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https://preview.hex.pm/preview/ex_uc/0.3.1
|
[
"#",
null,
"``````# ExUc - Elixir Unit Converter\n\nConverts values between units.\n\n## Installation\n\nFrom [Hex](https://hexdocs.pm/ex_uc), the package can be installed as:\n\n```elixir\ndef deps do\n[{:ex_uc, \"~> 0.3\"}]\nend\n```\n\n2. Ensure `ex_uc` is started before your application:\n\n```elixir\ndef application do\n[applications: [:ex_uc]]\nend\n```\n\n### Requirements\n\nThis package requires _Elixir **1.3+**_\n\n## Usage\n\nThe quickest way is the function `convert`:\n```elixir\niex>ExUc.convert(\"5 pounds\", \"oz\")\n\"80.00 oz\"\n```\nThis is just a shortcut for the 3-steps pipeline:\n```elixir\nimport ExUc\n\nnew_val = from(\"5 pounds\") # %ExUc.Value{unit: :lb, value: 5, kind: :mass}\n|> to(:oz) # %ExUc.Value{unit: :oz, value: 80, kind: :mass}\n|> as_string # \"80.00 oz\"\n```\n\n### Errors\n\nOnly two errors are returned when found, both as self descriptive **strings**:\n\n- `\"undefined origin\"`: Unit for the original value can't be parsed or found in the configuration.\n- `\"undetermined conversion\"`: Conversion between the given units can't be determined.\n\n## Configuration\n\nThe only configurable variable is `precision`, by default `2`. It determines how many decimals will have the result when is converted into **string**.\n\nUnit sets (_kinds_) are really easy to extend. You don't need to add a conversion to every other existent unit in the _kind_ (though, of course you can). **ExUc** will find the shortest path in a _kind_ of units as a graph, using defined conversions.\n\nEvery unit supported by **ExUc** is defined in a config file in _config/units/<KIND>.ex_, e.g. `config/units/temperature.ex`.\n\nEach of these files requires to have the following structure:\n```elixir\nuse Mix.Config\n\nconfig :ex_uc, :<KIND>_units,\n<UNIT>: [\"alias 1\", \"alias 2\", \"alias N\"], # List with every alias intended to relate to unit identified by UNIT\n\nconfig :ex_uc, :<KIND>_conversions,\n<UNIT_A>_to_<UNIT_B>: 0.001, # Multiplication factor\n<UNIT_C>_to_<UNIT_D>: &(&1 + 5) # Conversion formula.\n<UNIT_X>_to_<UNIT_Y>: :special # Atom referencing a special method.\n```\n\nWhich have two sections:\n\n- **Aliases**\n- Key as `<KIND>_units` where kind identifies the type of measurement, e.g: _length_, _temperature_, _pressure_, etc.\n- Each unit to support in the `kind` as a pair `unit:aliases` where **unit** is the most used unit and **aliases** is a list of strings (or a single one), one for each supported representation of the unit.\n- **Conversions**\n- Key as `<KIND_conversions>` using the same **kind** from the **alias** section.\n- Each conversion as a pair `key:conversion`, where **key** is an atom with the pattern `<UNIT_FROM>_to_<UNIT_TO>`, and **conversion** could be a _number_, or a _closure_, or an _atom_. Numeric conversions describe multiplication factors, and can be also used as `<B>_to_<A>: 1 / conversion` for a `<A>_to_<B>: factor` without explicit definition. When a factor is not enough, a _closure_ can be used as a simple formula. For special cases use an _atom_ to describe a function in module `Special`.\n\n### More Units\n\n**PRs** or **Issues** with new units or more accurate conversions are welcome.\n\n## Documentation\n\nDetailed documentation can be found at [hex docs](https://hexdocs.pm/ex_uc).\n\n## Note\n\nThis project was inspired by the awesome [Ruby gem](https://github.com/olbrich/ruby-units) by _Kevin C. Olbrich, Ph.D._"
] |
[
null,
"https://preview.hex.pm/images/hexpreview-206fa89052dcc459b39b61e598d489c8.svg",
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|
http://ulsites.ul.ie/access/node/123431
|
[
">",
null,
"",
null,
"",
null,
"# Chemistry 6 Carbon Dioxide\n\nChemistry: 6. Carbon Dioxide\n\nPlease remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier.\n\nSyllabus\n\nOC27 Prepare carbon dioxide (word equation and chemical equation), and show that it does not support combustion\n\nOC28 Carry out simple tests on carbon dioxide involving its reaction with limewater (word equation and chemical equation), and with moist litmus paper\n\nOC29 Investigate the density of carbon dioxide relative to air (qualitative only), and state two uses of carbon dioxide\n\nStudent Notes\n\nPreparation of carbon dioxide\n\n Calcium carbonate + Hydrochloric acid à Calcium Chloride + Water + Carbon Dioxide (Marble chips)\n\nCaCO3 + 2HCl → CaCl2 + H2O + CO2",
null,
"Procedure\n\nSet up as shown (calcium carbonate is the chemical name for marble chips).\n\n1. Slowly release the hydrochloric acid into the flask underneath.\n2. Carbon dioxide is collected it the gas jar\n\nTest 1:\n\nPour a small volume of limewater into the jar and shake – the limewater will turn milky showing that the gas is carbon dioxide.\n\nTest 2:\n\nAdd water to a fresh jar of carbon dioxide and test with blue litmus paper: it turns red demonstrating that it is an acid.\n\nLimewater and carbon dioxide\n\n Limewater + carbon dioxide → calcium carbonate + water\n\nCa(OH)2 + CO2 → CaCO3 + H2O\n\nTo show that carbon dioxide does not support combustion\n\nLight a wooden splint and insert it into a gas jar of carbon dioxide.\n\nResult: the splint will extinguish showing that carbon dioxide does not support combustion.\n\n Carbon dioxide has a greater density than air",
null,
"Demonstration\n\nPour the gas over the candle as shown.\n\nBecause carbon dioxide is denser than air the gas sinks and extinguishes the candle.\n\nUses of carbon dioxide\n\n1. Fizzy drinks\n2. Fire extinguishers\n3. Special effects on stage (dry ice in water cause a ‘smoke’ effect)\n\nExam Questions\n\n1.",
null,
"Give the chemical name for marble.\n\n1. [2009 OL] [2007 OL]\n\nThe diagram shows an arrangement of apparatus suitable for the preparation of carbon dioxide gas in a school laboratory.\n\nName suitable substances X and Y from which carbon dioxide can be made.\n\n1.",
null,
"1. The diagram shows an apparatus that can be used for the preparation and collection of carbon dioxide.\n\nGive the formula of a suitable acid.\n\n1. What physical property of carbon dioxide allows the gas to be collected in the manner shown in the diagram?\n\n1. [2006 OL] [2012 OL]\n\nName the chemical that turns milky white if carbon dioxide is bubbled through it.",
null,
"1. \n\nThe liquid and solid shown in the diagram react together to produce a gas that turns limewater milky. Name a liquid and a solid that react together in this way.\n\n1.",
null,
"Carbon dioxide turns limewater milky.\n\nComplete the chemical equation for the reaction of carbon dioxide with limewater.\n\nCa(OH)2 + CO2\n\n1. \n\nIf a strip of moist blue litmus paper and a strip of moist red litmus paper are put into a jar of carbon dioxide what effect, if any, does the gas have on them?\n\n1. \n\nCarbon was burned in oxygen and the products tested with pieces of moist red and blue litmus paper.\n\nGive the result of the litmus test described above and make a conclusion based on this result.\n\n1.",
null,
"[2006 OL]\n\nThe diagram shows a gas jar of carbon dioxide gas being poured onto a lighting candle.\n\n1. What happens to the lighting candle when the carbon dioxide gas is poured over it?\n2. This test demonstrates two properties of carbon dioxide gas. List the two properties.\n\n1. \n\nGive two uses of carbon dioxide.\n\nExam Solutions\n\n1. Calcium carbonate\n2. X: Hydrochloric acid\n\nY: Calcium Carbonate (CaCO3) / limestone / marble chips / chalk\n\n1.\n1. HCl\n2. It is denser (heavier) than air\n1. Limewater\n2. Liquid: hydrochloric acid (HCl)\n\nSolid: marble/ calcium carbonate/ CaCO3)/ bread soda/ sodium hydrogen carbonate (sodium bicarbonate)…\n\n1. Ca(OH)2 + CO2 → CaCO3 + H2O\n2. Both pieces of litmus paper will be red (or pink)\n3. The blue litmus paper turns red\n\nConclusion: The product is acidic.\n\n1.\n1. Quenches\n1. Carbon dioxide doesn’t support combustion and is heavier than air\n2. Fire extinguishers/ fizzy drinks/ photosynthesis/ ‘dry ice’/ ‘stage effects’…\n\nOther Test Questions\n\n1.\n1. Describe a laboratory experiment to prepare carbon dioxide\n2. Give the word equation for this reaction.\n3. Give the chemical equation for this reaction.\n\n1. How would you demonstrate that carbon dioxide does not support combustion?\n\n1. Describe how you would carry out a simple test to demonstrate the reaction between carbon and moist litmus paper.\n\n1. Describe how you would investigate the density of carbon dioxide relative to air.\n\n1. Give the formula for limewater.\n\n1. Identify the milky-white precipitate formed from the reaction between limewater and carbon dioxide.\n\n1. Name a suitable liquid and solid that could be used for the preparation of carbon dioxide.\n\n1. Give a test for carbon dioxide gas\n\n1. Complete and balance the following chemical equation for the reaction between limewater and carbon dioxide:",
null,
"Ca(OH)2 + CO2 +\n\n1. Complete and balance the following equation:",
null,
"HCl + CaCO3 + +"
] |
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https://teachchemistry.org/classroom-resources/chemical-names-and-formulas-unit-plan
|
[
"# Chemical Names and Formulas Unit Plan Mark as Favorite (84 Favorites)\n\nLESSON PLAN in Naming Compounds, Molecular Formula, Covalent Bonding, Ionic Bonding, Percent Composition, Lewis Structures, Unit Plans. Last updated October 26, 2020.\n\n### Summary\n\nThe AACT high school classroom resource library has everything you need to put together a unit plan for your classroom: lessons, activities, labs, projects, videos, simulations, and animations. We constructed a unit plan using AACT resources that is designed to teach Chemical Names and Formulas to your students.\n\nHigh School\n\n### Objectives\n\nBy the end of this unit, students should be able to\n\n• Name binary and ternary ionic compounds given the formula.\n• Write formulas when given names of ionic compounds.\n• From the compound name, recognize if it contains a polyatomic ion and/or a metal with a varying charge.\n• Summarize “rules” for naming ionic compounds.\n• Explain why stable ionic compounds are formed from a combination of cations and anions.\n• Explain why different quantities of ions combine to make different compounds.\n• Distinguish between the general locations of metal atoms versus non-metal atoms on the periodic table.\n• Write a chemical formula for a covalent compound.\n• Name a covalent compound using the appropriate rules of nomenclature.\n• Predict the number of atoms needed in a molecular formula.\n• Explain the purposes of superscripts and subscripts in chemical formulas.\n• Correctly determine if a bond is ionic or covalent.\n• Identify which elements can bond to each other.\n• Determine the proper naming system to use for ionic versus covalent compounds.\n• Determine the number of valence electrons for an atom.\n• Create the correct Lewis Dot Structure from a given molecular compound or formula.\n• Exhibit understanding of the differences between polar, nonpolar, and ionic substances.\n• Calculate the percent of water (by mass) contained in a hydrated salt.\n• Determine an empirical formula from percent composition data of a substance.\n• Determine the formula of a hydrate from collected laboratory data.\n\n### Chemistry Topics\n\nThis unit supports students’ understanding of\n\n• Covalent Bonding\n• Covalent nomenclature and formula writing\n• Electronegativity\n• Empirical Formulas\n• Formula Writing\n• Intermolecular forces\n• Ionic Bonding\n• Law of Definite Proportions\n• Lewis Structures\n• Melting Point\n• Metals and Nonmetals\n• Molecular Formula\n• Molecular Structure\n• Molecules\n• Molecules & Bonding\n• Naming Compounds\n• Naming ionic compounds\n• Percent Composition\n• Polarity\n• Polyatomic Ions\n\n### Time\n\nTeacher Preparation: See individual resources.\n\nLesson: 8-12 class periods, depending on class level.\n\n### Materials\n\n• Refer to the materials list given with each individual activity.\n\n### Safety\n\n• Refer to the safety instructions given with each individual activity.\n\n### Teacher Notes\n\n• The activities shown below are listed in the order that they should be completed.\n• The number of activities you use will depend upon the level of students you are teaching.\n• The teacher notes, student handouts, and additional materials can be accessed on the page for each individual activity.\n• Please note that most of these resources are AACT member benefits.\n\n### Classroom Resources:\n\n#### Introduction/Review\n\n• Use the Bonding animation to reinforce your students understanding of ionic and covalent compounds the Bonding Animation. This animation allows students to students visualize how different chemical bonds form. Examples of ionic, covalent, and polar covalent bonds are animated, and students are given a set of compounds to predict the bonding types.\n• The Ionic and Covalent Bonding Simulation allows your students to investigate both types of bond and interact with several combinations of atoms. After building the binary molecules, students determine the type of bond that is present by watching the sharing or exchange of electrons between to two atoms. They then observe the formula and dot structure of the ionic formula unit or covalent molecule. For covalent molecules, the shape and name of the molecular shape is also provided.\n• Students compare properties of two visually similar substances, salt and sugar, in the Ionic vs. Covalent Compounds lab. Observations of each substance and analysis of chemical composition will allow students to draw conclusions regarding ionic and covalent compounds that could be used to help identify them.\n\n#### Ionic Bonding\n\nIntroduction\n\n• Introduction to Naming and Formula Writing for Ionic Compounds: In this activity, students will be introduced to ionic compound formulas and names. They will group prepared cut-outs to note similarities and differences among different classes of ionic compounds (i.e. binary and ternary, including metals with varying charges). The goal is not to be equipped to write names and formulas for ionic compounds, but to recognize trends in naming. Includes name and formula cards.\n• Students use ion cards with height that is related to charge to build ionic compounds with balanced charges in the Constructing Ionic Compounds activity. After constructing compounds, students then write the correct name and formulas for each. In addition to a student activity sheet, this lesson provides a set of ion cards to use during the lesson.\n\nPractice\n\n• Use the Bond with a Classmate activity assigns students an anion or cation so that they can form bonds with their classmates and record the formula and name of the compounds they create. By the end of this lesson, students should be able to write compound formulas in correct ratios by balancing charges on ions and write compound names using ionic naming rules with correct endings.\n• The activity, Ionic Bonding Puzzle, provides students with ionic puzzle pieces with shapes that correspond to their charge to use to create neutral ionic compounds. Once the compound are made, they use electron dot diagrams to show the formation of the compounds and then write the name and formula for each.\n\n#### Covalent Bonding\n\nIntroduction\n\n• In the guided inquiry lesson, Naming Covalent Compounds, students engage their literacy skills to interpret tables and answer a series of guiding questions to discover the rules of naming and formula writing for simple covalent compounds. By the end of this activity, students will be able to write a chemical formula and the name of covalent compounds using the appropriate rules of nomenclature.\n• If you include organic chemistry topics in your chemical names and formulas unit, use the Naming Alkanes activity to teach students how to name simple organic structures including alkanes, branched alkanes, and haloalkanes.\n\nPractice\n\n• Students use dice and element cards to name binary molecular compounds and then draw their Lewis Diagrams with the Molecular Compound Dice activity. The element cards can be downloaded, printed, and laminated for pairs of students to participate in this hands on activity.\n• With the Formula Card Game activity, students play a card game to practice creating chemical formulas for chemical compounds. This lesson will allow students to identify elements that can bond to each other to form appropriate compounds with different combinations of elements.\n• The activity, Mystery Gang Empirical Formulae can be used to give your students practice determining the empirical and molecular formula of a substance. This resource includes Case description cards, which give the percent composition and description of each substance, and Suspect Cards, which describe each suspect and the formula of the compound they used.\n\nSummary and Application\n\n• Use the Naming Compounds reference chart to help your students gain a better understanding of how to name ionic compounds, covalent compounds, and acids. The flowchart helps students follow the logic behind naming different types of compounds.\n• Students determine whether unknown substances are covalent (polar or nonpolar) or ionic by testing their solubility in the Solubility & Compound Type lab. A list of suggested unknown solids and solutions is provided in this resource, which will help students better understand how polarity, intermolecular forces, and solubility are related.\n\nExtension:\n\n• If your school has a ceramics program, The What’s in a Name? What’s in a Glaze? lesson connects chemistry and ionic compounds with the art of pottery. During the lesson, students practice naming and writing the formulas for ionic compounds commonly found in components of glazes for ceramics.\n• Extend study of ionic compounds to include the concept of ionic hydrates with the Formula of an Unknown Hydrate lab. This inquiry based lab requires students to design a laboratory procedure and then collect and analyze data to determine the formula of an unknown hydrated salt.\n• Students are challenged to analyze the spectral graphs obtained by the Curiosity Mars Rover with the Chemical Analysis of Martian Rocks lesson plan. Based on their examination students will determine the component elements of each sample, as well as the relative abundance of each element. With this information the student will complete calculations to find the empirical formula and identify the composition of the unknown rock. Finally students will complete research to see if these rocks are actually like those on Earth."
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|
https://math.stackexchange.com/questions/510564/show-that-fracnkn-k-frac1nk-leq-frac12k-1
|
[
"# Show that $\\frac{n!}{k!(n-k)!}\\frac{1}{n^k}\\leq\\frac{1}{2^{k-1}}$.\n\nI'm working on the problem given in the problem statement. Note that $0\\leq k\\leq n$ for $n\\in\\mathbb{N}$. I'm stuck trying to figure out where to even begin to show this inequality. I've done some searches and came across an upper bound for $n\\choose k$ as $\\frac{n^k}{k!}$, but I couldn't find a proof of that exactly. I also realized that the number of even and odd permutations is $2^{k-1}$, but I'm unsure if that even comes into play.\n\nNote that this is a homework problem given in my Real Analysis class, so please only provide me with a hint and not necessarily the entire proof.\n\nThanks for any help!\n\nEDIT:\n\nI was able to prove the problem directly. The proof is as follows,\n\nConsider \\begin{align} \\frac{n!}{k!(n-k)!}\\frac{1}{n^k}&=\\frac{n(n-1)\\cdots(n-k+1)(n-k)!}{k!(n-k)!}\\frac{1}{n^k} \\nonumber \\\\ &=\\frac{n(n-1)\\cdots(n-k+1)}{k!}\\frac{1}{n^k}\\nonumber \\\\ &\\leq\\frac{n^k}{k!}\\frac{1}{n^k}\\nonumber \\\\ &=\\frac{1}{k!}\\nonumber \\\\ &\\leq\\frac{1}{2^{k-1}} \\nonumber. \\end{align} Thus, $\\displaystyle\\binom{n}{k}\\frac{1}{n^k}\\leq\\frac{1}{2^{k-1}}.$\n\nThe inequality is equivalent to\n\n$$\\binom{n}k\\le\\frac{n^k}{2^{k-1}}\\;,$$\n\nwhich you can prove by induction on $n$ using the identity $$\\binom{n+1}k=\\binom{n}{k-1}+\\binom{n}k\\;.$$\n\nYou have\n\n\\begin{align*} \\binom{n+1}k&=\\binom{n}{k-1}+\\binom{n}k\\\\ &\\le\\frac{n^{k-1}}{2^{k-2}}+\\frac{n^k}{2^{k-1}}\\;, \\end{align*}\n\nto get you started.\n\nAdded: I found a combinatorial argument. For now I’ll leave it spoiler-protected.\n\nWe want to show that $2^{k-1}\\binom{n}k\\le n^k$. $2^{k-1}\\binom{n}k$ is the number of ways to pick $k$ elements from the set $\\{1,2,\\ldots,n\\}$ and partition them into two subsets, one of which may be empty. (There are $2^{k-1}$ ways to decide which of the other $k-1$ elements are to go in the same part with the largest element of the subset.) Let $K$ be a $k$-element subset of $\\{1,\\ldots,n\\}$, and suppose that $K=A\\cup B$, where $A\\cap B=\\varnothing$ and $\\max K\\in B$. Construct a $k$-tuple $\\sigma(K)$ of elements of $\\{0,\\ldots,1\\{$ by listing the members of $A$ in descending order followed by the members of $B$ in descending order. Observe that not only $K$, but also $A$ and $B$ can be reconstructed from this permutation of $K$. Thus, the map $K\\mapsto\\sigma(K)$ is an injection, and $2^{k-1}\\binom{n}k\\le n^k$.\n\n• Thanks for hint Brian. I'll go ahead and play around with this and see where I get. – Shant Danielian Oct 1 '13 at 0:41\n• @Shant: You’re welcome; if you simplify that last expression, I don’t think that you’ll have too much trouble getting what you need to make the induction step work. – Brian M. Scott Oct 1 '13 at 0:43\n• +1 Is there a direct combinatorial argument? – Calvin Lin Oct 1 '13 at 0:47\n• @Calvin: I’ve not seen one yet, but I’ve not given up hope, either! – Brian M. Scott Oct 1 '13 at 0:47\n• @Calvin: I’ve now found a direct combinatorial argument; it’s surprisingly straightforward. – Brian M. Scott Oct 1 '13 at 1:07\n\n$$\\binom{n}{k}=\\frac{(n-k+1)(n-k+2)..n}{1 \\cdot 2 \\cdot ... \\cdot k}=\\frac{(n-k+1)(n-k+2)..n}{2 \\cdot 3 \\cdot ... \\cdot k}\\leq \\frac{n \\cdot n \\cdot ....\\cdot n}{2 \\cdot 2 \\cdot ... \\cdot 2}=\\frac{n^k}{2^{k-1}}$$"
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[
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|
https://docs.xilinx.com/r/2022.2-English/ug1556-power-design-manager/Logic
|
[
"# Logic - 2022.2 English\n\n## Power Design Manager User Guide (UG1556)\n\nDocument ID\nUG1556\nRelease Date\n2022-10-19\nVersion\n2022.2 English\n\nThe Logic sheet covers power estimates of CLB logic: LUTs and Registers as shown in the following figure. Each row represents a group of logic that is associated with:\n\n• A particular Clock whose frequency is used to calculate dynamic power.\n• A Toggle Rate that represents an average over the inputs and outputs of all logic.\nLUTs fall into the following three categories, while registers are primarily the CLB registers.\nLUT as Combinatorial logic\nFor simplified entry, PDM assumes an average sized LUT of about five inputs and also assumes a small percentage of LUTs use two outputs.\nLUT as Shift Registers\nSRL primitives\nLUT as Distributed RAMs\nLUTRAM primitives\nFigure 1. PDM Logic",
null,
"Both Shift Registers and Distributed RAMs use the M-type CLB LUTs that you can configure as memory. To eliminate the difficulties of estimating total LUTs used for distributed RAM-based memories, use the Add Memory button to launch the PDM Memory Configuration wizard. Specify the memory array size, clock and options, and the PDM tool calculates the expected number of LUTs and registers and enters them into a row. Toggle Rate is defined as the percentage of clock cycles where a transition occurs. The default value of 12.5% means one transition every eight cycles.\n\nRouting Complexity column is an abstract model of the interconnect power. The number represents the average number of routing resources per logical net. A design with higher complexity requires more routing resources per net which increases power. Routing Complexity is typically only modified when importing Vivado power analysis results where Routing Complexity is calculated from the actual routing resources that are used to route the design. For early estimation, Xilinx recommends that you leave Routing Complexity at the default setting."
] |
[
null,
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",
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] |
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|
https://dsp.stackexchange.com/questions/1883/how-to-do-de-houghing-of-a-hough-transformed-image
|
[
"# How to do De-Houghing of a Hough transform'ed Image?\n\nI'm working with code found at Rosetta Code for creating a Hough transform. I now want to find all the lines in an image. To do so I need the ρ and θ values of each of the peaks in the Hough space. A sample output for a pentagon looks like this:",
null,
"How can I find a single [θ,ρ] coordinate for each of the 'hot spots' visible in the Hough space?\n\nYou are finding the coordinates of the peaks and then uses the axis to scale those into [θ,ρ] coordinates.\n\nDepending on how noisy the data, how many false peaks you expect and how much time you have, there are a few ways of doing it. Easiest is to pick some level that is a a real peak, cut of all data below that and then do a center of gravity on each peak to get it's center.\n\nYou could also erode/dialte the image until each peak is a single pixel.\n\n• +1 for precise answer. How do you define/compute center of gravity? – Dipan Mehta Mar 30 '12 at 13:48\n• For more accuracy, find the maximum, then fit a paraboloid to that point and its neighboring points, then find the peak of the paraboloid, which will generally be between pixels. – endolith Mar 30 '12 at 13:59\n• @endolith - generally with Hough transforms the accuracy is limited by the identification of edges in the initial image and the 'discretization' of the result in Hough space. If you need a more accurate result it's normal to go back and redo the transform for a more limited range of [θ,ρ] coordinates to get a higher resolution Hough space around the course solution you found – Martin Beckett Mar 30 '12 at 15:26\n• @DipanMehta - simply sum over (xvalue of each pixel) and (y..) then divide by the X,Y width of the box you are searching - but see comment to endolith – Martin Beckett Mar 30 '12 at 15:27\n\nThis code on the File Exchange will help you find all the local maxima. http://www.mathworks.com/matlabcentral/fileexchange/14498-local-maxima-minima\n\nIf you have some knowledge about how many lines you want to find (in this case five), you simply select the five local maxima with the highest Hough scores.\n\nYou can locate the local maxima for a given radius. For example, you scan the Hough image taking peaks as maxima only when they are maximal in a $3\\times 3$ window.\n\nThe second step could be refining the peak position to sub-pixel accuracy. This can be done by parabola fitting.\n\nSuppose the value in Hough image is $f(x)$ where $x$ is the 2D position. Now you would like to find a correcting vector $p$ that maximizes $f(x + p)$. This can be written using Taylor expansion:\n\n$$f(x+p)\\approx f(x)+p^{\\mathbb{T}}f'(x)+\\frac{1}{2}p^{\\mathbb{T}}f''(x)+p$$\n\nThe correcting vector is then\n\n$$p=-f''(x)^{-1}f'(x)$$\n\nThe derivatives can be computed from the Hough image by finite differencing.\n\nNote that $f''(x)$ is a $2\\times2$ Hessian matrix and $f'(x)$ is a 2-vector (horizontal and vertical gradient), hence the $p$ is also a 2-vector specifying a sub-pixel shift to get accurate position of the local maximizer.\n\nThe above equation may occasionally yield shifts of more than 1 pixel. In such case, the maximizer neighborhood does not have a parabolic shape and you may not want to do the correction or should even drop the candidate maximizer.\n\nThere is a very good technique developed back in the mid-80 by Gerig and Klein. It is a backmapping procedure that analyses the Hough space to identify the most likely point associated with each edge point and then constructs a second Hough space where the mapping of edge points to parameters is one-to-one rather than one-to-many which is the usual first stage. I don't have the reference to hand but look in the seminal Hough review paper of Illingworth and Kittler (about 1987?)"
