0/1/0/all/0/1	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8211084604263306, "perplexity": 1353.7398965609282}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657119220.53/warc/CC-MAIN-20140914011159-00343-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
http://mathhelpforum.com/calculus/88616-directional-derivative-help.html	# Math Help - Directional derivative..help.. 1. ## Directional derivative..help.. Is this question asking for us to find the saddle point,maximum,minimum?I'm confused,how would I go about doing this? Suppose you are climbing a hill of height z whose shape is given by the equation z(x,y)=1000-0.01x^2-0.04y^2 and you are standing at the point with the coordinates(240,80,168). In which direction is the line of greatest steepness? Give your answer as unit vector. Use a directional derivative to find the rate of climb in this direction. 2. Gradient - Wikipedia, the free encyclopedia The gradient points in the direction where the function has the greatest rate of increase. Directional derivative - Wikipedia, the free encyclopedia In particular, the rate of climb in this direction is $\|\nabla z(x,y)\|$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6999586820602417, "perplexity": 831.4767922495449}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398450745.23/warc/CC-MAIN-20151124205410-00220-ip-10-71-132-137.ec2.internal.warc.gz"}
https://math.eretrandre.org/tetrationforum/showthread.php?mode=threaded&tid=424&pid=4809	• 1 Vote(s) - 5 Average • 1 • 2 • 3 • 4 • 5 using sinh(x) ? sheldonison Long Time Fellow Posts: 640 Threads: 22 Joined: Oct 2008 06/08/2010, 01:59 PM (This post was last modified: 06/09/2010, 12:18 AM by sheldonison.) (06/07/2010, 12:34 AM)tommy1729 Wrote: (06/02/2010, 10:56 PM)sheldonison Wrote: After that, do you agree that converting from your f(y) to g(y) by iterating natural logarithms would appear to be exactly the same? ... The value I'm using for k is 0.067838366. $\operatorname{TommySexp_e}(z)= \lim_{n \to \infty } \ln^{[n]} ( \operatorname{superfunc}(z+n+k))$ no , i use iterations of exp(x) ! you only use logaritms and the superfunction of 2sinh(x) ... i use logaritms , superfunction of 2sinh(x) and exp(x). numerically it might not be a big difference for large values ( since 2sinh(x) and exp(x) are close for large x ) , but for small x or properties it might be a huge difference ... maybe that is why you get 0.92715... ? i dont know if i need a correcting 'k'. and btw as for the diff-eq , i made a correction to that post (typo mainly but important ) , maybe it will help. regards tommy1729The correcting factor is k=$\lim_{n \to \infty}\operatorname{superfunc}^{-1}\exp^{[n]}(0)$ If you try your equations to calculate TommySexp(0.5) with x=0, y=0.5, and k=3 Quote:let g(x,y) be the y'th iterate of exp(x) evaluated at x. let f(x,y) be the y'th iterate of 2 sinh(x) evaluated at x. then g(x,y) = lim k -> oo log log log ... (k times ) [f( g(x,k) ,y)] then g(0,0.5) = (for k=3) log log log (3 times) [f( g(0,3), 0.5)] g(0,3) is $\exp^{[3]}(0)$=3814279.104.... Calculating f( g(3,0) ,0.5) is a a somewhat complex operation, and I'd like to understand if you would calculate that expression the same way I would. My approach would be to use the inverse superfunction, then add 0.5, then calculate the superfunction. $x=\exp^{[3]}(0) ; y=0.5$ $\text{f(x,y)=}\operatorname{superfunc}(\operatorname{superfunc}^{-1} (x) + y)$ Update or alternatively, iterate $\text{f(x,y)=}\lim_{n \to \infty}\operatorname{2sinh}^{[n]}((\operatorname{2sinh^{-1 [n times]}(x))2^y)$ $\text{f( g(0,3) ,0.5)=}\lim_{n \to \infty}\operatorname{2sinh}^{[n]}((\operatorname{2sinh^{-1 [n times]}(g(0,3)))\sqrt 2)$ The inverse superfunction gives 3.0678383... which is 3 plus the normalization constant, then adding 0.5 ... then calculate the superfunction of 3.5678383.... 8.10306E+77 Finally, take the logarithm three times, and you get (for Tommy's k=3) TommySexp(0.5) =~ f(0,0.5) =~ 0.4987433... Numerically, this is exactly what the limit equations I've posted give. - Sheldon - Sheldon « Next Oldest \| Next Newest » Messages In This Thread using sinh(x) ? - by tommy1729 - 02/28/2010, 12:22 AM RE: using sinh(x) ? - by tommy1729 - 03/06/2010, 12:35 PM RE: using sinh(x) ? - by bo198214 - 03/07/2010, 11:19 AM using 2* sinh(x) ! - by tommy1729 - 03/09/2010, 01:31 PM RE: using 2* sinh(x) ! - by bo198214 - 03/10/2010, 11:38 AM RE: using 2* sinh(x) ! - by tommy1729 - 03/11/2010, 12:50 AM RE: using 2* sinh(x) ! - by tommy1729 - 03/14/2010, 01:07 AM RE: using 2* sinh(x) ! - by sheldonison - 06/02/2010, 04:47 PM RE: using 2* sinh(x) ! - by tommy1729 - 06/02/2010, 10:13 PM RE: using 2* sinh(x) ! - by sheldonison - 06/02/2010, 10:56 PM RE: using 2* sinh(x) ! - by tommy1729 - 06/07/2010, 12:34 AM RE: using 2* sinh(x) ! - by sheldonison - 06/08/2010, 01:59 PM RE: using 2* sinh(x) ! - by tommy1729 - 06/09/2010, 12:18 PM RE: using 2* sinh(x) ! - by mike3 - 06/11/2010, 02:23 AM RE: using 2* sinh(x) ! - by bo198214 - 06/12/2010, 04:36 AM RE: using 2* sinh(x) ! - by mike3 - 06/12/2010, 11:14 AM RE: using 2* sinh(x) ! - by tommy1729 - 06/21/2010, 09:14 PM RE: using 2* sinh(x) ! - by sheldonison - 06/23/2010, 06:06 PM RE: using 2* sinh(x) ! - by tommy1729 - 06/23/2010, 09:11 PM RE: using 2* sinh(x) ! - by tommy1729 - 06/23/2010, 09:31 PM RE: using 2* sinh(x) ! - by bo198214 - 06/27/2010, 09:16 AM RE: using 2* sinh(x) ! - by sheldonison - 06/04/2010, 04:48 AM RE: using sinh(x) ? - by tommy1729 - 04/24/2010, 11:47 PM RE: using sinh(x) ? - by bo198214 - 05/31/2010, 05:52 AM RE: using sinh(x) ? - by tommy1729 - 06/01/2010, 10:58 PM RE: using sinh(x) ? - by bo198214 - 06/02/2010, 02:58 AM RE: using sinh(x) ? - by tommy1729 - 06/22/2010, 11:18 PM RE: using sinh(x) ? - by tommy1729 - 06/23/2010, 10:44 PM RE: using sinh(x) ? - by tommy1729 - 06/24/2010, 12:29 PM RE: using sinh(x) ? - by tommy1729 - 06/24/2010, 07:22 PM RE: using sinh(x) ? - by bo198214 - 06/26/2010, 12:04 PM RE: using sinh(x) ? - by tommy1729 - 06/26/2010, 09:19 PM attracting fixed point of 2sinh - by sheldonison - 06/27/2010, 03:31 AM RE: attracting fixed point of 2sinh - by tommy1729 - 06/28/2010, 11:23 PM RE: attracting fixed point of 2sinh - by sheldonison - 06/29/2010, 03:18 AM RE: attracting fixed point of 2sinh - by tommy1729 - 06/29/2010, 10:45 PM RE: attracting fixed point of 2sinh - by sheldonison - 06/30/2010, 01:12 AM RE: attracting fixed point of 2sinh - by tommy1729 - 06/30/2010, 02:35 PM RE: attracting fixed point of 2sinh - by sheldonison - 06/30/2010, 03:34 PM RE: using sinh(x) ? - by tommy1729 - 07/18/2010, 10:41 PM RE: using sinh(x) ? - by sheldonison - 07/19/2010, 09:37 PM RE: using sinh(x) ? - by tommy1729 - 07/20/2010, 08:24 PM RE: using sinh(x) ? - by tommy1729 - 07/19/2010, 10:20 PM RE: using sinh(x) ? - by sheldonison - 07/20/2010, 03:13 PM RE: using sinh(x) ? - by tommy1729 - 07/20/2010, 08:31 PM RE: using sinh(x) ? - by sheldonison - 07/21/2010, 03:19 AM RE: using sinh(x) ? - by tommy1729 - 07/21/2010, 10:34 PM RE: using sinh(x) ? - by sheldonison - 07/22/2010, 12:23 PM RE: using sinh(x) ? - by tommy1729 - 07/28/2010, 02:24 PM RE: using sinh(x) ? - by tommy1729 - 07/28/2010, 02:53 PM RE: using sinh(x) ? - by tommy1729 - 12/04/2010, 11:09 PM RE: using sinh(x) ? - by tommy1729 - 12/08/2010, 02:31 PM RE: using sinh(x) ? - by sheldonison - 01/17/2011, 07:43 PM RE: using sinh(x) ? - by tommy1729 - 01/17/2011, 11:36 PM RE: using sinh(x) ? - by tommy1729 - 07/02/2011, 10:32 PM RE: using sinh(x) ? - by tommy1729 - 07/04/2011, 10:56 PM RE: using sinh(x) ? - by sheldonison - 07/05/2011, 01:09 AM RE: using sinh(x) ? - by tommy1729 - 07/05/2011, 12:06 PM RE: using sinh(x) ? - by tommy1729 - 11/18/2012, 11:41 PM RE: using sinh(x) ? - by sheldonison - 11/20/2012, 12:01 AM RE: using sinh(x) ? - by tommy1729 - 11/20/2012, 10:53 PM RE: using sinh(x) ? - by sheldonison - 11/20/2012, 11:01 PM RE: using sinh(x) ? - by tommy1729 - 11/20/2012, 11:32 PM RE: using sinh(x) ? - by sheldonison - 11/20/2012, 11:46 PM RE: using sinh(x) ? - by tommy1729 - 11/28/2012, 06:59 PM RE: using sinh(x) ? - by tommy1729 - 11/28/2012, 08:07 PM RE: using sinh(x) ? - by tommy1729 - 12/17/2012, 04:34 PM RE: using sinh(x) ? - by tommy1729 - 02/10/2015, 12:02 AM RE: using sinh(x) ? - by tommy1729 - 04/22/2015, 12:27 PM RE: using sinh(x) ? - by tommy1729 - 04/23/2015, 04:49 PM RE: using sinh(x) ? - by tommy1729 - 10/26/2015, 12:56 AM RE: using sinh(x) ? - by tommy1729 - 11/26/2015, 11:56 PM RE: using sinh(x) ? - by sheldonison - 11/27/2015, 03:41 PM RE: using sinh(x) ? - by tommy1729 - 11/28/2015, 01:21 PM RE: using sinh(x) ? - by sheldonison - 11/29/2015, 03:03 PM RE: using sinh(x) ? - by tommy1729 - 12/01/2015, 01:22 PM RE: using sinh(x) ? - by sheldonison - 12/01/2015, 02:58 PM RE: using sinh(x) ? - by tommy1729 - 12/02/2015, 12:04 AM RE: using sinh(x) ? - by tommy1729 - 12/01/2015, 08:18 PM RE: using sinh(x) ? - by tommy1729 - 12/02/2015, 12:28 AM RE: using sinh(x) ? - by tommy1729 - 02/23/2016, 10:36 PM RE: using sinh(x) ? - by tommy1729 - 02/24/2016, 01:27 PM RE: using sinh(x) ? - by tommy1729 - 03/01/2016, 10:38 PM RE: using sinh(x) ? - by tommy1729 - 03/05/2016, 01:27 PM RE: using sinh(x) ? - by tommy1729 - 03/05/2016, 11:38 PM RE: using sinh(x) ? - by sheldonison - 03/06/2016, 03:16 PM RE: using sinh(x) ? - by tommy1729 - 03/06/2016, 10:54 PM RE: using sinh(x) ? - by tommy1729 - 03/07/2016, 01:48 AM RE: using sinh(x) ? - by tommy1729 - 03/07/2016, 10:46 AM RE: using sinh(x) ? - by tommy1729 - 03/07/2016, 09:36 PM RE: using sinh(x) ? - by tommy1729 - 03/08/2016, 12:26 AM RE: using sinh(x) ? - by tommy1729 - 03/11/2016, 01:27 PM RE: using sinh(x) ? - by tommy1729 - 03/12/2016, 01:12 PM RE: using sinh(x) ? 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http://openstudy.com/updates/52379bbfe4b0af32a079fd8b	Here's the question you clicked on: 55 members online • 0 viewing ## anonymous 3 years ago F(x)= ∫cos(e^t)dt top limit ln(x) bottom limit pi, what is the derivative of F(x) Delete Cancel Submit • This Question is Open 1. anonymous • 3 years ago Best Response You've already chosen the best response. 0 When the lower limit is a constant it drops out when taking the derivative, so it doesn't matter whether it's pi or 0 or any other constant. The question is how to deal with ln(x) as the upper limit. How about this:$\cos(e^{\ln x})\frac{ 1 }{ x }=\frac{ \cos x }{ x }$because e^(ln x) is just x. 2. anonymous • 3 years ago Best Response You've already chosen the best response. 0 Thans a lot, but one more question where did you get 1/x from? 3. anonymous • 3 years ago Best Response You've already chosen the best response. 0 We substituted ln x for t, so we need to substitute d(ln x) for dt. 4. Not the answer you are looking for? Search for more explanations. • Attachments: Find more explanations on OpenStudy ##### spraguer (Moderator) 5→ View Detailed Profile 23 • Teamwork 19 Teammate • Problem Solving 19 Hero • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9987283945083618, "perplexity": 5662.526422256496}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541864.24/warc/CC-MAIN-20161202170901-00123-ip-10-31-129-80.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1153750/galois-group-over-the-field-of-rational-functions	# Galois group over the field of rational functions I am looking to find the Galois group of $x^3-x+t$ over $\mathbb{C}(t)$, the field of rational functions with complex coefficients. I have shown that the automorphisms of the rational function field $F(t)$ for fixed $F$ are precisely the fractional linear transformations that is $t \rightarrow \frac{at +b}{ct+d}$ for $a,b,c,d \in \mathbb{C}$. Is this useful? Also is there anyway to factor $x^3-x+t$ nicely? I slept on this for a little bit and developed an idea to show this. I used Cardano's method to explicitly solve for the roots of this polynomial and show that there exist no linear factors in $\mathbb{C}(t)$ and $f(x)$ is therefore irreducible. This is because the polynomial is cubic, and if there are no linear factors then there cannot be any quadratic factors. Thus, you have to adjoin some root let's call it $\theta$ to $\mathbb{C}(t)$. The degree of this field over $\mathbb{C}(t)$ is a Galois extension and must have degree 3. The only group with order 3 is $\mathbb{Z}_3$, which implies this is the Galois group. • You can easily determine the Galois group of a cubic polynomial simply by computing its discriminant and deciding whether it is a square or not. – Mariano Suárez-Álvarez Feb 17 '15 at 23:33 • See www.math.uconn.edu/~kconrad/blurbs/galoistheory/cubicquarticallchar.pdf – Mariano Suárez-Álvarez Feb 17 '15 at 23:36 • Ah because if the discriminant is square then the Galois group is isomorphic to $A_3$ and $S_3$ otherwise. Thank you! – KangHoon You Feb 17 '15 at 23:42 • What you wrote is not correct. Your argument is, essentially, that as the polynomial is irreducible, adjoining one of its roots gives a normal extwnsion, and that is very false. – Mariano Suárez-Álvarez Feb 24 '15 at 5:26 • Chiming in with Mariano. Why do you get a Galois extension by adjoining $\theta$? – Jyrki Lahtonen Feb 24 '15 at 7:12 I don't see how to use Eisenstein here. But the polynomial is a cubic, so if it factors, then one of the factors is linear, and the polynomial would have a zero $x=\frac{p(t)}{q(t)}\in\Bbb{C}(t)$ with some polynomials $p(t),q(t)\in\Bbb{C}[t]$, $q\neq0$. To exclude this possibility we use a line of reasoning analogous to the familiar rational root test - taking advantage of the fact that $\Bbb{C}[t]$ is a UFD. So assume that all common factors of $p(t)$ and $q(t)$ have been cancelled. Then $$x^3-x+t=\frac{p^3-pq^2+tq^3}{q^3}=0.$$ Here the numerator has to be zero, so from $$p^3-pq^2=-tq^3$$ we can conclude that $p$ divides the left hand side, hence also the right hand side. But $p$ has no common factors with $q$, so it has to be a factor of $t$. Similarly from $$p^3=pq^2-tq^3$$ we see that $q$ divides the right hand side, hence also $p^3$. But, as above, this implies that $q$ must be a constant. The non-zero constants are the units of $\Bbb{C}[t]$, so we can conclude that $x=p/q$ is either a constant or, $x=at$ for some $a\in\Bbb{C}$. I'm sure that you can show that neither of those work. Therefore this cubic has no linear factors over $\Bbb{C}(t)$ and hence it is irreducible. • thank you for your help. I offer an alternative solution, do you see any problems with it? – KangHoon You Feb 24 '15 at 5:21 Hint: Show that the polynomial is irreducible over $\mathbb C[t]$ (which shows irreducibility over $\mathbb C(t)$ by Gauss) and then compute the discriminant as usual. • I know showing irreducibility over $\mathbb{Q}$ can be done using Eisenstein's Criterion. Is there a similar trick for $\mathbb{C}$? – KangHoon You Feb 17 '15 at 23:43 • Eisenstein's criterion works over the field of fractions of a UFD, such as $\mathbb Z$ or $\mathbb C[t]$. – Mariano Suárez-Álvarez Feb 17 '15 at 23:47 • After substituting $x+a$ for some integer $a$, I believe then I will be able to show the polynomial to satisfy Eisenstein's critertion. Thank you @MarianoSuárez-Alvarez and @Mesih! – KangHoon You Feb 17 '15 at 23:53 • By Gauss, irreducibility in $\mathbf C(T)[X]$ is (essentially) equivalent to irreducibility in $\mathbf C[T,X]$, which (here) follows from the fact that the degree in $T$ is $1$. – ACL Jun 26 at 15:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9385594129562378, "perplexity": 130.59019505235963}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314638.49/warc/CC-MAIN-20190819011034-20190819033034-00298.warc.gz"}
https://codegolf.stackexchange.com/questions/74553/robot-on-a-ladder?noredirect=1	Background I have a ladder leaning on a wall, and a remote-controlled robot that can climb it. I can send three different commands to the robot: • UP: the robot takes one step upwards. If it was on the highest step, it trips over, falls down and explodes. • DOWN: the robot takes one step downwards. If it was on the lowest step, nothing happens. • RESET: the robot returns to the lowest step. I can also send a series of commands, and the robot will execute them one by one. Your task is to predict its movements. Input Your inputs are a positive integer N, representing the number of steps in the ladder, and a non-empty string C over UDR, representing the commands I have sent to the robot. You can assume that N < 1000. The robot is initialized on the lowest step of the ladder. Output It is guaranteed that at some point, the robot will climb over the highest step and explode. Your output is the number of commands it executes before this happens. Example Consider the inputs N = 4 and C = "UDDUURUUUUUUUDDDD" The robot, denoted by @, moves along the 4-step ladder as follows: \|-\| \|-\| \|-\| \|-\| \|-\| \|-\| \|-\| \|-\| \|-\| \|@\| \|-\|\| \|-\| \|-\| \|-\| \|-\| \|-\| \|@\| \|-\| \|-\| \|@\| \|-\| \|-\|\| \|-\| \|@\| \|-\| \|-\| \|@\| \|-\| \|-\| \|@\| \|-\| \|-\| \|-\|v \|@\| U \|-\| D \|@\| D \|@\| U \|-\| U \|-\| R \|@\| U \|-\| U \|-\| U \|-\| U \|-\|# Boom! The remaining commands are not executed, since the robot has exploded. The explosion took place after 10 commands, so the correct output is 10. Rules and scoring You can write a full program or a function. The lowest byte count wins, and standard loopholes are disallowed. Test cases 1 U -> 1 1 DDRUDUU -> 4 4 UDDUUUUURUUUUDDDD -> 7 4 UDDUURUUUUUUUDDDD -> 10 6 UUUUUDRUDDDDRDUUUUUUDRUUUUUUUDR -> 20 10 UUUUUURUUUUUUURUUUUUUUURUUUUUUUUUUUUUU -> 34 6 UUUDUUUUDDDDDDDDDDDDDDRRRRRRRRRRRUUUUUU -> 8 6 UUUDUUUDURUDDDUUUUUDDRUUUUDDUUUUURRUUDDUUUUUUUU -> 32 20 UUDDUDUUUDDUUDUDUUUDUDDUUUUUDUDUUDUUUUUUDUUDUDUDUUUUUDUUUDUDUUUUUUDUDUDUDUDUUUUUUUUUDUDUUDUDUUUUU -> 56 354 UUDDUUDUDUUDDUDUUUUDDDUDUUDUDUDUDDUUUUDUDUUDUDUUUDUDUDUUDUUUDUUUUUDUUDUDUUDUDUUUUUDUDUUDUDUDUDDUUUUUUUDUDUDUDUUUUUDUDUDUDUDUDUDUDUUDUUUUUURUUUDUUUUDDUUDUDUDURURURUDUDUUUUDUUUUUUDUDUDUDUDUUUUUUDUDUUUUUUUDUUUDUUDUDUDUUDUDUDUUUUUUUUUUDUUUDUDUUDUUDUUUDUUUUUUUUUUUUUDUUDUUDUDUDUUUDUDUUUUUUUDUUUDUUUDUUDUUDDUUUUUUUUDUDUDUDUDUUUUDUDUUUUUUUUDDUUDDUUDUUDUUDUDUDUDUUUUUUUUUDUUDUUDUUUDUUDUUUUUUUUUUUDUDUDUDUUUUUUUUUUUUDUUUDUUDUDDUUDUDUDUUUUUUUUUUUUDUDUDUUDUUUDUUUUUUUDUUUUUUUUUDUDUDUDUDUUUUUUDUDUDUUDUDUDUDUUUUUUUUUUUUUUUDUDUDUDDDUUUDDDDDUUUUUUUUUUUUUUDDUDUUDUUDUDUUUUUUDUDUDUDUDUUUUDUUUUDUDUDUUUDUUDDUUUUUUUUUUUUUUUUUUDUUDUUDUUUDUDUUUUUUUUUUUDUUUDUUUUDUDUDUUUUUUUUUDUUUDUUUDUUDUUUUUUUUUUUUDDUDUDUDUUUUUUUUUUUUUUUDUUUDUUUUDUUDUUDUUUUUUUUUUUDUDUUDUUUDUUUUUUDUDUDUUDUUUUUUUUUUUUDUUUDUUDUDUDUUUUDUDUDUDUDUUUUUUUUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUUU -> 872 • Related – Peter Taylor Mar 1 '16 at 20:50 • I'm disappointed the task isn't to generate that ASCII art. – user253751 Mar 2 '16 at 2:34 • @immibis You know what to do... – Martin Ender Mar 2 '16 at 12:31 • Instead of a string, can we take a list of character codes? – Cyoce Mar 3 '16 at 3:04 • @Cyoce Only if your language has no other means to represent a string. – Zgarb Mar 3 '16 at 3:57 CJam, 2625 22 bytes 0l{i"()~ "=~0e>_}%ri#) Input format is the instructions on the first line and the ladder height on the second. Test it here. Explanation 0 e# Push a 0 - the initial position of the robot. { e# Map this block over the instruction... i e# Convert to character code. D -> 68, U -> 85, R -> 82. "()~ "= e# We use these as cyclic indices into this array. Note that the values e# modulo 4 are 0, 1 and 2, respectively. So U -> ) (increment), e# D -> ( (decrement), R -> ~ (bitwise NOT, i.e negated and decrement). ~ e# Evaluate the character as code. 0e> e# Clamp to non-negative numbers. So D can't go below 0, and since R is e# guaranteed to yield something negative, this resets it to zero. _ e# Duplicate, so we keep one copy of the current position on the stack. }% e# Since this was a map, the result will be wrapped in an array. ri e# Read the ladder height and convert it to an integer. # e# Find its first occurrence in the list of positions. ) e# The result is off by one, so we increment it. • Good idea to process all commands even after the explosion. I'll borrow that to save a few bytes – Luis Mendo Mar 1 '16 at 22:36 C, 83 71 + 4 = 75 bytes Thanks @Josh for showing me the K&S style, which allowed 8 bytes off !! f(i,s,z,a)chars;{z-=s<82?z>0:s>82?-1:z;return z-i?f(i,s+1,z,a+1):a;} Explaining: f(i,s,z,a)chars;{ // function needs one integer and one "string" z-= // z is the bot's height s<82? // if 'Down' z>0 // then subtract 1 when z>0 or nothing otherwise :s>82? // else if 'Up' -1 // increase height z-=-1 :z; // else reset z=z-z return z-i? // if z is not the max height f(i,s+1,z,a+1) // try next step :a; // else print how many calls/steps were made } // end of function Example call: f(1,"U",0,1); // I've added 4 bytes in the score because of ",0,1" Live test on ideone • Nice answer, but it might be worth noting that the function can effectively only be used once since globals z and a are not reset. – Josh Mar 2 '16 at 22:06 • @Josh. I've updated. :) – removed Mar 3 '16 at 13:00 • Awesome! You can also save a couple characters by playing around with the type declarations in your function: codegolf.stackexchange.com/a/40266/13877 – Josh Mar 3 '16 at 13:43 • @Josh. Wow this is awesome! thanks – removed Mar 3 '16 at 14:19 JavaScript (ES6), 54 53 bytes n=>c=>(f=p=>n-p?f({D:p&&p-1,U:p+1}[c[i++]]\|0):i)(i=0) Explanation Uses a recursive function internally. var solution = n=>c=>( f=p=> // f = recursive function, p = position of robot on ladder n-p? // if p != n f({ // execute the next command D:p&&p-1, // D -> p = max of p - 1 and 0 U:p+1 // U -> p = p + 1 }[c[i++]] // get current command then increment i (current command index) \|0 // R -> p = 0 ) :i // else return the current command index )(i=0) // initialise p and i to 0 for the first recurse N = <input type="number" id="N" value="354" /><br /> C = <input type="text" id="C" value="UUDDUUDUDUUDDUDUUUUDDDUDUUDUDUDUDDUUUUDUDUUDUDUUUDUDUDUUDUUUDUUUUUDUUDUDUUDUDUUUUUDUDUUDUDUDUDDUUUUUUUDUDUDUDUUUUUDUDUDUDUDUDUDUDUUDUUUUUURUUUDUUUUDDUUDUDUDURURURUDUDUUUUDUUUUUUDUDUDUDUDUUUUUUDUDUUUUUUUDUUUDUUDUDUDUUDUDUDUUUUUUUUUUDUUUDUDUUDUUDUUUDUUUUUUUUUUUUUDUUDUUDUDUDUUUDUDUUUUUUUDUUUDUUUDUUDUUDDUUUUUUUUDUDUDUDUDUUUUDUDUUUUUUUUDDUUDDUUDUUDUUDUDUDUDUUUUUUUUUDUUDUUDUUUDUUDUUUUUUUUUUUDUDUDUDUUUUUUUUUUUUDUUUDUUDUDDUUDUDUDUUUUUUUUUUUUDUDUDUUDUUUDUUUUUUUDUUUUUUUUUDUDUDUDUDUUUUUUDUDUDUUDUDUDUDUUUUUUUUUUUUUUUDUDUDUDDDUUUDDDDDUUUUUUUUUUUUUUDDUDUUDUUDUDUUUUUUDUDUDUDUDUUUUDUUUUDUDUDUUUDUUDDUUUUUUUUUUUUUUUUUUDUUDUUDUUUDUDUUUUUUUUUUUDUUUDUUUUDUDUDUUUUUUUUUDUUUDUUUDUUDUUUUUUUUUUUUDDUDUDUDUUUUUUUUUUUUUUUDUUUDUUUUDUUDUUDUUUUUUUUUUUDUDUUDUUUDUUUUUUDUDUDUUDUUUUUUUUUUUUDUUUDUUDUDUDUUUUDUDUDUDUDUUUUUUUUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUUU" /><br /> <button onclick="result.textContent=solution(+N.value)(C.value)">Go</button> <pre id="result"></pre> Perl, 47 + 2 = 49 bytes $z-=-/U/\|\|$z&&/D/;$z=!/R/;$^I<=$z&&last}{$_=$. Requires the -p flag, -i$N for latter height and a newline separated list of moves: $perl -pi10 ladderbot.pl <<<<$'U\nU\nU\nU\nU\nU\nR\nU\nU\nU\nU\nU\nU\nU\nR\nU\nU\nU\nU\nU\nU\nU\nU\nR\nU\nU\nU\nU\nU\nU\nU\nU\nU\nU\nU\nU\nU\nU' 34 How it works: # '-p' wraps the code in (simplified): # while($_=<>) {...print$_} $z-=-/U/\|\|$z&&/D/; # Subtract -1 if UP. subtract 1 if DOWN $z=!/R/; # If R then times by zero$^I<=$z&&last # Break while loop if N is reached }{ # Eskimo operator: # while($_=<>){...}{print$_}$_=$. # $. contains number of lines read from input. Deparsed: LINE: while (defined($_ = <ARGV>)) {$z -= -/U/ \|\| $z && /D/;$z = !/R/; last if $^I <=$z; } { $_ =$.; } continue { die "-p destination: $!\n" unless print$_; } -e syntax OK JavaScript (SpiderMonkey 30+), 65 64 bytes (n,s,i=0)=>[for(c of s)if(i<n)c<'E'?i&&i--:c>'T'?i++:i=0].length How it works We first set the variable i to 0. This will keep track of how many steps the robot has climbed up. Then for each char c in the input string, we run the following logic: 1. If i is larger than or equal to n, don't do anything. 2. If c is "D": • If i is 0, leave it as is. • Otherwise, decrement it by 1. 3. If c is "U", increment i by 1. 4. Otherwise, set i to 0. By cutting off if i>=n, we avoid adding any more items to the array after the robot has reached the top. Thus, we can simply return the length of the resulting array. x%'U'=x+1 x%'D'=max(x-1)0 x%_=0 f n=length.fst.span(<n).scanl(%)0 Usage example: f 4 "UDDUURUUUUUUUDDDD" -> 10. % adjusts the current position on the ladder, scanl makes a list of all positions, fst.span(<n) takes the part before the explosion and length counts the steps. • Nice job with the combination of named arguments and composition/currying – Cyoce Mar 3 '16 at 2:23 JavaScript (ES6), 65 bytes (n,s)=>[...s].map(_=>i=_<'E'?i&&i-1:_>'T'?i+1:0,i=0).indexOf(n)+1 • – ETHproductions Mar 1 '16 at 21:28 • I think 0,i=0 can be changed to i=0 – Cyoce Mar 3 '16 at 0:29 • @Cyoce hmm, fails for me in a new tab (works on this page b/c i is already defined) – Charlie Wynn Mar 3 '16 at 14:04 • @CharlieWynn sorry, got my precedence mixed up – Cyoce Mar 3 '16 at 18:18 MATL, 37 34 bytes Oj"t@4\1=?Q}6M?x0}qt0>]]]N$h=f1)q Try it online! Explanation Position is 0-based. Each new position is pushed onto the stack keeping the older positions. So the stack size represents the number of movements up to now, plus 1. A loop is used to process each command. The loop is exited when position reaches ladder height processes all commands, even after the explosion (idea taken from Martin's answer). The final result is given by the index of the first position that equals the ladder height. O % push a 0: initial position (0-based) j % take first input (commands) as a string " % for each command t % duplicate current position @ % push command 4\ % modulo 4. This gives 1, 2, 0 for 'U','R', 'D' 1=? % if result equals 1 (command 'U') Q % increase position by 1 } % else 6M? % if result was nonzero (command 'R') x0 % delete current position and push 0 } % else (command 'D') q % decrement by 1 t0>* % turn negative values into 0 ] % end if ] % end if ] % end for each N$h % pack all numbers in the stack into an array f1)q % find first position equal to that, and subtract 1. % Implicitly display Python 2, 63 62 bytes f=lambda n,s,h=0:h^n and-~f(n,s[1:],-[2%~h,~h,0][ord(s[0])%4]) For example, f(4, 'UDDUURUUUUUUUDDDD') is 10. xnor found an even shorter expression: 2%~h is really cool :) • Nice find with the %4. If I'm not mistaken, you can save a character by doing -[2%~h,~h,0][ord(s[0])%4]. – xnor Mar 2 '16 at 5:15 PowerShell, 86 79 bytes param($a,[char[]]$b)$b\|%{$d++;if(($c-=((1,0)[!$c],-1,$c)[$_%4])-ge$a){$d;exit}} A slight retooling of my When does Santa enter the basement? answer. Takes input $a and $b, explicitly casting $b as char-array. We then loop with \|%{...} over all of $b. Each iteration we increment our counter $d. Then, an if statement to check whether we've hit the top with -ge$a. If so, we output $d and exit. The if statement is constructed from a pseudo-ternary created by assigning $c minus-equal to the result of several indexes into an array. We have a trick that the ASCII values of D, R, and U correspond to 0, 2, and 1 when taken modulo-4, so $_%4 serves as our first index. If it's R, that sets $c equal to $c-$c, doing the reset. If U, that means we need to go up, so the $c-(-1) result. Otherwise it's a D, so we need to check if we're already at the bottom (that's the !$c - in PowerShell, "not-zero" is "true" or 1) and set $c equal to $c-0 or $c-1 respectively. Edit - Saved 7 bytes by using minus-equal assignment rather than direct assignment Perl 5, 61 bytes Includes two bytes for -F -i. (-M5.01 is free.) Input of the integer (e.g. 10) is as perl -M5.01 -F -i10 robot.pl; input of the ladder commands is as STDIN. for(@F){($i+=/U/)-=/R/?$i:$i&&/D/;$j++;last if$^I<=$i}say$j • using perl 5.12.5, i also had to explicitly enable autosplit mode with -anF before it would print anything for me. but it seems to get implicitly enabled with only -F in 5.20.3. can you verify this? – ardnew Mar 2 '16 at 2:23 • @ardnew, just -F sufficed for me (5.20 or 5.22 or so). Iirc the current perldoc perlrun says it implies -a and -a implies -n. – msh210 Mar 2 '16 at 3:55 • How much does we count -i for? I can see you count it as 1 but I would guess it should actually be counted as 3? :-) – andlrc Mar 3 '16 at 9:48 • @dev-null, why three? I think the convention on PPCG.SE is to count the letters in a flag but not the hyphen-minus characters, but please correct me if I'm wrong. (It looks like you're using the same counting convention for yoru own answer to this question, too. (Incidentally, nice answer.)) – msh210 Mar 3 '16 at 15:09 • @msh210 I was just counting the difference when using -i and without perl -i10 -pe';' vs perl -pe';' 3 characters more and then the input number - which I guess we shouldn't count. But I might be wrong just though about it this morning :-) – andlrc Mar 3 '16 at 15:57 Vitsy, 44 bytes There probably could be some reductions - I'll figure out some more things if I can. 0vVWl:X[4M1+mDvV-);]lvXv?v-N vD([1-] v1+ vX0 Explanation (in progress): 0vVWl:X[4M1+mDvV-);]lvXv?v-N 0v Save 0 as our temp var to edit. V Save the input as a global var. W Grab a line of STDIN. l Push the length of the stack. : Clone the stack. This is for later use. X Remove the top item of the stack (we don't need the length right now. [ ] Do the stuff in the brackets infinitely. 4M Modulo 4. m Go to the line index as specified by the top item of the stack. Dv Duplicate the top item, save it in the temp var. V-); If the top value is equal to the input number, exit the loop. l Push the length of the stack. vXv Dump the temp var, then save the top item. ? Rotate back to the original stack. v- Subtract the top item (the original length) by the temp var (new length) N Output the top item of the stack of the number. vD([1-] v Push the temp variable to the stack. D([ ] If this value is not zero... 1- Subtract one from it. v1+ Push the temp variable to the stack, then add one to it. vX0 Dump the temp var and replace it with zero. Try It Online! (big test case) PHP, 88 bytes This generates some (3+2n where n is the number of commands run) notices but that doesn't matter for golfing, right? <?php for(;$x++<$argv[1];)switch($argv[2][$i++]){case R;$x=2;case D;--$x?