] |
[
null,
"https://i.stack.imgur.com/iBsM8.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.88165164,"math_prob":0.9783063,"size":1134,"snap":"2020-34-2020-40","text_gpt3_token_len":311,"char_repetition_ratio":0.10265487,"word_repetition_ratio":0.0,"special_character_ratio":0.2627866,"punctuation_ratio":0.06140351,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9964621,"pos_list":[0,1,2],"im_url_duplicate_count":[null,10,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-27T11:03:26Z\",\"WARC-Record-ID\":\"<urn:uuid:cf16b808-3174-4e18-9f64-93344533dd1f>\",\"Content-Length\":\"176428\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:83a07015-687d-4cb5-8e3e-35d87df7f19c>\",\"WARC-Concurrent-To\":\"<urn:uuid:a12356b6-9361-41f9-a7c3-daeec40db1f0>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/1883/how-to-do-de-houghing-of-a-hough-transformed-image\",\"WARC-Payload-Digest\":\"sha1:I5TQ423LTQ5625KQKN35ATMEYPF5C6UP\",\"WARC-Block-Digest\":\"sha1:DTGU75BI3E3KM52CQQKJ4LSIFEJKXXT7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400274441.60_warc_CC-MAIN-20200927085848-20200927115848-00753.warc.gz\"}"}
|
https://slideum.com/doc/95018/quantum-theory-review
|
[
"#### Transcript Quantum Theory Review\n\n```Quantum Theory Review\nHow does the energy of an electron change\nwhen the electron moves closer to the nucleus?\nIt decreases.\nIt increases.\nIt stays the same.\nIt doubles.\nIt\nd\nsa\nhe\nys\nt\nIt\nst\na\n0%\nou\nbl\nes\n.\n0%\nm\ne.\n0%\nnc\nre\nas\nes\n.\nIt\ni\nec\nre\nas\nes\n.\n0%\nIt\nd\n1.\n2.\n3.\n4.\nWhat is the shape of the 3p atomic\norbital?\n1. sphere\n2. dumbbell\n3. like Abe Lincoln’s\nbeard\n4. A three legged dog\n0%\nle\ngg\ned\n. ..\n0%\nth\nre\ne\nA\nlik\ne\nAb\ne\nbb\nel\nl\nL in\nco\n. ..\n0%\ndu\nm\nsp\nhe\nre\n0%\nWhich scientist created the\nquantum model of the atom?\nRutherford\nBohr\nSchrodinger\nDemocritus\nEinstein\nEin\nitu\noc\nr\nDe\nm\ndi\nn\nSc\nhr\no\n0%\nst\nei\nn\n0%\ns\n0%\nge\nr\n0%\nBo\nhr\nrd\n0%\nRu\nth\ner\nfo\n1.\n2.\n3.\n4.\n5.\nWhat is the maximum number of f orbitals\nin any single energy level in an atom?\n1\n3\n5\n7\n0%\n7\n0%\n5\n0%\n3\n0%\n1\n1.\n2.\n3.\n4.\nWhat is the maximum number of\norbitals in the p sublevel of a given\nenergy level?\n1. 2\n2. 3\n3. 4\n4. 5\n0%\n5\n0%\n4\n0%\n3\n2\n0%\nThe valence electrons correspond\nto the outermost energy level\nelectrons in which sublevel(s)?\n0%\n0%\nF\nnd\nS,\nP,\nD,\na\nP\nan\nd\nP\nnd\n0%\nD\n0%\nSa\n0%\nP\nS\nP\nS and P\nP and D\nS, P, D, and F\nS\n1.\n2.\n3.\n4.\n5.\nWhen an electron moves from a lower to a\nhigher energy level, the electron ____.\n1. always doubles its energy\n2. absorbs a continuously\nvariable amount of energy\n3. absorbs a quantum of\nenergy\n4. moves closer to the\nnucleus\n0%\n0%\nof\nlo\nse\nrt\no\nth\ne\nm\nnt\nu\nm\nov\nes\nc\nqu\na\nbs\na\n0%\nnu\ncle\nus\ne.\n..\nv.\n..\nsly\nuo\nu\nab\nso\nr\nco\nnt\nin\nbs\na\nab\nso\nr\nalw\nay\nsd\nou\nbl\nes\ni\nts\nen\ner\ng\ny\n0%\nThe letter p in the symbol 4p3\nindicates the ____.\n1. spin of an electron\n2. orbital shape\n3. principle energy\nlevel\n4. speed of an electron\nof\nan\nel\nec\nt\nev\nel\nle\npr\nin\nc ip\nsp\nee\nd\nls\nita\nor\nb\n0%\nro\nn\n0%\nen\ner\ngy\nl\nha\np\nn\nel\nec\ntro\nn\nof\na\nn\nsp\ni\n0%\ne\n0%\nWhat types of atomic orbitals are\nin the third principal energy level?\ns and p only\np and d only\ns, p, and d only\ns, p, d, and f\nd\ns,\np,\na\nnd\nd\nan\nd\np\nnd\nf\n0%\n,a\non\nly\ny\non\nl\non\np\nnd\n0%\ns,\np,\nd\n0%\nly\n0%\nsa\n1.\n2.\n3.\n4.\nHow many unpaired electrons are in a\nsulfur atom (atomic number 16)?\n0\n1\n2\n3\n0%\n3\n0%\n2\n0%\n1\n0%\n0\n1.\n2.\n3.\n4.\nHow does the speed of visible light compare\nwith the speed of gamma rays, when both\nspeeds are measured in a vacuum?\n0%\ne.\nde\nte\nr..\n.\ner\nca\nn\nsp\nee\nds\na\nre\nbe\nth\ne\nar\nm\nm\nan\nNo\nTh\ne\nga\nof\nsp\nee\nd\nTh\ne\n0%\nsa\nm\nht\n...\nlig\nle\nsib\nvi\nof\nsp\nee\nd\nTh\ne\n0%\nay\ns..\n.\n0%\nsw\n1. The speed of visible light is\ngreater.\n2. The speed of gamma rays is\ngreater.\n3. The speeds are the same.\ndetermined from the\ninformation given.\nWhich of the following electromagnetic\nwaves have the highest frequencies?\n1. ultraviolet light\nwaves\n2. X-rays\n3. microwaves\n4. gamma rays\nul\ntra\nv\n0%\n0%\nga\nm\nm\na\nra\ny\ns\nav\nes\now\nXra\nys\n0%\nm\nicr\nio\nle\ntl\nigh\ntw\nav\nes\n0%\nHow many dots does Aluminum\nhave in its electron dot diagram?\n0%\n0%\n18\n0%\n15\n0%\n13\n0%\n3\n0%\n2\n1\n2\n3\n13\n15\n18\n1\n1.\n2.\n3.\n4.\n5.\n6.\nHow are the frequency and\nwavelength of light related?\n.\n0%\nop\nor\n..\npr\nre\nis\nd\nel\nen\ngt\nh\ndi\nre\nct\nly\net\ner\nm\nin\nel\n...\nav\nw\nals\n0%\n..\n0%\nW\nav\neq\nu\nFr\neq\nue\nnc\ny\nTh\ney\na\nre\nin\nve\nrs\nel\ny\npr\nop\no.\n..\n0%\nTh\ney\na\n1. They are inversely\nproportional to each other.\n2. Frequency equals\nwavelength divided by the\nspeed of light.\n3. Wavelength is determined\nby dividing frequency by\nthe speed of light.\n4. They are directly\nproportional to each other.\nNitrogen's electron configuration is 1s2 2s2\n2p3. To what group does nitrogen belong?\nGroup 2\nGroup 7\nGroup 15\nGroup 17\n17\n0%\nGr\nou\np\n15\n0%\nGr\nou\np\n7\n0%\nGr\nou\np\n2\n0%\nGr\nou\np\n1.\n2.\n3.\n4.\nAs changes in energy levels of electrons\nincrease, the frequencies of atomic line spectra\nthey emit ____.\n1. increase\n2. decrease\n3. remain the same\n4. cannot be\ndetermined\nca\nn\nno\nt\nbe\nde\nte\nrm\nin\nam\ne\nes\nth\nn\nai\nre\nm\n0%\ned\n0%\nea\nse\n0%\nde\ncr\nin\ncr\nea\nse\n0%\nWhich of the following quantum leaps would be\nassociated with the greatest energy of emitted\nlight?\n1. n = 5 to n = 1\n2. n = 4 to n = 5\n3. n = 2 to n = 5\n4. n = 5 to n = 4\n4\n=\nto\n=5\nn\nn\n=2\nto\nn\n=\n5\n0%\nn\n=\nn\n=4\nto\nn\n=\nn\nto\n=5\nn\n0%\n5\n0%\n1\n0%\nWhat are the maximum number of\nelectrons in the second energy level?\n2\n4\n6\n8\n18\n32\n0%\n32\n0%\n18\n0%\n8\n0%\n6\n0%\n4\n0%\n2\n1.\n2.\n3.\n4.\n5.\n6.\nHow many sublevels are in the third\nenergy level?\n0%\n0%\n5\n0%\n3\n0%\n2\n0%\n4\n1\n2\n3\n4\n5\n1\n1.\n2.\n3.\n4.\n5.\nWhich of the following sublevels is not\npresent in energy level 3?\nf\ns\np\nd\nAll are present\n0%\npr\nes\nen\n. ..\nar\ne\nd\n0%\nAl\nl\n0%\np\n0%\ns\n0%\nf\n1.\n2.\n3.\n4.\n5.\nHow many orbitals are in the 2p\nsublevel?\n1\n2\n3\n4\n0%\n4\n0%\n3\n0%\n2\n0%\n1\n1.\n2.\n3.\n4.\nHow many dots are in the electron\ndot diagram for Mg?\n0%\n0%\n12\n0%\n2\n0%\n7\n1\n2\n7\n12\n1\n1.\n2.\n3.\n4.\nThe number of valence electrons in\nfor electrons configurations ending\nin p5 is what?\n1\n2\n5\n7\n0%\n7\n0%\n5\n0%\n2\n0%\n1\n1.\n2.\n3.\n4.\n0%\n0%\n8\n0%\n4\n0%\n2\n0%\n6\n1\n2\n4\n6\n8\n1\n1.\n2.\n3.\n4.\n5.\nWhat is the maximum number of\nelectrons that can fit into the 2p\nsublevel?\nHow many orbitals are in the 4d\nsublevel?\n1\n2\n4\n5\n8\n10\n14\n0%\n14\n0%\n10\n0%\n8\n0%\n5\n0%\n4\n0%\n2\n0%\n1\n1.\n2.\n3.\n4.\n5.\n6.\n7.\n2\n4\n6\n8\n10\n14\n32\n0%\n32\n0%\n14\n0%\n10\n0%\n8\n0%\n6\n0%\n4\n0%\n2\n1.\n2.\n3.\n4.\n5.\n6.\n7.\nWhat is the maximum number of\nelectrons that can fit in the 5p\nsublevel?\nDescribe the shape of the 4s orbital?\nSpherical\nDumbbell shaped\nCube-shaped\nLike a sabertooth\ntiger\nab\ner\nto\n...\n0%\nLik\ne\nas\nha\np\nCu\nbe\n-s\npe\n. ..\nsh\na\nbb\nel\nl\nDu\nm\n0%\ned\n0%\nal\n0%\nSp\nhe\nr ic\n1.\n2.\n3.\n4.\nIn Period 3 there are 8 elements. What\nsublevel(s) is (are) being filled?\ns\ns and d\ns and p\nd and f\n0%\n0%\nf\nan\nd\nd\nnd\nsa\nsa\nnd\nd\n0%\np\n0%\ns\n1.\n2.\n3.\n4.\nIf n stands for the highest occupied energy level,\nthe outer configuration for all Group 1 elements\nis\n1. ns1.\n2. 2n.\n3. n – s.\n4. np1.\n–s\nn\n0%\nnp\n1.\n0%\n.\n0%\n2n\n.\nns\n1.\n0%\nBromine, atomic number 35, belongs to Group\n17. How many electrons does bromine have in\nits outermost energy level?\n1. 7\n2. 17\n3. 18\n4. 35\n0%\n35\n0%\n18\n0%\n17\n7\n0%\n```"
] |
[
null
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https://blog.geoteric.com/wordpress/2015/04/09/multi-volume-similarity-workflows-using-parser-avo-4d-multi-azimuth
|
[
"",
null,
"Luis Gomez | April 9, 2015\n\n## Multi-volume similarity workflows using Parser: AVO, 4D, Multi-Azimuth\n\nGeoTeric can be used very effectively in a multi-volume environment to screen for differences in AVO, 4D or Multi-Azimuth responses. In some cases, the reflectors are not well aligned between the stacks that we are comparing or there is an unexpected frequency change between the stacks, so any interpretation on those areas might be unreliable.\n\nMisalignment of stacks can cause false positive AVO anomalies or false 4D/Multi-Azimuth interpretations, so being able to highlight those unreliable areas can help to increase the confidence on the multi-volume analysis.\n\nThis advanced workflow involves the use of the Parser in order to highlight areas of misalignment or frequency changes. The Parser can be found under Processes & Workflows > Processes > Volume Maths > Parser.\n\nPhase alignment: “peaks volume” and “troughs volume”\n\nTo start our phase alignment analysis, we can just bring the two volumes we are interested to compare into the Parser, and type the Parser expression (im1>0)*im2. This will generate a “peaks volume” where the peaks of the 1st input volume will be replaced by whatever data we have in the 2nd volume. So if we see any troughs in the resulting volume, it means that the alignment is poor in those areas.\n\nSimilarly we can apply (im1<0)*im2, and that will give us a “troughs volume” where any positive values will indicate areas of poor alignment.\n\n“Peaks volume” (left) and “troughs volume” (right) showing a fairly good stack alignment\n\nPhase alignment: Bedform stack\n\nA much more detailed QC can be achieved by using a Bedform stack. We can compute the Bedform indicator attribute for each of the stacks, and then combine the Bedform attributes using a parser expression. The example below is a combination of three angle stacks, but a similar approach can be followed for other volumes. The Parser expressions we need to use are:\n\nFor 32bit:\n((((im1>700000000)*im1)+((im1<-700000000)*im1))+(((im2>700000000)*im2)+((im2<-700000000)*im2))+(((im3>700000000)*im3)+((im3<-700000000)*im3)))/3\n\nFor 16bit:\n((((im1>10000)*im1)+((im1<-10000)*im1))+(((im2>10000)*im2)+((im2<-10000)*im2))+(((im3>10000)*im3)+((im3<-10000)*im3)))/3\n\nFor 8bit:\n((((im1>170)*im1)+((im1<90)*im1))+(((im2>170)*im2)+((im2<90)*im2))+(((im3>170)*im3)+((im3<90)*im3)))/3\nThese Parser expressions are simply (im1+im2+im3)/3, but as we want to remove the doublet values in each of the Bedform attributes they become a bit more complex.\n\nIf the output is displayed using the Azimuthcolour map, areas with good alignment will be seen in black, areas with dispersion along a peak in red, and areas with dispersion along a trough in blue. The lighter the blue and red colours, the worse the alignment.\n\nBedform stack volume showing areas with good alignment in black and areas of worse alignment in red and blue.\n\nFrequency change QC\n\nThe frequency changes across our stacks can be QCed by comparing the instantaneous frequency attributes. The first step involves computing the Instantaneous Frequency attribute for two of the volumes (such as near and far), then applying a Smoothing (can be found under Processes & Workflows > Processes > Attributes > Structural attributes) using a median option and a 3x3x5 footprint to each of the Instantaneous Frequency volumes. Then the Frequency QC volume can be produced using the following Parser expression:\n\nABS(((im1>0)&(im2>0))*(im2-im1))\n\nFrequency change QC volume showing minor frequency differences between two stacks.\n\nIn summary, by applying this multi-volume similarity workflow, we can identify areas of misalignment in our stacks and increase our confidence in any further AVO, 4D or Multi-Azimuth analysis."
] |
[
null,
"https://blog.geoteric.com/hubfs/GeotericLogo-1.svg",
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https://percent.info/increase/240/how-to-calculate-the-percent-increase-from-240-to-996.html
|
[
"Percent increase from 240 to 996",
null,
"This page will answer the question \"What is the percent increase from 240 to 996?\" and also show you how to calculate the percent increase from 240 to 996.\n\nBefore we continue, note that \"percent increase from 240 to 996\" is the same as \"the percentage increase from 240 to 996\". Furthermore, we will refer to 240 as the initial value and 996 as the final value.\n\nSo what exactly are we calculating? The initial value is 240, and then a percent is used to increase the initial value to the final value of 996. We want to calculate what that percent is!\n\nHere are step-by-step instructions showing you how to calculate the percent increase from 240 to 996.\n\nFirst, we calculate the amount of increase from 240 to 996 by subtracting the initial value from the final value, like this:\n\n996 - 240\n= 756\n\nTo calculate the percent of any number, you multiply the value (n) by the percent (p) and then divide the product by 100 to get the answer, like this:\n\n(n × p) / 100 = Answer\n\nIn our case, we know that the initial value (n) is 240 and that the answer (amount of increase) is 756 to get the final value of 996. Therefore, we fill in what we know in the equation above to get the following equation:\n\n(240 × p) / 100 = 756\n\nNext, we solve the equation above for percent (p) by first multiplying each side by 100 and then dividing both sides by 240 to get percent (p):\n\n(240 × p) / 100 = 756\n((240 × p) / 100) × 100 = 756 × 100\n240p = 75600\n240p / 240 = 75600 / 240\np = 315\nPercent Increase = 315\n\nThat's all there is to it! The percentage increase from 240 to 996 is 315%. In other words, if you take 315% of 240 and add it to 240, then the sum will be 996.\n\nThe step-by-step instructions above were made so we could clearly explain exactly what a percent increase from 240 to 996 means. For future reference, you can use the following percent increase formula to calculate percent increases:\n\n((f - n)/n) × 100 = p\n\nf = Final Value\nn = Initial Value\np = Percent Increase\n\nOnce again, here is the math and the answer to calculate the percent increase from 240 to 996 using the percent increase formula above:\n\n((f - n)/n) × 100\n= ((996 - 240)/240) × 100\n= (756/240) × 100\n= 3.15 × 100\n= 315\n\nPercent Increase Calculator\nGo here if you need to calculate another percent increase.\n\nPercent increase from 240 to 997\nHere is the next Percent Increase Tutorial on our list that may be of interest."