--$x:0;}echo$i; ungolfed: <?php # actually 1 byte shorter not as a function for(;$x++<$argv[1];) # not initialising the $x causes a notice but still works # post increment$x by 1 regardless of the command (saves us writing a U case) switch($argv[2][$i++]) # get next command, increment number of commands {case R; # R gets treated as a constant with value 'R'. and a notice $x=2; # falling through to D which will double decrement so set to 2 case D; # same trick as R --$x?--$x:0;} # decrement once then again if >0 echo$i; # output • Notices are fine, as long as the code can still be run. – Zgarb Mar 2 '16 at 19:44 Python, 121 bytes def f(a,n): i=c=0 while i<n:i={'U':lambda x:x+1,'D':lambda x:0 if x==0 else x-1,'R':lambda x:0}[a[c]](i);c+=1 return c • Welcome to PPCG! Here we require by default that answers are either full programs that take input from STDIN and print to STDOUT, or functions that take inputs as arguments and return the output value. Your solution hard-codes the inputs, which is not allowed. – Zgarb Mar 1 '16 at 23:39 • Corrected by forming into function, I was using interpreter when I wrote it. – Alex Burge Mar 1 '16 at 23:48 • Thank you! You should also add a header of the form ## Python, <N> bytes to show others your score. – Zgarb Mar 1 '16 at 23:58 • I don't think there can be an unnamed function. – user48538 Mar 2 '16 at 8:08 • You can save bytes by replacing 0 if x==0 else x-1 with x and x-1 – Cyoce Mar 3 '16 at 0:22 JavaScript, 131 106 Bytes- I know this won't win a Code Golf competition, but this was a fun and stupid solution to implement: l=>s=>Function('i=c=0;'+s.replace(/./g,x=>c++;i${{R:"=0",U:++;if(i>=${l})re‌turn c,D:"--"}[x]};))() I kinda went the opposite of a "functional" route by making a dynamically-generated imperative solution, any instance of an instruction is replaced with an increment or decrement, and a counter increment. Thanks to Cycoce for saving me 29 bytes! • Here, I golfed off 29 bytes: l=>s=>Function('i=c=0;'+s.replace(/./g,x=>c++;i${{R:"=0",U:++;if(i>=${l})return c,D:"--"}[x]};))() – Cyoce Mar 3 '16 at 3:55 Python 3, 90 Saved 6 bytes thanks to DSM. Pretty simple right now. def f(c,n): f=t=0 for x in c: f+=1\|-(x<'E');f=(x!='R')&(f>=0);t+=1 if f>=n:return t Test cases: assert f('U', 1) == 1 assert f('DDRUDUU', 1) == 4 assert f('UDDUUUUURUUUUDDDD', 4) == 7 assert f('UDDUURUUUUUUUDDDD', 4) == 10 assert f('UUDDUUDUDUUDDUDUUUUDDDUDUUDUDUDUDDUUUUDUDUUDUDUUUDUDUDUUDUUUDUUUUUDUUDUDUUDUDUUUUUDUDUUDUDUDUDDUUUUUUUDUDUDUDUUUUUDUDUDUDUDUDUDUDUUDUUUUUURUUUDUUUUDDUUDUDUDURURURUDUDUUUUDUUUUUUDUDUDUDUDUUUUUUDUDUUUUUUUDUUUDUUDUDUDUUDUDUDUUUUUUUUUUDUUUDUDUUDUUDUUUDUUUUUUUUUUUUUDUUDUUDUDUDUUUDUDUUUUUUUDUUUDUUUDUUDUUDDUUUUUUUUDUDUDUDUDUUUUDUDUUUUUUUUDDUUDDUUDUUDUUDUDUDUDUUUUUUUUUDUUDUUDUUUDUUDUUUUUUUUUUUDUDUDUDUUUUUUUUUUUUDUUUDUUDUDDUUDUDUDUUUUUUUUUUUUDUDUDUUDUUUDUUUUUUUDUUUUUUUUUDUDUDUDUDUUUUUUDUDUDUUDUDUDUDUUUUUUUUUUUUUUUDUDUDUDDDUUUDDDDDUUUUUUUUUUUUUUDDUDUUDUUDUDUUUUUUDUDUDUDUDUUUUDUUUUDUDUDUUUDUUDDUUUUUUUUUUUUUUUUUUDUUDUUDUUUDUDUUUUUUUUUUUDUUUDUUUUDUDUDUUUUUUUUUDUUUDUUUDUUDUUUUUUUUUUUUDDUDUDUDUUUUUUUUUUUUUUUDUUUDUUUUDUUDUUDUUUUUUUUUUUDUDUUDUUUDUUUUUUDUDUDUUDUUUUUUUUUUUUDUUUDUUDUDUDUUUUDUDUDUDUDUUUUUUUUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUDUUUUDUDUUUUUU', 354) == 872 PHP, 129 bytes function r($h,$s){$i=0;$c=1;while($x=$s[$i++]){if($x=='U'){$c++;}elseif($x=='D'){--$c<1?$c=1:0;}else{$c=1;}if($c>$h){return$i;}}} Not winning, but fun to create. PHP seems to dislike empty parts in the ternary operator (it throws a Syntax Error), so I had to put a 0 there. Ungolfed version: function r($h,$s) { // $h - height of ladder;$s - instructions $i = 0; // Instruction index$c = 1; // Position on ladder while ($x =$s[$i++]){ // Set$x to current instruction and increment index if ($x == 'U'){ // If instruction is U...$c++; // Increment ladder position } elseif ($x == 'D') { // If instruction is D... --$c < 1 ? $c = 1 : 0; // Decrement ladder position, if under 1 set to 1 } else { // If instruction is anything else (in this case R)$c = 1; // Reset ladder position } if ($c >$h) { // If ladder position is larger than height... return $i; // Return current instruction index } } } PHP, 113 bytes Smaller version of https://codegolf.stackexchange.com/a/74575/13216 function r($h,$s){$i=0;$c=1;while($x=$s[$i++]){$c+=($x=='U'?1:($x=='D'?($c>1?-1:0):1-$c));if($c>$h){return$i;}}} Ungolfed: // $h - height of ladder;$s - instructions function r($h,$s) { $i = 0;$c = 1; while ($x =$s[$i++]) {$c += ( $x=='U'? 1 : ($x=='D'? ( $c>1? -1 : 0 ): 1-$c ) ); if ($c >$h) { return \$i; } } } • Great first post! I edited your post for better readability. Happy golfing! – GamrCorps Mar 2 '16 at 4:42 Pyth, 19 bytes x.u@[tWNNhN00)CYz0Q Try it online: Demonstration or Test Suite Explanation: x.u@[tWNNhN00)CYz0Q implicit: z = input string, Q = input number .u z0 reduce z: for each char Y in z manipulate N = 0 with: [ ) create a list with tWNN N-1 if N>0 else N hN * N+1 0 * 0 0 * 0 @ CY replace N by the ord(Y)-th element (mod 4) .u .u give us a list with all intermediate values of N x Q print the index of Q in this list Java, 250 bytes int cmds(int n, String s) { int steps=1; int count=0; for (int i=0;i< s.length();i++) { count++; char c=s.charAt(i); switch(c){ case 'D': steps=(steps==1)?1:--steps; break; case 'R': steps=1; break; case 'U': ++steps; break; } if(steps>n) return count; } return 0; } • When answering a code-golf-challenge, you should start your answer with # <language_name>, XX bytes. Also you can reduce your variable names to one character each and remove extra whitespaces, this way your byte count will reduce (which is the objective here)... Ah, and welcome to PPCG! – removed Mar 2 '16 at 11:47 • Some tips: To indent your code as code add 4 spaces at the line's start. You removed some spaces, but you can still remove more (ex: instead of int steps=1; int count=0; you can use int s=1,c=0; - look I changed the variable name - and so on). You can still show your ungolfed version below the golfed version with an explanation (this way is easy for someone help you golfing more bytes). – removed Mar 2 '16 at 14:39 C, 91 bytes No warnings with gcc -Wall. Recursion and comma-separated expressions. r.c contains bare function: int r(int N,int n,int s,charC){returnC&&s<=N?s+=C&2?-s:C&1?1:-1,r(N,n+1,s?s:1,C+1):n;} Commented, int r(int N, // number of steps on ladder int n, // result, seed with 0 int s, // current step, seed with 1 char C // command string ) { s+= // increment step value by... C&2? // bit test if 'R' but not 'U' or 'D'. -s // negate to 0, will set to 1 in call if needed :C&1? // Not 'R', is it 'U'? :-1, // Must be 'D', subtract 1 r(N,n+1,s?s:1,C+1) // Recursive call, and fix case where s==0. :n; // end of string or fell off ladder } For reference, 'U'.charCodeAt(0).toString(2) "1010101" 'D'.charCodeAt(0).toString(2) "1000100" 'R'.charCodeAt(0).toString(2) "1010010" roboladder.c wrapper, #include <stdio.h> #include <stdlib.h> #include "r.c" int main(int argc, char argv[]) { int N = atoi(argv[1]); int n = r(N,0,1,argv[2]); int check = atoi(argv[3]); printf("%d : %d\n", n, check); return 0; } Makefile for testing, run: @wc -c r.c Mathematica, 114 120 bytes (d=#~Max~1-1&;u=#+1&;r=1&;s=StringToStream@ToLowerCase@#;l=1;t=1;While[(l=ToExpression[s~Read~Character]@l)<=#2,t++];t)& Anonymous function, which takes the two arguments (C,N). Careful using this, as it doesn't close the stream it opens. Also it assigns all its variables globally. Edited to replace d=#-1& with d=#~Max~1-1&, so that robie doesn't go digging. • Wait: I don't think this is valid. It allows the robot to go down negative rungs. Whoops. That'll teach me to test non-comprehensively... I'll put a corrected one up when I get the chance. – hYPotenuser Mar 3 '16 at 3:07 Mathematica, 112 Bytes i=0;First@Position[ToExpression["{"<>#~StringReplace~{"U"->"i++,","D"->"i=i~Max~1-1,","R"->"i=0,"}<>"0}"],#2-1]& Clojure, 92 84 bytes Counts n to zero instead zero to n, can utilize take-while pos?. #(count(take-while pos?(reductions(fn[p o](if o(min(o p 1)%)%))%(map{\U -\D +}%2)))) Original: #(count(take-while(partial > %)(reductions(fn[p o](if o(max(o p 1)0)0))0(map{\U +\D -}%2)))) Maps 2nd argument U to +, D to - and others to nil. Reducing function runs (operand position 1) with non-null operand and 0 otherwise. Takes values until we are higher than the 1st input argument and counts how many we've got. Mathematica, 67 bytes (p=i=0;While[p<#,p=Switch[#2[[++i]],"U",p+1,"D",1~Max~p-1,_,0]];i)& Unnamed functions of two arguments, a positive integer and a list of characters, that returns a positive integer. A more straightforward While implementation than the other Mathematica entries, that manages to result in a more competetive length.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23170463740825653, "perplexity": 5751.318096067588}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250592261.1/warc/CC-MAIN-20200118052321-20200118080321-00018.warc.gz"}
https://www.physicsforums.com/threads/riemann-curvature-tensor-derivation.57670/	# Riemann curvature tensor derivation 1. Dec 23, 2004 ### weio Hey, when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field $$V$$, ie like this :- $$[\bigtriangledown_a, \bigtriangledown_b]$$ = $$\bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a$$ = $$V;_a_b - V;_b_a$$ But why does this difference of antisymmtery give us the Riemman tensor? thanks 2. Dec 24, 2004 ### Rob Woodside In addition to the commutator of the covariant derivatives, you need the commutator of the basis vectors too. Ignore torsion. Think of your covariant derivative as a change along your basis. In a coordinate basis (defined by vanishing basis commutators) two different basis vectors span a plane. Think of a small quadrilateral spanned by the two basis vectors. When the vector V is carried around this quadrilateral your commutator of covariant derivatives gives the change in V. It's length can't change, but its direction does. So with R the full Riemann curvature: [grada , gradb] V = R(.,V,a,b) . Riemann set up his geometry so it would look flat in the small. However, he was amazed that this difference resulting from taking a vector to nearby points could be described by an object (the full curvature tensor) that lived solely at the base point. This made him realize the importance of the curvature tensor and gave substance to his geometry. 3. Dec 24, 2004 ### weio Hey So far this is how I understand it, though I know I could be very wrong. If you have two geodesics parallel to each other, with tangents $$V$$ and $$V'$$ , in which the coordinate $$x^\alpha$$ point along both geodesics. There is some connecting vector $$w^\alpha$$ between them. Let the affine parameter on the geodesics be $$\lambda$$ Riemman tensor calculates the acceleration between these two geodesics. so you calculate the acceleration at some point A, A' on each geodesic , and subtract them. this gives you an expression telling how the components of $$w^\alpha$$ change. $$\frac{d^2w^\alpha} {d\lambda^2} = \frac{d^2x^\alpha} {d\lambda^2} \| A' - \frac {d^2x^\alpha} {d\lambda^2} \| A = - \Gamma^\alpha_0_0_\beta w^\beta$$ After that you calculate the full 2nd covariant derivative along V, ie , you get something like $$\bigtriangledown v \bigtriangledown v w^\alpha = (\Gamma^\alpha_\beta_0_0 - \Gamma^\alpha_0_0,\beta) w^\beta$$ $$= R^a_0_0\beta w^\beta$$ $$= R^a_u_v_\beta V^u V^v w^\beta$$ That's where the tensor arises. so basically it's a difference in acceleration as geodesics don't maintain their seperation in curved space. 4. Dec 24, 2004 ### Rob Woodside Yes it arises there and in many other places, including the one you asked about and that I told you about. 5. Dec 27, 2004 ### weio Thanks! I understand the derivation now. I found a simple one which fully explains it. for the curious, here is the link :- http://www.anasoft.co.uk/physics/gr/reimann/reimann.html [Broken] weio Last edited by a moderator: May 1, 2017	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9111636281013489, "perplexity": 732.340359913456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511203.16/warc/CC-MAIN-20181017153433-20181017174933-00430.warc.gz"}
https://wiki.q-researchsoftware.com/wiki/T-Test_of_a_Probability_%25	# T-Test of a Probability % Where $\displaystyle{ \hat{a} }$ is a probability % from a ranking question, $\displaystyle{ \mu }$ is the mean probability %, $\displaystyle{ n }$ is the effective number of observations (note that this is different to the effective sample size where repeated observations exist for each respondent) and $\displaystyle{ se_{a} }$ is the standard error of $\displaystyle{ \hat{a} }$, the test statistic is: $\displaystyle{ t=\frac{\hat{a}-\mu}{se_{a}} }$, $\displaystyle{ p = 2\Pr(t_{n-k+1} \ge \|t\|) }$, $\displaystyle{ k }$ is the number of alternatives.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.985694169998169, "perplexity": 445.0607422589567}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711162.52/warc/CC-MAIN-20221207121241-20221207151241-00509.warc.gz"}
http://www.zentralblatt-math.org/zmath/en/search/?q=an:1056.60029	Language: Search: Contact Zentralblatt MATH has released its new interface! For an improved author identification, see the new author database of ZBMATH. # Simple Search Query: Enter a query and click »Search«... Format: Display: entries per page entries Zbl 1056.60029 Bendikov, A.; Saloff-Coste, L. On the sample paths of diagonal Brownian motions on the infinite dimensional torus. (English) [J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 2, 227-254 (2004). ISSN 0246-0203 Let $T=R/2\pi Z$ be the circle group and $T^\infty=\prod_1^\infty T_i$ be the countable product of circles $T_i$. The group $T^\infty$ is equipped with the product topology and its normalized Haar measure $\mu$. Let $\cal C$ be the set of all smooth functions on $T^\infty$ which depend only on a finite number of coordinates. On the circle $T$ denote by $\nu_t$ the standard heat kernel measure associated to the infinitesimal generator $(\frac d{dx})^2$. The convolution semigroup $(\nu_t)_{t>0}$ is associated with a stochastic process $\xi=(\xi_t)_{t\ge0}$ which is simply Brownian motion runned at twice the usual speed in classic probabilistic notation and wrapped around the circle. For any fixed sequence ${\bold a}=(a_1,\ldots)$ of positive numbers let us consider the product measures $\mu_t=\mu_t^{\bold a}=\bigotimes_1^\infty\nu_{a_it}$. The family $(\mu_t)_{t>0}$ forms a convolution semigroup of measures on $T^\infty$ and $\mu_t$ is the marginal at time $t$ of a diffusion process $X=X^{\bold a}=(X_t)_{t\ge0}$ which is simply the product of independent circle Brownian motions $X^i=(X^i_t)_{t\ge0}$ where $X^i_t=\xi_{a_it}$. The intrinsic distance is defined by $$d(x,y)=d^{\bold a}(x,y)= \sup\left\{f(x)-f(y):f\in{\cal C},\ \sum_1^\infty a_i \vert \partial_if \vert ^2\le1\right\} \text{ and } d(x)=d^{\bold a}(x)=d^{\bold a}(e,x),$$ where $e=(0,0,\ldots)$ is the neutral element in $T^\infty$. $d$ is continuous and defines the topology of $T^\infty$ if and only if $\sum_1^\infty \frac 1{a_i}<\infty$. The last condition is assumed to hold throughout the paper under review. Under this condition for any $t>0$ the measure $\mu_t=\mu_t^{\bold a}$ is absolutely continuous with respect to the Haar measure $\mu$ and admits a continuous density $\mu_t^{\bold a}(x)$ given by $\mu_t^{\bold a}(x)=\prod_1^\infty \nu_{a_it}(x_i)$. Given a sequence ${\bold a}=(a_i)$ of positive numbers define $N(s)= N^{\bold a}(s)=\#\{i: a_i\le s\}$ and for a given function $f:(0, \infty)\to(0,\infty)$ define the transform $f^{\#}$ by $f^{\#}(z)= \int_0^z f(x)\,\frac{dx}{x}$. The main result of the paper is Theorem 4.4. Let ${\bold a}=(a_i)$ be a sequence of positive numbers such that $N=N^{\bold a}$ is slowly varying. Then $\log\mu_t(e)\sim(1/2)N^{\#}(1/t)$ as $t$ tends to $0$ and the sample paths of the process $X^{\bold a}$ have the following properties: (1) We always have $P_e$-almost surely $\liminf_{t\to 0} (d(X_t)/\sqrt{tN(1/t)})<\infty$. (2) If $N(s)=o(\log s)$ at infinity, then $P_e$-almost surely $$\limsup_{t\to 0} \frac {d(X_t)} {\sqrt{4t\log\log 1/t}}=1,\qquad \lim_{\varepsilon\to 0}\sup_{0<s<t \le1,\,t-s\le\varepsilon} \frac {d(X_s,X_t)} {\sqrt{4(t-2) \log(1/(t-s))}}=1$$ and $$\liminf_{t\to 0} \frac{d(X_t)} {\sqrt{4t\log\log 1/t}}=0.$$ (3) If $N(s)=o(\log s)$ and $\log\log s=O(N(s))$ at infinity, then $P_e$-almost surely $$0<\liminf_{t\to 0} \frac {d(X_t)} {\sqrt{tN(1/t)}}\le \limsup_{t\to 0} \frac {d(X_t)} {\sqrt {tN(1/t)}} <\infty,$$ and $$\lim_{\varepsilon\to 0}\sup_{0<s<t\le1, \,t-s \le\varepsilon} \frac{d(X_s,X_t)} {\sqrt{4(t-s)\log(1/(t-s))}}=1.$$ (4) If $\log\log s=O(N(s))$ at infinity, then $P_e$-almost surely $$0<\liminf_{t\to 0} \frac{d(X_t)} {\sqrt{tN(1/t)}} \le\limsup_{t\to 0} \frac{d(X_t)} {\sqrt{tN(1/t)}}<\infty.$$ (5) If $\log s=O(N(s))$ at infinity, then $P_e$-almost surely $$0< \lim_{\varepsilon\to 0}\sup_{0<s<t\le1,\,t-s\le \varepsilon} \frac{d(X_s,X_t)} {\sqrt{4(t-s)\log(1/(t-s))}}<\infty.$$ The authors note that the different cases in this theorem are not exclusive. Broadly speaking for a slowly varying $N$ there are three cases to consider: (a) If $N$ is smaller than $\log\log$, then we obtain a classical Lévy-Khinchin law of iterated logarithm $$\limsup_{t\to 0} \frac {d(X_t)} {\sqrt{4t\log\log 1/t}}=1$$ and a classical Lévy modulus of continuity $$\lim_{\varepsilon \to 0}\sup_{0<s<t\le1,\,t-s\le \varepsilon} \frac{d(X_s,X_t)} {\sqrt{4(t-s)\log(1/(t-s))}}=1.$$ (b) If $N$ is larger than $\log \log$ but smaller than $\log$, then we still have a classical Lévy modulus of continuity, but the Lévy-Khinchin-type result is not classical any more ($d(X_t)$ is now controlled by the function $\sqrt{tN(1/t)})$. (c) If $N$ is larger than $\log$, but still slowly varying, then all regularity behaviors are controlled by the function $\sqrt{tN(1/t)}$. [Vakhtang V. Kvaratskhelia (Tbilisi)] MSC 2000: *60G17 Sample path properties 60B15 Probability measures on groups 60J60 Diffusion processes Keywords: sample paths; modulus of continuity; diagonal Brownian motion; infinite-dimensional torus; intrinsic distance; law of iterated logarithm Highlights Master Server	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9858067631721497, "perplexity": 165.82917427700434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705318091/warc/CC-MAIN-20130516115518-00018-ip-10-60-113-184.ec2.internal.warc.gz"}
https://blog.federico.codes/posts/parens/	(some (context)) In the early 60s, computer scientist John McCarthy developed a programming system called LISP. This system defined this new notion of syntax called: S-expression or sexpr, for short. If you have never written in a LISP, this is what a sexpr looks like: (function param1 param2) On the left-most side of the parenthesis, we have the function to apply, and the rest are its arguments. Its simple, concise, and practical. One question arises: how do we do arithmetic? Simple: (+ 1 2) evaluates to: 3 You can also nest expressions together, and create bigger expressions, like: (* (- 14 5) (+ 4 6 3)) You get the idea… What is an sexpr, exactly? A sexpr is just an n-ary tree, where the leaves are atoms, and the nodes that branch are other sexprs. An atom is almost like a primitive type, except it also includes symbols, bound variables and some other oddities specific to each language Don’t believe that (+ (* 2 3) 7) is just a tree? More precisely, you could define an S-expression using algebraic data types as: 1 2 3 type sexp = \| Atom of string \| SList of sexp list LISP, the family LISP isn’t only a language, it’s a family of languages. Pretty much, every language that uses parenthesized prefix notation is considered a LISP. This is why I don’t say “in LISP” but rather “in a LISP”. Modern LISPs include: Racket, Scheme, Clojure and Common Lisp. “This is hideous, how can you like it so much?” Truth to be told, I didn’t at first. My first experience with a LISP was with a newer dialect, called Racket. In my freshmen year at Northeastern University I took the famous Fundies 1 course, where we read through the HtDP book and learned how to design programs, functionally, in the language. I hated the first few weeks. The language we used constrained me too much, it didn’t show me its shiny side and didn’t let me play with its internals. That all changed when I discovered that sexprs are not only part of the grammar, they are part of the data. That meant that an AST can be a sexpr, and that AST had sexprs with sexprs. That meant I could write a LISP interpreted by a LISP, interpreted by a LISP, interpreted by a LISP … That, for me, was mind-blowing and my passion for PL emerged. Macros Modern LISPs have this notion of “macros”, where you can write pieces of code that get cut and glued together with expressions and symbols. These macros make the code more concise and abstract, and give the programmer more flexibility over the language. This is very common amongst LISPs, in fact, in Racket, the boolean or and and operations aren’t functions or primitives, those are macros (for short-circuiting reasons I believe). You adapt the language to the problem, not the problem to the language Usually, programmers tend to program around the language they are using. If you are writing in Java, you are going to see a lot of SingletonAbstractFactoryStrategyHelloWorld situations. If you are writing in Rust (I love Rust, please don’t come after me) you will often have Box<(dyn std::error::Error, Arc<RwLock<IJustWantedConcurrency>>)> moments. Meanwhile, LISP code all look different, this is because its programmer didn’t adapt the problem to the language, they adapted the language to the problem. An Example Let’s take finite-state machines as an example. With finite-state machines, you can create state in a purely functional language, without using any mutation or side effects. Let’s say I want to simulate traffic lights with a finite state automata, the state should become green after being red, yellow after being green, and red after yellow, repeat… My code in Racket will roughly look like this: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 (define (traffic-state tape) (local ([define (start tape) (cond [(empty? tape) #true] [else (case (first tape) [("green") (middle (rest tape))] [else #false])])] [define (middle tape) (cond [(empty? tape) #false] [else (case (first tape) [("yellow") (end (rest tape))] [else #false])])] [define (end tape) (cond [(empty? tape) #false] [else (case (first tape) [("red") (start (rest tape))] [else #false])])] [define (process state tape) (cond [(string=? state "Start") (start tape)] [(string=? state "Middle") (middle tape)] [(string=? state "End") (end tape)])]) (process "Start" tape))) In essence, we have this function called tree-state that takes in an init state, either "Start", "Middle" or "End", and a tape with the history of the states the traffic light needs to go through. This function will produce #true if the states are well-formed (i.e. in the right order: ... -> "green" -> "yellow" -> "red" -> ... ending with "red") or #false if they aren’t. For example, (traffic-state '("green" "yellow" "red" "green" "yellow" "red")) produces #true, but (traffic-state '("green" "yellow" "green" "red")) or (traffic-state '("green" "yellow" "red" "green")) produces #false. If we wanted to adapt this state machine to another problem or add another case, we would have to change a lot of things. This is where macros come into play. Let’s define a macro to help us (credits, PDF page 10): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 (define-syntax state-automata (syntax-rules (: ->) [(state-automata init-state (state-name : (state-case -> next-state) ...) ... final-state) (lambda (tape) (local ([define (state-name tape) (cond [(empty? tape) (equal? state-name final-state)] [else (case (first tape) [(state-case) (next-state (rest tape))] ... [else #false])])] ...) (init-state tape)))])) And, we redefine our traffic-state function as: 1 2 3 4 5 6 (define traffic-state/v2 (state-automata START (START : ("green" -> MIDDLE)) (MIDDLE : ("yellow" -> END)) (END : ("red" -> START)) START)) Much better! Interestingly, if we count the lines of our unabstracted function, we get 28 lines of code. Meanwhile, the macro and the newer function are only 23 lines of code combined. laughs uncontrollably while staring at Java’s abstract classes The syntax of our state-automata macro is roughly: 1 2 3 4 (state-automata initial-state (state-name : (case-name -> state-name) ...) ... end-statisfied-state) This is all thanks to the power of S-expressions, they let us match and substitute nodes in the AST with ease and granular control. Macros are not only part of LISPs, other languages have them as well, but they are not as advanced. For example, here I have a macro in C that will produce the size of an array given the array and the type: 1 2 3 4 5 6 #define len(arr, type) (sizeof(arr) / sizeof(type)) int main() { int arr[3] = {1, 2, 3}; return len(arr, int); } I have picked this example because types in C are not values, yet you can pass them into this macro. How C handles macros is very cave-man-like: when this macro is reached by the pre-processor, the raw source code gets pasted, nothing more nothing less. Let’s check out a more “advanced” language, Rust. In Rust, we can define some pretty cool macros, even recursive ones. For example, here is a linked-list implementation that has a macro for initialization that takes in variadic parameters (with list implementations omitted for conciseness): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 #[macro_export] macro_rules! list { // it's recursive!!! () => { // base case Empty::new() }; // reads variadic args like a cons list ( $first:expr$( , $rest:expr )* ) => {{ Cons::new($first, Box::new(list!($($rest ),))) }}; } pub trait List { / omitted */ } struct Empty; impl Empty { fn new() -> Self { Empty } } struct Cons { first: T, rest: Box>, } impl Cons { pub fn new(first: T, rest: Box>) -> Self { Self { first, rest } } } #[cfg(test)] mod tests { #[test] fn it_works() { let l123 = Cons::new( // ughh.... this is ugly!!!! 1, Box::new(Cons::new(2, Box::new(Cons::new(3, Box::new(Empty::new()))))), ); let l123_macro = list!(1, 2, 3); // calling the macro assert_eq!(l123_macro, l123); // lets just imagine List derives PartialEQ... } } Here is another Rust example where we reduce code duplication by using macros for trait implementations (snippet from SxLang’s source code): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 /// Defines a trait for a tag, which allows the tag to be wrapped into another tag. pub trait TagWrappable { type WrappedAST; /// Gets the tag wrapped into this tag. fn take_ast(self) -> Self::WrappedAST where Self: Sized; /// Wraps the given ast into this tag. fn wrap(ast: Self::WrappedAST) -> Self; /// Wraps the given ast node with a previous wrappable tag, into this tag fn change_wrap>(self) -> IntoWrap where Self: Sized; } /// Defines a tag for an AST node, which symbolizes that the node was uniquely tagged. pub struct Tagged(pub ASTNode); /// Defines a tag for an AST node, which symbolizes that the node was well-formed, thus the node is /// well-formed by the definition of the language. pub struct WellFormed(pub ASTNode); /// Defines a tag for an AST node, which symbolizes that the node was typechecked, thus the node is /// type safe by the definition of the type system. pub struct TypeChecked(pub ASTNode); /// Macro to implement tag wrappable for a given type. macro_rules! impl_tagwrappable { ($t:ident) => { impl TagWrappable for$t { type WrappedAST = ASTNode; fn wrap(ast: Self::WrappedAST) -> Self { $t(ast) } fn change_wrap>( self, ) -> IntoWrap { IntoWrap::wrap(self.take_ast()) } fn take_ast(self) -> Self::WrappedAST { self.0 } } }; } // these macros implement the trait for all three structs impl_tagwrappable!(TypeChecked); impl_tagwrappable!(WellFormed); impl_tagwrappable!(Tagged); Cool! This gets close to a LISP, but not quite. Rust macros can get pretty painful to write, as you might have noticed. Additionally, Rust has some problems with blending together the macro system and the type system, as generics get eagerly type-checked, but macros are lazily expanded. This is why we were able to pull off the $t<D> trick in the example above. We wouldn’t be able to change $t<D> to just $t and expand the macro with impl_tagwrappable!(TypeChecked<D>), as the generic parameter D would need to be evaluated first (the syntax does not allow you to do this anyway). Programming Language Development Writing macros is like writing mini programming languages, but why do mini when you can do big? sexprs are perfect for creating programming languages of any scale from scratch. The reason is simple: writing the parser is the worst part of writing a language, especially if you are just making a toy language. With sexprs, you can just make a trivial recursive function that transforms s-expression concrete syntax into an abstract syntax tree. Sure, you could call that a parser, but it’s not the same thing as using lex and yacc. Here is one example “parser” in Racket for a sexpr-based grammar to an AST (some functions omitted): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 (define (parse-type sexp) (match sexp ['number (numType)] ['bool (boolType)] [(,args ... -> ,ret) (funType (map parse-type args) (parse-type ret))] [else (error 'parse (string-append (symbol->string sexp) " is not a parsable type"))])) (define (parse sexp) (match sexp ['true (boolE #t)] ['false (boolE #f)] [n #:when (number? n) (numE n)] [id-sym #:when (symbol? id-sym) (idE id-sym)] [(,op ,l ,r) #:when (binop-symbol? op) (binopE (binop-table op) (parse l) (parse r))] [(fun ([,params : ,param-types] ...) : ,ret-type ,body) (if (symbol-duplicates? params) (error 'parse "duplicate id in fun params") (funE params (map parse-type param-types) (parse body) (parse-type ret-type)))] [(loc ([,bound-ids : ,ids-types ,named-exprs] ...) : ,ret-type ,body) (if (symbol-duplicates? bound-ids) (error 'parse "duplicate id in loc bound ids") (appE (funE bound-ids (map parse-type ids-types) (parse body) (parse-type ret-type)) (map parse named-exprs)))] [(if ,cond-expr ,true-body ,false-body) (ifE (parse cond-expr) (parse true-body) (parse false-body))] [(rec ([,bound-ids : ,ids-types ,fun-exprs] ...) : ,ret-type ,body) (if (symbol-duplicates? bound-ids) (error 'parse "duplicate id in rec bound ids") (recE (map (lambda (id expr) (recBind id (parse expr))) bound-ids fun-exprs) (map parse-type ids-types) (parse body) (parse-type ret-type)))] [else (error 'parse (string-append (symbol->string sexp) " is not a parsable expression"))])) And here is a parser for position-annotated S-Expression in Rust (some parts omitted, parse_primitive is straight-forward): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 impl ASTParser { pub fn parse_from_sexpr<'a>( input: &'a Sexpr, ) -> Result>, ParsingError<'a>> { match input { Sexpr::Atom(a, _) => Self::parse_primitive(a), Sexpr::List(list, span) => Self::parse_list(list, span), } } fn parse_list<'a>( input: &'a [Sexpr], outer_span: &'a Span<'a>, ) -> Result>, ParsingError<'a>> { match input { [Sexpr::Atom(Atom::Symbol(letstr, _), _), Sexpr::List(letbinds, _), expr] if let ("let", Ok(result_binds)) = (letstr.as_ref(), Self::parse_letbinds(letbinds)) => { Ok(ASTNode::Let(result_binds, Box::new(Self::parse_from_sexpr(expr)?), outer_span.clone())) } [Sexpr::Atom(Atom::Symbol(ref s, _), _), expr] if let Ok(op) = UnaryOp::from_str(s) => { Ok(ASTNode::UnaryOp( op, Box::new(Self::parse_from_sexpr(expr)?), outer_span.clone(), )) } [Sexpr::Atom(Atom::Symbol(ref s, _), _), e1, e2] if let Ok(op) = BinaryOp::from_str(s) => { Ok(ASTNode::BinaryOp( op, Box::new(Self::parse_from_sexpr(e1)?), Box::new(Self::parse_from_sexpr(e2)?), outer_span.clone(), )) } [Sexpr::Atom(Atom::Symbol(ref s, _), _), Sexpr::List(params, _), expr] if s == "fun" => { let mut parsed_params = Vec::new(); for param in params { if let Sexpr::Atom(Atom::Symbol(id, _), _) = param { parsed_params.push(id.to_string()); } else { return Err(ParsingError::InvalidSyntax( param.get_decorator().clone(), param.to_string(), Some("expected a parameter".to_string()), )); } } Ok(ASTNode::Function(parsed_params, Box::new(Self::parse_from_sexpr(expr)?), outer_span.clone())) } // else, must be a func call, or something bad [first, rest @ ..] => { let mut args = Vec::new(); for expr in rest { args.push(Self::parse_from_sexpr(expr)?); } Ok(ASTNode::Call( Box::new(Self::parse_from_sexpr(first)?), args, outer_span.clone(), )) }, [] => Err(ParsingError::InvalidSyntax( outer_span.clone(), "()".to_string(), Some("expected an expression".to_string()), )), } } } Conclusion Overall, I think that S-expressions are a great tool for many needs, PL or not PL, and everyone should know how and when to use them. 1 2 3 4 [federico:~]\$ racket Welcome to Racket v8.5 [cs]. > (better? 'parens) "You decide." Built with Hugo Theme Stack designed by Jimmy	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4590701162815094, "perplexity": 7451.073943493162}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945472.93/warc/CC-MAIN-20230326111045-20230326141045-00178.warc.gz"}