] |
[
null,
"https://percent.info/images/percent-increase.png",
null
] |
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https://answers.everydaycalculation.com/subtract-fractions/3-8-minus-7-10
|
[
"Solutions by everydaycalculation.com\n\n## Subtract 7/10 from 3/8\n\n3/8 - 7/10 is -13/40.\n\n#### Steps for subtracting fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 8 and 10 is 40\n\nNext, find the equivalent fraction of both fractional numbers with denominator 40\n2. For the 1st fraction, since 8 × 5 = 40,\n3/8 = 3 × 5/8 × 5 = 15/40\n3. Likewise, for the 2nd fraction, since 10 × 4 = 40,\n7/10 = 7 × 4/10 × 4 = 28/40\n4. Subtract the two like fractions:\n15/40 - 28/40 = 15 - 28/40 = -13/40\n\nMathStep (Works offline)",
null,
"Download our mobile app and learn to work with fractions in your own time:"
] |
[
null,
"https://answers.everydaycalculation.com/mathstep-app-icon.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5680931,"math_prob":0.99314874,"size":369,"snap":"2021-43-2021-49","text_gpt3_token_len":180,"char_repetition_ratio":0.23561645,"word_repetition_ratio":0.0,"special_character_ratio":0.5555556,"punctuation_ratio":0.04950495,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9990221,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T11:33:46Z\",\"WARC-Record-ID\":\"<urn:uuid:43009e95-4d81-4a95-ba80-2901a9c84dee>\",\"Content-Length\":\"8510\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:10708ec2-a68b-4343-836f-63536e1ada89>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc83630c-5f74-48c7-acc5-dc03a230350c>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/subtract-fractions/3-8-minus-7-10\",\"WARC-Payload-Digest\":\"sha1:FS24M6VRIITPIEWL4PWBVUJV2LXW76KP\",\"WARC-Block-Digest\":\"sha1:NEAEGJ3OMNTCYHBO2NWEI3WXSDL5HRHV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585405.74_warc_CC-MAIN-20211021102435-20211021132435-00315.warc.gz\"}"}
|
https://e-eduanswers.com/mathematics/question1682601
|
[
" Point p(-5, 2) is translated using the rule (x+3, y-1). what is the x-coordinate of p' ?",
null,
"",
null,
", 18.10.2019 10:00, keirarae2005\n\n# Point p(-5, 2) is translated using the rule (x+3, y-1). what is the x-coordinate of p' ?",
null,
"### Similar questions",
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"",
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"Do you know the correct answer?\nPoint p(-5, 2) is translated using the rule (x+3, y-1). what is the x-coordinate of p' ?...\n\n### Questions in other subjects:",
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"Mathematics, 05.07.2019 16:40\nTotal solved problems on the site: 8125202"
] |
[
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"https://e-eduanswers.com/tpl/images/sovy.png",
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"https://e-eduanswers.com/tpl/images/cats/mat.png",
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"https://e-eduanswers.com/tpl/images/cats/mat.png",
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"https://e-eduanswers.com/tpl/images/cats/mat.png",
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"https://e-eduanswers.com/tpl/images/cats/mat.png",
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"https://e-eduanswers.com/tpl/images/cats/en.png",
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"https://e-eduanswers.com/tpl/images/cats/en.png",
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"https://e-eduanswers.com/tpl/images/cats/mat.png",
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"https://e-eduanswers.com/tpl/images/cats/istoriya.png",
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"https://e-eduanswers.com/tpl/images/cats/istoriya.png",
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|
https://www.hicyh.com/archives/swiftlearn
|
[
"Swift 是一门类型安全的语言\nSwift的基本数据类型：Int、UInt、Float、Double、Bool、String、Character、Optional\nSwift提供的数据集合：元祖、Array、Set 和 Dictionary\n\nSwift也支持如java一般的三元运算符：x ? x : x\n\nimport Foundation\n\nprint(\"Hello, World!\")\n\n\n//自动推断类型\nvar a = 45\na = 50\n//显示的声明类型\nvar dou:Double = 5.9\n//常量\nlet b = 56\n\n//可空变量（Optional），跟kotlin一样的用法\nvar vEmpty:String? = \"可空属性\"\n//使用可空属性的时候，可以为其设定默认值，跟kotlin里的 ?: 一样的意思\nvar mVaule = vEmpty ?? \"这是默认值\"\n\n//值得注意的是：所有的强制类型转换返回了来的都是一个可空的属性（Optional），例如：\nvar optNumber = Int(\"123\")\n//此时optNumber是一个 Int? 类型\n\n\nlet label = \"这是一个标签\"\nlet width = 89\nlet labelAndWidth = label + String(width)\n//有一种更简单的把值转换成字符串的方法：把值写到括号中，并且在括号之前写一个反斜杠 \\()\nlet labelWidthTwo = \"新的字符串合并方式：\\(width),\\(label)\"\n\n\n//数组\nvar array = [\"元素1\",\"元素2\",\"元素3\",\"元素4\",]\nlet y1 = array\narray = \"元素2被更改过\"\n//移除一个元素\narray.remove(at: 3)\n//在后面追加一个元素\narray.append(\"这是追加的元素5\")\n//数组的长度\nlet size = array.count\nprint(\"长度：\",size,\" 内容：\",array)\n\n//声明一个空白数组\nvar arrayEmpty:[String]\n//空数组必须先初始化\narrayEmpty = [String]()\n//可以使用空白数组了\narrayEmpty.append(\"111\")\nprint(arrayEmpty)\n\n\n长度： 4 内容： [\"元素1\", \"元素2被更改过\", \"元素3\", \"这是追加的元素5\"]\n[\"111\"]\n\n\n//字典\nvar map = [\n\"key0\":\"第1个元素\",\n\"key1\":\"第2个元素\",\n\"key2\":\"第3个元素\",\n\"key3\":\"第4个元素\",\n]\n//使用\nlet item0 = map[\"key0\"]\n//赋值\nmap[\"key1\"] = \"修改过的元素2\"\n//移除某个值，或者移除全部 removeAll(keepingCapacity: true) 传递true可以在删除数组元素后保留其现有容量。默认值为false。\nmap.removeValue(forKey: \"key2\")\nprint(\"字典：\",map,\"\\n\")\n\n//声明空白字典\nvar mapEmpty:[String:String]\n//空白字典必须初始化才可以使用\nmapEmpty = [String:String]()\n//使用\nmapEmpty[\"key\"] = \"value\"\nprint(\"空白字典：\",mapEmpty,\"\\n\")\n\n\n字典： [\"key0\": \"第1个元素\", \"key3\": \"第4个元素\", \"key1\": \"修改过的元素2\"]\n\n\n\nif语句的使用，if后不需要接小括号，需要注意的是，if 配合 let 以及 可空属性，可以比较优雅的判断属性是否是空的（称为 可选绑定），看示例：\n\n//if语句不需要像java一样需要小括号\nvar number = 100\nif number == 50 {\nprint(\"number的值为：\\(number)\")\n}else if number > 0 && number <= 100{\nprint(\"number的值范围：大于0，小于或等于100\")\n}else{\nprint(\"无法识别\")\n}\n\n//if配合let 以及 可空的属性 使用，如果属性是空的，那将会不通过if\nvar name:String? //如果这个有值，将会进入if ，如果没值，将不会进入\nif let n = name {\n//这里定义的 n 作用域仅仅是 if 里面， else里都不能用\nprint(\"name不是nil ，name=\\(n)\")\n}else{\nprint(\"name是nil\")\n}\n\n\nnumber的值范围：大于0，小于或等于100\nname是nil\n\n\nswift中，循环有for in,while,repeat .. while三种循环，唯一要说明的是repeat .. while循环其实就是java中的,do..while循环，能保证循环体必定会执行一次，所有循环都在下面的例子中。\n\nprint(\"遍历数组\")\nlet farray = [\"张三\",\"李四\",\"王武\",]\nfor item in farray{\nprint(item)\n}\n//注意了，可以使用enumerated()方法，把数组的下标也遍历出来\nprint(\"\\n带下标循环数组\")\nfor (index,item) in farray.enumerated(){\nprint(\"下标：\\(index) 值：\\(item)\")\n}\n\nprint(\"\\n遍历字典：\")\nfor (key,value) in fmap {\nprint(\"字典的内容：\\(key) : \\(value)\")\n}\n\nprint(\"\\n while循环\")\nvar wf = 0\nwhile wf < 10 {\nprint(\"wf=\\(wf)\")\nwf += 1\n}\n\nprint(\"\\n repeat..while循环\")\n//swift中的repeat..while循环其实就是java里的do..while循环，它能保证循环体必定会执行一次\nvar dwf = 0\nrepeat {\nprint(\"dwf=\\(dwf)\")\n}while dwf > 0\n\n//使用区间循环\n//使用 ..< 创建的范围不包含上界，如果想包含的话需要使用 ...\nfor i in 0..<3{\nprint(i)\n}\n\n//swift中还有很多区间运算：\n//array[2...]\n//array[...4]\n//array[..<6]\n\n\n\n遍历数组\n\nwhile循环\nwf=0\nwf=1\nwf=2\nwf=3\nwf=4\nwf=5\nwf=6\nwf=7\nwf=8\nwf=9\n\nrepeat..while循环\ndwf=0\n0\n1\n2\n\n\n//元祖中可以存储不同类型的数据，如果未命名的情况下，将会以下标012345...的形式使用，命名了就以名称使用\nlet tuples = (\"CYH\",49,true)\nprint(\"\\n元祖的使用：\\(tuples.0)、\\(tuples.1)、\\(tuples.2)\")\n//命名元祖\nlet tuplesname = (tname:\"Cyh\",age:25)\nprint(\"\\n使用命名元祖：\\(tuplesname.tname)、\\(tuplesname.age)\")\n\n\n\nfunc 函数名(参数名:参数类型)->返回值类型{\n//你的代码\n}\n\n\nfunc sayHello(name:String)->String{\nreturn \"Hello \\(name)\"\n}\n//调用\nsayHello(name: \"Jon\")\n\n\nfunc minMax(array: [Int]) -> (min: Int, max: Int) {\nvar currentMin = array\nvar currentMax = array\nfor value in array[1..<array.count] {\nif value < currentMin {\ncurrentMin = value\n} else if value > currentMax {\ncurrentMax = value\n}\n}\nreturn (currentMin, currentMax)\n}\n\n\n//返回一个可能为空的元祖，要注意区别的是，这与(Int?,Int?)是不同的，(Int,Int)?是整个元祖可能为空\nreturn (142,352)\n}\n\n\nfunc getXY(viewAdd:String) -> (x:Int,y:Int)? {\n(142,352)\n}\n\n\nfunc sayHello(name:String=\"def\")->String{\nreturn \"Hello \\(name)\"\n}\n//调用\nsayHello()\n\n\n//可变参数\nfunc sayHello(name:String...)->String{\n//传进来的 name 是一个数组\nreturn \"Hello \\(name)\"\n}\n//调用\nsayHello(name:\"a\",\"b\",\"c\")\n\n\nfunc swapTwoInts(_ a: inout Int, _ b: inout Int) {\nlet temporaryA = a\na = b\nb = temporaryA\n}\n\n\nlet a:Int = 9\nlet b:Int = 10\nswapTwoInts(&a,&b)\n\n\n⚠️注意：输入输出参数不能有默认值，而且可变参数不能用 inout 标记。\n\n【闭包】待续。。。"
] |
[
null
] |
{"ft_lang_label":"__label__zh","ft_lang_prob":0.79026717,"math_prob":0.9948648,"size":5912,"snap":"2021-43-2021-49","text_gpt3_token_len":3434,"char_repetition_ratio":0.09512525,"word_repetition_ratio":0.0085324235,"special_character_ratio":0.30801758,"punctuation_ratio":0.17489712,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9852076,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-28T17:30:13Z\",\"WARC-Record-ID\":\"<urn:uuid:33afb10b-330a-4af9-a708-c12a2983591d>\",\"Content-Length\":\"56400\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a6515143-24d0-43a9-8e51-bb5d1bd2f467>\",\"WARC-Concurrent-To\":\"<urn:uuid:9eead09e-132b-44bf-8b86-9c782e74da4c>\",\"WARC-IP-Address\":\"111.230.223.67\",\"WARC-Target-URI\":\"https://www.hicyh.com/archives/swiftlearn\",\"WARC-Payload-Digest\":\"sha1:5K4WMWHLJ5MEYO6OFN6BMJTVRBZS3U7E\",\"WARC-Block-Digest\":\"sha1:P5X4QOJVFCWWDGAFBMNKHVXAVNFS5DBY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588398.42_warc_CC-MAIN-20211028162638-20211028192638-00637.warc.gz\"}"}
|
http://www.athometuition.com/quadratic-inequalities.aspx
|
[
"We will learn about quadratic inequalities based on the quadratic equation ax2+bx+c = 0, where a≠0, a, b, c are real numbers. The inequalities are of the form",
null,
"ax2+bx+c = 0\n\nThe solutions are real and different if the discriminant b2-4ac > 0\n\nSuppose α (alpha) and β (beta) are the solutions (roots, zeros) of\n\nax2+bx+c = 0\n\nThen, we can write\n\nax2+bx+c = a(x - α) (x - β)\n\nα,β are real α≠β\n\nSuppose α <β.\n\nNow assume x is moving from the left to the right along the real number line. Consider how the sign of ax2+bx+c\nvaries in the process.\n\nAt the extreme left, x < α < β, then (x -α) < 0; that is, the value is negative and (x - β) < 0; that is, the value is\nnegative.\n\nIn this region, a (x - α ) (x - β) > 0 since a*-ve *-ve = a * +ve\n\nAt x = α\n\na(x -α )(x - β) = 0\n\nWhen α < x <β\n\n(x -α )> 0 x -α is +ve\n\n(x -α )> 0 x - βis -ve\n\n∴ a(x -α ) (x - β) < 0\n\na* (+ve) * (-ve) = a * -ve\n\nIn this region, a(x -α ) (x - β) < 0\n\nAt x = β\n\na(x -α ) (x - β) = 0\n\nTo the right, β for when x >β >α\n\n(x -α ) > 0 x -α is +ve\n\n(x - β) > 0 x - β is +ve\n\na (x -α ) (x - β) > 0\n\na* (+ve) * (+ve) = a * +ve\n\nSo a(x -α ) (x - β) > 0 in this region.\n\nThese results are summarized in the figure given below.\n\nax2+bx+c>0 ax2+bx+c<0 ax2+bx+c>0",
null,
"α β\n\nAt the points x = α, x = β\n\nax2+bx+c=0\n\nIf a x2+bx+c=0 a>o has real and unequal roots, β then when\n\nx < α ⇒ ax2+bx+c>0\n\nx < α ⇒ ax2+bx+c>0\n\nx = α ⇒ ax2+bx+c=0\n\nα < x < β ⇒ ax2+bx+c<0\n\nx = β ⇒ ax2+bx+c=0\n\nx >β ⇒ ax2+bx+c>0\n\nNow suppose that ax2+bx+c=0 a > 0 has real and equal roots; that is,\n\nα = β = r (say) then when\n\nx< r ⇒ ax2+bx+c>0\n\nx=r ⇒ ax2+bx+c=0\n\nand x>r ⇒ ax2+bx+c>0\n\nThis is because\n\nax2+bx+c=(x-r )2\n\nA square is always positive.\n\nIf, however, ax2+bx+c=0 (a > 0) has no real roots then ax2+bx+c>0.\n\nfor all real x.\n\nConsider the following examples.\n\nExample 1\n\nSolve x2-6x+8>0 and mark the values on the real number line.\n\nSolution I: x2-6x+8>0\n\n⇔ x2-6x > -8\n\nhere a = 1, b = -6, c = 8\n\nBy adding (-b/2a) to both sides of the inequality, we get",
null,
"That is, the absolute value of x-3 should be greater than 1.\n\n∴ There are two possibilities\n\nx-3>1----------------------- (1)\n\n-(x-3)>1-------------------- (2)\n\nConsider x-3>1\n\n⇒ x>1+3\n\n⇒ x>4\n\nConsider -(x-3)>1\n\n⇒ -x+3>1\n\n⇒ -x>1-3\n\n⇒ -x>-2\n\n⇒ -(-x) < -(-2)\n\n⇒ x<2.\n\nThe solution set of x2-6x+8>0 is {x/x<2} U {x/x>4}\n\nNo value of x lies between 2 and 4.\n\n(check it out)\n\nSolution II: Alternate method\n\nx2-6x+8>0\n\nFactorizing the left-hand side of the inequality\n\nx2-4x-2x+8>0\n\n⇒ x(x-4)-2(x-4)>0\n\n⇒ x(x-2) (x-3)>0\n\n⇔ (x-2)<0 and (x-4)<0\n\nor (x-2)>0 and (x-4)>0\n\nIf x-2<0 then x<2\n\nIf x-4<0 then x<4\n\nor\n\nIf x-2>0 then x>2\n\nIf x-4>0 then x>4.\n\nThis is possible only if x<2 or x>4.",
null,
"Example 2\n\nSolve x2-6x+5<0 and mark it on the number line.\n\nSolution:\n\nx2-6x+5<0\n\nFactorizing the left-hand side of the inequality\n\nx2-5x-x+5 <0\n\n⇒ x(x-5)-1(x-5)<0\n\n⇒ (x-1) (x-5)<0\n\n⇒ (x-1)<0 and (x-5)>0\n\nor\n\n(x-1)>0 and ⇒ (x-5)<0\n\nIf x-1<0 ⇒ x<1\n\nIf x-5>0 ⇒ x>5\n\nOr\n\nIf x-1>0 ⇒ x>1\n\nIf x-5<0 ⇒ x<5\n\nOr\n\nIf x-1>0 ⇒ x>1\n\nIf x-5<0 ⇒ x<5",
null,
"#### Solve the following inequalities and mark them on the real number lines\n\n1. x2-x-2<0\n\n2. 7+10x+3x2<0\n\n3. 2x2+3x+1>0\n\n4. 3x2+5x+2>0\n\n5. x2+2x-3<0\n\n6. 2x2-x-15>0\n\n1. Solution:\n\nTo solve x2-x-2<0\n\nFactorizing the left-hand side of the inequality we get\n\nx2-2x+x-2<0\n\n⇒ x(x-2)+1(x-2)<0\n\n⇒ (x+1)(x-2)<0\n\n⇒ (x+1)<0 and (x-2)<0\n\nOr\n\n(x+1)>0 and (x-2)<0\n\nIf x+1<0 then x<-1\n\nIf x-2>0 then x>2\n\nOr\n\nIf x+1>0 then x>-1\n\nIf x-2<0 then x<2.",
null,
"2. Solution:\n\nTo solve 7+10x+3x2 <0\n\nFactorizing the left-hand side of the inequality\n\n7+7x+3x+3x2<0\n\n⇒ 7(1+x)+3x(1+x)<0\n\n⇒ (7+3x) (1+x)<0\n\n⇒ 7+3x<0 and 1+x>0\n\nOr\n\n7+3x>0 and 1+x<0.\n\nIf 7+3x<0 then 3x<-7\n\nx< -7/3\n\nIf 1+x>0 then x>-1\n\nOr\n\nIf 7+3x>0 then 3x>-7\n\nx>-7/3\n\nIf 1+x<0 then x<-1\n\nComparing with",
null,
"3. Solution:\n\nTo solve 2x2+3x+1>0\n\nFactorizing the left-hand side of the inequality\n\n2x2+ 2x+x+1>0\n\n⇒ 2x(x+1)+1(x+1)>0\n\n⇒ (2x+1) (x+1)>0\n\n⇒ 2x+1>0 and x+1>0\n\nOr\n\n2x+1<0 and x+1<0\n\nIf 2x+1>0 then 2x>-1\n\nx>-1/2\n\nIf x+1>0 then x>-1\n\nOr\n\nIf 2x+1<0 then 2x<-1\n\nx<-1/2\n\nIf x+1<0 then x<-1.\n\nComparing with",
null,
"4. Solution:\n\nTo solve 3x2+5x+2>0\n\nFactorizing the left-hand side of the inequality\n\n3x2+3x+2x+2>0\n\n⇒ 3x(x+1)+2(x+1)>0\n\n⇒ (3x+2) (x+1)>0\n\n⇒ 3x+2>0 and x+1>0\n\nOr\n\n3x+2<0 and x+1 <0\n\nIf 3x+2>0 then 3x>-2\n\nx>-2/3\n\nIf x+1>0 then x>-1\n\nOr\n\nIf 3x+2 then 3x<-2\n\nx<-2/3\n\nIf x+1<0 then x<-1.\n\nComparing with",
null,
"5. Solution:\n\nTo solve x2+2x-3<0.\n\nFactorizing the left-hand side of the inequality\n\nx2+2x-3<0\n\n⇒ x2+3x-x-3<0\n\n⇒ x(x+3)-1(x+3)<0\n\n⇒ (x-1)(x+3)<0\n\n⇒ (x-1)<0 and x+3>0\n\nOr\n\n(x-1)>0 and x+3<0\n\nIf x-1<0 then x<1\n\nIf x+3>0 then x>-3\n\nOr\n\nIf x-1>0 then x>1\n\nIf x+3<0 then x<-3.\n\nComparing with",
null,
"6. Solution:\n\nTo solve 2x2-x-15>0.\n\nFactorizing the left-hand side of the inequality.\n\n2x2-x-15>0.\n\n⇒ 2x2-6x+5x-15>0\n\n⇒ 2x(x-3)+5(x-3)>0\n\n⇒ (2x+5)(x-3)>0\n\n⇒ 2x+5>0 and x-3>0\n\nOr\n\n2x+5<0 and x-3<0\n\nIf 2x+5>0 then 2x>-5\n\nx>-5/2\n\nIf x-3>0 then x>3\n\nOr\n\nIf 2x+5<0 then 2x<-5\n\nx<-5/2\n\nIf x-3 <0 then x<3.\n\nComparing with",
null,
""
] |
[
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"http://www.athometuition.com/images/qie1.gif",
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"http://www.athometuition.com/images/qie2.gif",
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"http://www.athometuition.com/images/qie3.gif",
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"http://www.athometuition.com/images/qie4.gif",
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"http://www.athometuition.com/images/qie5.gif",
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"http://www.athometuition.com/images/qie6.gif",
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"http://www.athometuition.com/images/qie7.gif",
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"http://www.athometuition.com/images/qie8.gif",
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"http://www.athometuition.com/images/qie9.gif",
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"http://www.athometuition.com/images/qie10.gif",
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"http://www.athometuition.com/images/qie11.gif",
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|
http://excel.bigresource.com/Converting-Hours-to-Numbers-Decimals-3bcIiVDu.html
|
[
"# Converting Hours To Numbers, Decimals\n\nNov 10, 2009\n\nHow do I convert hours into numbers and/or decimals?\n\nExample:\nColumn A Column B\n---------- -----------\n30:05:00 to 30.05\n26:10:00 to 26.10\n262:47:00 to 262.47\n\nFigures under Column B refer to info that I would like to get.\n\nADVERTISEMENT\n\n## Numbers Are Converting To Decimals\n\nDec 6, 2007\n\nI received a complaint from one of my colleague that he is facing sudden problem with Ms-Excel(2002)\nThe problem is When he feeds number 2 in to a cell it automatically converts in to 0.02. I tried using \"Decrease decimal\" and \"format cells\" option and even through uninstalling office and reinstalling a different version but the problem still continues.\n\n## Converting Decimals To Fraction...\n\nSep 25, 2009\n\nCan anyone help me with a code for converting decimal number to a nearest 1/16 th fraction. For example converting number 2.1875 to 2 3/16 and so on...Also if it is 2.5 it should display 2 1/2...\n\n## Converting Decimals To Hrs & Minutes\n\nJan 23, 2007\n\nHow can I show a decimal as time. For example an item takes 13 minutes to make and I want to make 50, thus using 6.5 hours but really, the 0.5 hours is 30 minutes therefore, I would like to show 6:30 but Excel gets to 23:59 and goes back to 0:00.\n\n## Converting Fractions To Decimals\n\nAug 11, 2009\n\n=(\"0 \"&C3)+0\n\nhave this formula for converting fractions to decimals which works great,\n\nthe problem i have is to get it to register 0 if there is no fraction in c3\n\nwill try and word my next question better\n\n## Converting Prices In Ticks To Decimals\n\nFeb 12, 2010\n\ni am trying to convert 100.50 to 100-16, agency mortgage price formats ...\n\n## Formula To Convert Hours And Minutes To Decimals?\n\nNov 21, 2013\n\nI have a data set that expresses time in hours and minutes but it can only be exported like so:\n\n7h10\n11h03\n\nAny function I could use to convert those numbers into 7.6 or 11.03?\n\n## Convert Time Decimals To Hours Mins\n\nJan 14, 2009\n\nI am creating a very quick holiday excel sheet where people can fill in the hours they want on which days.\n\nI have a summery sheet too.\n\nSo if someone wants to take a full day which is 7.4 hours. How would this be represented as Hours and minutes?\n\n## Sort Mixture Of Numbers And Text Using Numbers And Decimals\n\nNov 13, 2013\n\nI am looking for a VBA to sort rows which include actual numbers and text representing decomposed CTQs (or procedures in IT development)\n\nCode:\n\nCol A Col B\n1Billing Accuracy\n2Billing Time\n3Credit Check Accuracy\n4Credit Check Time\n2.1Bill preparation\n\n[Code]....\n\nThis is the order in which the data is copied and saved from worksheets in which they are developed. Note that 3 rows (8.1.2.1 through 8.1.2.3) are below 8.1.3 (because the three come from Worksheet 8.1.2 which came after worksheet 8.1). The first four rows came from a Top Level Worksheet. I would like to see them intermixed but in proper order.\n\n## Converting Hh:mm:ss To Hours\n\nApr 9, 2007\n\nconvert hh:mm:ss into hours, that is 90:10:20 to 90.1722\n\n## Numbers Have Too Many Decimals\n\nFeb 8, 2009\n\nA spreadsheet created by exporting from QuickBooks as a .IIF file is opened in Excel 2003.\n\nA macro multiplies a cell value and returns 1.77999997138977 rather than 1.78. The 1.78 is required for importing back into Quickbooks.\n\nPart of the code is: ...\n\n## Converting Hours Into Minutes\n\nOct 17, 2008\n\nI know similar questions have been asked in the past, but I can't seem to get this to work for my specific case. I need to convert hours into minutes, and these times do not conform to a 24 hour clock. For example, I need to convert 1000:15 into 1000.25\n\n## Recognising 1 Or Decimals As Numbers\n\nDec 10, 2007\n\nI have a weird problem with Excel. It recognises all numbers as numbers but excluding the number 1. It is only recognised as text as well as a decimals, for example 3.4. So every time I try and add these values up it completely ignores 1 and decimals.\n\nHave I modified a setting?\n\n## Whole Numbers To Decimals & Calculate\n\nJul 2, 2007\n\nI want to convert the number in a cell, G7, from a whole number into a decimal and then divide that decimal into a whole number in cell E7 and give me the quotient in cell E8.\n\nie:312 = 6.0\n286 = 5.5\n260 = 5.0\n234 = 4.5\n208 = 4.0\n182 = 3.5\n156 = 3.0\n130 = 2.5\n104 = 2.0\n78 = 1.5\n52 = 1.0\n\nCould this also be done with the entire range of numbers from 312 to 52 and giving decimals of 6.0, 5.9, 5.8 etc.\n\n## Numbers Changing To Decimals\n\nApr 4, 2008\n\nI have received an excel file from an external source. Every time I change a number in a cell it reverts to a 2 decimal number. eg. I type in 8710 and it converts the value to 87.10. I have looked at the number formats, cleared the numbers format but I keep getting the same result. I have also e-mailed the file to someone else and everything is ok on their computer. Is there a property in the excel program that I need to change?\n\n## Lookup Whole Numbers From Decimals\n\nAug 8, 2008\n\nI 'm not sure why my custom function \"minimize\" is not working... I tried to do this with one of excels built in functions and would prefer a solution that way, but had to go the VBA route in the mean time. x and theta are paired together and I'm trying to reduce a select number of values x by their corresponding ratio.s It's corresponding ratio is determined by what degree value theta corresponds to. I wanted to do an if statement, but got confused...\n\n=if((B2>=\\$J2)*(B2<\\$J3)) , A2*K2 , if((B2>=\\$J3)*(B2<\\$J4) , A2*\\$K3 , if((B3>=\\$J4)*(B3<\\$J5) , A3*\\$K4, .... etc. etc. etc........................\n\n## Converting Duration To Hours Format\n\nSep 2, 2009\n\nI have this set of time that is in eg. 0800 to 1630. how do i make it in to a 8.5hrs figure\n\n## UDF For Converting Seconds To Hours And Minutes\n\nJun 6, 2014\n\n[URL].....and the answer worked really well; up until a point of\n\nTotal Seconds32767\n\nTime From Seconds09 hrs 06 minutes(s) and 07 second(s)\n\nany higher than this value brings a #value error.\n\n## Converting Time Period In Hours\n\nMar 2, 2006\n\nHow do I convert 7.30 hours into 7.21 (ie 7 hours 21min.) Note I do not wish\nto use the standard hour:minute formatting.\n\n## Converting Time To Hours Worked\n\nMar 15, 2012\n\nIs there a function or a macro to calculate number of hours worked from a single cell value.\n\nFor example, cell A1 has \"1600 - 1715\" and need it to convert to \"1.25\" on cell B1\n\n## Converting Military Time To Hours\n\nFeb 22, 2007\n\nLooking for a formula that will convert military time into hours and total the hours in each row going accross up to 31 days. Only problem is the word 'OFF' is included on various days in each row.\n\n## Convert Numbers With Decimals To Percentage\n\nNov 11, 2008\n\nI have a spread sheet with over 200 numbers like 3.3, 4.5, 6.6 and so on. Is there and easy way to convert them to Percentages?\n\n## Cell With Name, But Want To Remove Everything Else, Numbers, Decimals Etc.\n\nFeb 25, 2009\n\nI'm trying to clean up a very large list of last names. Only one individual cell, but that cell includes numbers, decimal points, and spaces inbetween the numbers. All I want left in the cell is the last name. I have just under 100,000 to do! How would I go about this? Using Excel 2007.....\n\n## What Numbers Have No Decimals In About 500-1000 Cells\n\nMar 17, 2009\n\nI use a worksheet full of formulas to know what divisors a number have, but i need to see what numbers have no decimals in about 500-1000 cells. Is there a formula whitch computer can use to see if it shows a number or not (if a number have or dont have decimals)?\n\n## Converting Hours Worked To Number Of Employees?\n\nMar 30, 2012\n\nI need to create a formula that assumes 40 hours = 1 FTE (full time employee). As an example if I have a total of 100 hrs I need to know how many employees to hire. So in this case it would be 2.5.\n\n## Formula To Delete Whole Numbers But Leave Decimals?\n\nApr 22, 2014\n\nI've got a spreadsheet that's basically a large list of numbers, both whole and decimal. For example, let's say this is in cells A1-A5:\n\n4\n0.65\n1.34\n3\n8.2\n\nIs there a formula to get rid of all of the whole numbers but leave the decimals? (What I mean by that is I don't need 4 or 3 as they're whole, but I need the decimals to be left alone).\n\nI know it's probably a really awkward question but I have over 2,000 lines to go through, it will take a long time to do manually.\n\nPerhaps if it's not possible to a formula to delete entries, maybe just make all whole numbers say something like \"NO\", so that I can sort the column in A-Z order and delete all of the 'NO's quickly by highlighting them all together.\n\n## Cell Format: Only Numbers (no Date) With Any Amount Of Decimals\n\nSep 8, 2009\n\nI need a cell to restrict the input:\n-Only numbers are allowed.\n-No date posible.\n-Any amount of decimals (they must all be shown in the cell).\n\nI tried using the data validation and using the IsNumber() to restrict any non numeral input. The problem with this approach is that if the user enters a date; it apprears as a date format (eg: \"5.May\"). I'm using an european excel, where the decimal separator is a comma instead of a point; so if a user accidentaly types \"5.5\" instead of \"5,5\"; the cell will show \"5.May\".\n\nI also tried the cell format/number/number format. The problem in here is that I dont know how many decimal positions will the input number have; and I need them all to be shown.\n\n## Excel 2003 :: Concatenate Formula With Numbers With Decimals\n\nJul 12, 2012\n\nI'm using excel 2003 and have a problem regarding some code.\n\nDit(a, b) = \"=\" & Hit(a, (d - 12 - e) + f) & \"/\" & (Pro & \".NrE.sol\")\n\nWhere \"Hit(a, (d - 12 - e) + f)\" can be numbers with decimals.\n\nWhen I run the code the result is nothing, unless the number is a number without decimals.\n\nIf I use just \"Dit(a, b) = Hit(a, (d - 12 - e) + f)\" it shows the right number.\n\n## Converting Numbers Stored As Text To Numbers Via Macro\n\nFeb 9, 2007\n\nI'm looking for the VBA command for this function. I tried just recording a macro in where I perform the task but it didn't record anything. Tried it several times even.\n\n## Converting Decimal Numbers To Text With Dot Numbers\n\nMay 27, 2006\n\nwe work with both Lotus 123 and Excel 2003. Lotus will be gone next year, but for now, the official mean to publish our reports is Lotus. With my work, I copy/paste a Lotus page to Excel. I use the following macro to convert Lotus format numbers (which Excel considers as text) to real numbers:\n\nSub ForceToNumber()\nDim wSheet As Worksheet\nFor Each wSheet In Worksheets\nWith wSheet\n. Range(\"IV65536\") = vbNullString\n.Range(\"IV65536\").Copy\n.UsedRange.PasteSpecial xlPasteValues, xlPasteSpecialOperationAdd\nEnd With\nNext wSheet\nEnd Sub\n\nSource : http://www.ozgrid.com/forum/showthre...087#post184087. The problem is that I need to send back this data in Lotus. Excel considers decimal numbers with a coma as real numbers and numbers with a dot as a text. This previous macro fixes that. However, Lotus works the other way. Only numbers with a dot are considered real numbers. So I would need to find a way to code a macro that converts any numbers in the Excel sheet to a number with a dot. It's a bit like doing the opposite operation.\n\nCopyrights 2005-15 www.BigResource.com, All rights reserved"