http://www.php.net/manual/pt_BR/language.namespaces.importing.php	PHP 7.1.0 Released Using namespaces: Aliasing/Importing (PHP 5 >= 5.3.0, PHP 7) The ability to refer to an external fully qualified name with an alias, or importing, is an important feature of namespaces. This is similar to the ability of unix-based filesystems to create symbolic links to a file or to a directory. All versions of PHP that support namespaces support three kinds of aliasing or importing: aliasing a class name, aliasing an interface name, and aliasing a namespace name. PHP 5.6+ also allows aliasing or importing function and constant names. In PHP, aliasing is accomplished with the use operator. Here is an example showing all 5 kinds of importing: Exemplo #1 importing/aliasing with the use operator <?php namespace foo; use My\Full\Classname as Another; // this is the same as use My\Full\NSname as NSname use My\Full\NSname; // importing a global class use ArrayObject; // importing a function (PHP 5.6+) use function My\Full\functionName; // aliasing a function (PHP 5.6+) use function My\Full\functionName as func; // importing a constant (PHP 5.6+) use const My\Full\CONSTANT; $obj = new namespace\Another// instantiates object of class foo\Another$obj = new Another// instantiates object of class My\Full\Classname NSname\subns\func(); // calls function My\Full\NSname\subns\func $a = new ArrayObject(array(1)); // instantiates object of class ArrayObject // without the "use ArrayObject" we would instantiate an object of class foo\ArrayObject func(); // calls function My\Full\functionName echo CONSTANT// echoes the value of My\Full\CONSTANT ?> Note that for namespaced names (fully qualified namespace names containing namespace separator, such as Foo\Bar as opposed to global names that do not, such as FooBar), the leading backslash is unnecessary and not recommended, as import names must be fully qualified, and are not processed relative to the current namespace. PHP additionally supports a convenience shortcut to place multiple use statements on the same line Exemplo #2 importing/aliasing with the use operator, multiple use statements combined <?php use My\Full\Classname as AnotherMy\Full\NSname;$obj = new Another// instantiates object of class My\Full\Classname NSname\subns\func(); // calls function My\Full\NSname\subns\func ?> Importing is performed at compile-time, and so does not affect dynamic class, function or constant names. Exemplo #3 Importing and dynamic names <?php use My\Full\Classname as AnotherMy\Full\NSname; $obj = new Another// instantiates object of class My\Full\Classname$a 'Another'; $obj = new$a; // instantiates object of class Another ?> In addition, importing only affects unqualified and qualified names. Fully qualified names are absolute, and unaffected by imports. Exemplo #4 Importing and fully qualified names <?php use My\Full\Classname as AnotherMy\Full\NSname; $obj = new Another// instantiates object of class My\Full\Classname$obj = new \Another// instantiates object of class Another $obj = new Another\thing// instantiates object of class My\Full\Classname\thing$obj = new \Another\thing// instantiates object of class Another\thing ?> Scoping rules for importing The use keyword must be declared in the outermost scope of a file (the global scope) or inside namespace declarations. This is because the importing is done at compile time and not runtime, so it cannot be block scoped. The following example will show an illegal use of the use keyword: Exemplo #5 Illegal importing rule <?php namespace Languages; function toGreenlandic() { use Languages\Danish; // ... } ?> Nota: Importing rules are per file basis, meaning included files will NOT inherit the parent file's importing rules. Group use declarations From PHP 7.0 onwards, classes, functions and constants being imported from the same namespace can be grouped together in a single use statement. <?php // Pre PHP 7 code use some\namespace\ClassA; use some\namespace\ClassB; use some\namespace\ClassC as C; use function some\namespace\fn_a; use function some\namespace\fn_b; use function some\namespace\fn_c; use const some\namespace\ConstA; use const some\namespace\ConstB; use const some\namespace\ConstC; // PHP 7+ code use some\namespace\{ClassAClassBClassC as C}; use function some\namespace\{fn_afn_bfn_c}; use const some\namespace\{ConstAConstBConstC}; User Contributed Notes 17 notes 41 k at webnfo dot com 3 years ago Note that you can not alias global namespace: use \ as test; echo test\strlen(''); won't work. 23 anon 2 years ago The <?php use ?> statement does not load the class file. You have to do this with the <?php require ?> statement or by using an autoload function. 19 cl 3 years ago Something that is not immediately obvious, particular with PHP 5.3, is that namespace resolutions within an import are not resolved recursively. i.e.: if you alias an import and then use that alias in another import then this latter import will not be fully resolved with the former import. For example: use \Controllers as C; use C\First; use C\Last; Both the First and Last namespaces are NOT resolved as \Controllers\First or \Controllers\Last as one might intend. kelerest123 at gmail dot com 1 year ago For the fifth example (example #5): When in block scope, it is not an illegal use of use keyword, because it is used for sharing things with traits. 20 x at d dot a dot r dot k dot REMOVEDOTSANDTHIS dot gray dot org 3 years ago You are allowed to "use" the same resource multiple times as long as it is imported under a different alias at each invocation. For example: <?php use Lend; use Lend\l1; use Lend\l1 as l3; use Lend\l2; use Lend\l1\Keller; use Lend\l1\Keller as Stellar; use Lend\l1\Keller as Zellar; use Lend\l2\Keller as Dellar; ... ?> In the above example, "Keller", "Stellar", and "Zellar" are all references to "\Lend\l1\Keller", as are "Lend\l1\Keller", "l1\Keller", and "l3\Keller". me at ruslanbes dot com 8 months ago Note the code use ns1\c1 may refer to importing class c1 from namespace ns1 as well as importing whole namespace ns1\c1 or even import both of them in one line. Example: <?php namespace ns1; class c1{} namespace ns1\c1; class c11{} namespace main; use ns1\c1; $c1 = new c1();$c11 = new c1\c11(); var_dump($c1); // object(ns1\c1)#1 (0) { } var_dump($c11); // object(ns1\c1\c11)#2 (0) { } ultimater at gmail dot com 2 months ago Note that "use" importing/aliasing only applies to the current namespace block. <?php namespace SuperCoolLibrary { class Meta { static public function getVersion() { return '2.7.1'; } } } namespace { use SuperCoolLibrary\Meta; echo Meta::getVersion();//outputs 2.7.1 } namespace { echo Meta::getVersion();//fatal error } ?> To get the expected behavior, you'd use: class_alias('SuperCoolLibrary\Meta','Meta'); 19 c dot 1 at smithies dot org 5 years ago If you are testing your code at the CLI, note that namespace aliases do not work! (Before I go on, all the backslashes in this example are changed to percent signs because I cannot get sensible results to display in the posting preview otherwise. Please mentally translate all percent signs henceforth as backslashes.) Suppose you have a class you want to test in myclass.php: <?php namespace my%space; class myclass { // ... } ?> and you then go into the CLI to test it. You would like to think that this would work, as you type it line by line: require 'myclass.php'; use my%space%myclass; // should set 'myclass' as alias for 'my%space%myclass' $x = new myclass; // FATAL ERROR I believe that this is because aliases are only resolved at compile time, whereas the CLI simply evaluates statements; so use statements are ineffective in the CLI. If you put your test code into test.php: <?php require 'myclass.php'; use my%space%myclass;$x = new myclass; //... ?> it will work fine. I hope this reduces the number of prematurely bald people. Anonymous 3 years ago The last example on this page shows a possibly incorrect attempt of aliasing, but it is totally correct to import a trait \Languages\Languages\Danish. dominic_mayers at yahoo dot com 2 months ago To clarify the distinction between inserting a trait in a class and importing a trait in a namespace, here is an example where we first import and then insert a trait. <?php namespace ns1; trait T { static $a = "In T"; } namespace ns2; use ns1\T; // Importing the name of trait ns1\T in the namespace ns2 class C { use T; // Inserting trait T in the class C, making use of the imported name. namespace main; use ns2\C; echo C::$a; // In T; dominic_mayers at yahoo dot com 2 months ago The keyword "use" has been recycled for three distinct applications: 1- to import/alias classes, traits, constants, etc. in namespaces, 2- to insert traits in classes, 3- to inherit variables in closures. This page is only about the first application: importing/aliasing. Traits can be inserted in classes, but this is different from importing a trait in a namespace, which cannot be done in a block scope, as pointed out in example 5. This can be confusing, especially since all searches for the keyword "use" are directed to the documentation here on importing/aliasing. thinice at gmail.com 6 years ago Because imports happen at compile time, there's no polymorphism potential by embedding the use keyword in a conditonal. e.g.: <?php if ($objType == 'canine') { use Animal\Canine as Beast; } if ($objType == 'bovine') { use Animal\Bovine as Beast; } $oBeast = new Beast;$oBeast->feed(); ?> -1 samuel dot roze at gmail dot com 4 years ago (All the backslashes in namespaces are slashes because I can't figure out how to post backslashes here.) You can have the same "use" for a class and a namespace. For example, if you have these files: <?php // foo/bar.php namespace foo; class bar { public function __toString () { return 'foo\bar\__toString()'; } } ?> <?php // foo/bar/MyClass.php namespace foo/bar; class MyClass { public function __toString () { return 'foo\bar\MyClass\__toString()'; } } ?> In another namespace, you can do: <?php namespace another; require_once 'foo/bar.php'; require_once 'foo/bar/MyClass.php'; use foo/bar; $bar = new bar(); echo$bar."\n"; $class = new bar/MyClass(); echo$class."\n"; ?> And it will makes the following output: foo\bar\__toString() foo\bar\MyClass\__toString() -3 nsdhami at live dot jp 6 years ago The "use" keyword can not be declared inside the function or method. It should be declared as global, after the "namespace" as: <?php namespace mydir; // works perfectly use mydir/subdir/Class1 as Class1; function fun1() { // Parse error: syntax error, unexpected T_USE use mydir/subdir/Class1 as Class1; } class Class2 { public function fun2() { // Parse error: syntax error, unexpected T_USE use mydir/subdir/Class1 as Class1; } } ?> -4 sernuzh at gmail dot com 1 year ago You'll get here the Fatal error: Cannot declare class others\name because the name is already in use So you can't get two classes <name> inside one namespace <?php namespace my { class name { public function __construct(){ echo 'my_namespace_object'; } } } namespace others{ use my\name; class name { public function __construct(){ echo 'others_namespace_object'; } } $newObject = new name(); } ?> -21 Jan Tvrdk 5 years ago Importing and aliasing an interface name is also supported. -25 Dr. Gianluigi "Zane" Zanettini 1 year ago I was attempting to use something like this: <?php use$my_variable_namespace ?> This is not supported. I did this instead: <?php if(..) use My\First\Namespace; else use My\Other\Namespace; ?>	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6534278392791748, "perplexity": 3832.835895876549}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541517.94/warc/CC-MAIN-20161202170901-00490-ip-10-31-129-80.ec2.internal.warc.gz"}
https://www.math.ku.dk/english/calendar/events/algtopseminar08062020/	# Algebra/Topology Seminar Speaker: Christian Dahlhausen Title: Continuous K-theory and cohomology of rigid spaces Abstract: Continuous K-theory is a derivative of algebraic K-theory for rigid analytic spaces. In this talk, I will prove three properties for the negative continuous K-theory of a rigid space of dimension d: Weibel vanishing in degrees smaller than -d, analytic homotopy invariance in degrees less or equal -d, and describing the edge group in degree -d as the cohomology in degree d with integral coefficients. These properties are analoguous to correponding properties of negative algebraic K-theory and the proof works by reduction to the algebraic case. The key ingredient is a comparison of Zariski-cohomology and rh-cohomology for certain (relative) Zariski-Riemann spaces. The content of this talk is based on my PhD thesis advised by Moritz Kerz and Georg Tamme, a condensed version can be found on the arXiv (1910.10437).	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8259079456329346, "perplexity": 1029.8728724468292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198868.29/warc/CC-MAIN-20200920223634-20200921013634-00180.warc.gz"}
https://www.intechopen.com/books/irrigation-in-agroecosystems/water-footprint-differences-of-producing-cultivars-of-selected-crops-in-new-zealand	Open access peer-reviewed chapter # Water Footprint Differences of Producing Cultivars of Selected Crops in New Zealand By Isaac R. Fandika, Peter D. Kemp, James P. Millner and Davie Horne Submitted: January 18th 2018Reviewed: April 23rd 2018Published: January 23rd 2019 DOI: 10.5772/intechopen.77509 ## Abstract Water footprint (WF) is a measure of the amount of water used to produce goods and services. It is a very important concept on indicating how much water can be consumed to complete a process of growing or processing a product at a particular location. However, paucity of water footprint information in countries facing increased competition for water resources between industries limits market access and profit optimization. Water footprint differences of producing selected cultivars of potato, oca and pumpkin squash were determined under irrigation and rain-fed regimes. All crop husbandry practices were followed in potato, oca (3.3 plants m−2) and pumpkin squash (2.2 plants m−2). Water footprint was determined as the ratio of volume of evapotranspiration for irrigated and rain-fed crops plus grey water to total yield. The consumptive water use for the rain-fed crop was 75, 65 and 69% of the irrigated oca, potato and pumpkin squash, respectively, with high water consumption in heritage cultivars. The water footprint was low in pumpkin squash and highest in oca, while potato cultivars were intermediate. Irrigation reduced water footprint especially in crops more responsive to irrigation. Farmers should focus on improving the harvest index and irrigation to reduce water footprint. ### Keywords • water footprint • irrigation • potato • oca • pumpkin squash ## 1. Introduction The agricultural industry in New Zealand consumes 77% of the freshwater resources [1]. Climate change alongside population and urbanisation has broaden this demand by increasing water utilisation per capita [2]. Water consumption and pollution associated with agriculture has created a great competition for water [3]. As of now groundwater withdrawal and rainwater evaporation, in addition to environmental pollution are accelerating [4]. Until the recent past, there has been little attention to how water is consumed and polluted in agriculture in New Zealand. As a result, the profitability of traditionally irrigated crops reduced [5]. Improved understanding of water footprint (WF) differences in cultivars can reduce the pressure on freshwater, while still maintaining their profits and sustaining the environment. This can be achieved if farmers can start using water sparingly under both modern and heritage crop cultivars [6]. Information on water footprint differences in selected heritage cultivars used by Maori for over 200 years is of significant importance because of their social and cultural value to the economy [7]. McFarlane stated that these heritage cultivars attract a niche market and provide a cultural economy [8]. For instance, the Taewa Maori potato and Kamokamo are a treasured heritage used to enforce land rights, values and sustainable development in New Zealand [9]. Lately, modern crop cultivars have made a significant advancement in productivity, above heritage cultivars. The increased interest in heritage cultivars is restricted by a lack of information on their water use. There is need of information on new ways to grow heritage or modern crops while leaving more water available for people, plants and animals. Idea of considering water use along supply chain can be well explained by the concept of water footprint (WF). ### 1.1. Definition and significance of water footprint Water footprint (m3 ton−1) is defined as the volume of water required to produce a given weight or volume of specific crop [10]. It is a multidimensional indicator showing water consumption volumes by source and polluted volumes by type of pollution where all components of total water footprint are specified geographically and temporally. This footprint is an important factor in future market access, water conservation and growing international trade in agriculture [11]. The study and literature on water footprint expose hidden uses of water resources in producing a crop product over a complete supply chain (producers to consumers). Discovery of such hidden links can form basis for the formulation of new strategies of water governance among growers and consumers. The knowledge of water footprint to final consumers, retailers, food industries and traders in water—intensive products can make them become agent of change in promoting sparing water use. Nevertheless, the water footprint of arable crops has not been sufficiently examined among standard and heritage crop cultivars in New Zealand. In this chapter, we discuss the water footprint differences of producing selected heritage and modern potato, oca and pumpkin squash cultivars grown under rain-fed and irrigated conditions, in New Zealand; and finally what the WF means in the context of the social-economic aspects of growers. ## 2. Method for assessing the process water footprint of growing selected crops ### 2.1. Site biophysical characteristics and crop management Water footprint study of the process of growing crops was conducted at Massey University’s Pasture and Crop Research Unit, Palmerston North, between November, 2009 and April, 2011. Massey University is located at a latitude of 40°22′ 54.02 S, longitude 175°36′ 22.80 E, and an altitude of 36 m a.s.l. The soil type is Manawatu sandy loam with Olsen P at 36 mg/L; K at 0.22 mg/100 g, available N at 106 kg ha−1 and anaerobically mineralised N kg−1 at 76.8 mg at the beginning of the experiment. Climatic data for the site is in Figure 1. The study crops were managed at both supplementary irrigation and rain-fed conditions. There were four cultivars of potato (Solanum tuberosum L., Solanum andigena Juz & Buk.), two of oca (Oxalis tuberosa Mol.) and two of pumpkin squash (Curcubita pepo Linn and Cucurbuta maxima Duchesne) in each water regime. Rainfall treatment measured green water (rain water) while supplementary irrigation measured both green and blue water footprint (water from river, sea or ocean or ground) [12]. The four-selected potato cultivars included two modern cultivars (Agria and Moonlight (S. tuberosum L.)) and two heritage cultivars (Moe Moe (S. tuberosum L.) and Tutaekuri (S. andigena Juz & Buk.)). The two selected pumpkin squash cultivars included buttercup squash, Ebisu (C. maxima Duchesne, a modern cultivar) and Kamokamo (C. pepo Linn, a heritage cultivar), while two unnamed oca cultivars with dark orange and scarlet coloured tubers were used. All crop husbandry practices were followed in potato, oca (3.3 plants m−2) and pumpkin squash (2.2 plants m−2). Potatoes and oca received 12 N:5.2 P:14 K:6 S + 2 Mg + 5 Ca, using 500 kg ha−1 Nitrophoska Blue TE at planting, followed by 100 kg N ha−1 of urea 21 days later. The pumpkin squash received 12 N:5.2 P:14 K:6 S + 2 Mg + 5 Ca, using 700 kg ha−1 Nitrophoska Blue TE at planting, followed by 66 kg N ha−1, when the vines started running. Pests and diseases were also controlled accordingly [13]. ### 2.2. Irrigation and crop water use measurement In order to measure the actual water use, a soil water balance was used to determine the soil moisture deficit (SMD) on a daily basis during the growth of the crops [14]. The potential evapotranspiration (ETp) in the soil water balance was computed using the FAO 56 Penman-Monteith method [15, 16]. The crop coefficient factors used in the computation were for potato, because this was the most sensitive crop to water use [17]. NIWA/Ag Research in Palmerston North provided daily weather data for running the soil water balance model. The soil water balance model helped to scheduling irrigation centering on refilling 25 mm of the soil moisture deficit when it reaches 30 mm. It was made sure that approximately half the readily available water was supplied. An equation of actual crop evapotranspiration (ETc) was used as in Eq. (1) [15]. Soil moisture was monitored using time-domain reflectometer (TDR) to determine soil moisture change (∆S) [13] and surface runoff (Ro) was negligible. ETc=P+IDpRo+∆SE1 Consumptive water use (CWU) for the entire growing cycle, for irrigation and rain-fed treatments, were referred to as blue and green components, respectively. The CWU was determined according to Hoekstra [10], as in Eq. (2), where ETcblueand ETcgreenis the accumulation of actual water use (evapotranspiration) over the complete growing cycle for irrigated and rain-fed crops, respectively. Factor of 10 was required to convert water depths of mm into volume in m3 ha−1 [10]. CWUblue+green=10×ETcblue+ETcgreenCWUgreen=10×ETgreenE2 ### 2.3. Determination of water footprint differences of cultivars of selected crops Water footprint (m3 t ha−1) was determined as the ratio of actual crop water use (m3 ha−1) to the total yield or total biomass yield (t ha−1) [10]. Total water footprint was the sum of blue, green and grey water footprint. Blue and green water footprint (m3 t ha−1) was a ratio of blue and green crop water use (mm), to the total yield or total biomass yield (t ha−1), respectively [18]. Grey water footprint (m3 t ha−1) was determined as a ratio of total volume of water (m3) required diluting nitrogen that reached the ground water, per ton of produce [19]. Grey water footprint was estimated by multiplying the leaching fraction by the nitrogen application (kg ha−1) and dividing the difference between the permissible limit and the natural concentration of nitrogen in the receiving water body. The study assumed a natural water nitrate concentration of 5.6 mg l−1 and the permissible limit of 11.3 mg l−1 [20]. Leaching fraction was assumed at 10% [18, 21]. This study compared the water footprint based on actual crop yield and crop water use, in order to remove the disparity of over-estimation, once hypothetical crop and crop water requirements are used [22, 23]. ### 2.4. Social-economic analysis of the selected crop cultivar An economic assessment of Taewa against modern potato varieties in relation to irrigation investments was done using the net present value (NPV) method. Net present value is an investment analysis also referred as a total of present value of a single project cashflow of the same unit [24]. In order to get NPV, fixed and annual operating costs and expected returns were estimated based on a 5-ha small scale irrigation using a Trail Travel Irrigator to obtain the economic implications of the system on crop production. The data in the study on marketable fresh tuber or marketable fruit yield were used to analyse the economics of Taewa and water footprint. Crop water use and total yield from the three crops were pooled, in order to determine their comparative water footprint differences. ## 3. Results ### 3.1. Crop water use and yield summary Total consumptive water use (blue plus green water) for oca, potato and pumpkin squash in rain-fed and irrigation ranged from 5061 to 6824, 3470 to 5685 and 2551 to 4132 m3 ha−1, respectively. Consumptive water use (m3 ha−1) was greatest in oca and lowest in pumpkin squash, while potatoes were intermediate, despite variation within cultivars. The modern and heritage crops differed in their relationship between their maximum water requirement and actual evapotranspiration, thus crop coefficient (kc) and maturity (Figure 2). Taewa and Kamokamo used more water compared to modern cultivars (Table 1). Green water was approximately 62, 65, 58 and 70% of consumptive water use, under irrigated modern potato, Taewa, pumpkin squash and oca, respectively. Blue water for oca and potato was 2000 m3 ha−1, while pumpkin squash received 1750 m3 ha−1, applied to meet at least 100% of the crop’s water requirement. Water regime/cultivarsPlanting dateHarvesting dateTotal yield (t ha−1)Total biomass (t ha−1)Consumptive water use (m3 ha−1)Grey water (m3 ha−1) Green waterBlue waterTotal CWU Irrigation Agria10-11-1017-05-1051.758.73326.620005326.6424.8 Moonlight10-11-1017-05-1059.476.63255.620005255.6424.8 Moemoe10-11-1017-05-1052.676.13685.220005685.2424.8 Tutaekuri10-11-1017-05-1027.654.73670.220005670.2424.8 Buttercup09-12-1029-03-1054.797.72325.817504075.8398.2 Kamokamo09-12-1031-03-1078.0149.12382.017504132.0398.2 Dark O10-11-1022-06-1023.255.84742.220006742.2424.8 Scarlet10-11-1022-06-1025.569.54824.220026824.2424.8 Rain-fed Agria10-11-1017-05-1034.043.33470.63470.6424.8 Moonlight10-11-1017-05-1039.752.13513.03513.0424.8 Moemoe10-11-1017-05-1040.160.03950.03950.0424.8 Tutaekuri10-11-1017-05-1030.052.83933.03933.0424.8 Buttercup09-12-1029-03-1047.489.62551.02551.0398.2 Kamokamo09-12-1031-031067.7142.72603.82603.8398.2 Dark O10-11-1022-06-1016.742.05094.25094.2424.8 Scarlet10-11-1022-06-1021.250.75061.05061.0424.8 Significance Cultivars<0.0001<0.0001<0.0001<0.0001<0.0001 Water regime<0.0001<0.0001<0.0001<0.0001<0.0001<0.0001 LSD0.05 Cultivar10.76.23 Water regime5.418.9 ### Table 1. Date of planting and harvesting, harvestable yield, total biomass yield and consumptive water use for heritage and modern potato, oca and pumpkin squash crop cultivars in New Zealand, 2010. Grey water also significantly differed between cultivars with the highest in potato and oca. An equivalency of diluting requirement to the grey water for the applied N in potato or oca and pumpkin squash was 425 and 398 m3 ha−1, respectively (Table 1). An increase in N rate application raised the grey water in potato and oca compared to pumpkin squash. The actual crop water use for rain-fed crop in oca, potato and pumpkin squash was 74.9, 65.1 and 69% of the irrigated crop, respectively (Table 1). The total consumptive water use (m3 ha−1) was greatest in oca and lowest in pumpkin squash, while potato was intermediate, despite variation within cultivars. Heritage crops (Maori potato, Kamokamo) used more water because of its long growing season. Differences in yields were observed to be influenced by water regime and crop cultivars among the eight selected crop cultivars. With exception of Tutaekuri, average yields continuously increased from rain-fed (16.7–67.7 t ha−1) to irrigated conditions (23.2–78 t ha−1). Kamokamo had the greatest yields while dark orange had the lowest yields under both water regimes. Average yields for other crops’ varieties such as Agria, Moonlight and Moe Moe were similar but greatly lower than Kamokamo. Out of the crop cultivars, oca varieties and Tutaekuri proved to have lowest yield levels. Agria, Moonlight and Moe Moe also demonstrated an ability of partitioning more dry matter to economic yields basing on its harvest index (HI). In summary, the heritage crop cultivars extremely partition more to biomass unlike most of the modern cultivars which partition more to economic yields (Table 1). ### 3.2. Water footprint differences of cultivars of selected heritage and modern crops #### 3.2.1. Blue, green and grey water footprint on total yield The green, blue and grey water footprint components varied with both crop cultivars and water regimes as presented in Tables 2 and 3 and Figure 2. The total water footprint of consumptive water use (blue plus green water footprint or pure green water footprint) of total yield ranges was high in irrigated field and low in rain-fed field (Table 2). Figure 1 evidently show that the blue water footprint in rain-fed crop was zero while the green water footprint of total yield and total biomass yield related to rain-fed environment were high compared to the green water footprint of the irrigated field. Water regime/cultivarGreen water footprint (m3 ton−1)Blue water footprint (m3 ton−1)Grey water footprint (m3 ton−1)Total water footprint (m3 ton−1) Irrigation Agria65.539.48.4113.3 Moonlight55.834.37.397.4 Moemoe70.138.08.1116.2 Tutaekuri139.876.216.2232.2 Buttercup42.832.27.382.3 Kamokamo33.824.85.764.3 Dark orange223.294.119.9337.3 Scarlet190.378.916.8285.9 Rain-fed Agria106.513.03119.5 Moonlight90.410.92101.3 Moemoe99.410.69111.1 Tutaekuri144.615.62160.2 Buttercup55.68.6864.3 Kamokamo44.36.7851.1 Dark orange331.827.67359.5 Scarlet244.820.55265.4 Significance Cultivarsp < 0.0001p < 0.0001p < 0.0001p < 0.0001 Water regimep < 0.0001p < 0.0001p < 0.001Ns LSD0.05 Cultivar44.310.74.1054.6 Water regime15.53.72.0227.3 ### Table 2. Total water footprint of heritage and modern potato, oca and pumpkin squash crop cultivars on total yield basis in New Zealand, 2010. Water regime/cultivarGreen water footprint (m3 ton−1)Blue water footprint (m3 ton−1)Grey water footprint (m3 ton−1)Total water footprint (m3 ton−1) Irrigation Agria57.534.67.399.4 Moonlight43.726.85.776.3 Moemoe48.826.55.680.9 Tutaekuri68.237.27.9113.2 Buttercup23.817.94.145.9 Kamokamo16.512.12.831.4 Dark orange94.639.98.5143.0 Scarlet71.429.66.3107.3 Rain-fed Agria82.910.293.1 Moonlight69.28.477.6 Moemoe66.57.173.6 Tutaekuri79.88.688.4 Buttercup30.24.734.9 Kamokamo19.73.022.7 Dark orange141.811.8153.6 Scarlet105.28.8114.0 Significance Cultivarsp < 0.0001p < 0.0001p < 0.0001p < 0.0001 Water regimep < 0.01p < 0.0001p < 0.01Ns LSD0.05 Cultivar25.575.082.3230.48 Water regime12.782.541.1615.24 ### Table 3. Total water footprint of heritage and modern potato, oca and pumpkin squash crop cultivars on total biomass basis in New Zealand, 2010. In the irrigated crops, the blue water footprint comprised 27–39% while the grey water footprint made up to 6–9% of the total water footprint of total yield (Figure 2). The total water footprint of consumptive water use increased with irrigation in Moe Moe, Tutaekuri, Ebisu, Kamokamo and scarlet oca whilst Agria, Moonlight and dark orange oca decreased total water footprint of consumptive water use with irrigation (Table 2). The dilution requirement for the applied nitrogen in potato, oca and pumpkin squash, had the equivalency of 424.8 and 398.2 m3 ha−1, grey water footprint, respectively (Table 1). The green, blue and grey water footprint reflected the inverse trend observed in total yield and total biomass yield above. All water footprint components above were largest in dark orange oca and smallest in pumpkin squash, Kamokamo (Figure 2). #### 3.2.2. Total water footprint of total yield and total biomass yield Total water footprint of potato, oca and pumpkin squash on total yield and total biomass yield basis varied with crop cultivars. The total water footprint on total yield basis ranged from 64.3 to 337.3 m3 ton−1 under irrigation and from 47.3 to 343.6 m3 ton−1 under rain-fed condition (Table 2). The total water footprint on total biomass yield basis was between 31.3 and 143 m3 ton−1 under irrigation, and 22.7 to 153.6 m3 ton−1 under rain-fed (Table 3). Regardless of a remarkable crop water use increase with irrigation, the total water footprint on total yield and total biomass yield basis under irrigation and rain-fed regimes were much different. Figure 3 shows that dark orange oca had the largest average total water footprint of total yield and total biomass while pumpkin squash, Kamokamo had the least. The total water footprint on total yield exceeded total water footprint on total biomass basis in all crop cultivars (Figure 3, Tables 2 and 3). The pumpkin squash cultivars and Moonlight were not much different on total water footprint of total yield but were considerable different to Moe Moe, Agria, Tutaekuri and oca cultivars. Tutaekuri had the greatest total water footprint of total yield and total biomass among potato cultivars though extremely lower to oca cultivars. Nevertheless, the total biomass water footprint for Tutaekuri was not much different from Agria. Moonlight and Moe Moe were second from pumpkin squash in low water footprint of total biomass (Table 3 and Figure 3). ### 3.3. Social-economic of the selected crop cultivars Gross revenue on investment income; present value per ha from irrigation in 1st year; net present value was highest in Moe Moe among potato cultivars. Moe Moe also displayed shortest repayment period. The high market value and its intermediary yield response to full irrigation and low N-assisted Moe Moe to have high economic value among the selected potato cultivars. Agria, despite its highest yield response to full irrigation and nitrogen, ended up being the least economic crop enterprise. Agria gross revenue on investment income was NZ$8740; present value per ha from irrigation in the 1st year was NZ$7159; net present value was NZ41,764.5; and its repayment period was longer (0.92 years) than other enterprises. Low market value in Agria compared to Taewa contributed to its lowest economic status. An intermediary economic value was reported in Tutaekuri which had intermediary gross revenue on investment income; present value; net present value and intermediary repayment period. Tutaekuri outperformed modern potatoes in economic terms regardless of its low yield response to irrigation and N just because of its novelty value and reduced water and nitrogen fertiliser requirement. ## 4. Discussion ### 4.1. Consumptive water use and yield differences of cultivars of selected crops Modern and heritage crops differ in their relationship between their maximum water requirement and actual evapotranspiration, thus crop coefficient (kc), in addition to maturity. Figure 1shows how the crop coefficient (or growing stages) overlapped during the growing season between different crops leading to different water use. Application of one irrigation schedule in crops with different kc would result in over-irrigating pumpkin squash. Thus, irrigation scheduling (timing) based on soil water monitoring rather than some approximate modelling approach can significantly improve the water management [25], that is, the total water footprint. Differences in growth stages and date to maturity might contribute to great differences in crop water requirement and water footprint among the selected crops cultivars [15]. From the study, it is definite that Taewa and oca have the longest duration of growth to maturity compared to the other selected crop cultivars [13]. Most of heritage crop cultivars used more water than modern cultivars. Likely, the large biomass and longer growth cycle in heritage crop cultivars (Kamokamo, Tutaekuri, oca and Moe Moe) made them use more water than modern cultivars. This study considered actual evapotranspiration and other discharges in determining the water footprint, as suggested by Maes [23]. In this case, the water requirement was not equal to the actual total consumptive water use, thus remedying the over-estimation. This is in contrast to water footprint determination in other studies, where hypothetical crop yield and evapotranspiration were used [26]. Apart from, expected enormous variability in crop water use within the area in future, the current results provide a great benchmark of heritage and modern crop water requirement and water footprint for the studied area. ### 4.2. Water footprint differences of cultivars of selected heritage and modern potato, pumpkin squash and oca Water footprint components differ with crop type or cultivars and water regimes as also reported in energy crops [27]. Pumpkin squash, Kamokamo, was the most efficient crop cultivar, while dark orange oca was the least efficient crop. Equivalency in water footprint could be noticed between pumpkin squash cultivar and Moonlight. Nevertheless, both were five times slighter than water footprint of oca. Likewise, Moonlight, Agria and Moe Moe equaled in water footprint. Tutaekuri has largest water footprint almost double that of other potato cultivars. There more benefits to grow Tutaekuri and pumpkin squash cultivars under rain-fed than under irrigated conditions. If not, there is no gain in growing oca under irrigation, excluding in the case of a likely premium price, which would offset low water productivity, compared to potato and pumpkin squash. The average water footprint of growing potato reported in this study (ranging from 46 m3 ton−1 to 335 m3 ton−1) were greater than that for the Netherlands and almost equal to USA and Brazil, except for Tutaekuri, which was equal to the water footprint of growing potato in Zimbabwe [27]. The water footprint of 72 m3 ton−1 was reported in Netherlands, 111 m3 ton−1 in USA, 106 m3 ton−1 in Brazil and 225 m3 ton−1 in Zimbabwe [27] for producing potatoes. Besides, our study demonstrates that water footprint of growing potato and pumpkin squash in New Zealand is either average, or smaller than that of crops with smallest water footprint in referred regions. Oca was found to have largest total water footprint. However, oca average water footprint in this study is within the range of smallest water footprint reported in Netherlands, USA, Brazil and Zimbabwe among sugar beet, sugarcane and maize [27]. An average of 12, 10, 11, 20, 7, 5, 35 and 28 l of water (in virtual water content form) would be required to produce 100 g of Agria, Moonlight, Moe Moe, Tutaekuri, Buttercup squash, Kamokamo, dark orange and scarlet oca, respectively. Efficient crop water management and crop cultivar choice might contribute to lower virtual water content of producing potato and pumpkin squash than 25 l/100 g for potato tuber [28] and 23.8 l/100 g for pumpkin [22], which were reported as average global and Indian virtual water content, respectively. On the other hand, oca virtual water content is still falling outside the 25 l/100 g for potato tuber. These disparities in water footprint are within or above those reported in the 1995–2006 global water footprint of pumpkin squash (336 m3 ton−1) and potato (287 m3 ton−1) [12]. The results suggest that there are great disparities in virtual water content and water footprint within global averages, which may be due to climate, cultivars and methodological differences, when estimating crop water use [22, 28]. This study used actual water use and actual yield, as suggested by Maes [22], while the study referred to used hypothetical crop yields and water use [26]. On the other hand, the virtual water content and water footprint in this study, outweigh the global water footprint put forward by Mekonnen [12]. The reason for such disparities with this study is that most referred global water footprint studies theoretically estimated crop water use while this study practically recorded the actual water used. The theoretically estimated water use might have been over-estimated while our study might sparely use the water resulting into lower water footprint. It is globally agreed that smart and efficient practices in agriculture, selection of efficient crop cultivars in water use and good weather patterns do assist in reducing water footprint of producing various crops. Irrigation increases total water use compared to rain-fed agriculture. In this study blue water raised total crop water use by 34, 48 and 59%, in oca, potato and pumpkin squash cultivars, respectively. Consequently, blue water clearly increased the total water footprint. Total water footprint increased by 5, 45, 28, 25 and 8% in irrigated Moe Moe, Tutaekuri, Buttercup squash, Kamokamo and Scarlet oca. However, irrigation reduced total water footprint in Agria, Moonlight and dark orange oca by 6, 4 and 7%. The earlier trends were reported in wheat whereas the later was reported in sugarcane and soybean, respectively [12]. For crop varieties which positively respond to irrigation, the intervention is indispensable to reduce the total water footprint, by improving the economic yields. Nevertheless, this is contrary to like Moe Moe, Tutaekuri, Buttercup squash, Kamokamo and scarlet because the intervention raised the actual evapotranspiration nearly to potential evapotranspiration resulting into reduced water footprint, even with improved yield. The findings emphasise that irrigation is very important for crop yield quality and yield enhancement as well as reduced water footprint where rainfall is limited. Apart from differences in water footprint influenced by crop varieties and differences and crops, water footprint also extensively differ in their water footprint at different irrigation management. Irrigation scheduling method would influence the water footprint of producing various crops—however, this is dependent on crop cultivars. Partial irrigation reduced water footprint in Tutaekuri while full irrigation reduced water footprint in Moe Moe and Agria. The differences about crop varieties response to different irrigation schedules are very significant because they indicate disparity of water use among crop varieties. This result is very useful in selection for crop varieties that are sparing in water use or drought tolerant and breeding for water use efficiency. Hedley proved that the water footprint of modern potato production is slighter small than that of maize and pasture [29]. Hedley report registered water footprint of 308 and 325 m3 ton−1in potato 622 and 654 m3 ton−1 in maize and 2651 and 2667 m3 ton−1 in pasture at varied rate irrigation and uniform rate irrigation, respectively. It is noted that the total water footprint of growing potato by Hedley et al. [29, 30], was higher than those reported by Hoekstra [31] and the water footprint for this study, except for Tutaekuri. Similarly, the study under this report vividly shows that water footprint differed between full irrigation and rain-fed that ranged from 95 to 111 m3 ton−1 (modern potato); 110–220 m3 ton−1 (Taewa) in 2009/2010. In 2010/2011 the water footprint for water regimes ranged from 163 to 586 m3 ton−1 (full irrigation), 173–406 m3 ton−1 (partial irrigation) and 198–505 m3 ton−1 (rain-fed). The lowest water footprint was found in Agria and the highest in Tutaekuri. From this discussion and Figure 3, it is well illustrated that water management within different crop cultivars influences levels of water footprint. Apart from differences in water footprint caused by varieties differences, water footprint may also extensively differ in their water footprint due to pests’ infestation. Farmers need to keep fields weed free to reduce pests and diseases incidences. Pests and diseases affect water footprint of producing selected crop cultivars because they reduce yields without affecting water input. In case of this study, water footprint of Taewa between seasons differed due to pests’ infestation. As weather variations between seasons Water footprint was greatly higher in 2011 than in 2010 (Figure 3). Potato psyllid infestation influenced the increase in water footprint in 2011. However, the water footprint of producing potato without psyllid infestation, in 2009/2010, was smaller than the global water footprint (160 m3 ton−1) for producing potato. Potato infested with psyllid in 2010/2011 behaved differently, only a well-managed full irrigation regime of modern potato and Moe Moe, obtained a water footprint approaching the global water footprint of 160 m3 ton−1. A combination of proper management of irrigation under pests’ infestation can help to reduce water footprint. The water footprint indicator suggests there are numerous disparities, with global averages and within country or seasons, arising from irrigation management and methodological differences when estimating crop water use, climate variability, cultivars and pest and disease infestation [22, 28]. However, the water footprint for crops grown in New Zealand can be reduced through good management [12]. For instance, pumpkin squash (especially Kamokamo) had the lowest water footprint, compared to oca, potato, maize and pasture in New Zealand, and compared well with small water footprint crops such as sugar beet and sugarcane, at the global level [26]. This observation suggests that some heritage crop cultivars can compare with (or outperform) modern cultivars in relation to water footprint, when the crop husbandry is appropriate. ### 4.3. Social-economics of the selected crop cultivars A premium that farmers get at market on crop cultivar has higher influence on smallholder farmer’s social-economic status than sole yield and sole irrigation response factors. In our case, fully irrigated Moe Moe and partially irrigated Tutaekuri production systems, were economically viable due to their high value at market. The novel value of most heritage crops are value which have been based on social preferences based on their superiority flavour, texture and colour. Fully irrigated Moe Moe and partially irrigated Tutaekuri production systems, with low N, would be profitable investments for Taewa growers because they have high value and low N use. For growers to maintain these economic benefits they should be advised to produce Tutaekuri under partial irrigation and low high N, and Moe Moe under full irrigation with low N. It is not advisable for growers to produce Agria under partial irrigation and low N, because this production system has negative NPV. Economic water productivity is expected to be high in Taewa because of the premiums at market. Premiums, socially and economically forces production of Taewa among the highest producer but low valued. It is evidenced that issue of water footprint requires financial attachment to attract farmers. ## 5. Conclusion and recommendations In the field, water regimes differently influence crop production and the value of water footprint for both heritage and modern crop cultivars, depending on the crop water use characteristics and field management. Pumpkin squash, Kamokamo, has a low water footprint, since it genetically uses water more sparingly, compared to all the other crop cultivars studied. In spite of this, the yield response to irrigation is highest in modern potato, while Kamokamo is comparable to Moe Moe and Buttercup squash and dark orange oca. It can be concluded that pumpkin squash requires only a small amount of water, in order to produce total fruit yield compared to potatoes and oca. Potatoes, except Tutaekuri, are more responsive to irrigation compared to pumpkin squash and oca. The yields and water footprint of heritage potato is greatly affected by cultivars used and water regimes, unlike the case of oca. It can be concluded that there are water footprint differences between cultivars of different crops and within crops in New Zealand. Knowledge of these water footprint differences can assist growers to manage their crops and water resources sparingly. It is therefore recommended that growers should be properly selecting crops and crop varieties according to their water availability, market price, properly schedule irrigation and nitrogen application as well as pests and disease control in order to reduce water footprint of growing their crops at field level. It is recommended that farmers should strive to reduce water footprint either by avoidance of using two much of other inputs or by replacement of inefficient technologies by very efficient technologies as detailed below: 1. Farmers should be advised to strive to reduce grey water footprint in their fields. Grey water footprint would be decreased if application of chemical fertilisers, pesticides and herbicides to the field is avoided or reduced or by following efficient ways of using fertilisers as well as applying better application techniques or use of organic fertilisers and proper timing of fertiliser and irrigation application. 2. Farmers should also be advised to decrease green water footprint and blue water footprint. The green and blue water footprints would be greatly lessened by enhancing green and blue water productivity. Our study indicates that application of less water through smart irrigation scheduling (replacing full irrigation by partial irrigation) and selection of water efficient crop cultivars (replacing heavy water users by efficient water users) would help to maximise water productivity (striving for higher yield per cubic of water used for production) thereby reducing both green and blue water footprint. 3. Agricultural Extension Officers need to be guided to assist farmers in defining their target of best agricultural technology practices for reducing water footprint and formulating targets to be achieved in order to contribute to reduction of water footprint. Where possible farmers should be assisted to monitor and measure their water footprint in their environment. This can be achieved by setting environmental and social safeguards plan that would help to reduce risk of water footprint by investing in reasonable water use, better-quality catchment water management and sustainable water use. 4. Governments should formulate policies that include goal of sustainable usage of water resources. The policies should promote smart agriculture: that is, efficient irrigation (drip irrigation), conservation agriculture, system of rice intensification (SRI), crops that are efficient in water use and organic fertilisers. ## More © 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ## How to cite and reference ### Cite this chapter Copy to clipboard Isaac R. Fandika, Peter D. Kemp, James P. Millner and Davie Horne (January 23rd 2019). Water Footprint Differences of Producing Cultivars of Selected Crops in New Zealand, Irrigation in Agroecosystems, Gabrijel Ondrašek, IntechOpen, DOI: 10.5772/intechopen.77509. Available from: ### Related Content #### Irrigation in Agroecosystems Edited by Gabrijel Ondrasek Next chapter #### Water Quality in Irrigated Paddy Systems By Jian Liu, Hongbin Liu, Ruliang Liu, MG Mostofa Amin, Limei Zhai, Haiming Lu, Hongyuan Wang, Xubo Zhang, Yitao Zhang, Ying Zhao and Xiaodong Ding First chapter #### Agricultural Systems in IGAD Region — A Socio-Economic Review By Osman Babikir, Solomon Muchina, Ameha Sebsibe, Adan Bika, Agol Kwai, Caroline Agosa, George Obhai and Samuel Wakhusama We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. We share our knowledge and peer-reveiwed research papers with libraries, scientific and engineering societies, and also work with corporate R&D departments and government entities. View all books	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.621027946472168, "perplexity": 10474.151112647714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318011.89/warc/CC-MAIN-20190823062005-20190823084005-00004.warc.gz"}
https://tug.org/pipermail/texhax/2007-October/009343.html	# [texhax] TeX command works for "1 Foo" but not for "11 Foo" Tue Oct 30 21:49:07 CET 2007 Hi list, This is a weird problem. I use the following for my thesis to force me to include a date with each link I refer to, or make it explicit that I don't need a date, e.g. \link{http://debian.org}{}: % not making #2 optional on purpose \burl{#1}% \if\@empty#2\relax\else{ }\begin{smaller}{[#2]}\end{smaller}\fi% } The problem is that this works fine for dates like 1 Oct 2007 or 15 Sep 2007, but as soon as the date is 11 or 22, something goes fishy: yields: http://debian.org/Bugs/server-control [10 Oct 2007] http://debian.org/Bugs/server-control Oct 2007 Either TeX is on drugs, or I am, or I simply don't understand what's going on. Could you help me figure this out, please? -- sed -e '/^[when][coders]/!d' \ -e '/^...[discover].$/d' \ -e '/^..[real].[code]$/!d' \ /usr/share/dict/words	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9617566466331482, "perplexity": 4375.878108337279}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526517.67/warc/CC-MAIN-20190720132039-20190720154039-00393.warc.gz"}
https://www.zora.uzh.ch/id/eprint/18483/	Estimation of the false negative fraction of a diagnostic kit through Bayesian regression model averaging Ranyimbo, A O; Held, L (2005). Estimation of the false negative fraction of a diagnostic kit through Bayesian regression model averaging. Statistics in Medicine, 25(4):653-667. Abstract In modelling we usually endeavour to find a single 'best' model that explains the relationship between independent and dependent variables. Selection of a single model fails to take into account the prior uncertainty in the model space. The Bayesian model averaging (BMA) approach tackles this problem by considering the set of all possible models. We apply BMA approach to the estimation of the false negative fraction (FNF) in a particular case of a two-stage multiple screening test for bowel cancer. We find that after taking model uncertainty into consideration the estimate of the FNF obtained is largely dependent on the covariance structure of the priors. Results obtained when the Zellner g-prior for the prior variance is used is largely influenced by the magnitude of g. Abstract In modelling we usually endeavour to find a single 'best' model that explains the relationship between independent and dependent variables. Selection of a single model fails to take into account the prior uncertainty in the model space. The Bayesian model averaging (BMA) approach tackles this problem by considering the set of all possible models. We apply BMA approach to the estimation of the false negative fraction (FNF) in a particular case of a two-stage multiple screening test for bowel cancer. We find that after taking model uncertainty into consideration the estimate of the FNF obtained is largely dependent on the covariance structure of the priors. Results obtained when the Zellner g-prior for the prior variance is used is largely influenced by the magnitude of g. Statistics Citations Dimensions.ai Metrics 4 citations in Web of Science® 4 citations in Scopus®	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8932499885559082, "perplexity": 709.3715921235455}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00214.warc.gz"}
http://mathhelpforum.com/advanced-algebra/129500-prove-w-symmetric.html	# Thread: Prove that W is symmetric 1. ## Prove that W is symmetric I know that: W = W transpose is symmetric, 2. $(W-I)^T = 2W \ \ (\star)$ Using the property that: $(A \pm B)^T = A^T \pm B^T$ we have that: $W^T - I = 2W \ \Leftrightarrow \ {\color{blue}I = W^T - 2W}$ Now take the transpose of both sides of $(\star)$ and solve for $I$. Compare this expression with what we have in blue and you should get what you want.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9220216274261475, "perplexity": 530.8111960477613}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720026.81/warc/CC-MAIN-20161020183840-00215-ip-10-171-6-4.ec2.internal.warc.gz"}