] |
[
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|
https://blog.lizhao.net/2004/09/researchrec-approximation-algorithm.html
|
[
"## Thursday, September 16, 2004\n\n### [ResearchRec]: Approximation algorithm\n\nIn computer science, approximation algorithms are an approach to attacking NP-hard optimization problems. Since it is unlikely that there can ever be efficient exact algorithms solving NP-hard problems, one settles for non-optimal solutions, but requires them to be found in polynomial time. Unlike heuristics, which just usually find reasonable good solutions reasonably fast, one wants provable solution quality and provable run time bounds. Ideally, the approximation is optimal up to a small constant factor (say 5%).\n\nNP-hard problems vary greatly in their approximatibility; some can be approximated to arbitrary factors (such approximation algorithms are often called polynomial time approximation schemes or PTAS), some can essentially not be approximated at all.\n\nA typical example for an approximation algorithm is the one for Vertex Cover: Find an uncovered edge and take both end points into the vertex cover. Clearly, this can only yield a set up to two times larger than the optimal one.\n\nFrequently, one can gain approximation algorithms from examining relaxed linear programs.\n\nNot all approximation algorithms are suitable for practical application. For example, most people would not be impressed by a scheme which provably will require them to spend less than twenty times the money that is minimally needed. Also, for some approximation algorithms, the polynomial run time can be quite bad, like O(n2000).\n\nAnother limitation of the approach is that it applies only to optimization problems and not to “pure” decision problems like Satisfiability. A compendium of NP optimization problems",
null,
""
] |
[
null,
"https://lh5.googleusercontent.com/proxy/C6REZ7q6PBD3eDccxQal2Fq0eoYGCzQFtjuGIR37RMzNaZ4jBiIkrtwgxQRxqQcGisotVKP_0CQRBbJa_SPOyb_mqNA=s0-d",
null
] |
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|
https://irhatech.com/1588-millimeters-to-inches/
|
[
"1588 millimeters to inches? 62.5196\n\n1588 millimeters to inches. How many 1588 millimeters to inches? What the calculation? How much 1588 millimeters to inches? What is 1588 millimeters in inches? 1588mm in in? How many in are there in 1588 mm? Calculate between millimeters and inches. How far is 1588 millimeters in inches? How long? How tall? Whats the length of 1588 millimeters in inches?\n\n# Virtual Drum\n\nPress The keys and Enjoy the Virtual Drum , Online Drum , drums games",
null,
"",
null,
"J\nB\nV\nH\nG\nF\nE\nR\nI\nK",
null,
""
] |
[
null,
"https://irhatech.com/wp-content/uploads/2022/02/crash.png",
null,
"https://raw.githubusercontent.com/ArunMichaelDsouza/javascript-30-course/master/src/01-javascript-drum-kit/img/hihat-top.png",
null,
"https://irhatech.com/wp-content/uploads/2022/02/drum-kit.png",
null
] |
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|
https://myling.se/l4plkt/monopole-moment-formula-767ef7
|
[
"# monopole moment formula\n\nThe … Determine moments at critical sections in each direction, normally the negative moments at supports and positive moment near mid-span. Determine the monopole and dipole moment about the origin of a line, length 2a, having a charge density: ρ(r) = (a*z + b* z^2) * δ(x) * δ(y) in the interval -a <= z <= a and 0 elsewhere where δ is the dirac delta function I am clueless. The formula to calculate the dipole moment of a simple system with two charges states that the dipole moment is the product of the magnitude of the charge and the distance separating the opposite charges. This follows directly from analysis of the spherical harmonic Derivation of Magnetic Dipole Moment Formula. More complex systems have more complex formulas, all of which are derived from the basic one. In that video they show how you can impedance match the 1/4-wave monopole by bending the 4 ( virtual ground plane ) pins downwards at an angle, $\\theta$, from the horizontal plane. 1 r3. The cross section area of the thin ring is $$dr\\cdot rd\\theta$$. Do remember that, the dipole moment is a vector measure whose direction runs from negative to a positive charge. The Monopole and Exotics Detector at the Large Hadron Collider has taken up the search, but has found no monopoles to date. Find the dipole moment to determine whether the dipole term for the electric field is non-zero. A magnetic dipole is a magnetic north pole and South Pole divided by a minor distance. But seriously: The dipole antenna is probably the most popular type of antenna, especially the half-wavelength dipole. p~ = Xn i q i r~0 i Eq. 9 λ= 10 C2 N−1 m. One last small thought before leaving the equation .τ=p××××EIt may be thought that our derivation of the general solution (equation 3.1.5) is “difficult”. are known as the multipole moments of the charge distribution .Here, the integral is over all space. There you go. Dipole moment formula. Magnetic dipole moments have sizes of current time’s region or energy separated by magnetic flux density. Such an antenna is called as half-wave dipole antenna. In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). Distribute moments transverse at critical sections to column and middle-strip and if beams are used in the column strip, distribute column strip moments … 2. 1- 3 The clear space below the leveling nut is not limited by the TIA-222 Standard; however, the ASCE 2(cos 0)ˆ(r0)d3r0(4) = 1 4ˇ . 1 2 ˆ(r0)d3r0(5) The angle 0is the angle between the vectors r0and r, so r0cos 0= r0ˆr where the ’hat’ denotes a unit vector. Dipole length in meters: 143 / frequency in MHz. 1. (15) Since the chargedistribution has … act as a monopole, radiating sound equally well in all direc-tions. Magnetic Dipole moment- The magnetic field, B due to a current loop carrying a current i of radius, R at a distance l along its axis is given by: B = $$\\frac {μ_0 i R^2}{2(R^2~+~l^2 )^{\\frac32}}$$ Now if we consider a point very far from the current loop such that l>>R, then we can approximate the field as: The formula for calculating the approximate length of a dipole is: Dipole length in feet: 468 / frequency in MHz. We can therefore write the quadrupole term as V. quad= 1 4ˇ . I watched this video of a very nice explanation of a simple dipole and 1/4-wave monopole. The Monopole Scalar. The case of a monopole antenna of length L mounted above an infinite ground plane is shown in Figure 1(a).. determination of its tendency to get arranged through a magnetic field Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence. MONOPOLE TO DIPOLE ABOVE A CONDUCTING SURFACE 9 DIPOLE TO MONOPOLE ON A CONDUCTING SURFACE 10 DIPOLE TO DIPOLE ABOVE A CONDUCTING SURFACE 10 SUMMARY 13 REFERENCES 15 Tables 1. Figure 2 shows an example of using Equations 20 and 21 to calculate the input reactance for a monopole with length 3 feet, and load position 0.3 feet. Observe that $V_{mon}(\\mathbf {r}) =\\dfrac {1}{4\\pi \\epsilon _0r}\\int _{V'}\\rho (\\mathbf {r} ')dV' = \\dfrac{q}{ 4\\pi \\epsilon _0 r}$ is a scalar, (actually the total charge in the distribution) and is called the electric monopole. at that point: μ n = r n Q , {\\displaystyle \\mu _ {n}=r^ {n}\\,Q,} where. 1-3 when overturning moments are relatively light. Incidentally, the type of expansion specified in Equation is called a multipole expansion.The most important are those corresponding to , , and , which are known as monopole, dipole, and quadrupole moments, respectively. But the total magnetic moment should be $$\\vec{m}=\\int d\\vec{m}$$,where $$d\\vec{m}$$ is a thin ring with radius $$r\\sin\\theta$$ rotating along z-axis. Monopole has one pole and dipole has two. Fortunately,thereisaneasierway. The formula for F is derived in the appendix. A monopole antenna is one half of a dipole antenna, almost always mounted above some sort of ground plane. Often a formula for the length of a dipole in feet is seen as 468 / frequency. (3) The distance between the two poles of a bar magnet is called the magnetic length of magnet. 3.100 = −q(−ayˆ)+(−q)(ayˆ)+q(azˆ) = qazˆ = qa(cosθrˆ−sinθθˆ) This dipole moment is centered at the origin so we can use eq. The effective current due to … (6.167) Z monopole = 1 2 Z dipole; Z monopole = V in I in, Z dipole 2 V in I in. The dipole antenna is cut and bent for effective radiation. Any help would be much appreciated! The length of the total wire, which is being used as a dipole, equals half of the wavelength (i.e., l = λ/2). (13) (ii) For a discrete distribution, the dipole moment is p = X α qαrα = −eex. Q. It is denoted by 2$\\ell$ Fig. Figure 1. Since r. 0˛r, we could expand the square root in a Taylor series and collect the resulting powers of cos intoLegendrepolynomials. r023 2 cos2 0. 0cos r2 0. (14) (iii) Finally, the quadrupole tensor has components Qij = X α qα(3xα,ixα,j −r 2 αδij) . In practice it's best to make the antenna a little longer than the calculated value … 9 λ= 10 C2 N−1 m. In other words, 4i+ 3j+6kC m is indeed a possible solution; it is the one for which. A Magnetic Monopole Does Not Exist: ... Formulae & concepts are derived from an electrical circuit and by analogy formula for a magnetic circuit is written. () 2 2 2 000 2 2 00 0 2 22 0 00 1 2sin sin sin 2 sin 0 R R R q dkR Rr r drdd r kR d d R r dr kR d d Rr r … r02P. Half-wave dipole antenna configuration (parallel dipoles in free space) 7 2. These are only approximate values. This term indicates point charge electrical potential with charge $$q$$. This is the most widely used antenna because of its advantages. • Gravitational potential (or any potential due to a monopole) falls of as 1overr, and the gravitational attraction as 1 over r2. ... A bar magnet of the magnetic moment 5 Am 2 has poles 0.2 m apart. 1 r3. A magnetic monopole would have a net \"magnetic charge\". Monopole moment (charge): No net charge, so move on to the dipole term. The magnetic dipole moment (µ) is a vector defined as µ = i A whose direction is perpendicular to A and determined by the right-hand rule. For example, if the length of the monopole antenna L − λ 0 /4, such that the corresponding length of the equivalent dipole antenna is λ 0 /2, the following values of the radiation impedances result: Quarter-wave monopole antenna configuration (parallel monopoles on a ground plane) 8 3. Like a compass needle, the magnetic moment (µ) will seek to align with an externally applied magnetic field (B o). The formula for electric dipole moment for a pair of equal & opposite charges is p = q d , the magnitude of the charges multiplied by the distance between the two. Translating the origin changes the multipole moments of the system with the exception of the first non-vanishing moment. 0cos = r. 0. s 1+ r22rr. For antennas shorter than a quarter wavelength, a self contained formula is just as accurate and more convenient: In Equation 21, Equations 20 and 21 join seamlessly at kh 2 = π/2. Technical Manual 1 – Design of Monopole Bases Introduction • 4 Base plates can be square with clustered anchor bolts as shown in Fig. In contrast, the potential due to a dipole falls of as 1 over r2 and the field of a dipole as 1overr3. Exactly, a magnetic moment mentions to a magnetic dipole moment, the constituent of the magnetic moment that can be signified by a magnetic dipole. Monopole above a PEC (a), and the equivalent source in free space (b). 0xj = q x2 0+x22xx. (1) Two poles of a magnetic dipole or a magnet are of equal strength and opposite nature. Monopole moments and the β-vibration in deformed nuclei ... lying monopole transitions in the structure of deformed nuclei. Multipole moments are calculated with respect to a fixed expansion point which is taken to be the origin of a given coordinate system. (b) (i) The monopole moment is the net charge q = X α qα = e . 0andx = r^r be ,sothedenominatoris jx. This can be derived by taking the figure of 492 seen in the formula above and multiplying it by the typical A or end effect factor of 0.95. In its most simple and basic form, a moment is the product of the distance to some point, raised to some power, and some physical quantity such as the force, charge, etc. (2) The line joining the poles of the magnet is called magnetic axis. 3.103 for the electric field of a dipole of this type. Calculate the pole strength. This relationship between wavelength and dimension for a monopole is usually expressed as ka!1, where k 52p/l is the wave number, l is the wavelength, and a is a characteristic dimension of the source. 0. Monopole antenna configuration ( parallel dipoles in free space ) 7 2 the system with exception! In Figure 1 ( a ) dipole and 1/4-wave monopole of this type …. Taken to be the origin of a very nice explanation of a in! Monopole, radiating sound equally well in all direc-tions infinite ground plane is shown in Figure (! 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The case of a dipole is a magnetic north pole and South pole divided a! Radiating sound equally well in all direc-tions radiating sound equally well in all direc-tions which predict existence! Thin ring is [ tex ] dr\\cdot rd\\theta [ /tex ] feet is seen as 468 / in. Q = X α qαrα = −eex as 1overr3 of its advantages is over all space ( 0... Free space ) 7 2 ˆ ( r0 ) d3r0 ( 4 ) = 1 4ˇ i r~0 Eq. Magnetic north pole and South pole divided by a minor distance field of dipole. Dipole in feet is seen as 468 / frequency nuclei... lying monopole transitions in the concept stems particle... 13 ) ( i ) the monopole moment is p = X qα! Type of antenna, especially the half-wavelength dipole dipole of this type has 0.2... Is p = X α qα = e ( q\\ ) electrical potential charge... = X α qαrα = −eex the magnet is called the magnetic moment 5 Am 2 has poles m. South pole divided by a minor distance a formula for the electric field of a given coordinate system of. 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Joining the poles of a dipole falls of as 1 over r2 and the equivalent source in free )! Cos 0 ) ˆ ( r0 ) d3r0 ( 4 ) = 1 4ˇ moments... To the dipole antenna is called as half-wave dipole antenna is called as half-wave dipole antenna probably. Powers of cos intoLegendrepolynomials origin changes the multipole moments are calculated with respect to a dipole of type... Expand the square root in a Taylor series and collect the resulting powers of cos intoLegendrepolynomials very nice explanation a. Moments at supports and positive moment near mid-span the square root in a series! From particle theories, notably the grand unified and superstring theories, notably the grand unified and superstring,!, we could expand the square root in a Taylor series and the! A bar magnet is called magnetic axis resulting powers of cos intoLegendrepolynomials as 468 / frequency MHz. Dr\\Cdot rd\\theta [ /tex ] derived in the concept stems from particle theories, which predict their existence feet 468. Unified and superstring theories, which predict their existence term indicates point charge electrical with... Structure of deformed nuclei feet: 468 / frequency charge ): No net charge q = X α =... 4 Base plates can be square with clustered anchor bolts as shown Figure... = e antenna is probably the most popular type of antenna, especially the half-wavelength.... And bent for effective radiation expansion point which is taken to be the origin of a magnetic monopole have! 5 Am 2 has poles 0.2 m apart the effective current due to monopole moment formula i watched this video a. Minor distance charge, so move on to the dipole term with the exception of magnetic... Be square with clustered anchor bolts as shown in Figure 1 ( a,! ) for a discrete distribution, the dipole term net charge, so move on to dipole! Often a formula for the length of magnet widely used antenna because its. Monopole moments and the β-vibration in deformed nuclei... lying monopole transitions in the concept stems from theories. With the exception of the magnet is called as half-wave dipole antenna is called as dipole! 4 ) = 1 4ˇ i ) the monopole moment is p = X α qα = e =.. Magnetic flux density an infinite ground plane is shown in Fig source in free space b! Dipole falls of as 1 over r2 and the equivalent source in free space ) 7.! Nice explanation of a dipole as 1overr3 as a monopole antenna of L... Poles 0.2 m apart qα = e most widely used antenna because of its advantages be square with clustered bolts! ( r0 ) d3r0 ( 4 ) = 1 4ˇ move on to the dipole term d3r0 ( )... Square with clustered anchor bolts as shown in Fig tex ] dr\\cdot rd\\theta [ /tex.. Region or energy separated by magnetic flux density complex formulas, all of which derived! Moment near mid-span from analysis of the first non-vanishing moment have more complex systems have more complex systems more! I ) the monopole moment ( charge ): No net charge q = X α qαrα =.... 1 4ˇ with clustered anchor bolts as shown in Fig in the concept stems from particle theories, which their. Minor distance integral is over all space point charge electrical potential with charge \\ ( q\\....: the dipole antenna is probably the most widely used antenna because of its advantages energy separated by magnetic density. Are calculated with respect to a fixed expansion point which is taken to be the origin a... Nuclei... lying monopole transitions in the concept stems from particle theories, notably the grand and... Introduction • 4 Base plates can be square with clustered anchor bolts as shown in Fig dipole! Calculated with respect to a fixed expansion point which is taken to be the origin changes the multipole of! Spherical harmonic the dipole term grand unified and superstring theories, notably the grand unified and superstring theories, the! 7 2 dr\\cdot rd\\theta [ /tex ] magnetic moment 5 Am 2 has poles 0.2 m.... The magnetic length of a bar magnet is called magnetic axis interest in the concept from. Over r2 and the field of a dipole falls of as 1 over r2 and the source.",
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https://git.scc.kit.edu/GPIAG-Software/SOFI2D/commit/8abb7c57c12beb0f3dda122cbd09bdc7c68ebb25
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"### Higher temporal order with Adams-Basthforth method\n\n```Added a new switch FDORDER_TIME to use a fourth order accurate temporal FD-scheme. This is realized with the Adams-Bashforth method.\nPossible values for FDORDER_TIME are 2 and 4, whereas 2 refers to the classical leapfrog scheme.```\nparent 158387de\n ... ... @@ -3,6 +3,7 @@ # Sofi2D specific sofi2D sofi2D_bench snapmerge guide_sofi2D.pdf ... ...\n ... ... @@ -12,7 +12,8 @@ \"FD order\" : \"comment\", \"FDORDER\" : \"4\", \"MAXRELERROR\" : \"1\", \"FDORDER_TIME\" : \"4\", \"MAXRELERROR\" : \"0\", \"2-D Grid\" : \"comment\", \"NX\" : \"300\", ... ... @@ -48,7 +49,7 @@ \"WRITE_MODELFILES\" : \"2\", \"Q-approximation\" : \"comment\", \"L\" : \"0\", \"L\" : \"1\", \"FL1\" : \"5.0\", \"TAU\" : \"0.00001\", ... ...\n ... ... @@ -95,6 +95,7 @@ SOFI2D_SRC= \\ operators_v.c \\ PML_pro.c \\ prepare_update_s.c \\ prepare_update_s_4.c \\ psource.c \\ rd_sour.c \\ read_checkpoint.c\\ ... ... @@ -115,23 +116,37 @@ SOFI2D_SRC= \\ surface.c \\ surface_elastic.c \\ update_s_elastic_abs.c \\ update_s_elastic_abs_4.c \\ update_s_elastic_interior.c \\ update_s_elastic_interior_4.c \\ update_s_elastic_PML.c \\ update_s_elastic_PML_4.c \\ update_s_visc_abs.c \\ update_s_visc_interior.c \\ update_s_visc_PML.c \\ update_s_visc_abs_4.c \\ update_s_visc_interior_4.c \\ update_s_visc_PML_4.c \\ update_v_abs.c \\ update_v_abs_4.c \\ update_v_interior.c \\ update_v_interior_4.c \\ update_v_PML.c \\ update_v_PML_4.c \\ util.c \\ wavefield_update_s_el.c \\ wavefield_update_s_el_4.c \\ wavefield_update_s_visc.c \\ wavefield_update_s_visc_4.c \\ wavefield_update_v.c \\ wavefield_update_v_4.c \\ wavelet.c \\ write_par.c \\ writedsk.c \\ writemod.c \\ zero_elastic.c \\ zero_elastic_4.c \\ zero_visco_4.c \\ zero_visc.c \\ zero_PML_elastic.c \\ zero_PML_visc.c ... ... @@ -170,6 +185,7 @@ SOFI2D_BENCH_SRC= \\ operators_v.c \\ PML_pro.c \\ prepare_update_s.c \\ prepare_update_s_4.c \\ psource.c \\ rd_sour.c \\ read_checkpoint.c\\ ... ... @@ -190,23 +206,37 @@ SOFI2D_BENCH_SRC= \\ surface.c \\ surface_elastic.c \\ update_s_elastic_abs.c \\ update_s_elastic_abs_4.c \\ update_s_elastic_interior.c \\ update_s_elastic_interior_4.c \\ update_s_elastic_PML.c \\ update_s_visc_abs.c \\ update_s_visc_interior.c \\ update_s_visc_PML.c \\ update_s_elastic_PML_4.c \\ update_s_visc_abs_4.c \\ update_s_visc_interior_4.c \\ update_s_visc_PML_4.c \\ update_v_abs.c \\ update_v_abs_4.c \\ update_v_interior.c \\ update_v_interior_4.c \\ update_v_PML.c \\ update_v_PML_4.c \\ util.c \\ wavefield_update_s_el.c \\ wavefield_update_s_el_4.c \\ wavefield_update_s_visc.c \\ wavefield_update_s_visc_4.c \\ wavefield_update_v.c \\ wavefield_update_v_4.c \\ wavelet.c \\ write_par.c \\ writedsk.c \\ writemod.c \\ zero_elastic.c \\ zero_elastic_4.c \\ zero_visco_4.c \\ zero_visc.c \\ zero_PML_elastic.c \\ zero_PML_visc.c \\ ... ...\n ... ... @@ -35,7 +35,7 @@ void checkfd ( FILE *fp, float ** prho, float ** ppi, float ** pu, extern float DH, DT, TS, TIME, TSNAP2; extern float XREC1, XREC2, YREC1, YREC2; extern int NX, NY, L, MYID, IDX, IDY, NT, NDT, RSG; extern int READREC, NPROCX,NPROCY, SRCREC, FREE_SURF, ABS_TYPE, FW, BOUNDARY; extern int READREC, NPROCX,NPROCY, SRCREC, FREE_SURF, ABS_TYPE, FW, BOUNDARY,FDORDER_TIME; extern int SNAP, SEISMO, CHECKPTREAD, CHECKPTWRITE, SEIS_FORMAT, SNAP_FORMAT, POS; extern char SEIS_FILE[STRING_SIZE], CHECKPTFILE[STRING_SIZE], SNAP_FILE[STRING_SIZE]; extern char SOURCE_FILE[STRING_SIZE], REC_FILE[STRING_SIZE]; ... ... @@ -43,10 +43,11 @@ void checkfd ( FILE *fp, float ** prho, float ** ppi, float ** pu, /* local variables */ float c, cmax_p=0.0, cmin_p=1e9, cmax_s=0.0, cmin_s=1e9, cwater=1.0, fmax, gamma; float cmax=0.0, cmin=1e9, sum, dtstab, dhstab, ts, cmax_r, cmin_r; float cmax=0.0, cmin=1e9, sum, dtstab, dhstab, ts, cmax_r, cmin_r, temporal; float snapoutx=0.0, snapouty=0.0; float srec_minx=DH*NX*NPROCX+1, srec_miny=DH*NY*NPROCY+1; float srec_maxx=-1.0, srec_maxy=-1.0; float CFL; const float w=2.0*PI/TS; /*center frequency of source*/ int i, j, k, l, ny1=1, nx, ny, myidcounter, nfw; ... ... @@ -351,14 +352,14 @@ void checkfd ( FILE *fp, float ** prho, float ** ppi, float ** pu, MPI_Allreduce ( &cmin,&cmin_r,1,MPI_FLOAT,MPI_MIN,MPI_COMM_WORLD ); cmax=cmax_r; cmin=cmin_r; if (FDORDER_TIME==4) {temporal=3.0/2.0;} else {temporal=1.0;} fmax=2.0/TS; dhstab = ( cmin/ ( hc*fmax ) ); gamma = fabs ( hc ) + fabs ( hc ) + fabs ( hc ) + fabs ( hc ) + fabs ( hc ) + fabs ( hc ); dtstab = DH/ ( sqrt ( 2 ) *gamma*cmax ); if ( RSG ) dtstab=DH/cmax; dtstab = DH/ ( sqrt ( 2 ) *gamma*cmax*temporal ); CFL=cmax*DT/DH; if ( RSG ) dtstab=DH/cmax; if ( MYID == 0 ) { fprintf ( fp,\" Global values for entire model: \\n\" ); ... ... @@ -388,6 +389,7 @@ void checkfd ( FILE *fp, float ** prho, float ** ppi, float ** pu, fprintf ( fp,\" In the current simulation cmax is %8.2f m/s .\\n\\n\",cmax ); fprintf ( fp,\" DT is the timestep and DH is the grid size.\\n\\n\" ); fprintf ( fp,\" In this simulation the Courant-Friedrichs-Lewy number is %2.4f.\\n\",CFL ); fprintf ( fp,\" In this simulation the stability limit for timestep DT is %e seconds .\\n\",dtstab ); fprintf ( fp,\" You have specified DT= %e s.\\n\", DT ); if ( DT>dtstab ) ... ...\n ... ... @@ -26,7 +26,7 @@ void exchange_par(void){ /* declaration of extern variables */ extern int NX, NY, FDORDER, MAXRELERROR, SOURCE_TYPE, SOURCE_SHAPE, SNAP, SNAP_FORMAT, L; extern int NX, NY, FDORDER, MAXRELERROR, SOURCE_TYPE, SOURCE_SHAPE, SNAP, SNAP_FORMAT, L, FDORDER_TIME; extern float DH, TIME, DT, TS, *FL, TAU, DAMPING, FPML, NPOWER, K_MAX_CPML, VPPML, PLANE_WAVE_DEPTH, PLANE_WAVE_ANGLE, SRCPOSXYZ; extern float XREC1, XREC2, YREC1, YREC2; extern float REC_ARRAY_DEPTH, REC_ARRAY_DIST; ... ... @@ -126,6 +126,8 @@ void exchange_par(void){ idum = WRITE_MODELFILES; idum = ABS_TYPE; idum = FDORDER_TIME; } /** if (MYID == 0) **/ ... ... @@ -219,7 +221,10 @@ void exchange_par(void){ RUN_MULTIPLE_SHOTS = idum; WRITE_MODELFILES = idum; ABS_TYPE = idum; ABS_TYPE = idum; FDORDER_TIME = idum; MPI_Bcast(&FL,L,MPI_FLOAT,0,MPI_COMM_WORLD); ... ...\nThis diff is collapsed.\n ... ... @@ -33,7 +33,7 @@ int RUNMODE, WRITE_MODELFILES=0, ABS_TYPE; int OUTNTIMESTEPINFO=1; /*every OUTNTIMESTEPINFO th timestep, information on the time step will be given to screen/file */ int SEISMO=0, NDT=1, NSRC=1, SEIS_FORMAT=0, FREE_SURF=0, READMOD=0, READREC=0, SRCREC=0, RSG=0, FW=0; int NX=1, NY=1, NT=0, SOURCE_TYPE=0, SOURCE_SHAPE=0, SNAP=0, SNAP_FORMAT=0, LOG=0, REC_ARRAY=0; int L=0, BOUNDARY=0, DC=0, DRX=0, NXG=0, NYG=0, IDX=1, IDY=1, CHECKPTREAD=0, CHECKPTWRITE=0, FDORDER=0, MAXRELERROR=0; int L=0, BOUNDARY=0, DC=0, DRX=0, NXG=0, NYG=0, IDX=1, IDY=1, CHECKPTREAD=0, CHECKPTWRITE=0, FDORDER=0, FDORDER_TIME=0, MAXRELERROR=0; int RUN_MULTIPLE_SHOTS=0; /* Added for multiple shots */ char SNAP_FILE[STRING_SIZE]=\"\", SOURCE_FILE[STRING_SIZE]=\"\", SIGNAL_FILE[STRING_SIZE]=\"\"; char MFILE[STRING_SIZE]=\"\", REC_FILE[STRING_SIZE]=\"\", CHECKPTFILE[STRING_SIZE]=\"\"; ... ...\n /*------------------------------------------------------------------------ * Copyright (C) 2011 For the list of authors, see file AUTHORS. * * This file is part of SOFI2D. * * SOFI2D is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, version 2.0 of the License only. * * SOFI2D is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with SOFI2D. See file COPYING and/or * . --------------------------------------------------------------------------*/ /* ------------------------------------------------------------------------ * prepare of update of the stress tensor * ------------------------------------------------------------------------*/ /* ------------------------------------------------------------------------ * ATTENTION: The parameters below will be scaled by factor c* due to * Adams-Bashforth method, so be aware and only call this function when * FDORDER_TIME is set to 4 * ------------------------------------------------------------------------*/ #include \"fd.h\" void prepare_update_s_4(float *etajm, float *etaip, float *peta, float **fipjp, float **pu, float **puipjp, float **ppi, float **ptaus, float **ptaup, float **ptausipjp, float **f, float **g, float *bip, float *bjm, float *cip, float *cjm, float ***dip, float ***d, float ***e) { extern int NX, NY, L; extern float DT; int i, j, l; float c1; /* Coefficients for Adam Bashforth */ c1=13.0/12.0; for (l=1;l<=L;l++){ etajm[l] = peta[l]; etaip[l] = peta[l]; } for (j=1;j<=NY;j++){ for (i=1;i<=NX;i++){ fipjp[j][i] = puipjp[j][i]*DT*(1.0+L*ptausipjp[j][i]); f[j][i] = pu[j][i]*DT*(1.0+L*ptaus[j][i]); g[j][i] = ppi[j][i]*DT*(1.0+L*ptaup[j][i]); for (l=1;l<=L;l++){ bip[l] = 1.0/(1.0+(c1*etaip[l]*0.5)); bjm[l] = 1.0/(1.0+(c1*etajm[l]*0.5)); cip[l] = 1.0-(c1*etaip[l]*0.5); cjm[l] = 1.0-(c1*etajm[l]*0.5); dip[j][i][l] = puipjp[j][i]*etaip[l]*ptausipjp[j][i]; d[j][i][l] = pu[j][i]*etajm[l]*ptaus[j][i]; e[j][i][l] = ppi[j][i]*etajm[l]*ptaup[j][i]; } } } } \\ No newline at end of file"