https://math.libretexts.org/Courses/Honolulu_Community_College/Math_75X%3A_Introduction_to_Mathematical_Reasoning_(Kearns)/04%3A_Fundamentals_of_Algebra/4.06%3A_Solving_Equations-_Keeping_the_Balance/4.6.03%3A_Equations_with_Decimals	$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ # 4.6.3: Equations with Decimals $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ We can add or subtract the same decimal number from both sides of an equation without affecting the solution. Example 1 Solve for x: x − 1.35 = −2.6. Solution To undo subtracting 1.35, add 1.35 to both sides of the equation. \begin{aligned} x - 1.35 = -2.6 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x - 1.35 + 1.35 = -2.6 + 1.35 ~ & \textcolor{red}{ \text{ Add 1.35 to both sides.}} \\ x = -1.25 ~ & \textcolor{red}{ \text{ Simplify: } -2.6 + 1.35 = -1.25.} \end{aligned}\nonumber Exercise Solve for x: $$x+1.25=0.6$$ −0.65 We can still multiply both sides of an equation by the same decimal number without affecting the solution. Example 2 Solve for x: $$\frac{x}{-0.35} = 4.2$$. Solution To undo dividing by −0.35, multiply both sides of the equation by −0.35. \begin{aligned} \frac{x}{-0.35} = 4.2 ~ & \textcolor{red}{ \text{ Original equation.}} \\ -0.35 \left( \frac{x}{-0.35} \right) = -0.35 (4.2) ~ & \textcolor{red}{ \text{ Multiply both sides by } -0.35.} \\ x = -1.470 ~ & \textcolor{red}{ \text{ Simplify: } -0.35 (4.2) = -1.470.} \end{aligned}\nonumber Exercise Solve for y: $$\frac{y}{0.37} = -1.52$$. −0.5624 We can still divide both sides of an equation by the same decimal number without affecting the solution. Example 3 Solve for x: $$−1.2x = −4.08$$. Solution To undo multiplying by −1.2, divide both sides of the equation by −1.2. \begin{aligned} -1.2x = -4.08 ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{-1.2x}{-1.2} = \frac{-4.08}{-1.2} ~ & \textcolor{red}{ \text{ Divide both sides by } -1.2} \\ x = 3.4 ~ & \textcolor{red}{ \text{ Simplify: } -4.08/(-1.2)=3.4.} \end{aligned}\nonumber Exercise Solve for z: $$-2.5z=1.4$$ −0.56 ## Combining Operations We sometimes need to combine operations. Example 4 Solve for x: $$−3.8x − 1.7 = −17.28$$. Solution To undo subtracting 1.7, add 1.7 to both sides of the equation. \begin{aligned} -3.8x-1.7=-17.28 ~ & \textcolor{red}{ \text{ Original equation.}} \\ -3.8x-1.7+1.7=-17.28+1.7 ~ & \textcolor{red}{ \text{ Add 1.7 to both sides.}} \\ -3.8x=-15.58 ~ & \textcolor{red}{ \text{ Simplify: } -17.28 + 1.7 = -15.58.} \end{aligned}\nonumber Next, to undo multiplying by −3.8, divide both sides of the equation by −3.8. \begin{aligned} \frac{-3.8x}{-3.8} = \frac{-15.88}{-3.8} ~ & \textcolor{red}{ \text{ Divide both sides by } -3.8.} \\ x = 4.1 ~ & \textcolor{red}{ \text{ Simplify: } -15.58/(-3.8) = 4.1.} \end{aligned}\nonumber Exercise Solve for u: $$-0.02u-3.2=-1.75$$. −72.5 ## Combining Like Terms Combining like terms with decimal coefficients is done in the same manner as combining like terms with integer coefficients. Example 5 Simplify the expression: $$−3.2x + 1.16x$$. Solution To combine these like terms we must add the coefficients. To add coefficients with unlike signs, first subtract the coefficient with the smaller magnitude from the coefficient with the larger magnitude. $\begin{array}{r} 3.20 \\ - 1.16 \\ \hline 2.04 \end{array}\nonumber$ Prefix the sign of the decimal number having the larger magnitude. Hence: $−3.2+1.16 = −2.04.\nonumber$ We can now combine like terms as follows: $−3.2x + 1.16x = −2.04x\nonumber$ Exercise Simplify: $$-1.185t+3.2t$$ 2.015t When solving equations, we sometimes need to combine like terms. Example 6 Solve the equation for x: $$4.2 − 3.1x + 2x = −7.02$$. Solution Combine like terms on the left-hand side of the equation. \begin{aligned} 4.2-3.1x+2x=-7.02 ~ & \textcolor{red}{ \text{ Original equation.}} \\ 4.2 - 1.1x = -7.02 ~ & \textcolor{red}{ \text{ Combine like terms: } -3.1x + 2x = -1.1x.} \\ 4.2 - 1.1x - 4.2 = -7.02 - 4.2 ~ & \textcolor{red}{ \text{ Subtract 4.2 from both sides.}} \\ -1.1x = -11.02 ~ & \textcolor{red}{ \text{ Subtract: } -7.02 - 4.2 = -11.22.} \\ \frac{-1.1x}{-1.1} = \frac{-11.22}{-1.1} ~ & \textcolor{red}{ \text{ Divide both sides by } -1.1.} \\ x = 10.2 ~ & \textcolor{red}{ \text{ Divide: } -11.22/(-1.1) = 10.2.} \end{aligned}\nonumber Thus, the solution of the equation is 10.2. Check Like all equations, we can check our solution by substituting our answer in the original equation. \begin{aligned} 4.2 - 3.1x +2x = -7.02 ~ & \textcolor{red}{ \text{ Original equation.}} \\ 4.2 - 3.1(10.2) + 2(10.2) = -7.02 ~ & \textcolor{red}{ \text{ Substitute 10.2 for } x.} \\ 4.2 - 31.62 + 20.4 = -7.02 ~ & \textcolor{red}{ \text{ Multiply: } 3.1(10.2) = 31.62, ~ 2(10.2) = 20.4.} \\ -27.42 + 20.4 = -7.02 ~ & \textcolor{red}{ \text{ Order of Ops: Add, left to right.}} \\ ~ & \textcolor{red}{ ~ 4.2 - 31.62 = -27.42.} \\ -7.02 = -7.02 ~ & \textcolor{red}{ \text{ Add: } -27.42 + 20.4 = -7.02.} \end{aligned}\nonumber Because the last line is a true statement, the solution x = 10.2 checks. Exercise Solve for r: $$-4.2 + 3.6r - 4.1r = 1.86$$ −12.12 ## Using the Distributive Property Sometimes we will need to employ the distributive property when solving equations. Distributive Property Let a, b, and c be any numbers. Then, $a(b + c) = ab + ac.\nonumber$ Example 7 Solve the equation for x: $$−6.3x − 0.4(x − 1.2) = −0.86$$. Solution We first distribute the −0.4 times each term in the parentheses, then combine like terms. \begin{aligned} -6.3x - 0.4(x-1.2) = -0.86 ~ & \textcolor{red}{ \text{ Original equation.}} \\ -6.3x-0.4x+0.48 = -0.86 ~ & \textcolor{red}{ \text{ Distribute. Note that } -0.4(-1.2)=0.48.} \\ -6.7x+0.48=-0.86 ~ & \textcolor{red}{ \text{ Combine like terms.}} \end{aligned}\nonumber Next, subtract 0.48 from both sides, then divide both sides of the resulting equation by −6.7. \begin{aligned} -6.7x+0.48-0.48 = -0.86 - 0.48 ~ & \textcolor{red}{ \text{ Subtract 0.48 from both sides.}} \\ -6.7x = -1.34 ~ & \textcolor{red}{ \text{ Simplify: } -0.86 - 0.48 = -1.34.} \\ \frac{-6.7x}{-6.7} = \frac{-1.34}{-6.7} ~ & \textcolor{red}{ \text{ Divide both sides by } -6.7.} \\ x = 0.2 ~ & \textcolor{red}{ \text{ Simplify: } -1.34/(-6.7)=0.2.} \end{aligned}\nonumber Exercise Solve for x: $$−2.5x − 0.1(x − 2.3) = 8.03$$ −3 ## Rounding Solutions Sometimes an approximate solution is adequate. Example $$\PageIndex{1}$$ Solve the equation $$3.1x+ 4.6=2.5 − 2.2x$$ for x. Round the answer to the nearest tenth. Solution We need to isolate the terms containing x on one side of the equation. We begin by adding 2.2x to both sides of the equation. \begin{aligned} 3.1x + 4.6 = 2.5 - 2.2x ~ & \textcolor{red}{ \text{ Original equation.}} \\ 3.1x + 4.6 + 2.2x = 2.5 - 2.2x + 2.2x ~ & \textcolor{red}{ \text{ Add } 2.2x \text{ to both sides.}} \\ 5.3x + 4.6 = 2.5 ~ & \textcolor{red}{ \text{ Combine terms: } 3.1x + 2.2x = 5.3x.} \end{aligned{\nonumber We need to isolate the terms containing x on one side of the equation. We begin by adding 2.2x to both sides of the equation. \begin{aligned} 5.3x + 4.6 - 4.6 = 2.5 - 4.6 ~ & \textcolor{red}{ \text{ Subtract 4.6 from both sides.}} \\ 5.3x = -2.1 ~ & \textcolor{red}{ \text{ Simplify: } 2.5 - 4.6 = -2.1.} \end{aligned}\nonumber To undo the effect of multiplying by 5.3, divide both sides of the equation by 5.3. \begin{aligned} \frac{5.3x}{5.3} = \frac{-2.1}{5.3} ~ & \textcolor{red}{ \text{Divide both side by 5.3.}} \\ x \approx -0.4 ~ & \textcolor{red}{ \text{ Round solution to nearest tenth.}} \end{aligned}\nonumber To round the answer to the nearest tenth, we must carry the division out one additional place. Because the “test digit” is greater than or equal to 5, add 1 to the rounding digit and truncate. Thus, −0.39 ≈ −0.4. Thus, −2.1/5.3 ≈ −0.39. Exercise Solve for x: $$4.2x − 1.25 = 3.4+0.71x$$ 1.33 Applications Let’s look at some applications that involve equations containing decimals. For convenience, we repeat the Requirements for Word Problem Solutions. Requirements for Word Problem Solutions 1. Set up a Variable Dictionary. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: 1. Statements such as “Let P represent the perimeter of the rectangle.” 2. Labeling unknown values with variables in a table. 3. Labeling unknown quantities in a sketch or diagram. 2. Set up an Equation. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement. 3. Solve the Equation. You must always solve the equation set up in the previous step. 4. Answer the Question. This step is easily overlooked. For example, the problem might ask for Jane’s age, but your equation’s solution gives the age of Jane’s sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in a sentence with appropriate units. 5. Look Back. It is important to note that this step does not imply that you should simply check your solution in your equation. After all, it’s possible that your equation incorrectly models the problem’s situation, so you could have a valid solution to an incorrect equation. The important question is: “Does your answer make sense based on the words in the original problem statement.” Example 9 Molly needs to create a rectangular garden plot covering 200 square meters (200 m2). If the width of the plot is 8.9 meters, find the length of the plot correct to the nearest tenth of a meter. Solution We will follow the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. We will use a sketch to define our variables. Note that L represents the length of the rectangle. 2. Set Up an Equation. The area A of a rectangle is given by the formula $A = LW,\nonumber$ where L and W represent the length and width of the rectangle, respectively. Substitute 200 for A and 8.9 for W in the formula to obtain $200 = L(8.9),\nonumber$ or equivalently, $200 = 8.9L.\nonumber$ 3. Solve the Equation. Divide both sides of the last equation by 8.9, then round your answer to the nearest tenth. \begin{aligned} \frac{200}{8.9} = \frac{8.9L}{8.9} ~ & \textcolor{red}{ \text{ Divide both sides by 8.9.}} \\ 22.5 \approx L ~ & \textcolor{red}{ \text{ Round to nearest tenth.}} \end{aligned}\nonumber To round the answer to the nearest tenth, we must carry the division out one additional place. Because the “test digit” is greater than or equal to 5, add 1 to the rounding digit and truncate. Thus, 200/8.9 ≈ 22.5. 4. Answer the Question. To the nearest tenth of a meter, the length of the rectangular plot is L ≈ 22.5 meters. 5. Look Back. We have L ≈ 22.5 meters and W = 8.9 meters. Multiply length and width to find the area. $\text{Area} \approx (22.5 \text{ m})(8.9 \text{ m}) ≈ 200.25 \text{ m}^2.\nonumber$ Note that this is very nearly the exact area of 200 square meters. The discrepancy is due to the fact that we found the length rounded to the nearest tenth of a meter Exercise Eta’s dog run is in the shape of a rectangle with area 500 square feet. If the length of the run is 28 feet, find the width of the run, correct to the nearest tenth of a foot. 17.9 feet Example 10 Children’s tickets to the circus go on sale for $6.75. The Boys and Girls club of Eureka has$1,000 set aside to purchase these tickets. Approximately how many tickets can the Girls and Boys club purchase? Solution We will follow the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. Let N represent the number of tickets purchased by the Boys and Girls club of Eureka. 2. Set Up an Equation. Note that $\begin{matrix} \colorbox{cyan}{Price per ticket} & \text{ times } & \colorbox{cyan}{Number of tickets} & \text{ is } & \colorbox{cyan}{Full Purchase Price} \\ 6.75 & . & N & = & 1,000 \end{matrix}\nonumber$ Hence, our equation is 6.75N = 1000. 3. Solve the Equation. Divide both sides of the equation by 6.75. \begin{aligned} \frac{6.75N}{6.75} = \frac{1000}{6.75} ~ & \textcolor{red}{ \text{ Divide both sides by 6.75.}} \\ N \approx 148 ~ & \textcolor{red}{ \text{ Truncate to nearest unit.}} \end{aligned}\nonumber Push the decimal point to the right-end of the divisor and the decimal point in the dividend an equal number of places. We’ll stop the division at the units position. 4. Answer the Question. The Boys and Girls club can purchase 148 tickets. 5. Look Back. Let’s calculate the cost of 148 tickets at $6.75 apiece. Thus, at$6.75 apiece, 148 tickets will cost $999. Because the Boys and Girls club of Eureka has$1,000 to work with, note that the club doesn’t have enough money left for another ticket. Exercise Adult tickets to the circus cost $12.25 apiece. If the club has$1,200 set aside for adult ticket purchase, how many adult tickets can they purchase? 97 Example 11 Marta has 20 feet of decorative fencing which she will use for the border of a small circular garden. Find the diameter of the circular garden, correct to the nearest hundredth of a foot. Use π ≈ 3.14. Solution The formula governing the relation between the circumference and diameter of a circle is $C = \pi d\nonumber$ The 20 feet of decorative fencing will be the circumference of the circular garden. Substitute 20 for C and 3.14 for π. $20 = 3.14d\nonumber$ Divide both sides of the equation by 3.14. \begin{aligned} \frac{20}{3.14} = \frac{3.14d}{3.14} \\ \frac{20}{3.14} = d \end{aligned}\nonumber Move the decimal point to the end of the divisor, then move the decimal point in the dividend an equal number of places (two places) to the right. Note that we must add two trailing zeros in the dividend. Thus, the problem becomes: $314 \overline{ )2000}\nonumber$ We need to round to the nearest hundredth. This requires that we carry the division one additional place to the right of the hundredths place (i.e., to the thousandths place). For the final step, we must round 6.369 to the nearest hundredth. In the schematic that follows, we’ve boxed the hundredths digit (the “rounding digit”) and the “test digit” that follows the “rounding digit.” Because the “test digit” is greater than or equal to 5, we add 1 to the “rounding digit,” then truncate. Therefore, to the nearest hundredth of a foot, the diameter of the circle is approximately $d ≈ 6.37 \text{ ft.}\nonumber$ Exercise Dylan has a circular dog pen with circumference 100 feet. Find the radius of the pen, correct to the nearest tenth of a foot. Use π ≈ 3.14. 15.9 feet ## Exercises In Exercises 1-16, solve the equation. 1. $$5.57x − 2.45x = 5.46$$ 2. $$−0.3x − 6.5x = 3.4$$ 3. $$−5.8x + 0.32 + 0.2x = −6.96$$ 4. $$−2.2x − 0.8 − 7.8x = −3.3$$ 5. $$−4.9x + 88.2 = 24.5$$ 6. $$−0.2x − 32.71 = 57.61$$ 7. $$0.35x − 63.58 = 55.14$$ 8. $$−0.2x − 67.3 = 93.5$$ 9. $$−10.3x + 82.4=0$$ 10. $$−1.33x − 45.22 = 0$$ 11. $$−12.5x + 13.5=0$$ 12. $$44.15x − 8.83 = 0$$ 13. $$7.3x − 8.9 − 8.34x = 2.8$$ 14. $$0.9x + 4.5 − 0.5x = 3.5$$ 15. $$−0.2x + 2.2x = 6.8$$ 16. $$−7.9x + 2.9x = 8.6$$ In Exercises 17-34, solve the equation. 17. $$6.24x − 5.2=5.2x$$ 18. $$−0.6x + 6.3=1.5x$$ 19. $$−0.7x − 2.4 = −3.7x − 8.91$$ 20. $$3.4x − 4.89 = 2.9x + 3.6$$ 21. $$−4.9x = −5.4x + 8.4$$ 22. $$2.5x = 4.5x + 5.8$$ 23. $$−2.8x = −2.3x − 6.5$$ 24. $$1.2x = 0.35x − 1.36$$ 25. $$−2.97x − 2.6 = −3.47x + 7.47$$ 26. $$−8.6x − 2.62 = −7.1x + 8.54$$ 27. $$−1.7x = −0.2x − 0.6$$ 28. $$3.89x = −5.11x + 5.4$$ 29. $$−1.02x + 7.08 = −2.79x$$ 30. $$1.5x − 2.4=0.3x$$ 31. $$−4.75x − 6.77 = −7.45x + 3.49$$ 32. $$−1.2x − 2.8 = −0.7x − 5.6$$ 33. $$−4.06x − 7.38 = 4.94x$$ 34. $$−4.22x + 7.8 = −6.3x$$ In Exercises 35-52, solve the equation. 35. $$2.3+0.1(x + 2.9) = 6.9$$ 36. $$−6.37 + 6.3(x + 4.9) = −1.33$$ 37. $$0.5(1.5x − 6.58) = 6.88$$ 38. $$0.5(−2.5x − 4.7) = 16.9$$ 39. $$−6.3x − 0.4(x − 1.8) = −16.03$$ 40. $$−2.8x + 5.08(x − 4.84) = 19.85$$ 41. $$2.4(0.3x + 3.2) = −11.4$$ 42. $$−0.7(0.2x + 5.48) = 16.45$$ 43. $$−0.8(0.3x + 0.4) = −11.3$$ 44. $$7.5(4.4x + 7.88) = 17.19$$ 45. $$−7.57 − 2.42(x + 5.54) = 6.95$$ 46. $$5.9 − 0.5(x + 5.8) = 12.15$$ 47. $$−1.7 − 5.56(x + 6.1) = 12.2$$ 48. $$−7.93 + 0.01(x + 7.9) = 14.2$$ 49. $$4.3x − 0.7(x + 2.1) = 8.61$$ 50. $$1.5x − 4.5(x + 4.92) = 15.6$$ 51. $$−4.8x + 3.3(x − 0.4) = −7.05$$ 52. $$−1.1x + 1.3(x + 1.3) = 19.88$$ In Exercises 53-58, solve the equation. 53. $$0.9(6.2x − 5.9) = 3.4(3.7x + 4.3) − 1.8$$ 54. $$0.4(−4.6x+ 4.7) = −1.6(−2.2x+ 6.9)−4.5$$ 55. $$−1.8(−1.6x + 1.7) = −1.8(−3.6x − 4.1)$$ 56. $$−3.3(−6.3x + 4.2) − 5.3=1.7(6.2x + 3.2)$$ 57. $$0.9(0.4x + 2.5) − 2.5 = −1.9(0.8x + 3.1)$$ 58. $$5.5(6.7x + 7.3) = −5.5(−4.2x + 2.2)$$ 59. Stacy runs a business out of her home making bird houses. Each month she has fixed costs of $200. In addition, for each bird house she makes, she incurs an additional cost of$3.00. If her total costs for the month were $296.00, how many bird houses did she make? 60. Stella runs a business out of her home making curtains. Each month she has fixed costs of$175. In addition, for each curtain she makes, she incurs an additional cost of $2.75. If her total costs for the month were$274.00, how many curtains did she make? 61. A stationary store has staplers on sale for $1.50 apiece. A business purchases an unknown number of these and the total cost of their purchase is$36.00. How many were purchased? 62. A stationary store has CD packs on sale for $2.50 apiece. A business purchases an unknown number of these and the total cost of their purchase is$40.00. How many were purchased? 63. Julie runs a business out of her home making table cloths. Each month she has fixed costs of $100. In addition, for each table cloth she makes, she incurs an additional cost of$2.75. If her total costs for the month were $221.00, how many table cloths did she make? 64. Stella runs a business out of her home making quilts. Each month she has fixed costs of$200. In addition, for each quilt she makes, she incurs an additional cost of $1.75. If her total costs for the month were$280.50, how many quilts did she make? 65. Marta has 60 feet of decorative fencing which she will use for the border of a small circular garden. Find the diameter of the circular garden, correct to the nearest hundredth of a foot. Use π ≈ 3.14. 66. Trinity has 44 feet of decorative fencing which she will use for the border of a small circular garden. Find the diameter of the circular garden, correct to the nearest hundredth of a foot. Use π ≈ 3.14. 67. Children’s tickets to the ice capades go on sale for $4.25. The YMCA of Sacramento has$1,000 set aside to purchase these tickets. Approximately how many tickets can the YMCA of Sacramento purchase? 68. Children’s tickets to the ice capades go on sale for $5. The Knights of Columbus has$1,200 set aside to purchase these tickets. Approximately how many tickets can the Knights of Columbus purchase? 69. A stationary store has mechanical pencils on sale for $2.25 apiece. A business purchases an unknown number of these and the total cost of their purchase is$65.25. How many were purchased? 70. A stationary store has engineering templates on sale for $2.50 apiece. A business purchases an unknown number of these and the total cost of their purchase is$60.00. How many were purchased? 71. Marta has 61 feet of decorative fencing which she will use for the border of a small circular garden. Find the diameter of the circular garden, correct to the nearest hundredth of a foot. Use π ≈ 3.14. 72. Kathy has 86 feet of decorative fencing which she will use for the border of a small circular garden. Find the diameter of the circular garden, correct to the nearest hundredth of a foot. Use π ≈ 3.14. 73. Kathy needs to create a rectangular garden plot covering 100 square meters (100 m2). If the width of the plot is 7.5 meters, find the length of the plot correct to the nearest tenth of a meter. 74. Marianne needs to create a rectangular garden plot covering 223 square meters (223 m2). If the width of the plot is 8.3 meters, find the length of the plot correct to the nearest tenth of a meter. 75. Children’s tickets to the stock car races go on sale for $4.5. The Boys and Girls club of Eureka has$1,300 set aside to purchase these tickets. Approximately how many tickets can the Boys and Girls club of Eureka purchase? 76. Children’s tickets to the movies go on sale for $4.75. The Lions club of Alameda has$800 set aside to purchase these tickets. Approximately how many tickets can the Lions club of Alameda purchase? 77. Ashley needs to create a rectangular garden plot covering 115 square meters (115 m2). If the width of the plot is 6.8 meters, find the length of the plot correct to the nearest tenth of a meter. 78. Molly needs to create a rectangular garden plot covering 268 square meters (268 m2). If the width of the plot is 6.1 meters, find the length of the plot correct to the nearest tenth of a meter. 79. Crude Inventory. US commercial crude oil inventories decreased by 3.8 million barrels in the week ending June 19. If there were 353.9 million barrels the following week, what were crude oil inventories before the decline? rttnews.com 06/24/09 80. Undocumented. In 2008, California had 2.7 million undocumented residents. This is double the number in 1990. How many undocumented residents were in California in 1990? Associated Press Times-Standard 4/15/09 81. Diamonds Shining. The index of refraction n indicates the number of times slower that a light wave travels in a particular medium than it travels in a vacuum. A diamond has an index of refraction of 2.4. This is about one and one-quarter times greater than the index of refraction of a zircon. What is the index of refraction of a zircon? Round your result to the nearest tenth. 1. 1.75 3. 1.3 5. 13 7. 339.2 9. 8 11. 1.08 13. −11.25 15. 3.4 17. 5 19. −2.17 21. 16.8 23. 13 25. 20.14 27. 0.4 29. −4 31. 3.8 33. −0.82 35. 43.1 37. 13.56 39. 2.5 41. −26.5 43. 45.75 45. −11.54 47. −8.6 49. 2.8 51. 3.82 53. −2.59 55. −2.9 57. −3 59. 32 61. 24 63. 44 65. 19.11 feet 67. 235 tickets 69. 29 71. 19.43 feet 73. 13.3 meters 75. 288 tickets 77. 16.9 meters 79. 357.7 million barrels 81. 1.9	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9721999764442444, "perplexity": 1952.6810389015984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363809.24/warc/CC-MAIN-20210302095427-20210302125427-00030.warc.gz"}
http://mathhelpforum.com/algebra/222336-reverse-ratios-percentages.html	# Thread: Reverse ratios and percentages.... 1. ## Reverse ratios and percentages.... The teachers were right.... we will need this one day!!! I didn't do so well in math class. Thank you for forums like this! I am working with dilutions of a concentrate. (I will give both gallons and lbs.) We have a diluted drum of 55 gallons/450lbs. Of that, 15 Gal/122.715 lbs is the concentrate. 40 Gal/327.285 lbs is the water. I think that is a 3:8 dilution ratio. When performing a solids/activity test on this diluted product, we find the finished drum has 11.65% solids/activity. We do not have the original concentrate and need to determine what the solids/activity of the original concentrate is. (I hope someone will tell me it is as simple as multiplying 11.56 by 3) On the flip side...... We often have a concentrate for which we know the % of solids/activity ie. 49%. Then I want to plug into a formula (which I don't have) to determine the resulting solids at a known ratio ie. 1:75, or 1:120 etc.... Again I hope I'm making this too complicated and there is some very simple formula that I missed that day I skipped class to go swimming! humbly in appreciation. 2. ## Re: Reverse ratios and percentages.... Hey lisach. Percentages are basically some ratio times 100%. So if your ratio is say 1/10 = 0.1 then the percentage is 1/10 * 100% = 0.1 * 100% = 10%. With regards to the dilution you calculate 15/40 = 3/8 just as you have done so yourself. Remember its just a ratio of one thing relative to another (in this case, concentrate relative to water). To convert that to a percentage we multiply that ratio by 100% which gives us 3/8 100 = 300/8 = 75/2 = 32.5% 3. ## Re: Reverse ratios and percentages.... Ok... Well that is the first step. I get so lost here ..... Yes the ratio of the finial diluted drum is 3:8 and the percentage of concentrate in the drum is 32.5%, that is part of what I need but all of it. Let me go here for a minute....On the reverse side. • A concentrated sugar solution that is 49% sugar and 51% water has 49% activity/solids in it. • I dilute it with water at 1:75 ratio to make 450lbs/55 Gal. The drum then has 76 parts. 55 Gal=7040 oz---- 7040 oz/76=92.63 oz---- 1 part = 92.63 oz. • If 1 part is the original concentrate, and it is 49% active then 92.63oz49%=45.389 oz. So if the sugar was all condensed in a little packet sitting in the bottom of the drum it would be 45.389 oz in 7040 oz. • 45.389/7040= 0.645% • Therefore, if a concentrate with 49% activity diluted at 1:75 ratio will have an activity of .645% as a final dilution activity. Please correct me at this point if I am wrong.... If I was using a formula to get this instead of drawing out visual representations, I would be able to plug in the known factors and figure the reverse. a) activity level of concentrate 49% b) dilution rate 1:75 c) volume of diluted product 55 Gal d) activity level of diluted product .645% A final diluted drum of 55 Gal that was diluted at 3:8 ratio has an activity of 11.65%. How do we determine what the percentage activity of the original concentrate was. (like a deer in headlights here.....) 4. ## Re: Reverse ratios and percentages.... drum contains 450 lbs of diluted concentrate assay of drum= 11.56% solids solids in drum=0.1156 * 450 = 52 lbs solids in concentrate =52/122.7=0.424 fraction 42.4% 5. ## Re: Reverse ratios and percentages.... Ok... That looks very good..... Now to expand on that further...... a=activity of concentrate c=volume of diluted product b=dilution rate d=activity of diluted product Is there a quick way to determine the following? 1. Unknown activity level of final diluted product X a=49% b=1:75 c=450lbs d=x 1. Unknown dilution rate X a=49% b=X c=450lbs d=12% 6. ## Re: Reverse ratios and percentages.... I assumed that activity was % solids.If you need to make dilutions based on solids content or some other concentration unit I can help but you must clearly define what you want. 7. ## Re: Reverse ratios and percentages.... yes activity is the same thing as % solids I'm not sure what else to clarify 8. ## Re: Reverse ratios and percentages.... given concentrate 49% solids specific gravity not given.I will assume 1.5 dilution rate by volume 1:75 1gal conc = 8.35* 1.5 * 0.49 = 6.14 lb solids 75 gal water = 8.35 * 75=626.4 lbs water Total wt of mix =632.4 lbs % solids = 6.14 / 632.4 *100=0.97% by wt	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9198095798492432, "perplexity": 3925.453099517532}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719027.25/warc/CC-MAIN-20161020183839-00555-ip-10-171-6-4.ec2.internal.warc.gz"}
https://www.nature.com/articles/s42005-019-0168-y?utm_source=other&utm_medium=other&utm_content=null&utm_campaign=JRPC_2_SC_NatureKorea_Cphys_Sep&error=cookies_not_supported&code=1039bc25-8c5c-4b59-9f94-ea33a7020ab2	## Introduction Since McCarthy and Parks1 found radiation-dose enhancements inside thunderclouds with an airborne detector in 1980s, high-energy phenomena associated with thunderstorms have been detected inside the Earth’s atmosphere and from space. Terrestrial gamma-ray flashes (TGFs) are burst-like emission with their photon energy extending up to 20 MeV that last for several hundred microseconds, coincident with lightning discharges. They were first detected from space by Compton Gamma-Ray Observatory2, and since then have been reported by many other satellites3,4,5,6,7,8. Similar phenomena but going downward have been found in recent years at ground level9,10,11,12,13,14,15,16,17. They, now called “downward TGFs”, share several features with TGFs observed from space, such as coincidence with lightning, sub-millisecond durations, and energy spectra extending to >10 MeV. Downward TGFs that contains enough photons above 10 MeV have been experimentally shown to trigger atmospheric photonuclear reactions, namely producing neutrons and positron-emitting radioactive nuclei13,14. These photoneutrons can be observed as a short-duration gamma-ray burst lasting for several hundreds of milliseconds, as they are absorbed by atmospheric nuclei via neutron-capture processes14,18. Gamma-ray glows, also referred to as long bursts19 or thunderstorm ground enhancements20, are energetic radiation from thunderclouds with energies up to tens of MeVs, lasting for a few seconds to several minutes. They have been observed by airborne detectors1,21,22,23, at mountain-top20,24,25,26,27,28,29 and sea-level observation sites19,30,31,32,33. Gamma-ray glows usually coincide with passage of thunderclouds, and sometimes cease at the moment when lightning discharges take place1,21,22,23,34,35,36,37,38. Although TGFs and gamma-ray glows are distinguished clearly by duration, brightness, and timing with regard to lightning discharges, both of them are thought to originate from a common fundamental mechanism, called relativistic runaway electron avalanches (RREAs39,40). According to Wilson’s hypothesis41, seed electrons (provided by, e.g., cosmic rays) can be accelerated up to an energy of tens of MeVs in strong electric fields, producing secondary electrons. The number of multiplied and accelerated electrons exponentially increases, and the accelerated electrons finally emit bremsstrahlung gamma rays as they interact with ambient atmospheric nuclei. Dwyer42 proposed additional electron-seeding processes by positrons and backscattered gamma rays into the RREA mechanism, called “relativistic feedback model”. This model can achieve a higher multiplication factor than that of a RREA alone, and thus are thought to explain extraordinarily high brightness of TGFs. Despite an increasing number of respective observation samples of TGFs and gamma-ray glows, connections between them remain poorly understood. This is primarily because there has been no report of simultaneous detection of both, except for a very recent short report on a marginal detection17. In this paper, we report the first unequivocal simultaneous detection of them at sea level and discuss its implications. ## Results ### Observation of high-energy phenomena in winter thunderstorms The Gamma-ray Observation of Winter Thunderclouds (GROWTH) collaboration31,32,35,43 has been engaged with a multi-point observation campaign of atmospheric high-energy phenomena in coastal areas of Japan Sea14,44. Winter thunderstorms in Japan are ideal targets to observe this type of phenomena due to their unique characteristics; most notably typical altitude of clouds is significantly lower than ordinary38,45,46, which makes sea-level observations of gamma-ray glows viable. We have developed portable radiation detectors dedicated to the multi-point observation. They have a 25 cm × 8 cm × 2.5 cm Bi4Ge3O12 (BGO) scintillation crystal coupled with two photo-multiplier tubes (PMTs; HAMAMATSU R1924A). Outputs from the PMTs are amplified, and then read out by a 50 MHz digitiser onboard a data acquisition system. The data acquisition system stores 20-μs waveforms of the amplified analogue outputs once a pulse is detected, and extracts the maximum and minimum value as well as the timing of the pulse (see also Detector calibration). The maximum value corresponds to the energies of the pulse, and the minimum the analogue baseline voltage. The data acquisition system also records counts of discarded photon events due to buffer overflow, which are used for dead-time correction. Three detectors were deployed at three observation sites in Kanazawa City, the capital of Ishikawa Prefecture, by the Japan Sea coast (Fig. 1) and have been operated since October 2016. Lightning discharges were monitored by a broadband low-frequency (LF: 0.8–500 kHz) lightning mapping network (hereafter LF network), for which detectors are installed along Toyama Bay and in Noto peninsula. Another receiver in the extreme-low-frequency band (ELF: 1–100 Hz) is installed at Kuju, as summarised in the section Radio observations. We also utilise lightning location data of Japanese Lightning Detection Network (JLDN) operated by Franklin Japan Co., Ltd. ### Detection of gamma-ray glow and downward TGF On 9 January 2018, two of our detectors shown in Fig. 1 recorded gamma-ray glows. Figure 2a, b shows long-term count-rate histories of detectors A and B, respectively. At around 17:54 in coordinated universal time (UTC), detector A at Kanazawa Izumigaoka High School (36.538°N, 136.649°E) recorded a radiation increase for ~60 s. Then, ~30 s later, detector B at Kanazawa University High School (36.539°N, 136.664°E, 1.3 km east from detector A) also recorded a gamma-ray glow. No radiation enhancements were observed by detector C at Kanazawa University Kakuma Campus (36.546°N, 136.709°E; 4 km from detector B) in the period. The glow then suddenly terminated, coincident with a lightning discharge, while it was still being observed by detector B. An snapshot image of the X-band radar network at 17:55 shows a heavy precipitation area, corresponding to a thundercloud, located between detectors A and B (Fig. 1a). The radar data suggest that the thundercloud passed over the two detectors towards east-northeast with a speed of 19.3 ± 1.4 m s−1 (see Wind estimation with X-band radar). Since the temporal separation between the glow detection by the two detectors is consistent with the time for the thundercloud to travel the distance between the two detectors, we consider that the gamma-ray glows recorded by the two detectors are from the same cloud and hence of the same origin. At the same time as the glow termination and the lightning discharge, both detectors A and B recorded a short-duration radiation burst lasting for ~200 ms simultaneously. The count-rate profiles of the 200-ms-lasting short burst shown in Fig. 2c, d exhibit a steep rise and decay with time constants of 52.0 ± 4.9 and 59.2 ± 1.7 ms for detectors A and B, respectively. Combining the timing analysis with spectral analysis (see Gamma-ray emission originating from neutrons), the short burst is found to originate from neutron captures by atmospheric nitrogen nuclei, which Rutjes et al.18 predicted as “TGF afterglow”, and Enoto et al.14 observationally demonstrated. In addition, detector B recorded a faint annihilation emission at 511 keV for 10 s after the short burst (see Positron production by beta-plus decay). These features imply that atmospheric photonuclear reactions such as 14N + γ→ 13N + n and 16O + γ→ 15O + n took place coincident with the lightning discharge, as discussed in Bowers et al.13 and Enoto et al.14. Figure 3a, b shows the maximum and minimum waveform values of photon events during the short burst recorded by detectors A and B, respectively. At the very beginning of the short burst, both detectors A and B recorded saturated pulses (the maximum values exceeding >4 V), and then significant negative values of the baseline (the minimum values) called “undershoot” for ~10 ms. Although detector B failed to acquire the main part of the undershoot due to buffer overflow in the data acquisition system, it recorded the saturated pulses and the last part of the undershoot. As demonstrated in Methods: Initial flash of Enoto et al.14, this feature manifests the existence of an extremely large energy deposit (much more than hundreds of MeVs) in the scintillation crystal within a few milliseconds, which is a clear sign of a downward TGF. In the following analysis we employ an elapsed time t from the onset of the downward TGF at 17:54:50.308892 UTC, recorded by detector B. The LF network recorded a consecutive series of waveforms of the lightning discharge lasting for ~400 ms (Fig. 3c). The downward TGF coincided with a large-amplitude pulse at the initial phase of the lightning discharge within 10 μs (Fig. 3d). We detected four or so precursory pulses shortly before the large-amplitude pulse. No pulses had been detected before the precursory pulses by the LF network. The ELF measurement also confirmed that the associated ELF pulse was coming from the LF source. In addition, JLDN also reported a negative intracloud/intercloud (IC) discharge of −197 kA at t = −13 μs, which is temporally associated with the large-amplitude pulse. Figure 1b shows the source positions of the large-amplitude and precursory pulses determined by the LF network. At the beginning, the small precursory pulses took place in a southwest region less than 3 km away from detector B. Then, the main large-amplitude pulse (the fifth one in Figs. 1b and 3c) occurred 0.6 km southwest of detector B at t = −5.5 μs. JLDN also located the large-amplitude pulse within 0.9 km from detector B. These temporal and spatial correlations lead us to conclude that the large-amplitude LF pulse is associated with the downward TGF. ### Production mechanism of gamma-ray glow The multi-point observation enables us to investigate characteristics of the gamma-ray glow preceding the lightning initiation and the downward TGF. First, we perform spectral analysis. Figure 4 shows the background-subtracted gamma-ray energy spectra, extracted from −69 s < t < −39 s and −30 s < t < −10 s for detectors A and B, respectively. The detector response function is calculated with the GEANT4 Monte Carlo simulation framework47, and is convolved with a model spectrum in spectral fitting using the XSPEC package48. The observed spectra, of which instrumental responses are corrected, are found to be well explained by an empirical power-law function with an exponential cutoff, ε−Γexp[(−ε/εcut)α], where ε, Γ, εcut, and α are the photon energy (MeV), power-law photon index, cutoff energy (MeV), and cutoff index, respectively. The best-fitting parameters are $${\mathrm{\Gamma }} = 0.90_{ - 0.08}^{ + 0.06}$$ and $$1.02_{ - 0.05}^{ + 0.04}$$, $$\varepsilon _{{\mathrm{cut}}} = 6.4_{ - 1.1}^{ + 1.0}$$ and $$8.5_{ - 0.9}^{ + 0.8}\,{\mathrm{MeV}}$$, $$\alpha = 1.21_{ - 0.14}^{ + 0.15}$$ and $$1.43_{ - 0.14}^{ + 0.15}$$, and the 0.4–20.0 MeV incident gamma-ray flux of $$1.5_{ - 0.5}^{ + 0.7} \times 10^{ - 5}$$ and $$2.4_{ - 0.6}^{ + 0.7} \times 10^{ - 5}$$ ergs cm−2 s−1 on average over −69 s < t < −39 s and −30 s < t < −10 s integration periods for detectors A and B, respectively. Here and after, all the errors are statistical at 1σ confidence level, unless otherwise mentioned. We then perform another set of Monte Carlo simulations, using GEANT4, and compare the obtained energy spectra and count-rate histories with the simulated ones to investigate atmospheric interactions and propagation of electrons and gamma rays (see Simulation of gamma-ray glow). We find a model of spatial and energy spectral distribution for avalanche electrons in the RREA region which can reproduce both the obtained gamma-ray spectra and count-rate histories, and summarise the results in Figs. 1 and 4. The best-fit value of the RREA terminus altitude hbase is 400 m, which means the electron avalanche took place in the lower part of the winter thundercloud, and the offsets from the centre of the RREA region are 540 and 80 m for detectors A and B, respectively. The electron flux distribution is consistent with being proportional to a function of a distance from the RREA centre r, exp(−r/150 m), providing the circularly symmetric distribution. Figure 1b shows the centre position of the RREA region at the moment of the termination. Normalising the simulation result, we estimate the total production rate of 1–50 MeV avalanche electrons to be 3.66 × 1012 electrons s−1. The electron flux F(r, ε) at the terminus of RREA is also estimated to be a function of r and ε $${F(r,\varepsilon ) = 4.1 \,\times 10^2\,{\mathrm{exp}}\left( { - \frac{r}{{{\mathrm{1}}50\,{\mathrm{m}}}}} \right){\mathrm{exp}}\left( { - \frac{\varepsilon }{{{\mathrm{7}}.3\,{\mathrm{MeV}}}}} \right) {\mathrm{electrons}}\,{\mathrm{cm}}^{ - 2}\,{\mathrm{s}}^{ - 1}\,{\mathrm{MeV}}^{ - 1}.}$$ (1) This model reproduces the observed count-rate histories and spectra, except the increase in the count rate of detector B during −5 s < t < 0 s. This period is discussed in the section Abrupt increase in count rates of gamma-ray glow before downward TGF. Let us consider the electron multiplication factor M = FRREA/Fseed, where FRREA and Fseed are the average electron flux at the RREA terminus and seed electron flux, respectively. Integrating Eq. (1) yields the 0.3–50 MeV average flux within r = 150 m of FRREA = 7.5 × 102 electrons cm−2 s−1. Assuming that the seed electrons are mainly produced by cosmic rays, the 0.3–50 MeV seed electron flux is a function of a vertical acceleration length L and hbase given by $$F_{{\mathrm{seed}}}(L) = 2.56 \,\times 10^{ - 3}{\mathrm{exp}}\left[ {(L + h_{{\mathrm{base}}})/1890\,{\mathrm{m}}} \right]{\mathrm{electrons}}\,{\mathrm{cm}}^{ - 2}\,{\mathrm{s}}^{ - 1}$$ (2) (see Seed electrons). The multiplication factor M is thus a function of L, with the fixed hbase (400 m). In the RREA region, electron flux is known to increase39 exponentially as a function of L, FRREA= Fseed exp(L/λ), assuming that change of the vertical atmospheric pressure is negligible for the RREA processes at the low altitude. The avalanche length λ is empirically determined (see ref. 49 and references therein) to be λ = 7.3 MeV/(eE − 0.276 MeV m−1), where eE is a product of the elementary charge and strength of the electric field. The value of λ is then calculated to be 304, 99, and 59 m for E = 0.3, 0.35, and 0.4 MV m−1, respectively. We note that the set of the trial values of E up to 0.4 MV m−1 we have assumed is suggested to be plausible inside thunderclouds39. Therefore, combining M(L) = FRREA/Fseed(L) = exp(L/λ), L and M are derived to be L = 3240, 1160, and 710 m, M = 4.3 × 104, 1.3 × 105, and 1.6 × 105 for E = 0.3, 0.35, and 0.4 MV m−1, respectively. As Dwyer50 pointed out, the multiplication factor would not exceed ~105 in the RREA-only case because thunderclouds cannot maintain an acceleration length required for it. Given that L can reach twice as high as the typical diameter of the RREA region50, L < 600 m is required in this case, where the typical radius r = 150 m is employed. The 0.3 MV m−1 case is not plausible because the required acceleration length L = 3240 m cannot be maintained inside the thundercloud. In the other cases, it is necessary to take into account the relativistic feedback processes to explain the estimated avalanche multiplication factor. The relativistic feedback processes are parameterised with a feedback factor γ, the fraction of the seed electrons provided by the steady-state relativistic feedback processes50. The flux of runaway electrons is then modified as FRREA = Fseed(L) exp(L/λ)/(1 − γ). Figure 5 shows this relation between L and γ to explain the observed flux at the RREA terminus. To satisfy the condition L < 600 m, γ should be larger than 0.998 and 0.846 for 0.35 and 0.4 MV m−1, respectively. This suggests that the number of feedback-origin seed electrons is higher than that of cosmic-ray seed electrons by a factor of >5.5 for our event. ### Abrupt increase in count rates of gamma-ray glow before TGF The count-rate history of detector B exhibited an additional increase during −5 < t < −0 s (Fig. 6a). Figure 6b shows the ratio of the simulated model to the observed history. Although the observed history is well reproduced by the simulation up to t = −5 s, the observed count rate is twice as high as the simulation in −5 s < t < −0 s. Figure 6c shows the three energy spectra extracted from the time regions of −10 s < t < −5 s, −5 s < t < −2 s, and −2 s < t < 0 s. All the spectra show a power-law function with an exponential cutoff, indicating that bremsstrahlung is still the main process of gamma-ray production. Since our simulations fail to reproduce this increase in count-rate, we speculate that the increase was caused by a fluctuation of the intrinsic electron fluxes, rather than by the movement of the RREA region with the ambient wind flow. Based on the working hypothesis of the speculated increase of the accelerated electron flux, at least one of the following is required to have taken place: (1) stronger electric fields of the RREA region, (2) longer acceleration length, and/or (3) increase in the feedback factor γ. However, since lightning did not occur during this period (−5 s < t < 0 s), atmospheric mechanism could not drastically change the meteorological conditions, such as electric fields and acceleration length, within 5 s. We thus conjecture that temporal variations of the relativistic feedback processes played an important role for the electron flux increase, then the abrupt rise of gamma rays in the 5-s period before the lightning discharge. Assuming the electric field of 0.4 MV m−1, the doubled rate of avalanche electrons can be explained by increasing γ from 0.846 to 0.923. The RREA and relativistic feedback processes remained stable until t = −5 s; this state corresponds to the “steady state” of relativistic feedback as defined by Dwyer50, namely γ < 1. In general, when γ exceeds 1, an electron flux would spontaneously increase, and an RREA region should collapse. The timescale of the flux increase depends on the types of the relativistic feedback processes. The feedback process by positrons can discharge RREA regions within microseconds50. This timescale is close to that of TGFs, and is much shorter than that of the observed abrupt increase (i.e. 5 s). Alternatively, the feedback by backscattered X-rays may trigger a second-order discharge in RREA regions50. At present, even though the 5-s abrupt flux rise seems to be of great importance, its origin is yet to be understood. ## Discussion To conclude the relation between the gamma-ray glow and the downward TGF, verifying their temporal and positional coincidence will give a strong clue. Our observation cannot clarify whether the glow termination or the downward TGF took place first because these phenomena seemed to be slightly overlapped. On the other hand, the positional coincidence of the gamma-ray glow and the downward TGF in the present case is precisely determined owing to the multiple gamma-ray detectors and the LF network. The discussion in the section Production mechanism of gamma-ray glow suggests that the gamma-ray glow ceased when the source cloud was moving 130 m southwest of detector B (Fig. 1b). Also, the TGF-associated LF pulse was located within 0.5 km from detector B. Therefore, it is clear that the two phenomena are physically related to one another. Our interpretation of the observed gamma-ray glow suggests that the electron acceleration site should have electric fields of 0.35 MV m−1 or higher in order to achieve the high electron multiplication factor of >105 with a plausible acceleration length. In such highly electrified regions, TGFs are thought to initiate more easily than in other less-electrified regions as Smith et al.17 suggested. From another point of view, we speculate that the avalanche electrons of the gamma-ray glow can behave as seed electrons of the downward TGF. At the point where the TGF-associated LF pulse was located (point 5 in Fig. 1b), the 0.3–50 MeV electron flux at 400 m altitude is estimated to be 1.7 × 102 electrons cm−2 s−1. By comparing this flux with that of the cosmic-ray-induced seed electrons (the canonical seed electron source), it is suggested that the highly-electrified region responsible for the gamma-ray glow can be the dominant source of seed electrons for the TGF which occurs in the close proximity of the gamma-ray glow. In addition, the abrupt count-rate increase monitored by detector B before the TGF (see section Abrupt increase in count rates of gamma-ray glow before downward TGF) suggests additional production of avalanche electrons for the gamma-ray glow, and might have predicted drastic changes in the electrified region such as the lightning discharge and the TGF. In the present high-energy event, the discussion above suggests a possibility that the high electron current in the gamma-ray glow assisted the initiation of the downward TGF. However, it still remains observationally unclear how gamma-ray glows and TGFs are related with each other in general. Among an increasing sample of glow terminations, TGF-associated events are still quite rare, i.e. only Smith et al.17 and the present event. For example, a termination event during a winter thunderstorm in 2017 (ref. 38) was associated with an intracloud/intercloud discharge but not related with any signals for TGF-like emissions. As another example, a TGF-like intensive emission associated with photonuclear reactions was reported14, where no gamma-ray glows were recorded before the event. In these cases, we lack sufficient evidences due to our present sparse observation sites on the ground to conclude that glow terminations are not always associated with TGFs. Our future gamma-ray monitoring network combined with radio-frequency lightning mapping systems will give a clue to reveal the relation between TGFs and gamma-ray glows. In summary, we detected a gamma-ray glow, terminated with a downward TGF which triggered atmospheric photonuclear reactions. The gamma-ray glow was so bright that the relativistic feedback processes are required. Although we cannot determine whether the glow termination or the downward TGF occurred first, the two high-energy phenomena in the atmosphere took place in an identical electrified region of a winter thundercloud, and hence are clearly related to each other in the present case. ## Methods ### Detector calibration Energy calibration of the detectors was performed to convert the maximum value of a pulse into photon energy. We measured the centre of environmental background lines of 40K (1.46 MeV) and 208Tl (2.61 MeV), and built a linear calibration function which is utilised to assign the energy of each photon. All the detectors record 0.4–20.0 MeV gamma rays. See also Instrumental calibration in Enoto et al.14 for details. Absolute timing is conditioned by pulse-per-second signals of the Global Positioning System (GPS). The timing-assignment logic employed from 2017 to 2018 winter provides absolute timing accuracy of each photon better than 1 μs. However, detector A failed to receive the GPS signals during the experiment. Instead, we performed the calibration of detector A, using the internal clock time with ~1 s accuracy, and then corrected the absolute timing so that the detection time of the downward TGF matches that with detector B. ### Wind estimation with X-band radar We utilised data of eXtended RAdar Information Network (XRAIN). XRAIN is a polarimetric weather radar network in the X band and has a spatial resolution of 280 m (east–west) × 230 m (north–south) mesh. It records two-dimensional precipitation maps with a 1-min interval. XRAIN also obtains three-dimensional maps of radar echoes and particle types with a 5-min interval by the constant-altitude plan position indicator technique. However, the three-dimensional data are not utilised in the present paper because the XRAIN observations have a moderate spatial resolution of altitude (≥1 km), which is insufficient to discuss charge structures in the thundercloud. Wind velocity and direction are estimated by overlaying and shifting precipitation maps at different time. First, 11 maps from 17:50 to 18:00 were extracted in the range of 36.4°N–36.7°N, 136.4°E–136.8°E. We then took a pair of maps with a 5-min interval (six pairs in total), and calculated the sum of precipitation residual at each mesh, given by $$\Sigma _{i,j}(P_{ij}^1 - P_{ij}^2)^2$$, where $$P_{ij}^1$$ and $$P_{ij}^2$$ are precipitation at each mesh on each map, and i and j are mesh indexes. With trial shifting of one map with several steps of the spatial resolution for four directions, we searched for the position which takes the minimum residual sum. The distance and direction for which the cloud moved in 5 min can be estimated from the amount of the map shift at the point of the minimum residual sum. Consequently, the wind direction and velocity at the moment of the glow detection were determined to be west-northwestwards and 19.3 ± 0.9 (systematic) ± 1.1 (statistic) m s−1, respectively. Here, the quoted statistical error was calculated from the the standard deviation (1σ) of six pairs. The systematic error was determined by the mesh size and temporal interval of the map pair. The wind velocity with the overall error is then calculated to be 19.3 ± 1.4 m s−1, where the standard error propagation in quadrature between the systematic and statistical errors is assumed to hold. Since the statistic error is smaller than 10% and is comparable with the systematic error, it is reasonable to assume that the wind parameters did not change considerably during the glow observation. ### Gamma-ray emission originating from neutrons Photonuclear reactions such as 14N + γ13N + n and 16O + γ→ 15O + n expel ~10 MeV neutrons from atmospheric nitrogen and oxygen nuclei51,52,53. The photoneutrons gradually lose their kinetic energy via elastic scatterings, and are eventually captured by atmospheric nuclei such as 14N. In the dominant reaction 14N + n15N + γ, 15N nuclei in excited states emit various de-excitation gamma-ray lines up to 10.8 MeV. In addition, de-excitation gamma rays from other nuclei such as Si and Al should be also emitted when photoneutrons were captured by ambient nuclei in soil, buildings, and components of the detectors. These de-excitation gamma rays originating from neutron captures are thought to compose the short burst14,18. The timescale of the short burst is determined by neutron thermalisation13,14,18. A numerical calculation predicts the neutron-capturing rate of exp(−t/τ) for 5 ms < t < 120 ms, where t is the elapsed time from the onset of the TGF and τ ≈ 56 ms is the decay constant14. The count-rate histories of the observed burst have decay constants of 52.0 ± 4.9 and 59.2 ± 1.7 ms for detectors A and B, respectively. These results are consistent with the calculation. Supplementary Fig. 1 shows the energy spectra of the burst with detectors A and B. Enoto et al.14 simulated the de-excitation emission, considering atmospheric scattering of the gamma rays and moderate energy resolution of BGO crystals. The emission model from 15N and ambient nuclei, such as Al and Si, well reproduces the results of both detectors A and B. From the spectral and temporal analyses, we confirm that the observed short burst is caused by neutrons produced via atmospheric photonuclear reactions. ### Positron production by beta-plus decay After neutrons are expelled from 14N and 16O, unstable nuclei 13N and 15O start emitting positrons via β+ decay with half-lives of 10 and 2 min, respectively. Positrons immediately annihilate and emit 511 keV annihilation gamma rays. Supplementary Fig. 2a–d shows count-rate histories in the 0.4–0.65 and 0.65–30.0 MeV bands. Whereas detector A recorded no enhancements after the short burst, detector B recorded an afterglow in the 0.4–0.65 MeV band for the period 0 s < t < 10 s. The count rates decreased with a decay constant of 6.0 ± 2.1 s. The background-subtracted photon count in the 0.4–0.65 MeV band for 1 s < t < 10 s is (2.0 ± 0.4) × 102 photons. The background-subtracted energy spectrum is shown in Supplementary Fig. 2e. The centre energy of the line emission is 528 ± 14 keV, which is consistent with 511 keV of the annihilation line within error. These results lead us to conclude that a positron-emitting region filled with 13N and 15O were produced in the atmosphere by the photonuclear reactions, and then passed over detector B flown by the ambient wind flow14. Considering that the count-rate history shows a monotonic decrease, the positron source might be generated somewhere above detector B or downwind. The LF network has five stations (Supplementary Fig. 3a). Each station has a flat plate antenna sensitive to 0.8–500 kHz. Analogue outputs from the antenna are sampled by a 4 MHz digitiser, whose absolute timing is calibrated with the GPS signals. The LF network can locate radio pulses with the time-of-arrival technique. Supplementary Fig. 3b, c shows the entire LF waveforms of the observed lightning discharge. The ELF receiver is installed in Kuju (33.059°N, 131.233°E) as a station of the Global ELF Observation Network operated by Hokkaido University. The station has two horizontal search coil magnetometers sensitive to 1–100 Hz magnetic-field perturbations in the east–west and north–south directions. The analogue output is sampled by a 400 Hz digitiser. The direction-of-arrival of the ELF pulses can be confirmed with the magnetic-detection-finder technique. Supplementary Fig. 3d shows the observed waveform in the ELF band. The JLDN reported two other discharges besides the TGF-associated radio-frequency pulse: an IC of −14 kA at t = 18.7 ms and a CG of −13 kA at t = 228.6 ms. Supplementary Fig. 3b, c shows the corresponding LF pulses. Since these pulses occurred long after the observed TGF, we consider that they were not associated with the high-energy phenomena. ### Simulation of gamma-ray glow We performed Monte Carlo simulations of electron propagation in the atmosphere to reproduce the count-rate histories and energy spectra, using GEANT4 (ref. 47). We assume that electron avalanches towards the ground developed in thundercloud, and that the electron spectrum of the RREA at the end of the region has the shape of exp(−ε/7.3 MeV)49, where ε is the electron energy. We also assume that the distribution of the electron flux in the avalanche region is circularly symmetric and has no intrinsic time fluctuation. These assumption should be reasonable, given that the count-rate history of detector A is symmetric about the peak, and that the wind velocity was approximately constant (see Wind estimation with X-band radar). The energy spectra of bremsstrahlung gamma rays from the avalanche electrons approximately follow ε−Γexp(−ε/7.3 MeV)54. The photon index Γ is determined from the source altitude h and offset from the source centre. Count-rate histories depend on the size of the RREA region, wind velocity, and h. The distribution of gamma rays is more diffuse at a higher source altitude due to atmospheric scattering, hence resulting in a longer and fainter gamma-ray glow. First, we tested a disk-like region with a uniform electron flux, varying h and disk radius in our simulations. Supplementary Fig. 4a shows some examples of the simulation results at various altitudes. Comparing the simulation results with the observation, h = 1500 m is required to reproduce the observed count-rate histories, whereas Γ of the energy spectra indicates h = 900 m. Since any other conditions cannot satisfy both the spectra and count-rate histories, this uniformed-disk model is thus rejected in this analysis. Then, we considered two disk-like models in which the spatial distribution of the electron flux follows either of the two functions of a distance from the RREA centre l: a Gaussian model, exp(−l2/2σ2) and an exponential model, exp(−l/L). The parameters σ and L are free parameters, which denote the spatial extent of the surface brightness of the emission. We found that both models can reproduce the obtained count-rate histories and spectra; The estimated parameters are h = 600 m and σ = 200 m for the Gaussian model, and h = 400 m and L = 150 m for the exponential model. Comparing these two best models, we found that the exponential model explains the observation better, particularly for the count-rate histories of detector B (Supplementary Fig. 4b). Therefore, we employ the exponential model as a working hypothesis to interpret the observation. ### Seed electrons We assume that the seed electrons of the RREA processes are mainly produced by cosmic rays. To calculate the electron fluxes of secondary cosmic rays, we employed Excel-based Program for calculating Atmospheric Cosmic-ray Spectrum (EXPACS)55,56, which calculates the flux and spectrum of cosmic-ray particles as a function of an altitude, latitude, longitude, and solar modulation. We extracted electron spectra at an altitude h of 300–2000 m, and then integrated the spectra to obtain the electron fluxes Fseed in the energy range of 0.3–50.0 MeV. The electron flux was found to increase exponentially as a positive function of altitude, given by Fseed = 2.56 × 10−3 × exp(h/1890 m) electrons cm−2 s−1. Carlson et al.57 have considered 1 MeV seed electrons produced by cosmic rays. Kelley et al.22 employed it, and derived the seed flux to be 0.25 cm−2 s−1 at 14.1 km. Our calculation with EXPACS gives the electron flux at 14.1 km of 0.86 cm−2 s−1. Given that Carlson et al. took a more thorough approach than ours by simulating the effective seeding efficiency for various particles, energies, and geometries, our method might have overestimated the seed electron flux. Regardless of the potential errors in our method, our conclusion that the gamma-ray glow requires relativistic feedback is unaffected, because overestimation of the seed flux, even if it was the case, would result in an underestimation of the multiplication factor.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9381633996963501, "perplexity": 1784.2110005914196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335054.79/warc/CC-MAIN-20220927162620-20220927192620-00476.warc.gz"}
https://www.gerad.ca/fr/events/859	Groupe d’études et de recherche en analyse des décisions Unit Commitment - Challenges and Wind Energy Bala Venkatesh – Ryerson University, Canada Unit commitment is a challenging problem to solve. Its key attributes include: (1) A set of nonlinear power balance equations that are hourly. The number of sets equal 24 for the day-ahead challenge. The number of equations in each set equals $$2N$$ where $$N$$ is the number of buses in the system. (2) A set of intertemporal constraints that bind the 24 hourly solutions together. These include generator status, ramping limits on generator outputs, etc. (3) A whole host of operating limits such as generator output limits, line flow MVA limits, bus voltage magnitude limits, etc are imposed on the solution. The objective for the problem is to minimize the total generation cost. This presentation outlines these challenges and discusses a possible solution process using sequential mixed integer linear programming algorithm. Further, the challenge of integrating wind energy to such an algorithm is also briefly discussed.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7922571897506714, "perplexity": 915.2565757104061}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178356232.19/warc/CC-MAIN-20210226060147-20210226090147-00182.warc.gz"}