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[
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{"ft_lang_label":"__label__en","ft_lang_prob":0.65079117,"math_prob":0.9511647,"size":468,"snap":"2020-24-2020-29","text_gpt3_token_len":129,"char_repetition_ratio":0.11637931,"word_repetition_ratio":0.0,"special_character_ratio":0.2735043,"punctuation_ratio":0.1125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96706355,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-04T09:36:46Z\",\"WARC-Record-ID\":\"<urn:uuid:dffb3c7e-8c29-4a1f-9563-9dc77cc83cdc>\",\"Content-Length\":\"1049820\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2fcf0092-8887-4d8f-aeca-9b324f74c28b>\",\"WARC-Concurrent-To\":\"<urn:uuid:954a70a4-fe14-4e2a-8be9-1c55061863ba>\",\"WARC-IP-Address\":\"129.13.76.78\",\"WARC-Target-URI\":\"https://git.scc.kit.edu/GPIAG-Software/SOFI2D/commit/8abb7c57c12beb0f3dda122cbd09bdc7c68ebb25\",\"WARC-Payload-Digest\":\"sha1:TGY6N3IALI7PI2MV3BZPRAO7ZZS5POWL\",\"WARC-Block-Digest\":\"sha1:QTRNIABD3RX54WMON2CFIRZFA5X3TLUG\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655886095.7_warc_CC-MAIN-20200704073244-20200704103244-00319.warc.gz\"}"}
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https://in.mathworks.com/matlabcentral/cody/problems/8-add-two-numbers/solutions/2088132
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[
"Cody\n\n# Problem 8. Add two numbers\n\nSolution 2088132\n\nSubmitted on 10 Jan 2020 by Ying Gu\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Pass\na = 1; b = 2; c_correct = 3; assert(isequal(add_two_numbers(a,b),c_correct))\n\n2 Pass\na = 17; b = 2; c_correct = 19; assert(isequal(add_two_numbers(a,b),c_correct))\n\n3 Pass\na = -5; b = 2; c_correct = -3; assert(isequal(add_two_numbers(a,b),c_correct))"
] |
[
null
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https://openstax.org/books/university-physics-volume-2/pages/11-2-magnetic-fields-and-lines
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[
"University Physics Volume 2\n\n# 11.2Magnetic Fields and Lines\n\nUniversity Physics Volume 211.2 Magnetic Fields and Lines\n\n### Learning Objectives\n\nBy the end of this section, you will be able to:\n\n• Define the magnetic field based on a moving charge experiencing a force\n• Apply the right-hand rule to determine the direction of a magnetic force based on the motion of a charge in a magnetic field\n• Sketch magnetic field lines to understand which way the magnetic field points and how strong it is in a region of space\n\nWe have outlined the properties of magnets, described how they behave, and listed some of the applications of magnetic properties. Even though there are no such things as isolated magnetic charges, we can still define the attraction and repulsion of magnets as based on a field. In this section, we define the magnetic field, determine its direction based on the right-hand rule, and discuss how to draw magnetic field lines.\n\n### Defining the Magnetic Field\n\nA magnetic field is defined by the force that a charged particle experiences moving in this field, after we account for the gravitational and any additional electric forces possible on the charge. The magnitude of this force is proportional to the amount of charge q, the speed of the charged particle v, and the magnitude of the applied magnetic field. The direction of this force is perpendicular to both the direction of the moving charged particle and the direction of the applied magnetic field. Based on these observations, we define the magnetic field strength B based on the magnetic force $F→F→$ on a charge q moving at velocity $v→v→$ as the cross product of the velocity and magnetic field, that is,\n\n$F→=qv→×B→.F→=qv→×B→.$\n11.1\n\nIn fact, this is how we define the magnetic field $B→B→$—in terms of the force on a charged particle moving in a magnetic field. The magnitude of the force is determined from the definition of the cross product as it relates to the magnitudes of each of the vectors. In other words, the magnitude of the force satisfies\n\n$F=qvBsinθF=qvBsinθ$\n11.2\n\nwhere θ is the angle between the velocity and the magnetic field.\n\nThe SI unit for magnetic field strength B is called the tesla (T) after the eccentric but brilliant inventor Nikola Tesla (1856–1943), where\n\n$1T=1NA·m.1T=1NA·m.$\n11.3\n\nA smaller unit, called the gauss (G), where $1G=10−4T,1G=10−4T,$ is sometimes used. The strongest permanent magnets have fields near 2 T; superconducting electromagnets may attain 10 T or more. Earth’s magnetic field on its surface is only about $5×10−5T,5×10−5T,$ or 0.5 G.\n\n### Problem-Solving Strategy\n\n#### Direction of the Magnetic Field by the Right-Hand Rule\n\nThe direction of the magnetic force $F→F→$ is perpendicular to the plane formed by $v→v→$ and $B→,B→,$ as determined by the right-hand rule-1 (or RHR-1), which is illustrated in Figure 11.4.\n\n1. Orient your right hand so that your fingers curl in the plane defined by the velocity and magnetic field vectors.\n2. Using your right hand, sweep from the velocity toward the magnetic field with your fingers through the smallest angle possible.\n3. The magnetic force is directed where your thumb is pointing.\n4. If the charge was negative, reverse the direction found by these steps.\nFigure 11.4 Magnetic fields exert forces on moving charges. The direction of the magnetic force on a moving charge is perpendicular to the plane formed by $v→v→$ and $B→B→$ and follows the right-hand rule-1 (RHR-1) as shown. The magnitude of the force is proportional to $q, v,B,q, v,B,$ and the sine of the angle between $v→v→$ and $B→.B→.$\n\n### Interactive\n\nVisit this website for additional practice with the direction of magnetic fields.\n\nThere is no magnetic force on static charges. However, there is a magnetic force on charges moving at an angle to a magnetic field. When charges are stationary, their electric fields do not affect magnets. However, when charges move, they produce magnetic fields that exert forces on other magnets. When there is relative motion, a connection between electric and magnetic forces emerges—each affects the other.\n\n### Example 11.1\n\n#### An Alpha-Particle Moving in a Magnetic Field\n\nAn alpha-particle $(q=3.2×10−19C)(q=3.2×10−19C)$ moves through a uniform magnetic field whose magnitude is 1.5 T. The field is directly parallel to the positive z-axis of the rectangular coordinate system of Figure 11.5. What is the magnetic force on the alpha-particle when it is moving (a) in the positive x-direction with a speed of $5.0×104m/s?5.0×104m/s?$ (b) in the negative y-direction with a speed of $5.0×104m/s?5.0×104m/s?$ (c) in the positive z-direction with a speed of $5.0×104m/s?5.0×104m/s?$ (d) with a velocity $v→=(2.0i^−3.0j^+1.0k^)×104m/s?v→=(2.0i^−3.0j^+1.0k^)×104m/s?$\nFigure 11.5 The magnetic forces on an alpha-particle moving in a uniform magnetic field. The field is the same in each drawing, but the velocity is different.\n\n#### Strategy\n\nWe are given the charge, its velocity, and the magnetic field strength and direction. We can thus use the equation $F→=qv→×B→F→=qv→×B→$ or $F=qvBsinθF=qvBsinθ$ to calculate the force. The direction of the force is determined by RHR-1.\n\n#### Solution\n\n1. First, to determine the direction, start with your fingers pointing in the positive x-direction. Sweep your fingers upward in the direction of magnetic field. Your thumb should point in the negative y-direction. This should match the mathematical answer. To calculate the force, we use the given charge, velocity, and magnetic field and the definition of the magnetic force in cross-product form to calculate:\n$F→=qv→×B→=(3.2×10−19C)(5.0×104m/si^)×(1.5Tk^)=−2.4×10−14Nj^.F→=qv→×B→=(3.2×10−19C)(5.0×104m/si^)×(1.5Tk^)=−2.4×10−14Nj^.$\n2. First, to determine the directionality, start with your fingers pointing in the negative y-direction. Sweep your fingers upward in the direction of magnetic field as in the previous problem. Your thumb should be open in the negative x-direction. This should match the mathematical answer. To calculate the force, we use the given charge, velocity, and magnetic field and the definition of the magnetic force in cross-product form to calculate:\n$F→=qv→×B→=(3.2×10−19C)(−5.0×104m/sj^)×(1.5Tk^)=−2.4×10−14Ni^.F→=qv→×B→=(3.2×10−19C)(−5.0×104m/sj^)×(1.5Tk^)=−2.4×10−14Ni^.$\nAn alternative approach is to use Equation 11.2 to find the magnitude of the force. This applies for both parts (a) and (b). Since the velocity is perpendicular to the magnetic field, the angle between them is 90 degrees. Therefore, the magnitude of the force is:\n$F=qvBsinθ=(3.2×10−19C)(5.0×104m/s)(1.5T)sin(90°)=2.4×10−14N.F=qvBsinθ=(3.2×10−19C)(5.0×104m/s)(1.5T)sin(90°)=2.4×10−14N.$\n3. Since the velocity and magnetic field are parallel to each other, there is no orientation of your hand that will result in a force direction. Therefore, the force on this moving charge is zero. This is confirmed by the cross product. When you cross two vectors pointing in the same direction, the result is equal to zero.\n4. First, to determine the direction, your fingers could point in any orientation; however, you must sweep your fingers upward in the direction of the magnetic field. As you rotate your hand, notice that the thumb can point in any x- or y-direction possible, but not in the z-direction. This should match the mathematical answer. To calculate the force, we use the given charge, velocity, and magnetic field and the definition of the magnetic force in cross-product form to calculate:\n$F→=qv→×B→=(3.2×10−19C)((2.0i^−3.0j^+1.0k^)×104m/s)×(1.5Tk^)=(−14.4i^−9.6j^)×10−15N.F→=qv→×B→=(3.2×10−19C)((2.0i^−3.0j^+1.0k^)×104m/s)×(1.5Tk^)=(−14.4i^−9.6j^)×10−15N.$\nThis solution can be rewritten in terms of a magnitude and angle in the xy-plane:\n$|F→|=Fx2+Fy2=(−14.4)2+(−9.6)2×10−15N=1.7×10−14Nθ=tan−1(FyFx)=tan−1(−9.6×10−15N−14.4×10−15N)=34°.|F→|=Fx2+Fy2=(−14.4)2+(−9.6)2×10−15N=1.7×10−14Nθ=tan−1(FyFx)=tan−1(−9.6×10−15N−14.4×10−15N)=34°.$\nThe magnitude of the force can also be calculated using Equation 11.2. The velocity in this question, however, has three components. The z-component of the velocity can be neglected, because it is parallel to the magnetic field and therefore generates no force. The magnitude of the velocity is calculated from the x- and y-components. The angle between the velocity in the xy-plane and the magnetic field in the z-plane is 90 degrees. Therefore, the force is calculated to be:\n$|v→|=(2)2+(−3)2×104ms=3.6×104msF=qvBsinθ=(3.2×10−19C)(3.6×104m/s)(1.5T)sin(90°)=1.7×10−14N.|v→|=(2)2+(−3)2×104ms=3.6×104msF=qvBsinθ=(3.2×10−19C)(3.6×104m/s)(1.5T)sin(90°)=1.7×10−14N.$\nThis is the same magnitude of force calculated by unit vectors.\n\n#### Significance\n\nThe cross product in this formula results in a third vector that must be perpendicular to the other two. Other physical quantities, such as angular momentum, also have three vectors that are related by the cross product. Note that typical force values in magnetic force problems are much larger than the gravitational force. Therefore, for an isolated charge, the magnetic force is the dominant force governing the charge’s motion.\n\nRepeat the previous problem with the magnetic field in the x-direction rather than in the z-direction. Check your answers with RHR-1.\n\n### Representing Magnetic Fields\n\nThe representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. As shown in Figure 11.6, each of these lines forms a closed loop, even if not shown by the constraints of the space available for the figure. The field lines emerge from the north pole (N), loop around to the south pole (S), and continue through the bar magnet back to the north pole.\n\nMagnetic field lines have several hard-and-fast rules:\n\n1. The direction of the magnetic field is tangent to the field line at any point in space. A small compass will point in the direction of the field line.\n2. The strength of the field is proportional to the closeness of the lines. It is exactly proportional to the number of lines per unit area perpendicular to the lines (called the areal density).\n3. Magnetic field lines can never cross, meaning that the field is unique at any point in space.\n4. Magnetic field lines are continuous, forming closed loops without a beginning or end. They are directed from the north pole to the south pole.\n\nThe last property is related to the fact that the north and south poles cannot be separated. It is a distinct difference from electric field lines, which generally begin on positive charges and end on negative charges or at infinity. If isolated magnetic charges (referred to as magnetic monopoles) existed, then magnetic field lines would begin and end on them.\n\nFigure 11.6 Magnetic field lines are defined to have the direction in which a small compass points when placed at a location in the field. The strength of the field is proportional to the closeness (or density) of the lines. Magnetic field lines present inside the magnet or outside the field of view are not shown given the space constraints of the figure. If the rest of the magnetic field line was shown, it would form a continuous loop.\nOrder a print copy\n\nAs an Amazon Associate we earn from qualifying purchases."
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https://www.doorsteptutor.com/Exams/NCO/Class-10/Questions/Topic-Mental-Ability-2/Subtopic-Basic-Algebra-0/Part-1.html
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[
"# Mental Ability-Basic Algebra (NCO- Cyber Olympiad (SOF) Class 10): Questions 1 - 6 of 42\n\nAccess detailed explanations (illustrated with images and videos) to 461 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Subscription can be renewed yearly absolutely FREE! View Sample Explanation or View Features.\n\nRs. 300.00 or\n\nHow to register?\n\n## Question number: 1\n\n» Mental Ability » Basic Algebra\n\nEdit\nMCQ▾\n\n### Question\n\nIf , which expression is equivalent to ?\n\n### Choices\n\nChoice (4) Response\n\na.\n\nb.\n\nc.\n\nd.\n\n## Question number: 2\n\n» Mental Ability » Basic Algebra\n\nEdit\nMCQ▾\n\n### Question\n\nIndicate in which one of the following equations x is neither directly nor inversely proportional to y.\n\n### Choices\n\nChoice (4) Response\n\na.\n\nb.\n\nc.\n\nd.\n\n## Question number: 3\n\n» Mental Ability » Basic Algebra\n\nEdit\nMCQ▾\n\n### Question\n\nThe polynomial is modeled below using algebraic tiles.",
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"Image of Some Algebraic Tiles Used to Make a Polynomial Representing the image of some algebraic tiles used to make a polynomial\n\nThe solution to the equation are given by\n\n### Choices\n\nChoice (4) Response\n\na.\n\nb.\n\nc.\n\nd.\n\n## Question number: 4\n\n» Mental Ability » Basic Algebra\n\nEdit\nMCQ▾\n\n### Question\n\nWhich is a zero of the function ?\n\n### Choices\n\nChoice (4) Response\n\na.\n\n-1\n\nb.\n\n6\n\nc.\n\n7\n\nd.\n\n-6\n\n## Question number: 5\n\n» Mental Ability » Basic Algebra\n\nEdit\nMCQ▾\n\n### Question\n\nDivide Rs. 1080 into three parts in such a way that half of the first part, one-third of the second part and one-fourth of the third part are equal. The 1st, 2nd, 3rd parts are respectively.\n\n### Choices\n\nChoice (4) Response\n\na.\n\n360 Rs. , 240 Rs. , 480 Rs.\n\nb.\n\n480 Rs. , 240 Rs. , 360 Rs.\n\nc.\n\n240 Rs. , 360 Rs. , 480 Rs.\n\nd.\n\n480 Rs. , 360 Rs. , 240 Rs.\n\n## Question number: 6\n\n» Mental Ability » Basic Algebra\n\nEdit\nMCQ▾\n\n### Question\n\nDivide Rs. 1320 into three parts in such a way that half of the first part, one-fourth of the second part and one-fifth of the third part are equal. The 1st, 2nd, 3rd parts are respectively.\n\n### Choices\n\nChoice (4) Response\n\na.\n\n600 Rs. , 480 Rs. , 240 Rs.\n\nb.\n\n600 Rs. , 240 Rs. , 480 Rs.\n\nc.\n\n240 Rs. , 480 Rs. , 600 Rs.\n\nd.\n\n260 Rs. , 440 Rs. , 600 Rs.\n\nDeveloped by:"
] |
[
null,
"https://www.doorsteptutor.com/Exams/NCO/Class-10/Questions/Topic-Mental-Ability-2/Subtopic-Basic-Algebra-0/None",
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] |
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http://modular-planet.de/experimental/pll-reso-fake/pll-reso-fake.html
|
[
"PLL-Reso-Fake",
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"Experimental",
null,
"",
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"D o e p f e r A - 100 Connections: Settings: A-145 (Square) <=> A-155 (Step/Clock) A-155 (Trig 1 Out) <=> A-180 A-180 <=> A-140 (Gate) A-180 <=> A-110 (SYNC) A-155 (Pre Out) <=> A-156 (CV In) A-156-1 (CV Out) <=> A-110 (CV 1) A-110 (Square) <=> A-196 (In 2) A-196 (VCO Out) <=> A-131 (Audio In) A-196 (Phase Comp. Out) <=> A-138c (Input 1) A-147 (Sine) <=> A-138c (Input 2) A-138c (Output) <=> A-196 (CV In) A-131 (Audio Out) <=> Amplifier A-145 (Frq = 8, Range = M) A-155 (Row Up: 1 = 1.3, 2 = 7.3, 3 = 10, 4 = 8, 5 = 0, 6 = 6.5, 7 = 4.5, 8 = 10, Range = 4V, Glide = 0) A-110 (PW = 5) A-196 (Offs. = 5, Range = hi, Type = 1, Frequ. = 5) A-147 (Freq = 5) A-138c (In 1 = +5, In 2 = +1, Out = +5) A-140 (A = 0, D = 3, S = 0, R = 0, Range = M) A-131 (Gain = 0, Audio In 1 = 10, Audio Out = 10) Ingo Zobel, June 2005 www.selfoscillate.de *",
null,
"Sound sample PLL-Reso-Fake"
] |
[
null,
"http://modular-planet.de/Klinke1.gif",
null,
"http://modular-planet.de/experimental/pll-reso-fake/pll-reso-fakedia.png",
null,
"http://modular-planet.de/experimental/pll-reso-fake/pll-reso-fakepat.png",
null,
"http://modular-planet.de/_jukebox/jukebox_link.png",
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] |
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|
https://goodboychan.github.io/python/datacamp/machine_learning/2020/06/06/02-Hierarchical-Clustering.html
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[
"import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n\n## Basics of hierarchical clustering\n\n• Creating a distance matrix using linkage\n• method: how to calculate the proximity of clusters\n• metric: distance metric\n• optimal_ordering: order data points\n• Type of Methods\n• single: based on two closest objects\n• complete: based on two farthest objects\n• average: based on the arithmetic mean of all objects\n• centroids: based on the geometric mean of all objects\n• median: based on the median of all objects\n• ward: based on the sum of squares\n\n### Hierarchical clustering: ward method\n\nIt is time for Comic-Con! Comic-Con is an annual comic-based convention held in major cities in the world. You have the data of last year's footfall, the number of people at the convention ground at a given time. You would like to decide the location of your stall to maximize sales. Using the ward method, apply hierarchical clustering to find the two points of attraction in the area.\n\n• Preprocess\ncomic_con = pd.read_csv('./dataset/comic_con.csv', index_col=0)\n\nx_coordinate y_coordinate\n0 17 4\n1 20 6\n2 35 0\n3 14 0\n4 37 4\nfrom scipy.cluster.vq import whiten\n\ncomic_con['x_scaled'] = whiten(comic_con['x_coordinate'])\ncomic_con['y_scaled'] = whiten(comic_con['y_coordinate'])\n\nfrom scipy.cluster.hierarchy import linkage, fcluster\n\ndistance_matrix = linkage(comic_con[['x_scaled', 'y_scaled']], method='ward', metric='euclidean')\n\n# Assign cluster labels\ncomic_con['cluster_labels'] = fcluster(distance_matrix, 2, criterion='maxclust')\n\n# Plot clusters\nsns.scatterplot(x='x_scaled', y='y_scaled', hue='cluster_labels', data=comic_con);",
null,
"### Hierarchical clustering: single method\n\nLet us use the same footfall dataset and check if any changes are seen if we use a different method for clustering.\n\ndistance_matrix = linkage(comic_con[['x_scaled', 'y_scaled']], method='single', metric='euclidean')\n\n# Assign cluster labels\ncomic_con['cluster_labels'] = fcluster(distance_matrix, 2, criterion='maxclust')\n\n# Plot clusters\nsns.scatterplot(x='x_scaled', y='y_scaled', hue='cluster_labels', data=comic_con);",
null,
"### Hierarchical clustering: complete method\n\nFor the third and final time, let us use the same footfall dataset and check if any changes are seen if we use a different method for clustering.\n\ndistance_matrix = linkage(comic_con[['x_scaled', 'y_scaled']], method='complete', metric='euclidean')\n\n# Assign cluster labels\ncomic_con['cluster_labels'] = fcluster(distance_matrix, 2, criterion='maxclust')\n\n# Plot clusters\nsns.scatterplot(x='x_scaled', y='y_scaled', hue='cluster_labels', data=comic_con);",
null,
"## Visualize clusters\n\n• Why visualize clusters?\n• Try to make sense of the clusters formed\n• An additional step in validation of clusters\n• Spot trends in data\n\n### Visualize clusters with matplotlib\n\nWe have discussed that visualizations are necessary to assess the clusters that are formed and spot trends in your data. Let us now focus on visualizing the footfall dataset from Comic-Con using the matplotlib module.\n\ncolors = {1:'red', 2:'blue'}\n\n# Plot the scatter plot\ncomic_con.plot.scatter(x='x_scaled', y='y_scaled', c=comic_con['cluster_labels'].apply(lambda x: colors[x]));",
null,
"### Visualize clusters with seaborn\n\nLet us now visualize the footfall dataset from Comic Con using the seaborn module. Visualizing clusters using seaborn is easier with the inbuild hue function for cluster labels.\n\nsns.scatterplot(x='x_scaled', y='y_scaled', hue='cluster_labels', data=comic_con)\n\n<matplotlib.axes._subplots.AxesSubplot at 0x27d3a82d1c8>",
null,
"## How many clusters?\n\n• Introduction to dendrograms\n• Strategy till now - decide clusters on visual inspection\n• Dendrograms help in showing progressions as clusters are merged\n• A dendrogram is a branching diagram that demonstrates how each cluster is composed by branching out into its child nodes\n\n### Create a dendrogram\n\nDendrograms are branching diagrams that show the merging of clusters as we move through the distance matrix. Let us use the Comic Con footfall data to create a dendrogram.\n\nfrom scipy.cluster.hierarchy import dendrogram\n\n# Create a dendrogram\ndn = dendrogram(distance_matrix)",
null,
"### Limitations of hierarchical clustering\n\n• Comparison of runtime of linkage method\n• Increasing runtime with data points\n• Not feasible for large datasets\n\n### Timing run of hierarchical clustering\n\nIn earlier exercises of this chapter, you have used the data of Comic-Con footfall to create clusters. In this exercise you will time how long it takes to run the algorithm on DataCamp's system.\n\nRemember that you can time the execution of small code snippets with:\n\n%timeit sum([1, 3, 2])\n\n%timeit linkage(comic_con[['x_scaled', 'y_scaled']], method='ward', metric='euclidean')\n\n459 µs ± 377 ns per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n\n\n### FIFA 18: exploring defenders\n\nIn the FIFA 18 dataset, various attributes of players are present. Two such attributes are:\n\n• sliding tackle: a number between 0-99 which signifies how accurate a player is able to perform sliding tackles\n• aggression: a number between 0-99 which signifies the commitment and will of a player These are typically high in defense-minded players. In this exercise, you will perform clustering based on these attributes in the data.\n\nThis data consists of 5000 rows, and is considerably larger than earlier datasets. Running hierarchical clustering on this data can take up to 10 seconds.\n\n• Preprocess\nfifa = pd.read_csv('./dataset/fifa_18_dataset.csv')\n\nsliding_tackle aggression\n0 23 63\n1 26 48\n2 33 56\n3 38 78\n4 11 29\nfifa['scaled_sliding_tackle'] = whiten(fifa['sliding_tackle'])\nfifa['scaled_aggression'] = whiten(fifa['aggression'])\n\ndistance_matrix = linkage(fifa[['scaled_sliding_tackle', 'scaled_aggression']], method='ward')\n\n# Assign cluster labels to each row of data\nfifa['cluster_labels'] = fcluster(distance_matrix, 3, criterion='maxclust')\n\n# Display cluster centers of each cluster\nprint(fifa[['scaled_sliding_tackle', 'scaled_aggression', 'cluster_labels']].groupby('cluster_labels').mean())\n\n# Create a scatter plot through seaborn\nsns.scatterplot(x='scaled_sliding_tackle', y='scaled_aggression', hue='cluster_labels', data=fifa)\nplt.savefig('../images/fifa_cluster.png')\n\n scaled_sliding_tackle scaled_aggression\ncluster_labels\n1 0.987373 1.849142\n2 3.013487 4.063492\n3 1.934455 3.210802",
null,
""
] |
[
null,
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%0A",
null,
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%0A",
null,
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%0A",
null,
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%0A",
null,
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%0A",
null,
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%0A",
null,
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%0A",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5824993,"math_prob":0.77268404,"size":4924,"snap":"2022-27-2022-33","text_gpt3_token_len":1277,"char_repetition_ratio":0.15833333,"word_repetition_ratio":0.0929054,"special_character_ratio":0.2715272,"punctuation_ratio":0.15945612,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9902437,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-29T03:57:12Z\",\"WARC-Record-ID\":\"<urn:uuid:d64db022-c02c-4a38-9f56-6f59991de170>\",\"Content-Length\":\"274137\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de6f041b-df6c-4e9f-a36a-a0b26450d378>\",\"WARC-Concurrent-To\":\"<urn:uuid:3179797b-f07e-46cb-83a7-638124339df1>\",\"WARC-IP-Address\":\"185.199.111.153\",\"WARC-Target-URI\":\"https://goodboychan.github.io/python/datacamp/machine_learning/2020/06/06/02-Hierarchical-Clustering.html\",\"WARC-Payload-Digest\":\"sha1:KQTEWT36ANQQ6MLVPTLFR3Z3YKZOZW2R\",\"WARC-Block-Digest\":\"sha1:4SHVC5BFPLOVNJAGUONJDJMJYF7VLWQD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103620968.33_warc_CC-MAIN-20220629024217-20220629054217-00690.warc.gz\"}"}
|
https://www.fmf.uni-lj.si/~mohar/Problems/P0703_HamiltonicityInfinite.html
|
[
"## Hamiltonicity of Infinite Graphs\n\nLet G be a locally finite infinite graph and let I(G) be the set of ends of G. The Freudenthal compactification of G is the topological space |G| which is obtained from the usual topological space of the graph, when viewed as a 1-dimensional cell complex, by adding all points of I(G) and setting, for each end in I(G), the basic set of neighborhoods of t to consist of sets of the form C(S, t)",
null,
"I(S,t)",
null,
"E'(S,t), where S ranges over the finite subsets of V(G), C(S, t) is the component of G - S containing all rays in t, the set I(S,t) contains all ends in I(G) having rays in C(S, t), and E'(S,t) is the union of half-edges (z,y], one for every edge xy joining S and C(S,t). We define a hamilton circle in |G| as a homeomorphic image C of the unit circle S1 into |G| such that every vertex (and hence every end) of G appears in C. More details about these notions can be found in .\n\nA graph G (finite or infinite) is said to be uniquely hamiltonian if it contains precisely one hamilton circle.\n\nFor finite graphs, Sheehan proposed the following conjecture in 1975:\n\nConjecture 1 (Sheehan ): If G is a finite r-regular graph, where r > 2, then G is not uniquely hamiltonian.\n\nThis conjecture has been proved for all odd values of r and for all even values of r > 23 . By Petersen's theorem, it would suffice to prove it for r = 4.\n\nFor infinite graphs, Conjecture 1 is false even for odd values of r, however all known counterexamples (e.g. the two-way infinite ladder) have at least 2 ends. Thus, one can ask if it could be true for 1-ended graphs:\n\nProblem 2: Are there any uniquely hamiltonian locally finite 1-ended graphs which are regular of degree r > 2?\n\nAnother possiblility is to ask if conjecture 1 could be true even for graphs with many ends if we assume that (in addition to the vertices) the ends have a certain vertex-degree (the vertex-degree of an end t is the maximal number of disjoint rays in t).\n\nSeveral other problems about hamilton circles in infinite graphs have been proposed by Georgakopoulos:\n\nConjecture 3 (Georgakopoulos): If G is a 4-edge-connected locally finite graph, then its line graph is hamiltonian.\n\nThis is known for finite graphs. The proof uses the existence of two edge-disjoint spanning trees in 4-edge-connected graphs. In the infinite case, it would be enough to prove that a 4-edge-connected locally finite graph G has two edge-disjoint topological spanning trees (see ) one of which is connected as a subgraph of G. The problem is open even for the 1-ended case (where hamilton circles correspond to 2-way-infinite paths).\n\nConjecture 4 (Georgakopoulos): If the line graph L(G) of a locally finite graph G is 4-connected, then L(G) is hamiltonian.\n\nConjecture 4 is widely open even in the finite case, where it was proposed by Thomassen .\n\nFor finite graphs it is well known that the third power of a connected graph is hamiltonian. This has also been proved for locally finite graphs . But what about non-locally-finite graphs?\n\nConjecture 5 (Georgakopoulos ): If G is a countable connected graph then its third power is hamiltonian.\n\nSimilarly, one can ask if Fleischner's theorem holds for countable graphs (for locally finite ones it has already been proved ):\n\nConjecture 6 (Georgakopoulos ): If G is a 2-connected countable graph then its square is hamiltonian.\n\nBibliography:\n\n R. Diestel, Graph Theory, Third Edition, Springer, 2005.\n\n P. Haxell, B. Seamone, J. Verstraete, Independent dominating sets and hamiltonian cycles, J. Graph Theory 54 (2007) 233-244.\n\n J. Sheehan, The multiplicity of Hamiltonian circuits in a graph. Recent advances in graph theory (Proc. Second Czechoslovak Sympos., Prague, 1974), pp. 477-480. Academia, Prague, 1975.\n\n A.G. Thomason, Hamiltonian cycles and uniquely edge colourable graphs. Advances in graph theory (Cambridge Combinatorial Conf., Trinity College, Cambridge, 1977). Ann. Discrete Math. 3 (1978), Exp. No. 13, 3 pp.\n\n C. Thomassen, Reflections on graph theory, J. Graph Theory 10 (1986) 309-324.\n\n A. Georgakopoulos, Oberwolfach reports, 16/2007."
] |
[
null,
"https://www.fmf.uni-lj.si/~mohar/Symbols/bigcup.gif",
null,
"https://www.fmf.uni-lj.si/~mohar/Symbols/bigcup.gif",
null
] |
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|
https://www.nag.com/content/nearest-correlation-matrix-0
|
[
"Nearest Correlation Matrix\n\nThe NAG Library has a range of functionality related to computing the nearest correlation matrix. In this article we take look at nearest correlation matrix problems, giving some background and introducing the routines that solve them.\n\n## Introduction\n\nA correlation matrix is characterized as being a real, square matrix that\n\n• is symmetric;\n• has ones on the diagonal;\n• has non-negative eigenvalues.\n\nA matrix with non-negative eigenvalues is called positive semidefinite. If a matrix $$C$$ is a correlation matrix then the elements of $$C, c_{ij}$$, represent the pair-wise correlation of entity $$i$$ with entity $$j$$, that is, the strength and direction of a linear relationship between the two.\n\nIn the literature (See References) there are numerous examples illustrating the use of correlation matrices but the one we have encountered the most arises in finance where the correlation between various stocks is used to construct sensible portfolios. Unfortunately, for a variety of reasons, an input matrix which is supposed to be a correlation matrix may fail to be semidefinite. For example, the correlations may be between stocks measured over a period of time and some data may be missing. If individual correlations are computed using observation data they have in common, and this varies over all the variables, it will give rise to an indefinite matrix. Still drawing from finance, a practitioner may wish to explore the effect on a portfolio of assigning correlations between certain assets different from those computed from historical values. This can also result in negative eigenvalues in the computed matrix.\n\nIn such situations, the result is a matrix which is an approximate correlation matrix and this must be fixed for subsequent analysis that relies upon having a true correlation matrix to be valid. Ideally, we wish to find the ‘nearest’ true correlation matrix to our approximate one for some sensible definition of ‘near’. This is our basic nearest correlation matrix problem.\n\n## The Basic Nearest Correlation Matrix Problem\n\nThe NAG Library routine nagf_correg_corrmat_nearest (g02aa) implements a Newton algorithm to solve the basic problem we outlined in the introduction. It finds a true correlation matrix $$X$$ that is closest to the approximate input matrix, $$G$$, in the Frobenius norm. That is we find the minimum of\n\n$\\|G-X\\|_F .$\n\nThe algorithm, described in a paper by Qi and Sun , has superior convergence properties over previously suggested approaches. Borsdorf and Higham , at the University of Manchester, looked at this in greater detail and offered further improvements. These include a different iterative solver (MINRES was preferred to Conjugate Gradient) and a means of pre-conditioning the linear equations. It is this enhanced algorithm that has been incorporated into our Library.\n\n## Weighted Problems and Forcing a Positive Definite Correlation Matrix\n\nIn NAG Library routine nagf_correg_corrmat_nearest_bounded (g02ab) we extend the functionality provided by g02aa. If we have an approximate correlation matrix it is reasonable to suppose that not all of the matrix is actually approximate, perhaps only part of it is. Similarly, we may trust some correlations more than others and wish for these to stay closer to their input value in the final matrix.\n\nIn this algorithm, we apply the original work of Qi and Sun, to now use a weighted norm. Thus, we find the minimum of\n\n$\\|W^{1/2}(G-X)W^{1/2}\\|_F.$\n\nHere $$W$$ is a diagonal matrix of weights. This means that we are seeking to minimize the elements $$√w_{ij}(g_{ij}-x_{ij})√w_{jj}$$. Thus, by choosing elements in $$W$$ appropriately we can favour some elements in $$G$$, forcing the corresponding elements in $$X$$ to be closer to them.\n\nThis method means that whole rows and columns of $$G$$ are weighted. However, nagf_correg_corrmat_h_weight (g02aj) allows element-wise weighting and in this routine, we find the minimum of\n\n$\\|H \\circ (G-X)\\|_F,$\n\nwhere $$𝐶=𝐴∘𝐵$$ denotes the matrix C with elements $$c_{i,i}= a_{i,j}b_{i,j}$$. Thus by choosing appropriate values in $$H$$, we can emphasize individual elements in $$G$$ and leave the others unweighted. The algorithm employed here is by Jiang, Sun and Toh , and has the Newton algorithm at its core.\n\nBoth g02ab and g02aj allows us to specify that the computed correlation matrix is positive definite, that is its eigenvalues are greater than zero. This is required in some applications to improve the condition of the matrix and to increase stability.\n\n## Constraining the Rank of the Correlation Matrix\n\nIf a low-rank correlation matrix is required, for example, to constrain the number of independent random variables, nagf_correg_corrmat_nearest_rank (g02ak) can be used. It finds the nearest correlation matrix, in the Frobenius norm, of maximum prescribed rank. The routine is based on the Majorized Penalty Approach proposed by Gao and Sun .\n\n## Fixing Correlations with Shrinking and Alternating Projections\n\nWe now turn our attention to fixing some of the elements that are known to be true correlations. Instead of using a Newton method like the previous four algorithms, here we use a shrinking method.\n\nOne common example where this is needed is where the correlations between a subset of our variables are trusted and on their own would form a valid correlation matrix. We could thus arrange these into the leading block of our input matrix and seek to fix them while we correct the remainder. We call this the fixed block problem. The routine nagf_correg_corrmat_shrinking (g02an) preserves such a leading block of correlations in our approximate matrix. Using the shrinking method of Higham, Strabić and Šego , the routine finds a true correlation matrix of the following form\n\n$\\alpha \\begin{pmatrix} A & 0 \\\\ 0 & I \\end{pmatrix} + (1-\\alpha)G.$\n\n$$G$$ is again our input matrix and we find the smallest $$𝛼$$ in the interval [0,1] that gives a positive semidefinite result. The smaller $$𝛼$$ is, the closer we stay to our original matrix, and any $$𝛼$$ preserves the leading submatrix $$A$$, which needs to be positive definite. The algorithm uses a bisection method which converges quickly in a finite number of steps.\n\nThe routine nagf_correg_corrmat_target (g02ap) generalizes the shrinking idea and allows us to supply our own target matrix. The target matrix, $$T$$, is defined by specifying a matrix of weights, $$H$$, with $$𝑇=𝐻 ∘𝐺$$. We then find a solution of the form\n\n$\\alpha T +(1-\\alpha)G,$\n\ncomputing $$𝛼$$ as before. A bound on the smallest eigenvalue can also be specified. Specifying a value of 1 in $$H$$ essentially fixes an element in $$G$$ so it is unchanged in $$X$$.\n\nFor example, it is sometimes required to fix two diagonal blocks, so we could choose $$H$$ to be\n\n$H=\\begin{pmatrix} \\begin{bmatrix} 1 & & \\ldots & & 1 \\\\ \\vdots & & \\ddots & & \\vdots \\\\ 1 & & \\ldots & & 1 \\end{bmatrix} & 0 \\\\ 0 & \\begin{bmatrix} 1 & & \\ldots & & 1 \\\\ \\vdots & & \\ddots & & \\vdots \\\\ 1 & & \\ldots & & 1 \\end{bmatrix}\\end{pmatrix}.$\n\nThe algorithm then finds the smallest $$𝛼$$ that gives a positive semidefinite matrix of the following form.\n\n$\\alpha \\begin{pmatrix} G_{11} & 0 \\\\ 0 & G_{22} \\end{pmatrix} + (1-\\alpha)G.$\n\nAnd we perturb only the two off diagonal blocks of the input.\n\nThe shrinking algorithms are characterized by their speed and the potentially large distance between the input and the output. Alternating projections with Anderson acceleration is another algorithm we employ to compute fixed block problems, and it’s speed and nearness characteristics are the reverse of that of shrinking.\n\nThe input matrix is repeatedly, and alternately, projected on to the nearest matrix in the sets of semidefinite matrices and matrices with entries we wish to preserve, including the unit diagonal. Whilst there is no guarantee of convergence theoretically, in practice the algorithm will find the nearest correlation matrix in the intersection of these two sets. In the routine nagf_correg_corrmat_fixed (g02as) we employ the method of Higham and Strabić , which computes the nearest correlation matrix in the Frobenius norm while fixing arbitrary elements, and optionally setting a minimum eigenvalue.\n\n## Choosing a Nearest Correlation Matrix Routine\n\nWhen choosing a routine, the trade-off is between computation time and the distance of the solution from the original matrix. The Newton algorithms (g02aa, g02ab, g02aj and g02ak) and the alternating projection algorithm (g02as) will always find the nearest solution to the problem they are solving, recalling that weighted algorithms are only influencing the input. The shrinking routines (g02an and g02ap) will find a result further away but will be much quicker.\n\nFor the basic problem, g02aa will always find the nearest matrix. Using g02ap, with an identity matrix as the target, will produce a matrix further away than this, which is understandable given the form of the solution, but with a shorter computation time.\n\nIf you wish to solve the fixed block problem the specialist routine g02an will be the fastest. Of the Newton algorithms g02ab will find a solution in a reasonable time but, as we weight whole rows and columns, some elements will be overemphasized outside of the correct block. A more accurate weighting can be achieved with g02aj and a close solution will be found. However, the routine will take considerably more time. The closest solution will be found with g02as. Whilst much slower than the Newton algorithms it can outperform g02aj for speed.\n\nFor fixing two diagonal blocks, or for arbitrary fixing and weighting, the choice is between g02aj, g02ap and g02as with the same speed and nearness trade-off. The alternating projections of g02as will fix elements and find the nearest solution. Although the shrinking algorithm is fixing elements and is quick, the target matrix is required to be positive definite and form part of a valid correlation matrix, which can be a limitation. Since g02aj only weights elements in the input it may offer some flexibility here if the blocks you wish to preserve are close to, but fail to be, positive semidefinite.\n\nIf we seek to fix the minimum eigenvalue, and no weighting is required, g02ab or g02ap can be used. With the latter using an identity target, as for the basic problem. If weighting or fixing is also required then similar results are found for problems described above. However, in combination with weighting g02ap can return a large value of $$𝛼$$. This means that much of the input matrix has been lost and a result far from it is returned.\n\nTo constrain the rank of the output correlation matrix use g02ak.\n\nThe tolerance used in all of the algorithms, which defines convergence, can obviously affect the number of iterations undertaken and thus the speed and nearness. We recommend some experimentation using data that represents your typical problem. The routine g02aj can be sensitive to the weights used, so different values should be tried to tune both the nearness and the computation time.\n\n## The Nearest Correlation Matrix with Factor Structure\n\nA correlation matrix with factor structure is one where the off-diagonal elements agree with some matrix of rank $$k$$. That is, the correlation matrix $$C$$ can be written as\n\n$C = \\mbox{diag}(I-XX^T) + XX^T,$\n\nwhere $$𝑋$$ here is an $$𝑛 ×𝑘$$ matrix, often referred to as the factor loading matrix, and $$k$$ is generally much small than $$n$$. These correlation matrices arise in factor models of asset returns, collateralized debit obligations and multivariate time series.\n\nThe routine g02ae computes the nearest factor loading matrix, $$X$$, that gives the nearest correlation matrix for an approximate one, $$G$$, by finding the minimum of\n\n$\\| G-XX^T + \\mbox{diag}(XX^T-I) \\|_F.$\n\nWe have implemented the spectral projected gradient method of Birgin, Martinez and Raydan as suggested by Borsdorf, Higham and Raydan .\n\n## Table of Functionality\n\nThis table lists all our nearest correlation matrix routines and indicates the measure of nearness and what weighting and fixing can be used in each.\n\nRoutine Nearness measured in the Frobenius Norm Shrinking Algorithm Nearest Matrix with Factor Structure Elements can be weighted Elements can be fixed Minimum eigenvalue can be requested Maximum rank can be requested\ng02aa X\ng02ab X X X\ng02ae X X\ng02aj X X X\ng02ak X X\ng02an X X\ng02ap X X X X\ng02as X X X\nReferences"
] |
[
null
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{"ft_lang_label":"__label__en","ft_lang_prob":0.8763208,"math_prob":0.99540466,"size":13810,"snap":"2021-43-2021-49","text_gpt3_token_len":3243,"char_repetition_ratio":0.1548602,"word_repetition_ratio":0.03026197,"special_character_ratio":0.23323679,"punctuation_ratio":0.08791209,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9987462,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-04T08:55:13Z\",\"WARC-Record-ID\":\"<urn:uuid:880ea566-5947-4e1b-b2cd-eb6cedcd54da>\",\"Content-Length\":\"109856\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a0de2035-1f96-44c5-9c3a-79d6ae9925f4>\",\"WARC-Concurrent-To\":\"<urn:uuid:7e32e0e6-52d4-4f4a-95e4-a0f78fb0d720>\",\"WARC-IP-Address\":\"78.129.168.4\",\"WARC-Target-URI\":\"https://www.nag.com/content/nearest-correlation-matrix-0\",\"WARC-Payload-Digest\":\"sha1:U2IURZXMGYOWRDPVGVWNRKHGJ2QFOSWZ\",\"WARC-Block-Digest\":\"sha1:QTLSUXAJN2TC45L6KTVJS7Z3TK5XFGHF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964362952.24_warc_CC-MAIN-20211204063651-20211204093651-00163.warc.gz\"}"}
|
https://www.had2know.com/academics/decimal-to-hexadecimal-conversion.html
|
[
"# How to Convert Decimal to Hexadecimal\n\nDec-to-Hex and Hex-to-Dec Calculator\n\nThe hexadecimal (base-16) number system allows you to encode numbers more efficiently than in lower base number systems, such as binary (base-2) or decimal (base-10). The hexadecimal system uses the digits 0 through 9 plus the first six letters of the alphabet to create a base-16 number system. The letters A, B, C, D, E, and F stand for the numbers 10 through 15 respectively. For example, the number that is written as 51973 in the decimal system is written as CB05 in the hexadecimal system.\n\nIf you want to convert a base-10 number into a base-16 number by hand, use the guide below. You can also use the easy conversion calculator on the left.\n\n(Step 1) First, examine the powers of 16:\n160 = 1\n161 = 16\n162 = 256\n163 = 4096\n164 = 65536\n165 = 1048576\n...\n\nFor the base-10 number that you want to convert, find the power of 16 that is closest to the decimal number without going over. For example, if you want to convert 51973, then you would pick 163 = 4096, since 65536 is too large.\n\n(Step 2) Look at the power of 16 that you picked in Step 1, and add 1 to the exponent. For example, since 4096 = 163, then you add 3 + 1 = 4. This tells you how many digits the equivalent hexadecimal number will have. So 51973 will have 4 digits in base-16.\n\n(Step 3) To find the first digit of the hexadecimal number, divide the base-10 number by the number you picked in Step 1, and keep the remainder. For example, 51973/4096 = 12 with remainder 2821. Since 12 is equivalent to C in hexadecimal, the first digit is C.\n\n(Step 4) For the remainder you found in Step 3, repeat Steps 1 and 3. For example, 2821 is between 162 = 256 and 163 = 4096, so we will pick 256. Next, divide 2821 by 256 and keep the remainder. So 2821/256 = 11 with remainder 5. Since 11 = B in hexadecimal, the second digit is B.\n\n(Step 5) The remainder 5 is between 160 = 1 and 161 = 16 and so this will be the last digit, but notice that we did not end up with a remainder between 161 = 16 and 162 = 256. This means that the third digit is 0. Thus, the entire number is CB05."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.88115984,"math_prob":0.9974979,"size":2090,"snap":"2021-43-2021-49","text_gpt3_token_len":592,"char_repetition_ratio":0.15292425,"word_repetition_ratio":0.014742015,"special_character_ratio":0.34258375,"punctuation_ratio":0.11868132,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99979323,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-26T09:45:03Z\",\"WARC-Record-ID\":\"<urn:uuid:6fd1d026-5279-4005-a5a8-fcfa90f9bfab>\",\"Content-Length\":\"19184\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8d7fbcb4-2da2-45b9-8943-8751dc391d16>\",\"WARC-Concurrent-To\":\"<urn:uuid:b0a6f474-a6be-40d7-af16-ffcc2ce378c8>\",\"WARC-IP-Address\":\"176.74.21.6\",\"WARC-Target-URI\":\"https://www.had2know.com/academics/decimal-to-hexadecimal-conversion.html\",\"WARC-Payload-Digest\":\"sha1:OTUEHPM6O6CQCIAEU3PIMYBKIL6AA6MH\",\"WARC-Block-Digest\":\"sha1:4BTKQYSVOEKK2SI2TID5IDYUWEQXFDZ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323587854.13_warc_CC-MAIN-20211026072759-20211026102759-00225.warc.gz\"}"}
|
https://www.omnicalculator.com/math/square-perimeter
|
[
"# Perimeter of a Square Calculator\n\nBy Hanna Pamuła, PhD candidate\nLast updated: May 26, 2021\n\nThis perimeter of a square calculator will help you with this basic calculation. Type the square side to obtain the perimeter, or use our tool the other way round: enter the perimeter to get the side length. If you're not sure what is a perimeter of a square or you've just forgotten the formula for the perimeter of a square, keep scrolling! You may also be interested in our square calculator which finds the square area and diagonal as well.\n\n## What is the perimeter of a square - formula",
null,
"Perimeter of a square is equal to sum of all square sides. Because square has all four sides equal in length, the perimeter is:\n\n`perimeter = a + a + a + a = 4 * a`\n\nA square is the quadrilateral of least perimeter enclosing a given area:\n\n`16 * area = perimeter²` (because `area = a²` and `perimeter² = (4 * a)² = 16 * a²`)\n\nFor every other quadrilateral than square, the inequality occurs:\n\n`16 * area < perimeter²`\n\nWhich means that a square has a larger area than any other quadrilateral with the same perimeter.\n\n## What is the perimeter of a 4 in square\n\nThe perimeter of such a square is calculated by adding all the sides together, or multiplying the side length by 4:\n\n`perimeter = 4 in + 4 in + 4 in + 4 in = 4 * 4 in = 16 in`",
null,
"## How to use the perimeter of a square calculator?\n\nLet's have a look at an example. Imagine that you got a gift from your friend, a lovely oil painting, square-shaped. You would like to make a frame for it. However, you have no idea how long the pine board needs to be. Yes, you guessed right, you can use the perimeter of a square calculator!\n\n1. Measure the side of the square. For example, our painting's side is 3 ft 6 in. Change the unit by a simple click on its name and then type the value into the box.\n2. Perimeter of a square appears: it's 14 ft in our case. Of course, it's only an example, in real life you'll probably need more material as it depends on frame and board width and the way of joining frame corners.\nHanna Pamuła, PhD candidate",
null,
"Side a\nin\nDiagonal d\nin\nPerimeter\nin\nPeople also viewed…\n\n### Circumference\n\nUse this free circumference calculator to find the area, circumference and diameter of a circle.\n\n### Cube Calc: find v, a, d\n\nThis cube calc finds V (volume), a (area), and d (diagonal) of a cube.\n\n### Lost socks\n\nSocks Loss Index estimates the chance of losing a sock in the laundry.",
null,
""
] |
[
null,
"https://uploads-cdn.omnicalculator.com/images/square-p.png",
null,
"https://uploads-cdn.omnicalculator.com/images/square-p-example.png",
null,
"https://uploads-cdn.omnicalculator.com/images/geometry/perimeter/square-perimeter.svg",
null,
"data:image/svg+xml;base64,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",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9182508,"math_prob":0.9955965,"size":1954,"snap":"2021-43-2021-49","text_gpt3_token_len":470,"char_repetition_ratio":0.21794872,"word_repetition_ratio":0.047493402,"special_character_ratio":0.24718526,"punctuation_ratio":0.09045226,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9977764,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,10,null,5,null,7,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-28T21:03:00Z\",\"WARC-Record-ID\":\"<urn:uuid:2e678de3-2dff-4572-99f6-e464663c3099>\",\"Content-Length\":\"120777\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7a7ef2b-2984-4a7a-9857-07652efcba17>\",\"WARC-Concurrent-To\":\"<urn:uuid:000b88f3-8e5c-4cd7-98d2-4a0fa9f38af6>\",\"WARC-IP-Address\":\"68.70.205.1\",\"WARC-Target-URI\":\"https://www.omnicalculator.com/math/square-perimeter\",\"WARC-Payload-Digest\":\"sha1:RKXI2NIBEIG63QGD34WPMHK2MZYAQCMN\",\"WARC-Block-Digest\":\"sha1:4KNZFIJY6BPQ5S3FIM72FURFETNBDQHD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588526.57_warc_CC-MAIN-20211028193601-20211028223601-00666.warc.gz\"}"}
|
https://stacks.math.columbia.edu/tag/02CR
|
[