https://en.wikipedia.org/wiki/Color_wheel_graphs_of_complex_functions	# Color wheel graphs of complex functions In mathematics, a complex function is a function with the complex numbers (see the imaginary numbers and the complex plane) as both its domain and codomain. The complex color wheel method assigns a color to each point of the complex plane. ## Methods HL plot of z, as per the first definition in the text: the origin is black, −1 is red, 1 is cyan, and a point at infinity is white Color wheel graph of complex function sin 1/z (according to the second definition). Black parts inside refer to numbers having large absolute values. This function has an essential singularity at z = 0. A graph of the complex logarithm using a different coloring method. Here, red is 1, cyan is -1. Brightness represents magnitude, with white at infinity The assignment of color to complex point could be diverse, but often one of the following two: • the origin is black, −1 is red, 1 is cyan, and a point at infinity is white: {\displaystyle {\begin{aligned}H&=\pi +\arg z,\\L&=\left(1-2^{-\left\|z\right\|}\right)\times 100\%,\\S&=100\%.\end{aligned}}} • the origin is white, 1 is red, −1 is cyan, and a point at infinity is black: {\displaystyle {\begin{aligned}H&=\arg z,\\L&=2^{-\left\|z\right\|}\times 100\%,\\S&=100\%.\end{aligned}}} More precisely, the argument (angle) of the complex number defines the hue value while the modulus defines the light value of the color in the HLS (hue, lightness, saturation) color model; for a given (H,L) pair we choose the maximal saturation value. In both assignments, vivid colors of the rainbow are rotating in a continuous way on the complex unit circle, so the sixth roots of unity (starting with 1) are, according to the second definition: red, yellow, green, cyan, blue, and magenta. In addition, it is common in the assignments that the gradations of colors belonging to two complex numbers close to each other are close to each other, and that colors of complex numbers of the same argument are gradations of the same color – the one which has greater absolute value is lighter (according to the first definition) or darker (according to the second definition). However, the HSL color space is not perceptually uniform, leading to streaks of perceived brightness at yellow, cyan, and magenta (even though their absolute values are the same as red, green, and blue) and a halo around L = 1/2. Use of the Lab color space corrects this, making the images more accurate, but also makes them more drab/pastel.[1] To make images comparable, it is highly recommended to use the standardised color schemes of the Digital Library of Mathematical Functions.[2] ## History The color wheel method was probably first used in publication in the late 1980s by Larry Crone and Hans Lundmark.[3]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.629305899143219, "perplexity": 903.4244361277351}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123048.37/warc/CC-MAIN-20170423031203-00640-ip-10-145-167-34.ec2.internal.warc.gz"}
https://dsp.stackexchange.com/questions/40518/frequency-translation-or-pitch-shifting-through-linear-interpolation-in-frequenc	# frequency translation or pitch shifting through linear interpolation in frequency domain I want to perform pitch shifting with the method described in NEW PHASE-VOCODER TECHNIQUES FOR PITCH-SHIFTING, HARMONIZING AND OTHER EXOTIC EFFECTS. Basically, it involves: 1. Locate the spectral peaks and their indices in spectrums. 2. Determine the region of influence (ROI) for each detected peak. 3. Perform peak shifting according to the amount of frequency shift. Specifically, peaks and their ROI are shifted by an amount of frequency. 4. Update the phase to maintain the phase coherence, as in phase vocoder for time-scaling. I am stuck in step 3. The paper describes that with a fractional number of frequency bin shifting (rather than integer number of frequency bin), one should use interpolation since the frequency bins are discrete: If the amount of frequency shift is a fractional number of frequency bins, then frequency-domain interpolation is required, since the sinusoidal peak is only known at discrete frequencies. My problem is that how do I perform peak shifting through, say, linear interpolation? And, assume a shifted spectrum is obtained, as interpolation insert values between the original discrete bins, how is it finally istf to the pitch-shifted output? I appreciate for any help. EDIT: I've realized my question can be simply be phrased as "fractional shifting of spectrum components". The following code is an example to achieve fractional shifting with a random signal using linear interpolation: import numpy as np import matplotlib.pyplot as plt np.random.seed(5) y = np.random.random(20) alpha = 3.2 # shifting factor # Pad the signal with zero # to avoid spill-out caused by # large shifting factor xInt = x[0:len(y)]*alpha # the 'xp' in function interp yInt = y # the 'fp' in function interp # Now define 'x' in function interp start = np.ceil(xInt[0]) end = np.ceil(xInt[-1]) if float(xInt[-1]).is_integer(): xQue = np.arange(start, end+1, 1).astype(int) else: xQue = np.arange(start, end, 1).astype(int) yNew = np.interp(xQue, xInt, yInt) # linear interpolation shifted[xQue] = yNew plt.plot(shifted, 'r') plt.show() The above example uses a randomly generated signal to illustrate fractional shifting of a spectrum. However, in the real case, a spectrum shouldn't be padded with zero in the first case as I do in the code. So, how to deal with the "spill" with spectrum component if the shifting factor is too large?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.738584578037262, "perplexity": 2908.4689954044184}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999130.98/warc/CC-MAIN-20190620024754-20190620050754-00430.warc.gz"}
https://mathlesstraveled.com/2011/04/14/triangular-number-equations-via-pictures-solutions/	## Triangular number equations via pictures: solutions Here are some solutions to my previous post. However, they are almost certainly not the only solutions! If you have other cool ways to visualize any of these (or any other triangular number equations) feel free to post in the comments — either a link to an image if you have one, or just a description if you don’t have a good way to make an image. $3T_n + T_{n-1} = T_{2n}$ $3T_n + T_{n+1} = T_{2n+1}$ $(2k+1) T_n + T_{kn - 1} = T_{(k+1)n}$ $T_n T_k + T_{n-1} T_{k-1} = T_{nk}$ Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus. This entry was posted in arithmetic, pattern, pictures, proof, solutions and tagged , , , . Bookmark the permalink. ### 10 Responses to Triangular number equations via pictures: solutions 1. Fergal Daly says: I didn’t actually attempt them before you posted your solution but the solutions are beautiful. I wonder is there a nice way of turning each picture into an algebraic proof. • Brent says: Well, algebraic proofs for these are all pretty simple: just plug in the formula for triangular numbers and do some algebra. I don’t know whether there’s a way to see a connection between the pictures and the specific algebraic manipulations required; there might be! • jd2718 says: If we flipped the odd triangles to the center, eg on the first row flipped the red ones down and brought the blue up, at least we have a suggestion. There are 3 blue triangles, each reaching halfway up the “perimeter” of the big one to meet the next, and leaving a gap, one smaller, in the center. Maybe that’s a subtraction I’m looking at? Jonathan 2. Excellent solutions Brent. And nice graphics too. 3. By the way, I have included you in my blogroll. 4. Tom says: Very pretty! The final solution is particularly impressive. Congrats on recognising that pattern amidst your M&M’s 🙂 BTW, what program are you using to generate these graphics??? I’ve been hunting around for some free software which could quickly generate pretty mathematical drawings, and these drawings do look quite impressive. • Brent says: I was wondering if someone would ask that. =) The short answer is that I used software I wrote myself, which I’ve been working on in fits and starts over the past two and a half years. I hope to make it more widely available soon (free and open source), at which point I’ll probably write about it. The short version is that it is a domain-specific language for describing pictures and diagrams, embedded within the Haskell programming language. To make simple diagrams doesn’t really require knowing much (if any) Haskell; you just use the supplied primitive shapes, transformations, and ways of combining diagrams. But when you want to start doing more sophisticated things you have the entire power of Haskell at your disposal. • Tom says: Wow, that’s pretty cool. Yet another reason to learn Haskell… 🙂	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5143544673919678, "perplexity": 1038.7735671409923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119225.38/warc/CC-MAIN-20170423031159-00470-ip-10-145-167-34.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/conditions-for-using-stokes-theorem.695228/	Conditions for using Stokes' Theorem 1. Jun 3, 2013 Mandelbroth I'm back with more questions! I'm wondering what conditions must a manifold satisfy to be able to use Stokes' Theorem. I understand that it must be orientable, but does it have to necessarily be smooth? I tried to see if it was possible to prove Cauchy's Residue Theorem and Cauchy's Integral Formula using Stokes' Theorem, but I got stuck with results that don't make sense. Both require that an integrand can be meromorphic, so I'm not sure that Stokes' Theorem will necessarily apply to nonsmooth manifolds. 2. Jun 3, 2013 3. Jun 3, 2013 Mandelbroth I didn't know. :tongue: I figured it out, though. I think it's cool, so I might as well share it here to explain what I was trying to do to see if there's any more information to be had. Let $z\in\mathbb{C}:z=x+iy$ and $f(z)=u(x,y)+iv(x,y)$ be a meromorphic function such that f is undefined for all $z_0\in\mathcal{A}\subseteq D:\mathcal{A}=\{a_1, a_2, \cdots , a_n\}$. Then, what I wanted to say was $$\oint\limits_{\partial D}f(z) \, dz = \iint\limits_D d(f(z) \, dz) = \iint\limits_D \left(\left(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}\right)+i\left(\frac{\partial v}{\partial y}-\frac{\partial u}{\partial x}\right)\right)dy\wedge dx$$ which makes the Cauchy Integral Theorem rather trivially evident. However, this is not necessarily the most fun to use to prove the more general Residue Theorem. What I noted instead was that I could make the integral become $$\iint\limits_{D\setminus\mathcal{A}} \left(\left(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}\right)+i\left(\frac{\partial v}{\partial y}-\frac{\partial u}{\partial x}\right)\right)dy\wedge dx + \sum_{k=1}^{n}\left[\, \oint\limits_{\beta(a_k)}f(z) \, dz \,\right]$$ where $\beta(a_k)$ traces an infinitesimally small circle around $a_k$. I'm working in a similar way to get the Cauchy Integral Formula. 4. Jun 4, 2013 lavinia Stokes theorem applies to smooth singular chains.These exist on both oriented and non-oriented manifolds. The real and complex parts of a holomorphic differential are closed. This just restates the Cauchy-Riemann equations. Stokes theorem tells you that the integral of the differential must be zero around any piecewise smooth closed curve within its domain of holomorphy. Except for the term of degree minus 1, the terms in a Laurent series when multiplied by dz are all exact forms and so by Stokes Theorem integrate to zero around a circle. So the integral of a meromorphic function around a pole is its residue by Cauchy's theorem. Last edited: Jun 5, 2013 5. Jun 5, 2013 Mandelbroth I understand everything else about your post, but this is new to me. I was aware that Stokes' Theorem had something to do with chains, but I was unaware that you could use that fact to apply it to non-orientable manifolds. But then, I don't understand how that would work, since all of the integration I've done preserved some form of orientation (id est, $\int_{a}^{b}f^\prime(x) \, dx = \int\limits_{[a,b]} f^\prime(x) \, dx = f(b) - f(a)$). Can you please elaborate how you would integrate over a non-orientable manifold using Stokes' Theorem? 6. Jun 5, 2013 WannabeNewton See chapter 4 of Spivak's Calculus on Manifolds. 7. Jun 5, 2013 lavinia i am sorry I was so brief. A smooth singular simplex has two natural orientations. One can always integrate a differential form over an oriented simplex whether it is in an oriented or unoriented manifold. A smooth singular chain is a finite formal sum of oriented smooth simplexes. The integral of a differential form over the chain is the sum of its integrals over each oriented simplex in the chain. When you talk about "integrating over a manifold" you mean expressing the fundamental cycle of the manifold as a smooth singular chain then integrate over that chain. An unorientable manifold does not have a fundamental cycle so there is no smooth singular chain to integrate over. Last edited: Jun 5, 2013 8. Jun 6, 2013 lavinia As an after thought here is something to think about. Suppose you have a function on a non-orientable manifold. Pull this function back to the orientable 2 fold cover and multiply it by any orientation form you want. Integrate this then divide by 2. Similar Discussions: Conditions for using Stokes' Theorem	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9651029706001282, "perplexity": 380.56695605280333}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823284.50/warc/CC-MAIN-20171019122155-20171019142155-00811.warc.gz"}
https://www.physicsforums.com/threads/meaning-of-this-operator.134916/	# Meaning of this operator 1. Oct 5, 2006 From the "Lie Group" theory point of view we know that: $$p$$ := is the generator for traslation (if the Lagrangian is invariant under traslation then p is conserved) $$L$$:= s the generator for rotation (if the Lagrangian is invariant under traslation then L is conserved) (I'm referring to momentum p and Angular momentum L, although the notation is obvious ) My question is if we take the "Lie derivative" and "covariant derivative" as a generalization of derivative for curved spaces.. if we suppose they're Lie operators..what's their meaning?..if the momentum operator acts like this: $$pf(x)\rightarrow \frac{df}{dx}$$ derivative of the function..could the same holds for Lie and covariant derivative (covariant derivative is just a generalization to gradient, and i think that Lie derivatives can be expressed in some cases as Covariant derivatives, in QM the momentum vector applied over the wave function is just the gradient of the $$\psi$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.995743453502655, "perplexity": 768.9913017349189}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267163146.90/warc/CC-MAIN-20180926022052-20180926042452-00370.warc.gz"}
https://pypi.org/project/fwdpy11/0.6.0rc0/	Forward-time population genetic simulation in Python ## Project description This is the README for fwdpy11, which is a Python package for forward-time population genetic simulation. It uses fwdpp as its C++ back-end. Master: Development: ## Manual Latest/master: Development branch: ## Features • Picklable population objects • Parallel computation via multiprocessing or concurrent.futures. • Custom temporal samplers to analyze populations during a simulation may be written in pure Python. ## Dependencies The following must be present on your system: • GSL. This is a C library. It is available via conda. fwdpy11 requires version 2.3 or greater. • pybind11. This should be installed conda as appropriate for your system, or via your system’s package manager or manually. See note below. • cmake. This should be installed by conda or your favorite package manager. fwdpy11 also uses fwdpp, which is included as a submodule. Note The C++ modules are built using cmake, which requires that pybind11’s cmake macros are visible. Installing pybind11 via pip does not install the macros. However, installs using conda, apt-get, or manual installation from source will install both the Python module and the cmake macros. GPLv3 or later (See COPYING) ## Suppored Python version fwdpy11 is written for Python 3. We will not modify the package to be compatible with Python 2.7. ## Installation Building from the git repository: git submodule init git submodule update python setup.py build_ext -i python -m unittest discover tests Using pip on macOS and Linux (or pip3 as appropriate for your system): pip install --upgrade fwdpy11 It is possible that the cmake macros to detect the GSL can fail to detect the correct version. Issues like this are a basic weakness of cmake. I’ve seen this in conda environments, where the macro prefers the system version over the newer version in the environment. To “fix” this, give it a hint: GSL_ROOT_DIR=/path/to/gsl python3 setup.py build_ext -i ### macOS On Apple’s macOS, we strongly encourage that you use conda with their compiler packages: conda install clang_osx-64 clangxx_osx-64 Installing these packages will mean that you can get away from the relatively old versions of these compilers that ship with Xcode. However, you do need to add the following flag when building the package: On macOS versions prior to “Mojave”: CONDA_BUILD_SYSROOT=/ python3 setup.py build_ext -i For later versions, you may omit the environment variable prefix. Do the same for a pip install from the source directory. ### Windows We have heard positive reports of using fwdpy11 on Windows 10 with the Ubuntu subsystem installed. For such a system, you may use a Linux conda installer and then install fwdpy11 via bioconda. The developers do not have access to this platform, but we are keen to hear of any issues. ### Caution We use the GitHub “release” mechanism to make stable versions available. However, GitHub releases to not include the sub-modules, meaning that the releases themselves cannot be used for installation. (A related irony is that the Zenodo DOI for the releases are somewhat meaningless.) To install a specific release: 1. Use pip (see above). This is the recommended approach if you do not use conda. 2. Install from bioconda. This is the recommended approach. 3. Clone the repo, checkout the release, and update submodules: git clone http://github.com/molpopgen/fwdpy11 cd fwdpy11 git submodule init git submodule update The latter method is probably the least appealing. We have a strict policy of putting releases on PyPi and bioconda. If there is a release on PyPi but not on bioconda, then that is because we identified a bug and pushed a new release before the bioconda build happend. It happens. That’s life. ## Enabling code profiling By default, fwdpy11 is compiled with aggressive optimizations to help reduce the library size. One side effect is that it becomes impossible to accurately profile the code. To override these defaults: python setup.py build_ext -i --enable-profiling Note The package should not be installed with profiling enabled. This method of building is for developers who need to accurately profile the C++ back-end. Also note that only the main package is affected. Building the unit test modules is not affected. ## Enabling debugging symbols in the C++ code python setup.py build_ext -i --debug Debug mode disables all compiler optimizations, allows C-like assertions, and generated debug symbols. Note Never install the package compiled in debug mode! First, things will run much more slowly. Second, triggering an assertion will cause the Python interpreter to crash. These assertions exist as a brute-force method to help developers quickly identify bugs. ## Enabling assertions in the C++ code The fwdpp library code uses C’s assert macros in several places. These are disabled by default. However, it can be useful to enable them when hacking the code. To do so, you must manually set your compiler flags with cmake: cmake . -DCMAKE_CXX_FLAGS="-UNDEBUG -O2 -g" When compiling this way, fwdpy11 makes some extra checks that will throw RuntimeError if they fail. The fwdpp back end also makes extra checks. If those fail, abort will be called, which will crash the Python interpreter. Thus, compiling with this option is a “serious debugging mode only” option. ## Enabling aggressive debugging of C++ STL templates using GCC Use the following flags to enable an “extreme” debugging mode of the C++ standard template library: CXXFLAGS="-D_GLIBCXX_CONCEPT_CHECKS -D_GLIBCXX_DEBUG -D_GLIBCXX_DEBUG_PEDANTIC" \ CPPFLAGS="-D_GLIBCXX_CONCEPT_CHECKS -D_GLIBCXX_DEBUG -D_GLIBCXX_DEBUG_PEDANTIC" python3 setup.py build_ext -i ### Bioconda fwdpy11 is available through bioconda for Linux and for macOS: conda install -c bioconda fwdpy11 ## Project details Uploaded source	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23138533532619476, "perplexity": 9677.5585680644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571847.45/warc/CC-MAIN-20220812230927-20220813020927-00570.warc.gz"}
https://indico.math.cnrs.fr/event/1577/timetable/?print=1&view=standard	# Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows Europe/Paris Amphi Hermite (Institut Henri Poincaré) ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Description Flows with liquid-vapor transfer occur at many different scales in the atmosphere as well as in many industrial processes. It would be interesting to have a general review of the topic before focusing on the simpler geometry involving a single liquid-vapor interface. An objective of the workshop will be to discuss the relative merits and to compare different numerical methods (if the single liquid-vapor interface is still too complex, the comparison could be made on a liquid-gas interface without mass transfer). It could be also interesting to find clear-cut problems in order to make quantitative comparisons between different models or with experimental results. The registration is free of charge but mandatory. Lunch and coffee break will be offered. Where : Institut Henri Poincaré, Paris, France (map here). When : december 12-13, 2016. Program (pdf) : see here. Registration : see here. A 3D bubble with Adaptative Mesh Refinement (A. Talpaert - CEA Paris-Saclay) Invited speakers : • Marie Béchereau (Ecole normale supérieure de Cachan, Paris-Saclay) • Guillaume Bois (CEA Paris-Saclay) • Hélène Mathis (Université de Nantes) • Richard Saurel (Université d'Aix-Marseille) • Arthur Talpaert (CEA et Ecole Polytechnique, Paris-Saclay) • Laurette Tuckerman (Ecole Supérieure de Physique et de Chimie Industrielle de Paris) • Stéphane Zaleski (Université Pierre et Marie Curie, Paris) 3D bubbles with averaging plane (G. Bois - CEA Paris-Saclay) Participants • Anne Burbeau • Anouar MEKKAS • Antoine du Cluzeau • Arthur Talpaert • Benjamin Graille • Benoit-Joseph Grea • Bertrand Mercier • Bérénice Grec • Caterina Calgaro • Cedrick Copol • Chaouki HABCHI • Christophe Chalons • Christophe Josserand • Colette Nicoli • Daniel Fuster • Daouda SANGARE • Dena Kazerani • Elie Hachem • Emmanuel Creusé • Florian De Vuyst • François Dubois • François-Xavier Demoulin • Garon André • Giovanni Ghigliotti • Grégoire Allaire • Guillaume BOIS • Guillaume Sahut • Gérard Gallice • Gérard Liger-Belair • HASSAN BARKAI ALLATCHI • Hélène Mathis • Ibrahima CISSE • Jean-Marc CARRAT • Julien CARLIER • Julien Derr • Karol Cascavita • Laurent Martin Witkowski • Laurette Tuckerman • Lucien Vienne • Marc Massot • Marc Medale • Marco De Lorenzo • Maria Giovanna Rodio • Marica Pelanti • Marie Bechereau • Marié Simon • Mehdi Khalloufi • Michel Delfour • Nicolas Grenier • Nicolas Maquignon • Olivier Heuzé • Philippe Cordier • Philippe Lafon • Picella Francesco • Pierre HALDENWANG • Pietro Marco Congedo • Rafael Lugo • Raviart Pierre-Arnaud • Renaud Motte • Renée Gatignol • Richard Saurel • Rudy Valette • Rémi Abgrall • Saira Pineda • Shanggui Cai • Simon PELUCHON • Songzhi Yang • Stephan Fauve • Stéphane Dellacherie • Stéphane Zaleski • Sébastien Tanguy • Thibaut Ménard • Thomas Leroy • Vincent Giovangigli • Vitoriano Ruas • Wen YANG • Yannick Hoarau • Yohan Penel Support • Monday, December 12 • 8:30 AM 9:00 AM WELCOME 30m Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 9:00 AM 9:45 AM Effervescence in champagne and sparkling wines: Recent advances and future prospects 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Bubbles in a glass of champagne may seem like the acme of frivolity to most of people, but in fact they may rather be considered as a fantastic playground for any fluid physicist. In a glass of champagne, about a million bubbles will nucleate and rise if you resist drinking from your flute. The so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the result of the complex interplay between carbon dioxide (CO2) dissolved in the liquid phase, tiny air pockets trapped within microscopic particles during the pouring process, and some both glass and liquid properties. The journey of yeast-fermented CO2 is reviewed (from its progressive dissolution in the liquid phase during the fermentation process, to its progressive release in the headspace above glasses). The physicochemical processes behind the nucleation, and rise of gaseous CO2 bubbles, under standard tasting conditions, have been gathered hereafter. Moreover, when a bubble reaches the air-champagne interface, it ruptures, projecting a multitude of tiny droplets in the air. Based on the model experiment of a single bubble bursting in simple liquids, we depict each step of this process, from bubble bursting to droplet evaporation. In particular, we demonstrate how damping action of viscosity produces faster and smaller droplets and more generally how liquid properties enable to control the bubble bursting aerosol characteristics. We demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. Conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of aerosol characteristics and flavor release during sparkling wine tasting, a major issue of the sparkling wine industry. Speaker: Prof. Gérard Liger-Belair (CNRS) • 9:45 AM 10:30 AM Direct Numerical Simulation of Bubbles with Adaptive Mesh Refinement with Distributed Algorithms 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France This talk presents the implementation of the simulation of two-phase flows in conditions of water-cooled nuclear reactors, at the scale of individual bubbles. To achieve that, we study several models for Thermal-Hydraulic flows and we focus on a technique for the capture of the thin interface between liquid and vapour phases. We thus review some possible techniques for Adaptive Mesh Refinement (AMR) and provide algorithmic and computational tools adapted to patch-based AMR, which aim is to locally improve the precision in regions of interest. More precisely, we introduce a patch-covering algorithm designed with balanced parallel computing in mind. This approach lets us finely capture changes located at the interface, as we show for advection test cases as well as for models with hyperbolic-elliptic coupling. The computations we present also include the simulation of the incompressible Navier-Stokes system, which models the shape changes of the interface between two non-miscible fluids. We highlight two canonical test cases: the (one-phase) lid-driven cavity as well as the Rayleigh-Taylor instability. Speaker: Mr Arthur Talpaert (CEA and Ecole Polytechnique (Paris-Saclay)) • 10:30 AM 11:00 AM PAUSE 30m Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 11:00 AM 11:30 AM Numerical simulations of gas/vapor bubble oscillations 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France In this work we numerically investigate the effect of heat and mass transfer on the dynamic response of gas-vapor bubbles. The numerical solution of the full non-linear 1D equations is compared with the analytical solution of the equations obtained for the oscillation of an spherical gas/vapor bubble in response of a weak pressure perturbation (linear solution). For a system with known gas/vapor/liquid properties, we identify various oscillation regimes as a function of an nondimensional oscillation frequency (e.g. the bubble's Peclet number) and the vapor content. Even at very low frequencies, there exist regimes where transient diffusion effects arise due to heat diffusion in the surrounding liquid and also due to vapor mass diffusion inside the bubble. These phenomena restrict the applicability of the commonly-adopted assumption of full-equilibrium conditions inside the bubble. Simulations of the oscillation of bubbles for strong perturbations shows that non-linear effects restrict even further the range of applicability of the isothermal equilibrium model when the vapor content becomes larger than a critical value. Speaker: Dr Daniel FUSTER (Institut D'Alembert, UPMC-CNRS 75005 Paris) • 11:30 AM 12:00 PM Simulation of free surface fluids in incompressible dynamique 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France In this work, we present a numerical scheme for solving free surface flows. The free surface is modeled using the level-set formulation. Besides, the mesh is anisotropic and adapted at each iteration. This adaptation allows us to obtain a precise approximation for the free- surface location. In addition, it enables us to solve the time-discretized fluid equation only on the fluid domain. The fluid here is considered incompressible. Therefore, its motion is described by the incompressible Navier–Stokes equation which is temporally discretized using the method of characteristics and is solved at each time iteration by a first order Lagrange–Galerkin method. The level-set function representing the free surface satisfies an advection equation which