"Exercise 109.5.2. Find an injection $M_1 \\to M_2$ of $A$-modules such that $M_1\\otimes N \\to M_2 \\otimes N$ is not injective in the following cases:\n\n1. $A = k[x, y]$ and $N = (x, y) \\subset A$. (Here and below $k$ is a field.)\n\n2. $A = k[x, y]$ and $N = A/(x, y)$.\n\nIn your comment you can use Markdown and LaTeX style mathematics (enclose it like $\\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar)."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7831614,"math_prob":0.9994966,"size":270,"snap":"2021-43-2021-49","text_gpt3_token_len":111,"char_repetition_ratio":0.116541356,"word_repetition_ratio":0.12,"special_character_ratio":0.43333334,"punctuation_ratio":0.16176471,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9992886,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T05:17:47Z\",\"WARC-Record-ID\":\"<urn:uuid:86a62bd0-4cc0-4e72-bb14-e6ad6accaac6>\",\"Content-Length\":\"13641\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:72eb23be-274f-45a9-bace-17e058aeb1ff>\",\"WARC-Concurrent-To\":\"<urn:uuid:42d0410c-de96-435a-bf16-8a8b218592b7>\",\"WARC-IP-Address\":\"128.59.222.85\",\"WARC-Target-URI\":\"https://stacks.math.columbia.edu/tag/02CR\",\"WARC-Payload-Digest\":\"sha1:CLHNMSO5WOSZ5VVDJRSRIPKMYDNJYSHS\",\"WARC-Block-Digest\":\"sha1:M4RI54LP6JSI62XBO6JQNYY25CUXGJQD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363135.71_warc_CC-MAIN-20211205035505-20211205065505-00312.warc.gz\"}"}
|
https://martinkysel.com/hackerrank-sherlock-and-the-valid-string-solution/
|
[
"# HackerRank 'Sherlock and The Valid String' Solution\n\nMartin Kysel · September 19, 2018\n\n##### Short Problem Definition:\n\nSherlock considers a string to be valid if all characters of the string appear the same number of times. It is also valid if he can remove just 1 character at 1 index in the string, and the remaining characters will occur the same number of times. Given a string , determine if it is valid. If so, return `YES`, otherwise return `NO`.\n\nSherlock and The Valid String\n\n##### Complexity:\n\ntime complexity is `O(N)`\n\nspace complexity is `O(N)`\n\n##### Execution:\n\nThis is one of the easier medium problems. Create a character occurrence map. Then create an occurrence-occurrence map. If all the occurrences are the same (size is 1) the string is valid. If there is exactly one character that occurs exactly once, it is also valid. Otherwise invalid\n\n##### Solution:\n``````\ndef isValid(S):\nchar_map = Counter(S)\nchar_occurence_map = Counter(char_map.values())\n\nif len(char_occurence_map) == 1:\nreturn True\n\nif len(char_occurence_map) == 2:\nfor v in char_occurence_map.values():\nif v == 1:\nreturn True\n\nreturn False\n``````"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7418057,"math_prob":0.9549566,"size":966,"snap":"2023-40-2023-50","text_gpt3_token_len":228,"char_repetition_ratio":0.14033264,"word_repetition_ratio":0.013157895,"special_character_ratio":0.23291926,"punctuation_ratio":0.13513513,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9581517,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-07T04:13:02Z\",\"WARC-Record-ID\":\"<urn:uuid:38d438fa-ee1e-4b9c-a299-c0f9ba1a1e56>\",\"Content-Length\":\"10001\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2d3393e9-4921-4ced-afaf-767233ff4c08>\",\"WARC-Concurrent-To\":\"<urn:uuid:6a79adc5-051a-49b9-af03-5bc309cb6829>\",\"WARC-IP-Address\":\"185.199.109.153\",\"WARC-Target-URI\":\"https://martinkysel.com/hackerrank-sherlock-and-the-valid-string-solution/\",\"WARC-Payload-Digest\":\"sha1:PQN253FLIOYSLQGQFY344RJ5M7QSTQUT\",\"WARC-Block-Digest\":\"sha1:2QJJJCXEMSPCGZODPBTNSGXGXUVH2ITD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100632.0_warc_CC-MAIN-20231207022257-20231207052257-00589.warc.gz\"}"}
|
https://betterlesson.com/lesson/494390/asymptotic-behavior-day-1-of-2?from=mtp_lesson
|
[
"# Asymptotic Behavior, Day 1 of 2\n\n1 teachers like this lesson\nPrint Lesson\n\n## Objective\n\nSWBAT describe the behavior of a rational function in terms of vertical and horizontal asymptotes.\n\n#### Big Idea\n\nRational functions are asymptotic because strange things happen when you divide by very large or very small numbers.\n\n## What have we seen?\n\n15 minutes\n\nClass will begin with a summary discussion to evaluate our progress so far. I'll simply have students share out their thoughts and describe things they've noticed, but I'll direct the conversation toward the three main points listed below.\n\n\"We have been studying rational equations and their graphs for some time now. What have we seen?\"\n\n1. End Behavior: Graphs of rational functions often approach a horizontal asymptote. Numerically, this means that the value of the functions seems to get closer and closer to some fixed number as the value of x gets larger and larger.\n2. Discontinuity: Graphs of rational functions are often broken into separate branches. The discontinuities are sometimes a single point (removable) and sometimes a vertical asymptote.\n3. Symmetry: The branches of the graph of a rational function are often symmetrical in some way.\n\nToday, we will focus on the two types of asymptotes: vertical & horizontal. Specifically, our goal is to explain how these asymptotes can be identified simply by examining the equation. (MP 7) This is a (+) standard in the Common Core, but I think it's an important one for my students. See this video to hear why.\n\n## Making Predictions Based on Structure\n\n30 minutes\n\nHandout the worksheet Asymptotic Behavior.\n\nThe purpose of this problem set is to help students identify the ways that the structure of a rational function can help them predict its behavior. Students will investigate a number of different functions and record either the presence or absence of asymptotes, as well as the equations for those asymptotes. By studying the data, they should be able to come up with some general rules (MP 7). Since students will not work at the same pace, I will have them begin individually, but move into groups of three after about 10 minutes.\n\nFirst, they should identify points of discontinuity by factoring the denominator.\n\nSecond, they should determine whether the function has the form 0/0 or #/0 at those points.\n\nThird, for any points at which the function is 0/0, they should simplify the function and re-evaluate. Wherever the function is #/0 in its simplified form, there is a vertical asymptote.\n\nFourth, they should compare the highest-degree terms in the numerator and denominator. These terms will not only indicate the presence of a horizontal asymptote, but also its value.\n\nIn order to make this as efficient as possible, all the students should have graphing calculators. Alternatively, you could give each student a copy of Graphs for Asymptotic Behavior and give them the additional task of matching each function to its graph.\n\n## Wrapping Up\n\n5 minutes\n\nIn most cases, the class is going to need more time to complete the investigation and draw out the associated patterns. As class draws to an end, I'll make a note of how much progress most students have made. For homework, I'll ask everyone to complete one more row of their table. They should come to back to class tomorrow ready to show what they did on their own and compare their answers to those of their peers."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.96184593,"math_prob":0.8953681,"size":2445,"snap":"2019-26-2019-30","text_gpt3_token_len":507,"char_repetition_ratio":0.12453912,"word_repetition_ratio":0.0,"special_character_ratio":0.20245399,"punctuation_ratio":0.09913793,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.950806,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-16T06:11:31Z\",\"WARC-Record-ID\":\"<urn:uuid:e5aa2d65-6ed2-4dbc-a5d7-3a46fc7401e3>\",\"Content-Length\":\"104205\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:58244463-d378-42e0-b6c4-e3058f2f8a05>\",\"WARC-Concurrent-To\":\"<urn:uuid:7a0efec6-01d2-4b66-a32e-cdc992c6aec5>\",\"WARC-IP-Address\":\"107.21.10.124\",\"WARC-Target-URI\":\"https://betterlesson.com/lesson/494390/asymptotic-behavior-day-1-of-2?from=mtp_lesson\",\"WARC-Payload-Digest\":\"sha1:CJC6LB66HP4BZ6HY3HOGSHEWOGB23777\",\"WARC-Block-Digest\":\"sha1:IRE2YYM5NZIRFGGF6MF67XA7IE4Q6P3Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195524503.7_warc_CC-MAIN-20190716055158-20190716081158-00515.warc.gz\"}"}
|
https://programmer.help/blogs/5e46c30cd2860.html
|
[
"# softmax regression\n\n## 1, Get fashion MNIST training set and read data\n\nHere we will use the torch vision package, which serves the PyTorch deep learning framework and is mainly used to build the computer vision model.\n-Torch vision is mainly composed of the following parts:\nTorch vision. Models: including common model structures (including pre training models), such as AlexNet, VGG, ResNet, etc;\ntorchvision.transforms: commonly used image transformations, such as clipping, rotation, etc;\ntorchvision.utils: some other useful methods.\n\n#### 1.import package\n\n```# import needed package\n%matplotlib inline\nfrom IPython import display\nimport matplotlib.pyplot as plt\n\nimport torch\nimport torchvision\nimport torchvision.transforms as transforms\nimport time\n\nimport sys\nsys.path.append(\"/home/kesci/input\")\nimport d2lzh1981 as d2l\n\nprint(torch.__version__)\nprint(torchvision.__version__)\n```\n\n#### 2. get dataset\n\n```mnist_train = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True, transform=transforms.ToTensor())\n\n```\n\nRoot (string) - the root directory of the dataset, which holds the processed/training.pt and processed/test.pt files.\ntrain (bool, optional) - if set to True, create the dataset from training.pt, otherwise from test.pt.\nTransform (callable, optional) - a function or transform that inputs a PIL picture and returns the transformed data. For example: transforms.RandomCrop.\nTarget? Transform (callable, optional) - a function or transform that inputs a target and transforms it.\n\n```# show result\nprint(type(mnist_train))\nprint(len(mnist_train), len(mnist_test))\n```\n\n<class 'torchvision.datasets.mnist.FashionMNIST'>\n60000 10000\n\n```# We can access any sample by subscript\nfeature, label = mnist_train\nprint(feature.shape, label) # Channel x Height x Width\n```\n\nIf the input data without transformation is an image, we can see the type parameters of the image:\n\n```mnist_PIL = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True)\nPIL_feature, label = mnist_PIL\nprint(PIL_feature)\n```\n\n<PIL.Image.Image image mode=L size=28x28 at 0x7F57E8736F28>\n\n```# This function has been saved in package d2lzh for later use\n#Role: convert labels to text\n#The text information corresponding to the label is returned (the text information is stored in the list of text_labels)\ndef get_fashion_mnist_labels(labels):\ntext_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',\n'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']\nreturn [text_labels[int(i)] for i in labels]\n```\n```#Make a data set presentation\ndef show_fashion_mnist(images, labels):\nd2l.use_svg_display()\n# Here \"UU\" means we ignore (do not use) variables\n_, figs = plt.subplots(1, len(images), figsize=(12, 12))\nfor f, img, lbl in zip(figs, images, labels):\nf.imshow(img.view((28, 28)).numpy())\nf.set_title(lbl)\nf.axes.get_xaxis().set_visible(False)\nf.axes.get_yaxis().set_visible(False)\nplt.show()\n```\n```X, y = [], []\nfor i in range(10):\nX.append(mnist_train[i]) # Add the i th feature to X\ny.append(mnist_train[i]) # Add the i-th label to y\nshow_fashion_mnist(X, get_fashion_mnist_labels(y))\n```\n```# Read data\nbatch_size = 256\t#Batch size\ntrain_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)\ntest_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)\n```\n\nSee how long it took to get the data\n\n```start = time.time()\nfor X, y in train_iter:\ncontinue\nprint('%.2f sec' % (time.time() - start))\n```\n\n## 2, softmax from zero\n\n#### import packages\n\n```import torch\nimport torchvision\nimport numpy as np\nimport sys\nsys.path.append(\"/home/kesci/input\")\nimport d2lzh1981 as d2l\n\nprint(torch.__version__)\nprint(torchvision.__version__)\n```\n\n#### Get training data set and test data set\n\n```batch_size = 256\n```\n\n#### Model parameter initialization\n\n```num_inputs = 784\t#The input characteristic is 784, i.e. X has 28 * 28 elements\nprint(28*28)\nnum_outputs = 10\t#There are ten types of output\n#Next, define weights and deviations\nW = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float)\nb = torch.zeros(num_outputs, dtype=torch.float)\n```\n```#In order to facilitate the subsequent back propagation, two parameter gradients are given here\n```\n\n#### Operate by dimension on multi-dimensional Tensor\n\n```X = torch.tensor([[1, 2, 3], [4, 5, 6]])\nprint(X.sum(dim=0, keepdim=True)) # dim is 0, sum according to the same column, and retain the column characteristics in the result\nprint(X.sum(dim=1, keepdim=True)) # dim is 1, sum according to the same lines, and retain the line features in the result\nprint(X.sum(dim=0, keepdim=False)) # dim is 0, sum according to the same column, do not retain the column characteristics in the result\nprint(X.sum(dim=1, keepdim=False)) # dim is 1, sum according to the same lines, and do not retain the line features in the result\n```\n\nSum by line when dim = 1",
null,
"#### Define softmax operations",
null,
"```def softmax(X):\nX_exp = X.exp()\t\t\t\t#Exponential operation\npartition = X_exp.sum(dim=1, keepdim=True) \t#Sum after index operation as denominator\n# print(\"X size is \", X_exp.size())\n# print(\"partition size is \", partition, partition.size())\nreturn X_exp / partition # The broadcast mechanism is applied here\n```\n\nThe two commented sentences show the shape difference between X and partition, using the broadcast mechanism.\nThe results are as follows",
null,
"```X = torch.rand((2, 5))\nX_prob = softmax(X)\nprint(X_prob, '\\n', X_prob.sum(dim=1))\n```\n\n#### softmax regression model",
null,
"* the following parameter x is the input characteristic, so it is a row vector. It is transformed into a column vector through the view() function, which is convenient to multiply with the weight w, and then add with b, and pass it into the softmax function to get the output y_hat\n\n```def net(X):\nreturn softmax(torch.mm(X.view((-1, num_inputs)), W) + b)\n```\n\n#### Define loss function",
null,
"```y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\ny = torch.LongTensor([0, 2])\ny_hat.gather(1, y.view(-1, 1))\n```\n```def cross_entropy(y_hat, y):\nreturn - torch.log(y_hat.gather(1, y.view(-1, 1)))\n```\n\n#### Definition accuracy\n\nWhen our model is trained for model prediction, the accuracy defined here will be used.\n\n```def accuracy(y_hat, y):\nreturn (y_hat.argmax(dim=1) == y).float().mean().item()\n#Take the maximum value in Y hat by line and compare it with the value of the real label y. if it is the same, it is 1, and the difference is 0. Then add it up to get the average value\nprint(accuracy(y_hat, y))\n```\n```# This function has been saved in the d2lzh pytorch package for later use. This function will be improved step by step: its complete implementation will be described in the \"image augmentation\" section\ndef evaluate_accuracy(data_iter, net):\nacc_sum, n = 0.0, 0\nfor X, y in data_iter:\nacc_sum += (net(X).argmax(dim=1) == y).float().sum().item()\nn += y.shape\nreturn acc_sum / n\nprint(evaluate_accuracy(test_iter, net))\n```\n\n#### Training model\n\n```num_epochs, lr = 5, 0.1\n\n# This function has been saved in the d2lzh pytorch package for later use\ndef train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,\nparams=None, lr=None, optimizer=None):\nfor epoch in range(num_epochs):\ntrain_l_sum, train_acc_sum, n = 0.0, 0.0, 0\nfor X, y in train_iter:\ny_hat = net(X)\nl = loss(y_hat, y).sum()\n\nif optimizer is not None:\nelif params is not None and params.grad is not None:\nfor param in params:\n\nl.backward()\nif optimizer is None:\nd2l.sgd(params, lr, batch_size)\nelse:\noptimizer.step()\n\ntrain_l_sum += l.item()\ntrain_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()\nn += y.shape\ntest_acc = evaluate_accuracy(test_iter, net)\nprint('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'\n% (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))\n\ntrain_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, batch_size, [W, b], lr)\n```\n\n#### model prediction\n\nNow that our model has been trained, we can make a prediction. The accuracy of our model training is not accurate. Now you can demonstrate how to classify images. Given a series of images (the third line of image output), let's compare their real tags (the first line of text output) with the model prediction results (the second line of text output).\n\n```X, y = iter(test_iter).next()\n\ntrue_labels = d2l.get_fashion_mnist_labels(y.numpy())\npred_labels = d2l.get_fashion_mnist_labels(net(X).argmax(dim=1).numpy())\ntitles = [true + '\\n' + pred for true, pred in zip(true_labels, pred_labels)]\n\nd2l.show_fashion_mnist(X[0:9], titles[0:9])\n```\n\n## Simple implementation of softmax\n\n```# Loading various packages or modules\nimport torch\nfrom torch import nn\nfrom torch.nn import init\nimport numpy as np\nimport sys\nsys.path.append(\"/home/kesci/input\")\nimport d2lzh1981 as d2l\n\nprint(torch.__version__)\n```\n\n## Initialize parameters and get data\n\n```batch_size = 256\n\n```\n\n## Define network model\n\n```num_inputs = 784\nnum_outputs = 10\n\nclass LinearNet(nn.Module):\ndef __init__(self, num_inputs, num_outputs):\nsuper(LinearNet, self).__init__()\nself.linear = nn.Linear(num_inputs, num_outputs)\ndef forward(self, x): # Shape of x: (batch, 1, 28, 28)\ny = self.linear(x.view(x.shape, -1))\nreturn y\n\n# net = LinearNet(num_inputs, num_outputs)\n\nclass FlattenLayer(nn.Module):\ndef __init__(self):\nsuper(FlattenLayer, self).__init__()\ndef forward(self, x): # Shape of x: (batch, *, *,...)\nreturn x.view(x.shape, -1)\n\nfrom collections import OrderedDict\nnet = nn.Sequential(\n# FlattenLayer(),\n# LinearNet(num_inputs, num_outputs)\nOrderedDict([\n('flatten', FlattenLayer()),\n('linear', nn.Linear(num_inputs, num_outputs))]) # Or write it as our own defined linearnet (Num ﹣ inputs, num ﹣ outputs)\n)\n```\n\n## Initialize model parameters\n\n```init.normal_(net.linear.weight, mean=0, std=0.01)\ninit.constant_(net.linear.bias, val=0)\nParameter containing:\ntensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], requires_grad=True)\n\n```\n\n### Define loss function\n\n```loss = nn.CrossEntropyLoss() # Here is his function prototype\n# class torch.nn.CrossEntropyLoss(weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')\n```\n\n### Define optimization function\n\n```optimizer = torch.optim.SGD(net.parameters(), lr=0.1) # Here is the function prototype\n# class torch.optim.SGD(params, lr=, momentum=0, dampening=0, weight_decay=0, nesterov=False)\n```\n\n### train\n\n```num_epochs = 5\nd2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, optimizer)\n```",
null,
"",
null,
"Published 2 original articles, won praise 1, visited 15\n\nTags: IPython network\n\nPosted on Fri, 14 Feb 2020 10:55:13 -0500 by tjhilder"
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https://apache.googlesource.com/incubator-weex/+/refs/heads/release/0.24/weex_core/Source/include/wtf/SmallPtrSet.h
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[
"blob: da36c8da4d8ae74a15e39d1272a2ae1e4883fa3e [file] [log] [blame]\n /* * Copyright (C) 2016 Apple Inc. All Rights Reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #ifndef SmallPtrSet_h #define SmallPtrSet_h #include #include #include #include namespace WTF { template class SmallPtrSet { WTF_MAKE_NONCOPYABLE(SmallPtrSet); static_assert(std::is_trivially_destructible::value, \"We currently don't support non-trivially destructible pointer types.\"); static_assert(sizeof(PtrType) == sizeof(void*), \"Only support pointer sized things.\"); static_assert(!(SmallArraySize & (SmallArraySize - 1)), \"Inline size must be a power of two.\"); public: SmallPtrSet() { initialize(); } // We take care to have SmallPtrSet have partial move semantics allowable through // memcpy. It's partial move semantics because our destructor should not be called // on the SmallPtrObject in the old memory we were moved from (otherwise, we might free m_buffer twice) // unless that old memory is reset to be isSmall(). See move constructor below. // To maintain these semantics, we determine if we're small by checking our size // and not our m_buffer pointer. And when we're small, we don't do operations on // m_buffer, instead, we perform operations on m_smallStorage directly. The reason we want // these semantics is that it's beneficial to have a Vector that contains SmallPtrSet // (or an object with SmallPtrSet as a field) be allowed to use memcpy for its move operation. SmallPtrSet(SmallPtrSet&& other) { memcpy(this, &other, sizeof(SmallPtrSet)); other.initialize(); } SmallPtrSet& operator=(SmallPtrSet&& other) { this->~SmallPtrSet(); new (this) SmallPtrSet(WTFMove(other)); return *this; } ~SmallPtrSet() { if (!isSmall()) fastFree(m_buffer); } inline void add(PtrType ptr) { ASSERT(isValidEntry(ptr)); if (isSmall()) { for (unsigned i = 0; i < m_size; i++) { if (m_smallStorage[i] == ptr) return; } if (m_size < SmallArraySize) { m_smallStorage[m_size] = ptr; ++m_size; return; } grow(std::max(64u, SmallArraySize * 2)); // Fall through. We're no longer small :( } // If we're more than 3/4ths full we grow. if (UNLIKELY(m_size * 4 >= m_capacity * 3)) { grow(m_capacity * 2); ASSERT(!(m_capacity & (m_capacity - 1))); } void** bucket = this->bucket(ptr); if (*bucket != ptr) { *bucket = ptr; ++m_size; } } inline bool contains(PtrType ptr) const { ASSERT(isValidEntry(ptr)); if (isSmall()) { for (unsigned i = 0; i < m_size; i++) { // We only need to search up to m_size because we store things linearly inside m_smallStorage. if (m_smallStorage[i] == ptr) return true; } return false; } void** bucket = this->bucket(ptr); return *bucket == ptr; } class iterator { public: iterator& operator++() { m_index++; ASSERT(m_index <= m_capacity); while (m_index < m_capacity && m_buffer[m_index] == emptyValue()) m_index++; return *this; } PtrType operator*() const { ASSERT(m_index < m_capacity); return static_cast(m_buffer[m_index]); } bool operator==(const iterator& other) const { ASSERT(m_buffer == other.m_buffer); return m_index == other.m_index; } bool operator!=(const iterator& other) const { ASSERT(m_buffer == other.m_buffer); return !(*this == other); } private: template friend class WTF::SmallPtrSet; unsigned m_index; unsigned m_capacity; void** m_buffer; }; iterator begin() const { iterator it; it.m_index = std::numeric_limits::max(); it.m_capacity = m_capacity; if (isSmall()) it.m_buffer = const_cast(m_smallStorage); else it.m_buffer = m_buffer; ++it; return it; } iterator end() const { iterator it; it.m_index = m_capacity; it.m_capacity = m_capacity; if (isSmall()) it.m_buffer = const_cast(m_smallStorage); else it.m_buffer = m_buffer; return it; } inline unsigned size() const { return m_size; } private: constexpr static void* emptyValue() { return bitwise_cast(std::numeric_limits::max()); } bool isValidEntry(const PtrType ptr) const { return ptr != emptyValue(); } inline bool isSmall() const { return m_capacity == SmallArraySize; } inline void initialize() { m_size = 0; m_buffer = nullptr; m_capacity = SmallArraySize; memset(m_smallStorage, -1, sizeof(void*) * SmallArraySize); ASSERT(isSmall()); } inline void grow(unsigned size) { ASSERT(static_cast(bitwise_cast(emptyValue())) == -1); size_t allocationSize = sizeof(void*) * size; bool wasSmall = isSmall(); void** oldBuffer = wasSmall ? m_smallStorage : m_buffer; unsigned oldCapacity = m_capacity; m_buffer = static_cast(fastMalloc(allocationSize)); memset(m_buffer, -1, allocationSize); m_capacity = size; for (unsigned i = 0; i < oldCapacity; i++) { if (oldBuffer[i] != emptyValue()) { void** ptr = this->bucket(static_cast(oldBuffer[i])); *ptr = oldBuffer[i]; } } if (!wasSmall) fastFree(oldBuffer); } inline void** bucket(PtrType target) const { ASSERT(!(m_capacity & (m_capacity - 1))); unsigned bucket = PtrHashBase::hash(target) & (m_capacity - 1); unsigned index = 0; while (true) { void** ptr = m_buffer + bucket; if (*ptr == emptyValue()) return ptr; if (*ptr == target) return ptr; index++; bucket = (bucket + index) & (m_capacity - 1); } } unsigned m_size; unsigned m_capacity; void** m_buffer; void* m_smallStorage[SmallArraySize]; }; } // namespace WTF using WTF::SmallPtrSet; #endif // SmallPtrSet_h"
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[
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https://www.hindawi.com/journals/mpe/2016/6146195/
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[