is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level-set function (redistancing) as well as the construction of a convenient flow for the level-set advection equation. Finally, some numerical results are presented. Speaker: Mrs Dena Kazerani (Laboratoire Jacques-Louis Lions (UPMC, Paris 6)) • 12:00 PM 12:30 PM Direct Numerical Simulation of Liquid-Vapor Phase Change. Applications to Leidenfrost Droplet and Nucleate Boiling 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Studies on two-phase flows are of interest in many fundamental problems and industrial applications, as the spray formation in internal combustion engine, the bubble formation in heat exchangers, the fluid management in satellites or space launcher tanks, the spray cooling or the interaction of bubbles with acoustic waves. The Direct Numerical Simulation is a powerful tool, which is complementary to experimental measurements, to provide accurate results in complex situations. However, unlike single-phase flows, currently the direct numerical simulation of two- phase flows cannot be considered as a fully mature field, especially in most configurations involving strong coupling between the interface motion with heat and mass transfer, acoustic or shock waves, and/or a solid boundary where a contact line can be formed. This presentation will emphasize on the development of new numerical methods [1,2,3,4,5] to perform accurate Direct Numerical Simulations of two-phase flows with phase change in the framework of sharp interface capturing numerical methods. The presentation will focus mainly on two specific configurations involving liquid vapor phase change, i.e. Leidenfrost droplets and nucleate boiling. We will discuss about suited numerical strategy to succeed numerical simulations in these configurations. Accurate comparison between experiments and fully-resolved numerical simulations will be presented in order to bring out the relevance of the proposed algorithms. [1] S. Tanguy, T. Menard, A. Berlemont, A level set method for vaporizing two-phase flows, J. Comput. Phys. 221 (2007) 837-853 [2] S. Tanguy, M. Sagan, B. Lalanne, F. Couderc, C. Colin, Benchmarks and numerical methods for the simulation of boiling flows. J. Comput. Phys. 264 (2014) 1-22. [3] L. Rueda Villegas, R. Alis, M. Lepilliez, S. Tanguy. A Level Set/Ghost Fluid Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect. J. Comp. Phys. 316 (2016) 789-813 [4] L. Rueda Villegas, S. Tanguy, G. Castanet, O. Caballina, F. Lemoine. Direct Numerical Simulation of the impact of a droplet onto a hot surface above the Leidenfrost temperature. Int. J. Heat Mass Transfer 104 (2017) 1090-1109 [5] G. Huber, M. Sagan, C. Colin, S. Tanguy. Direct Numerical Simulation of nucleate boiling at moderate Jakob number and high microscopic contact angle. In preparation to be submitted in Int. J. Heat Mass Transfer Speaker: Dr Sébastien Tanguy (Institut de Mécanique des Fluides de Toulouse) • 12:30 PM 2:15 PM LUNCH TIME 1h 45m Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 2:15 PM 3:00 PM Numerical simulation of flows with sharp interfaces by the Volume-Of-Fluid method 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France We discuss recent developments in the Volume-Of-Fluid (VOF) methods, such as the height function method for the approximation of the geometry of the interface, the balanced-force surface tension method, and the methods that conserve mass and momentum at machine accuracy. Applications at high Reynolds number,such as high speed liquid-gas flows, and low Reynolds and low Capillary numbers, are discussed. Problems of engineering and physical interest, such as jet atomisation or flow in porous media are investigated with these methods as will be shown. Speaker: Prof. Stéphane Zaleski (Université Pierre et Marie Curie (Paris)) • 3:00 PM 3:45 PM Applications of the Front-Tracking algorithm of TrioCFD to turbulent bubbly flows in plane channels 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France The Front-Tracking method has been implemented in TrioCFD and improved over the last decade. It has been widely used on large parallel architectures to study incompressible two- phase flows. The permanent increase in computing capabilities allows to perform simulations of fully turbulent bubbly flows in relatively small periodic domains. This talk will be organized in two parts. The numerical method used to perform Front-Tracking simulations will be presented. The code is capable to deal with phase change and specific Ghost-Fluid Methods have been implemented to guarantee a great accuracy of the solution, even in the presence of large jumps and phase change. Then, recent calculations on adiabatic two-phase turbulent bubbly flows will be presented. Averaged results are analyzed in great details in order to better understand the dominant processes in the exchange mechanisms at the interface and in the modulation of turbulence by the vapor inclusions and their wakes. Preliminary results and suggestions for the two-fluid model will conclude the presentation. This work was granted access to the HPC resources of TGCC under the allocation 20XX- t20142b7239 made by GENCI. Speaker: Dr Guillaume Bois (CEA (Paris-Saclay)) • 3:45 PM 4:30 PM PAUSE 45m Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 4:30 PM 5:00 PM High fidelity anisotropic adaptive FEM towards physical couplings occurring in turbulent boiling 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France We propose in this work an adaptive variational multiscale method for complex multiphase flows with surface tension: applications to 3D bubble dynamics, turbulent boiling and solid quenching with experimental comparisons will be presented. A new conservative level-set method is used to provide a precise position of the interfaces. An implicit implementation of the surface tension in the context of the Continuum Surface Force is proposed to circumvent the capillary time step restriction. The obtained system is then solved using a unified compressible-incompressible variational multiscale stabilized finite element method designed to handle the abrupt changes at the interface and large density and viscosity ratios. Combined with an a posteriori error estimator, we show that anisotropic mesh adaptation yields an accurate 3D modeling framework for turbulent multiphase flows with phase change. Speaker: Dr Elie Hachem • 5:00 PM 5:30 PM Modelling atomization with phase change 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France DNS[1], LES [2] and RANS [3] modelling of atomization have been developed for the last decade in our laboratory with a particular attention devoted on the behavior of the interface. In particular model equations for the liquid-gas surface density have been proposed based on the pioneering work of Borghi and Vallet [4]. The purpose of this approach is to determine the surface density that we believe is the first order parameter to determine the mass transfer rate, a key future of fuel injection system. In addition to well-developed procedures usually used to evaluate the vaporization rate for dispersed spray based on the resolution of Boltzmann-Williams kinetic equation, our focus has been to determine the phase change rate for any kind of interface geometry not only spherical droplet. To do so the interface capturing DNS code Archer has been extended to handle heat and mass transfer at the interface based on the method proposed by Tanguy et al. [5], [6]. From this work the turbulent mixing of a scalar quantity issued from an interface such has the vapor concentration has been studied showing the importance of interface boundary layer zone on the global statistic of the scalar field [7]. Further works concern the extension of interface capturing method generally based on incompressible scheme to fully compressible code to handle other phenomena occurring during the injection process such as cavitation. [1] T. Menard, S. Tanguy, et A. Berlemont, « Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet », Int. J. Multiph. Flow, vol. 33, n o 5, p. 510‐524, 2007. [2] J. Chesnel, J. Reveillon, T. Menard, et F. X. Demoulin, « Large eddy simulation of liquid jet atomization », At. Sprays, vol. 21, n o 9, p. 711‐736, 2011. [3] R. Lebas, T. Menard, P. A. Beau, A. Berlemont, et F. X. Demoulin, « Numerical simulation of primary break-up and atomization: DNS and modelling study », Int. J. Multiph. Flow, vol. 35, n o 3, p. 247‐260, 2009. [4] A. Vallet et R. Borghi, « Modélisation Eulerienne de L’atomisation d’un Jet Liquide », C R Acad Sci Paris Sér II B, vol. 327, p. 1015–1020, 1999. [5] S. Tanguy, T. Ménard, et A. Berlemont, « A Level Set Method for vaporizing two-phase flows », J. Comput. Phys., vol. 221, n o 2, p. 837‐853, 2007. [6] B. Duret, T. Menard, J. Reveillon, et F. X. Demoulin, « Two phase flows DNS of evaporating liquid-gas interface including interface regression, using Level Set and Coupled Level Set/VOF method », présenté à 8th International Conference on Multiphase Flow (ICMF 2013, 2013. [7] B. Duret, G. Luret, J. Reveillon, T. Menard, A. Berlemont, et F. X. Demoulin, « DNS analysis of turbulent mixing in two-phase flows », Int. J. Multiph. Flow, vol. 40, n o 0, p. 93‐105, 2012. Speaker: Dr François-Xavier Demoulin (CORIA) • 5:30 PM 6:00 PM Locally conservative approximation of (conservative) systems written in non conservation form: application to Lagrangian hydrodynamics and multifluid problems 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Since the celebrated Lax Wendroff theorem, it is known that the right way of discretising systems of hyperbolic equations written in conservation form is to use a flux formulation. However, in many occasions, the relevant formu- lation, from an engineering point of view, is not to consider this conservative formulation but one non conservative form. For example, with standard notations, a one fluid model writes [équation : voir résumé PDF] (1) but the interesting quantities are the mass, velocity and pressure, which evolution is described by: [équation : voir résumé PDF] (2) Unfortunately this form is not suitable to approximation. In the case of a multi-fluid system, the same problem occurs. In this talk, we will describe a method to overcome this issue. It does not use any flux formulation per se, but can be shown to provide the right solutions. In order to illustrate the method, we will consider several examples in Eulerian and Lagrangian hydrodynamics We will first start from the Residual Distribution (RD) (re-)interpretation of the Dobrev et al. scheme [1] for the numerical solution of the Euler equations in Lagrangian form. The first ingredient of the original scheme is the staggered grid formulation which uses continuous node-based finite element approximations for the kinematic variables and cell-centered discontinuous finite elements for the thermodynamic parameters. The second ingredient of the Dobrev et al. scheme is an artificial viscosity technique applied in order to make possible the computation of strong discontinuities. Using a reformulation in term of RD scheme, we can show that the scheme is indeed locally conservative while the formulation is stricto sensu non conservative. Using this, we can generalise the construction and develop locally conservative artificial viscosity free schemes. To demonstrate the robustness of the proposed RD scheme, we solve several one-dimensional shock tube problems from rather mild to very strong ones: we go from the classical Sod problem, to TNT explosions (with JWL EOS) via the Collela-Woodward blast wave problem. In a second part, we show how to extend this method to the Eulerian framework and give applications on single fluid and multiphase problems via the five equation model. References [1] V. Dobrev, T. Kolev, and R. Rieben. High order curvilinear finite element methods for Lagrangian hydrodynamics. SIAM J. Sci. Comput, 34:B606–B641, 2012. Speaker: Prof. Rémi Abgrall (Université de Zürich) • 6:00 PM 6:30 PM END OF DAY 1 30m • Tuesday, December 13 • 9:00 AM 9:45 AM Modelling liquid-vapor phase change with metastable states 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France We propose a model of liquid-vapor phase transition including metastable states of the van der Waals Equation of State. The first part of the talk concerns the thermodynamics model. Following the second principle, the problem boils down to a minimization problem with constraints of the mixture energy. This ”static” description allows to recover the classical equilibria: pure liquid/vapor states and a coexistence state (given by the Maxwell equal area rule). Then, when assuming a dependency with respect to time, we define a dynamical sys- tem with long time equilibria which are either the classical equilibria or the metastable states. In a second part of the talk, we use the dynamical system as a source term of a two-phase isothermal model. The homogeneous model is hyperbolic under condition. However for smooth solutions, we manage to prove that the regions of hyperbolically are invariant domains. We finish with some numerical experiments, obtained by a finite volume scheme and a splitting technique to handle the source term. Speaker: Dr Hélène Mathis (Université de Nantes) • 9:45 AM 10:30 AM Diffuse interfaces with compressible fluids, phase transition and capillarity 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Conventional models of capillary fluids with phase transition consider linked thermodynamics and capillarity. Such coupling has serious consequences, such as: - sound propagation, undefined in some critical regions, - very thin interfaces, causing serious issues in practical computations. In the present talk an approached based on hyperbolic systems with relaxation is promoted to solve interfaces with phase transition and surface tension. The method deals with arbitrary pressure and density jumps. The diffuse interface model consists in a set of balance equations of mass for each phase and momentum and energy for the mixture. When simple contact is considered (in the absence of heat diffusion), a volume fraction equation is needed as well. In this frame each phase is compressible and governed by its own (convex) equation of state, preserving sound propagation. The two equations of state are rendered compatible through appropriate constants determined from the phase diagram. Phase change is modeled through Gibbs free energy relaxation terms. Capillarity is modelled through mass fraction gradients at interfaces and is consequently decoupled of thermodynamics. Examples of cavitating, flashing and boiling flows with and without shocks are shown. Le Métayer, O., & Saurel, R. (2016). The Noble-Abel Stiffened-Gas equation of state. Physics of Fluids 28(4), 046102 Saurel, R., Le Metayer, O. and Boivin, P. (2016) A general formulation for cavitating, boiling and evaporating flows. Computers and Fluids 128, 53-64 Le Martelot, S., Saurel, R. and Nkonga, B. (2014) Toward the direct numerical simulation of boiling flows. Int. J. of Multiphase Flows 77, 62-78 Le Martelot, S., Nkonga,B. and Saurel, R. (2013) Liquid and liquid–gas flows at all speeds, Journal of Computational Physics 255(15), 53-82 Petitpas, F., Massoni, J., Saurel, R., Lapebie, E. and Munier, L. (2009) Diffuse interface model for high speed cavitating underwater systems. Int. J. Multiphase Flow 35, 747-759 Saurel, R., Petitpas, F. and Abgrall, R. (2008) Modeling phase transition in metastable liquids. Application to flashing and cavitating flows. Journal of Fluid Mechanics, 607:313-350 Speaker: Prof. Richard Saurel (Université Aix-Marseille) • 10:30 AM 11:00 AM PAUSE 30m Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 11:00 AM 11:45 AM Numerical simulation of Faraday wave patterns 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France In 1831, Faraday described the standing wave patterns that form on the surface of a layer of fluid subjected to periodic vertical vibration. These waves usually take the form of stripes, squares, or hexagons. However, other phenomena have been observed numerically, such as quasipatterns, supersquares, heteroclinic cycles, and oscillons. Until recently, numerical simulation of Faraday waves was out of reach. Since 2009, however, we have simulated not only simple wave patterns but also patterns which involve large-scale modulation. To do so, we have developed a massively parallel multiphase code, BLUE, whose treatment of the free surface uses a hybrid Front-Tracking/Level-Set technique, defining the interface both by a discontinuous density field on the Eulerian grid and by triangles on the Lagrangian interface mesh. We will discuss the various Faraday wave configurations we have studied: regular square and hexagonal lattices, patterns composed of spherical harmonics on a vibrated drop, and supersquares consisting of a four-by-four array of smaller squares. Speaker: Prof. Laurette Tuckerman (Ecole Supérieure de Physique et de Chimie Industrielle (Paris)) • 11:45 AM 12:30 PM Lagrange-Euler Lattice-Boltzmann Method And Its Application to Two-Fluid Flows Dynamics With Possibly High Density Ratio 45m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Two-fluid extensions of Lattice Boltzmann methods with free boundaries usually consider "microscopic'' pseudopotential interface models. In this paper, we rather propose an interface-capturing Lattice Boltzmann approach where the mass fraction variable is considered as an unknown and is advected. Several works have reported the difficulties of LBM methods to deal with such two-fluid systems especially for high-density ratio configurations. This is due to the mixing nature of LBM, as with Flux vector splitting approaches for Finite Volume methods. We here give another explanation of the lack of numerical diffusion of Lattice Boltzmann approaches to accurately capture contact discontinuities. To fix the problem, we propose an arbitrary Lagrangian-Eulerian (ALE) formulation of Lattice-Boltzmann methods. In the Lagrangian limit, it allows for a proper separated treatment of pressure waves and advection phenomenon. After the ALE solution, a remapping (advection) procedure is necessary to project the variables onto the Eulerian Lattice-Boltzmann grid. We explain how to derive this remapping procedure in order to get second-order accuracy and achieve sharp stable oscillation-free interfaces. It has been shown that mass fractions variables satisfy a local discrete maximum principle and thus stay in the range $[0,1]$. The theory is supported by numerical computations of the free fall of an initial square block of a dense fluid surrounded by a lighter fluid into a box. Figures 1 and 2 are showing the mass fraction field of the light fluid at two successive instants. The density ratio equal to 4 and the computational lattice grid is 400x400. One can appreciate the thickness of the numerical diffuse interface, the capture of complex structures and the capability to compute strong changes of free boundary topology. Even if our methods are currently used for inviscid flows (Euler equations) by projecting the discrete distributions onto equilibrium ones at each time step, we believe that it is possible to extend the framework formulation for multifluid viscous problems. This will be at the aim of a next work. Speaker: Mrs Marie Béchereau (Ecole normale supérieure de Cachan (Paris-Saclay)) • 12:30 PM 2:30 PM LUNCH TIME 2h Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 2:30 PM 3:00 PM Benchmarking rotating flow with free surface deformation 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France The free surface deformation generated by a disk rotating at the bottom of a container partially filled with fluid is an exciting challenge for numerical simulations. The shape of the free surface has shown surprising patterns in experiments performed by different research groups. However, for many regimes (non axisymmetric, dewetted disk, sloshing), an accurate comparison with numerical simulations is clearly missing. We will present the different existing regimes of such flow and show results of comparison between different numerical codes on few selected regimes. Some preliminary measurements on a recent experimental set up will also be presented and we will discuss the relevance of a benchmark on such flow. Speaker: Dr Laurent Martin Witkowski • 3:00 PM 3:30 PM Numerical simulation of a gas bubble collapse using the SPH-ALE method 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France A multiphase model developed in SPH-ALE is used to simulate the collapse of a gas bubble in water. This model does not diffuse the interface and guarantees the continuity of normal velocity and pressure at the interface between both fluids. This scheme is able to deal with interfaces of simple contact where normal velocity is continuous. The model solves the mass, momentum and energy conservation equations of Euler system using a non-isentropic equation of state for each phase, the Stiffened Gas EOS for water and the ideal gas EOS for the gas bubble. Both phases are compressible and the phase change is not modeled. A multiphase shock tube is presented for validation purpose, with satisfactory results in comparison with reference solutions. The dynamics of the Rayleigh collapse of a bubble in a free-field and near a planar rigid wall are analyzed. Collapse behavior, interfacial velocities and surface pressure as a function of time are analyzed for the free-field collapse case, and in addition, as a function of the initial bubble stand-off distance from the wall for the case of the bubble collapse near the wall. For the case of the bubble collapse near a wall, a re-entrant jet directed towards the surface is observed due to the non- symmetry initial configuration. The potential damage to the surface wall is estimated by measuring the wall pressure. Speaker: Mrs Saira Pineda • 3:30 PM 4:00 PM Simulations of a heated fluid at low Mach number: modelling of phase transition and numerical strategies 30m Amphi Hermite ### Amphi Hermite #### Institut Henri Poincaré 11 Rue Pierre et Marie Curie, 75005 Paris, France Thermohydraulic codes used in industry are based on the resolution of compressible Navier-Stokes equations in which acoustic waves are taken into account. This allows to describe fluid flows at any Mach number. However, many difficulties may arise in terms of CPU time, robustness and accuracy in the low Mach number regime. In this regime, an asymptotic expansion with respect to the Mach number leads to simpler models. Thus, the strategy of our work is to derive, investigate and simulate a system of PDE taking into account phase transition in the low Mach number regime but with possible high heat transfers. More precisely, we focus on the choice of the equation of state and its parameters, with emphasis on the gain due to the low Mach number hypothesis, and we present preliminary 2D numerical simulations with FreeFem++ showing the robustness of the approach. This is a joint work with S. Dellacherie, G. Faccanoni and Y. Penel. Speaker: Dr Bérénice Grec • 4:00 PM 4:30 PM PAUSE 30m Hall d'accueil, Institut Henri Poincaré ### Hall d'accueil, Institut Henri Poincaré • 4:30 PM 5:00 PM END OF DAY 2 30m	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7249583601951599, "perplexity": 2793.169065919385}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00278.warc.gz"}
https://nightingale.becomingcelia.com/category/maths	## POTW – What are the Possibilities? This is a problem originally published on Problem of the Week of University of Waterloo. The question was about finding the roots of a functions. I thought it would be really easy since Desmos seems to be able to solve all functions, however in this interesting question it fails, which is why I am posting […]	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9183711409568787, "perplexity": 294.22019264516274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704843561.95/warc/CC-MAIN-20210128102756-20210128132756-00678.warc.gz"}
https://www.physicsforums.com/threads/stealing-an-electron.764461/	# Stealing an electron 1. ### Meson080 100 Is the statement by wikipedia correct? Since, there is a probability of finding electron at any distance from the nucleus, when the electron comes far from the nucleus, I will block it, so that it won't return to its parent atom. Am I not stealing the electron? I can steal even the electron of your body being in India, be careful! That's what we layman think from those statements. What's the actual meaning of the wikipedia statement? Last edited: Aug 3, 2014 ### Staff: Mentor It means that if we perform a measurement to find out where the electron is, its location could technically be almost anywhere, including in India. But the probability of finding the electron further than about a nano-meter from the nucleus is so low that you could perform this measurement every second for a billion years and not find it there. 3. ### Meson080 100 Then I do have the chance of stealing your body's electron. Is that what you mean? Can I have the source for this? ### Staff: Mentor Have you checked the list of references at the bottom of the wikipedia article you quoted from? 5. ### Meson080 100 It will be helpful, if you can point the source among that bunch of reference links. 6. ### Meson080 100 The same question is also posted in Physics Stack Exchange. Interested folks can read this page: Can I steal your electron? The page might help to have better discussion. ### Staff: Mentor I don't have a specific source, it's just general knowledge how atomic orbitals work. My response wasn't meant to be taken literally, as I haven't done the math. I just know that the probability of an electron being found a few thousand miles away from its atom is exceedingly low. So low that we never worry about objects falling apart because they lose their electrons in this manner. ### Staff: Mentor See http://en.m.wikipedia.org/wiki/Hydrogen_atom#Wavefunction For the ground state electron this simplifies to a probability density of: $$\|\Psi(r)\|^2 = \frac{1}{a_0^3 \pi} e^{-2r/a_0}$$ Since ##a_0=5.29 \; 10^{-11} \; m## if you want to steal an electron in a 1 m cubic box located even just 10 m away, the probability is so small that it cannot be distinguished from 0 with even a million digits of precision, and the probability of finding it anywhere in the universe further than 1 m distance away is less than 1.6E-16419451091 Last edited: Aug 3, 2014 9. ### Khashishi Meson, you have a very, very, very small chance. This chance is really too small to worry about in any context. 10. ### Meson080 100 So, once electron comes far from its parent atom, it won't return to it? Did you mean this? ### Staff: Mentor I believe that's how it works. 12. ### Meson080 100 The question is, what provides energy to the electron to go any far distance from the nucleus? As there is the force which is holding the electron, it should not have any "probability" of going far from the nucleus, isn't it? How does QM tackle this discrepancy? ### Staff: Mentor To measure the position of the electron you have to interact with it, and that interaction supplies any necessary energy. The total energy of the system (nucleus, electron, and measuring device) is conserved. Understand also that the electron isn't anywhere until you interact with it. The function that DaleSpam posted does not give you the probability that the electron is at a given location, it gives you the probability that the electron will be found at that location if you make a measurement. Thus, there's no question about how the electron moved far away from the nucleus before you looked and found it out there - until you measured its position it didn't have a position, it wasn't far away from the nucleus, or near it, or anywhere else. That's how quantum mechanics works. If you don't like it, you're in good company - but like it or not, them's the rules. ### Staff: Mentor I believe energy conservation in QM is a bit more complicated than it is in classical physics, but you'd need to ask in the QM forum if you want to know about that. 1 person likes this. 15. ### Meson080 100 I felt this as the misconception of Heisenberg's Uncertainity principle. Isn't this? If it works that way, I need to learn more to unlearn as Feynman always says. Last edited: Aug 4, 2014 16. ### phinds 8,105 No, they have nothing do do with each other. That article is about the false presentation of the HUP as a measurement problem. It is not and never has been a measurement problem, it is a fundamental fact of nature. That presentation was a dumbed-down common language presentation that does not represent the math. As did we all when we first got into this stuff. EDIT: just to be sure I'm clear, when I say "they have nothing to do with each other", I'm saying that the fact that an electron has a probability distribution that gives a non-zero (but incredibly tiny) result for positions far away from its atom has nothing to do with the HUP. ### Staff: Mentor The formula I provided is for the ground state, meaning that it has the minimal amount of energy and is not excited. No energy is required for the electron to be measured in different locations in the ground state. Energy is only required to raise it to a different state. ### Staff: Mentor OP is capturing the electron ("stealing" in the thread title). The state in which the electron has been localized at some distance from the nucleus isn't an energy eigenstate. 19. ### Meson080 100 Can I have any reliable source which supports this idea? ### Staff: Mentor Any decent QM text book will work. To see it in modern terms you'll want one that stresses the statistical interpretation, but the idea that it makes no sense to talk about the value of quantities that haven't been measured goes all the way back to Bohr.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.635305643081665, "perplexity": 602.0974675719652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463378.98/warc/CC-MAIN-20150226074103-00119-ip-10-28-5-156.ec2.internal.warc.gz"}

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