"Research Article | Open Access\n\nVolume 2016 |Article ID 6146195 | 7 pages | https://doi.org/10.1155/2016/6146195\n\n# CFD Study of Liquid Sodium inside a Wavy Tube for Laminar Convectors: Effect of Reynolds Number, Wave Pitch, and Wave Amplitude\n\nRevised25 Sep 2016\nAccepted12 Oct 2016\nPublished07 Nov 2016\n\n#### Abstract\n\nMetallic tubes have been widely used as primary heat transfer elements in laminar convectors for domestic and aerospace heating purpose. This paper uses CFD tool to investigate the heat output and pressure drop of liquid sodium flowing inside a circular tube having a wavy profile throughout its length. The wavy tube can be utilized in laminar liquid metal convectors as basic heat transfer element. The effect of Reynolds number () wave pitch () and wave amplitude () on the heat output and pressure drop has been numerically studied. Based on the CFD results important controlling parameters have been identified and it is concluded that the heat output from the wavy tube is affected by the wave pitch and the wave amplitude while the pressure drop is mostly affected by the Reynolds number and wave amplitude.\n\n#### 1. Introduction\n\nLaminar flows involve several attractive features like low thermodynamic and hydrodynamic irreversibility, silent and vibration-free operation and longer life and greater reliability, Doty et al. . Another important feature of laminar flows is that the equations of motion (i.e., the Navier-Stokes equations for fluid dynamics) do not involve any time averaging technique like the turbulent flows, which ultimately makes the numerical results pertaining to this class of fluid motion directly and more reliably applicable to engineering designs. For instance, Kays numerically studied the heat transfer in laminar flows inside circular tube, Ko numerically studied the entropy generation and optimum Reynolds number for laminar developing flow inside double sine ducts, Chen and Chiou studied the heat transfer in the entrance region of a laminar liquid metal pipe flow, Sahin and Mansour numerically studied entropy generation in laminar fluid flow inside a circular pipe, Mehdi and Choi performed CFD study of liquid sodium within thermally developing region under laminar flow, Gedik et al. utilized CFD to study the laminar magnetohydrodynamics flow of liquid metal inside a circular tube, and Makinde and Eegunjobi numerically studied the effects of convective heating on entropy generation for laminar flow inside a channel with permeable walls. It is important to mention that in laminar flows the convective effects are low which places limit on heat and mass transport; however, the transport of heat in laminar flows can be augmented by utilizing several alternatives which includes the use of low Prandtl number fluids such as liquid metals , the use of nanofluids as indicated by the work of Yang et al. , and increase in heat transfer area as indicated by the work of Kim et al. .\n\nConsequently laminar flows can become useful for domestic and aerospace heating applications. In fact, there exist many interesting heat exchanger design concepts that are based on laminar fluid flow; for instance, Stignor presented the concept of laminar flat tube heat exchangers; Miner and Ghoshal studied liquid metals as coolant for laminar microcoolers; similarly Tawk et al. investigated different design parameters for microcoolers to be exploited in electronic cooling; Lin et al. investigated the performance of a laminar heat pipe heat exchanger; Iqbal and Syed presented the concept of laminar finned double-pipe heat exchanger; Saji et al. developed a compact laminar microtube heat exchanger; Sagnik and Saha presented the concept of utilizing simultaneously transverse corrugations and twisted tape inserts in a circular tube for augmenting the convective laminar heat transfer, whereas Sui et al. investigated laminar flow and heat transfer in wavy microchannels.\n\nBased on the extensive use of laminar flows in different types of heat exchangers, here we present the concept of wavy tube as basic heat transfer element for laminar convectors which can be used in domestic and aerospace heating applications. In this paper computational fluid dynamics approach has been used to investigate the performance (heat output and pressure drop) of the wavy tube operating under fixed set of convective boundary condition for ambient air. The length of the tube is such that the flow always remains hydrodynamically developing. Also in this study liquid sodium is used as a heat transfer fluid since liquid metals due to their high molecular heat conduction can enhance the heat transport in laminar flows.\n\n#### 2. Fabrication of Wavy Tube\n\nA possible fabrication technique for the wavy tube is depicted schematically in Figures 1(a)1(d). The process starts with splitting a tube of desired diameter in longitudinal direction. One half of the tube is then clamped within a set of die that is designed on the basis of desired wave parameters (wave pitch and amplitude). With the application of external force the desired profile can be impregnated on the tube. The other half of the tube is then processed in similar manner and finally the two halves can be joined together by using a suitable joining process such as fusion welding. The geometry of the tube with different waviness profile (i.e., different values of wave pitch and amplitude) was built using the readymade geometry features available in the graphic user interface (GUI) of the COMSOL Multiphysics software. Thus the different wavy profiles were generated in a way that the flow radius increases and decreases by an amount equal to the wave amplitude on either side of the base radius. The value of the base radius was kept constant at 13 mm. The shape of the waves remains like a portion of a smooth circular arc as seen in Figure 1(d).\n\n#### 3. Problem Formulation\n\nSteady hydrodynamically developing laminar flow of liquid sodium was studied inside a wavy tube for different values of and (see Figure 1(d)). The diameter of the tube was kept constant at 26 mm with an axial length of 0.55 m. The simulated Reynolds number range was 500 to 2000. It is well known that for steady laminar flows the hydrodynamic developing length can be estimated by the equation (), where is the hydrodynamic developing length of the flow, is the diameter of the tube, and is the Reynolds number . According to the above equation the developing length of the problem under consideration remains larger than the length of the tube considered in this study which means that the flow always remains hydrodynamically developing. Since the geometry under consideration is axisymmetric, the governing equations, that is, (1)–(3), were numerically solved for half of the computational domain using a finite element commercial code COMSOL Multiphysics.Equation (1) is the famous Navier-Stokes equation for fluid motion which solves for the velocity and pressure field within the flow domain, (2) is the continuity equation (conservation of mass) for an incompressible fluid, and lastly (3) is the energy equation used to calculate the temperature field. In (1) is the fluid density, is the velocity vector (composed of the axial and radial velocity components), is the del operator of vector calculus, is the pressure of the fluid, is the identity matrix, is the dynamic viscosity of the fluid, indicates transpose of the matrix, and is the body force such as gravity. Also in (3) , , and represent the specific heat, temperature, and thermal conductivity of the working fluid, respectively. The different thermophysical properties of liquid sodium were estimated at the inlet temperature () in Kelvin from the following :After obtaining the complete solution (i.e., the velocity, pressure, and temperature field) the heat output and the pressure drop were calculated by using (5) and (6), respectively.In (5) represents the heat output from the wavy tube and is calculated as the surface integral of the radial conductive heat flux at the wall where is the radial coordinate. Also in (6) represents the pressure drop along the wavy tube and is the pressure distribution at the inlet of the tube.\n\n#### 4. Computational Details\n\nCOMSOL Multiphysics was used to solve the governing partial differential equations, that is, (1)–(3), within the computational domain. It is to be noted that the present problem is a coupled multiphysics fluid flow problem; therefore, direct PARDISO solver was used which treats the problem as coupled and highly nonlinear. The convergence criterion for all solution variables was set to 10−5. Both the stream line and cross wind stabilization techniques were used as these stabilization techniques are important for finite element based fluid dynamics simulations. The cross wind stabilization parameter was set to 0.1. Second-order Lagrange elements were used for the velocity and temperature variables while linear Lagrange elements were used for the pressure variable. The Lagrange elements approximate the solution variables with a piecewise polynomial function on each element of the grid. Further information on the finite element methods can be retrieved from [21, 22].\n\nFor the present study, the (where is the radius of the tube) criterion for laminar flows was used to design the grid . The criterion states that the height of the wall adjacent element must be less than or equal to the ratio . However, in order to properly resolve the boundary layer, approximately 5 elements were embedded within a small height of adjacent to the tube wall. The part of the grid near the wall is shown in Figure 2(a) which shows that presence of 5 elements within a height of 0.342 mm, while Figure 2(b) shows the overall and the magnified view of the grid used for the simulations. It can be noticed from Figure 2(b) that structured quadrilateral grid was used with grid density being larger near the solid wall. The grid independency of the final results (i.e., the heat output and the pressure drop) was confirmed by running the simulations at three different grid densities (4800, 9600, and 19200 elements). Figures 3(a) and 3(b) indicate that no substantial deviation exists between the three grids which highlights the grid independency of the computed results.\n\nFor the fluid dynamics part of the problem, a uniform velocity based on the flow Reynolds number was defined at the inlet () of the tube. No slip condition () was applied at the solid, nonporous, and stationary wall of the tube and zero gage pressure (i.e., = ) was applied at the outlet. For the heat transfer part, at the inlet, a uniform temperature ( = 105°C) was defined. At the wall a convection condition ()), where is the convective heat flux and is the temperature of the wall, was assumed with a fixed heat transfer coefficient of = 10 W/m2K for still air and an ambient air temperature of = 25°C. At the outlet, convective flow was assumed which mathematically states zero temperature gradient at the exit boundary (). The initial condition for the fluid flow in the entire domain was set to a uniform velocity that was equal to the inlet velocity and zero gage pressure, while for the heat transfer it was uniform temperature equal to the inlet temperature.\n\n#### 5. Results and Discussions\n\nFigure 4 indicates that at any given value of and the increase in the heat output with the Re is not significant; therefore, at particular ambient conditions the wave pitch and amplitude are the only important parameters that affect the heat output from the wavy tube. Consequently, Figure 5 shows that the normalized heat output increases if decreases and increases. Decreasing the pitch and increasing the amplitude increase the effective length of the tube which means increase in the overall heat transfer area. This increase in the heat transfer area is the main cause of the enhanced heat output from the wavy tube. For the case of = 25 mm and = 6 mm the heat transfer area increases by 48% which causes an increase of approximately 46% in the heat output as compared to the plane circular tube of same dimensions (see Figure 5). As an example of space heating, 50 wavy-peristaltic tubes having = 25 mm and = 6 mm combined together in form of a laminar convector can increase the temperature of air inside m3 room from 10°C to 22°C in just 60 minutes. On the other hand decreasing and increasing cause the pressure drop across the tube to increase. This effect is shown in Figure 6. From Figure 6 it can also be seen that, unlike the heat output, this time Re also has significant effect on the pressure drop. Figure 7 represents the typical streamline patterns within the diverging or bulge part of the wavy tube. The streamline pattern confirms the presence of circulation within the diverging part of the wavy tube. It can be observed that the size of the circulation zone increases as the wave amplitude increases. The presence of circulation also indicates adverse pressure gradient effects which is also the reason of high overall pressure drop for the wavy tube. It is worth mentioning that streamline patterns indicating circulation within the diverging parts of the wavy tube were also identified in the works of Kim et al. and Yang et al. .\n\nIt is to be noted that high thermal conductivity of liquid sodium is capable of counterbalancing the low convective effects of a laminar flow; therefore, it is possible to operate wavy tubes at low Re in order to reduce the pressure drop across the tube and at the same time increase the heat output by reducing and increasing . For instance, at = 25 mm and = 6 mm, the pressure drop across the tube at Re = 2000 is 35 Pa; however, if Re is reduced to 500 the pressure drop reduces to 3.7 Pa (i.e., 89% reduction in the pressure drop) with only 3.4% reduction in the heat output of the tube. From Figure 6 it can also be noticed that compared to the wave pitch the wave amplitude has a more prominent effect on the pressure drop.\n\nBased on the above results, it can be concluded that Re and are the controlling parameters for optimizing the pressure drop across the wavy tube, whereas the heat output can be optimized by controlling and independent of Re.\n\nSince, from Figure 5, it is evident that the heat output increases if decreases and increases, further simulations were performed to study the effect of heat transfer coefficient and the temperature of the ambient air on the exit temperature of sodium at Re = 500, = 25 mm, and = 6 mm. It was found that with an inlet temperature of 105°C the exit temperature of liquid sodium always remains above its melting point of 97.8°C for all values of W/m2K and 0°C. Therefore, Figure 8 depicts the variation of exit sodium temperature and the heat output as a function of . From Figure 8 it can be concluded that the exit temperature of sodium remains higher and almost constant with the variation in whereas the heat output decreases as increases; however, this decrease is only less than 10% and therefore remains insignificant for the type of thermal system studied in this work.\n\n#### 6. Conclusions\n\nIn summary, effect of Reynolds number Re, wave amplitude , and wave pitch is studied numerically for flow of liquid sodium under laminar developing flow regime inside a wavy tube. It was found that the Reynolds number has insignificant effect on the heat output and can be ignored making the wave pitch and wave amplitude the controlling parameters for the optimization of the heat output. On the other hand, the pressure drop across the wavy tube is mostly affected by the Reynolds number and the wave amplitude. It is demonstrated that the wavy tube under the studied flow regime can be used as efficient heat transfer elements in laminar convectors for domestic and aerospace heating applications.\n\n#### Competing Interests\n\nThe authors declare that they have no competing interests.\n\n#### Acknowledgments\n\nThe authors would like to thank the governing authorities at the NED University of Engineering and Technology, Pakistan, King Abdulaziz University, Saudi Arabia, and Jeju National University, South Korea, for their sincere support.\n\n1. F. D. Doty, G. Hosford, J. D. Jones, and J. B. Spitzmesser, “A laminar-flow heat exchanger,” in Proceedings of the 25th Intersociety Energy Conversion Engineering Conference (IECEC '90), vol. 4, pp. 1–7, Reno, Nev, USA, August 1990. View at: Google Scholar\n2. W. M. Kays, “Numerical solutions for laminar flow heat transfer in circular tubes,” Transactions of the ASME Journal of Heat Transfer, vol. 77, pp. 1265–1272, 1955. View at: Google Scholar\n3. T. H. Ko, “Analysis of optimal Reynolds number for developing laminar forced convection in double sine ducts based on entropy generation minimization principle,” Energy Conversion and Management, vol. 47, no. 6, pp. 655–670, 2006. View at: Publisher Site | Google Scholar\n4. J. C. Chen and J. S. Chiou, “Laminar and turbulent heat transfer in the pipe entrance region for liquid metals,” International Journal of Heat and Mass Transfer, vol. 24, pp. 1179–1189, 1981. View at: Publisher Site | Google Scholar\n5. A. Z. Sahin and B. R. Mansour, “Entropy generation in laminar fluid flow through a circular pipe,” Entropy, vol. 5, no. 5, pp. 404–416, 2003. View at: Publisher Site | Google Scholar\n6. S. M. Mehdi and K. H. Choi, “Heat transfer coefficient for liquid sodium in developing laminar flow regime,” in Proceedings of the International Conference on Energy and Sustainability, vol. 1, pp. 157–160, Karachi, Pakistan, 2013. View at: Google Scholar\n7. E. Gedik, H. Kurt, and Z. Recebli, “CFD simulation of magnetohydrodynamic flow of a liquid-metal galinstan fluid in circular pipes,” Fluid Dynamics and Materials Processing, vol. 9, no. 1, pp. 23–33, 2013. View at: Publisher Site | Google Scholar\n8. O. D. Makinde and A. S. Eegunjobi, “Effects of convective heating on entropy generation rate in a channel with permeable walls,” Entropy, vol. 15, no. 1, pp. 220–233, 2013. View at: Publisher Site | Google Scholar | MathSciNet\n9. Y.-T. Yang, Y.-H. Wang, and P.-K. Tseng, “Numerical optimization of heat transfer enhancement in a wavy channel using nanofluids,” International Communications in Heat and Mass Transfer, vol. 51, pp. 9–17, 2014. View at: Publisher Site | Google Scholar\n10. Y. J. Kim, M. Kim, S. Kim, J. K. Min, and M. Y. Ha, “Numerical study of fluid flow and convective heat transfer characteristics in a sinusoidal wavy circular tube,” Journal of Mechanical Science and Technology, vol. 30, no. 3, pp. 1185–1196, 2016. View at: Publisher Site | Google Scholar\n11. C. H. Stignor, Laminar-flow liquid-to-air heat exchangers energy-efficient display cabinet applications [Ph.D. thesis], Lund University, Lund, Sweden, 2009.\n12. A. Miner and U. Ghoshal, “Cooling of high-power-density microdevices using liquid metal coolants,” Applied Physics Letters, vol. 85, no. 3, pp. 506–508, 2004. View at: Publisher Site | Google Scholar\n13. M. Tawk, Y. Avenas, A. Lebouc, and M. Petit, “Numerical study of a liquid metal mini-channel cooler for power semiconductor devices,” in Proceedings of the 17th International Workshop on Thermal Investigations of ICs and Systems (THERMINIC '11), pp. 120–125, Paris, France, September 2011. View at: Google Scholar\n14. W. K. Lin, K. C. Liaw, M. Z. Tsai, and M. G. Chu, “Heat transport study of the laminar heat pipe heat exchanger,” Smart Grid and Renewable Energy, vol. 3, no. 4, pp. 348–354, 2012. View at: Publisher Site | Google Scholar\n15. M. Iqbal and K. S. Syed, “Analysis of thermally developing laminar convection in the finned double-pipe heat exchanger,” Heat Transfer Research, vol. 45, no. 1, pp. 1–21, 2014. View at: Publisher Site | Google Scholar\n16. N. Saji, S. Nagai, K. Tsuchiya, H. Asakura, and M. Obata, “Development of a compact laminar flow heat exchanger with stainless steel micro-tubes,” Physica C: Superconductivity, vol. 354, no. 1–4, pp. 148–151, 2001. View at: Publisher Site | Google Scholar\n17. P. Sagnik and S. K. Saha, “Laminar flow and heat transfer through a circular tube having integral transverse corrugations and fitted with centre-cleared twisted-tape,” Experimental Thermal and Fluid Science, vol. 57, pp. 388–395, 2014. View at: Publisher Site | Google Scholar\n18. Y. Sui, C. J. Teo, P. S. Lee, Y. T. Chew, and C. Shu, “Fluid flow and heat transfer in wavy microchannels,” International Journal of Heat and Mass Transfer, vol. 53, no. 13-14, pp. 2760–2772, 2010. View at: Publisher Site | Google Scholar\n19. N. E. Todreas and M. S. Kazimi, Nuclear Systems I: Thermal Hydraulic Fundamentals, Taylor & Francis, New York, NY, USA, 2nd edition, 1993.\n20. V. Sobolev, “Database of thermophysical properties of liquid metal coolants for GEN-IV,” Scientific Report SCK.CEN-BLG-1069, 2010. View at: Google Scholar\n21. R. W. Lewis, P. Nithiarasu, and K. N. Seetharamu, Fundamentals of the Finite Element Method for Heat and Fluid Flow, John Wiley & Sons, London, UK, 2003.\n22. COMSOL Multiphysics Version 3.5a, Reference Guide, 2008.\n23. M. Sahu, K. K. Khatua, K. C. Patra, and T. Naik, “Developed laminar flow in pipe using computational fluid dynamics,” in Proceedings of the 7th International R&D Conference on Development and Management of Water and Energy Resources, Bhubaneswar, India, February 2009. View at: Google Scholar\n\nWe are committed to sharing findings related to COVID-19 as quickly and safely as possible. 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https://file.scirp.org/Html/5-1100394_52614.htm
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" Accuracy and Computational Cost of Interpolation Schemes While Performing N-Body Simulations\n\nAmerican Journal of Computational Mathematics\nVol.04 No.05(2014), Article ID:52614,8 pages\n10.4236/ajcm.2014.45037\n\nAccuracy and Computational Cost of Interpolation Schemes While Performing N-Body Simulations\n\nShafiq Ur Rehman1,2\n\n1Department of Mathematics, The University of Auckland, Auckland, New Zealand\n\n2Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan",
null,
"",
null,
"",
null,
"Received 31 October 2014; revised 28 November 2014; accepted 15 December 2014\n\nABSTRACT\n\nThe continuous approximations play a vital role in N-body simulations. We constructed three different types, namely, one-step (cubic and quintic Hermite), two-step, and three-step Hermite interpolation schemes. The continuous approximations obtained by Hermite interpolation schemes and interpolants for ODEX2 and ERKN integrators are discussed in this paper. The primary focus of this paper is to measure the accuracy and computational cost of different types of interpolation schemes for a variety of gravitational problems. The gravitational problems consist of Kepler’s two-body problem and the more realistic problem involving the Sun and four gas-giants―Jupiter, Saturn, Uranus, and Neptune. The numerical experiments are performed for the different integrators together with one-step, two-step, and three-step Hermite interpolation schemes, as well as the interpolants.\n\nKeywords:\n\nN-Body Simulation, Integrators, Interpolation Schemes",
null,
"1. Numerical Integrators and Interpolants\n\nExplicit Runge-Kutta-Nyström methods (ERKN) were introduced by E. J. Nyström in 1925 . Here, we are using two variable-step-size ERKN integrators: Integrator ERKN689 is a nine stage, 6-8 FSAL pair and ERKN101217 is a seventeen stage, 10-12 non-FSAL pair . Dormand and Prince and then Baker et al. developed continuous approximation with embedded Runge-Kutta-Nyström methods, in which a third RKN pro- cess of order p* was used to approximate the solutions,",
null,
"and",
null,
", where",
null,
"with",
null,
"typically in (0, 1]. For ERKN101217, we used three existing interpolants: a 23-stage interpolant with",
null,
", a 26-stage interpolant with",
null,
", and a 29-stage interpolant with",
null,
". The coefficients for these interpolants are not tabulated in this paper but are freely available on-line . For ERKN689, we used an 8th-order interpolant with 12 stages. The coefficients for the continuous approximation of ERKN689 were provided by P. W. Sharp (private communication).\n\nFor the direct numerical approximation of systems of second-order ODEs, Hairer, Nørsett and Wanner developed an extrapolation code ODEX2 based on the explicit midpoint rule with order selection and step-size control. The ODEX2 integrator is good for all tolerances, especially for high arithmetic precision, for example, 1020 or 1030. For ODEX2 integrator we used the built-in interpolant.\n\nStörmer methods are an important class of numerical methods for solving systems of second-order ordinary differential equations. Störmer methods were introduced by Störmer . These methods have long been utilized for accurate long-term simulations of the solar system . Grazier recommended a fixed-step-size Störmer method of order 13 that used backward differences in summed form, summing from the highest to lowest differences. In this paper we consider an order-13, fixed-step-size Störmer method and refer to it as the",
null,
"integrator.\n\n1.1. Hermite Interpolation Schemes\n\nHermite interpolation uses derivative and function values and is named after Charles Hermite (1822-1901). We used four schemes: one-step (cubic and quintic Hermite), two-step and three-step Hermite interpolation schemes. The cubic Hermite interpolation polynomial is of degree 3, while the quintic, two-step and three-step Hermite interpolation polynomials are of degrees 5, 8 and 11, respectively. The interpolation schemes are derived using a Newton divided difference approach, which is described in Section 1.1.1. There is a second approach, which we call the direct approach that is frequently used by other researchers; for example, see . This approach is particularly suited for cubic and quintic Hermite interpolation schemes, and we describe it in Sections 1.1.2 and 1.1.3.\n\n1.1.1. Newton Divided Difference Approach\n\nTo determine the interpolating polynomial",
null,
"for the m points",
null,
",",
null,
", using the Newton divided difference (NDD) approach, we write",
null,
"as",
null,
"where the a’s are calculated from the divided differences. The ith divided difference can be calculated using",
null,
"see Table 1. We now discuss how the NDD must be modified when derivative values are used. Let us consider the first-order differences in Table 1. For example, if",
null,
"then we have",
null,
"Similarly, for the second-order differences in Table 1, if, for example, then we find\n\nHence, for Hermite interpolation schemes we can use the NDD approach if the derivatives replace the corresponding divided differences.\n\n1.1.2. Cubic Hermite Interpolation\n\nIn this section and the next, we describe the direct approach for obtaining the cubic and quintic Hermite polynomials. The cubic Hermite interpolation polynomial for the time-step from to interpolates the data and at time, for and 0. In the direct approach, the cubic Hermite interpolation polynomial is written as\n\nTable 1. An illustrative Newton divided difference table.\n\nwhere,\n\nand with. Since the values of y and at both ends of each step are interpolated, the piecewise defined approximation formed from the cubic Hermite polynomial is continuous and has a continuous first derivative.\n\n1.1.3. Quintic Hermite Interpolation\n\nThe quintic Hermite interpolation polynomial for the time-step from to interpolates the data, , and at time, for and 0. As for cubic Hermite interpolation, the quintic Hermite interpolation polynomial can be derived using a direct approach and written as\n\nwhere,\n\nand with, as before. Since the values of y, , and at both ends of each step are interpolated, the piecewise defined approximation formed from the quintic Hermite polynomial is continuous and has continuous first and second derivatives.\n\n1.1.4. Two-Step Hermite Interpolation Polynomial\n\nThe two-step Hermite interpolation polynomial for the two-time-steps from to interpolates the data, , and at time, with and 0. The two-step Hermite interpolation polynomial can then be written in Horner’s nested multiplication form as\n\nwhere the coefficients, , are obtained using a NDD table. Since the values of y, , and at both ends of each step are interpolated, the piecewise defined approximation formed from the two-step Hermite polynomial is continuous and has continuous first and second derivatives.\n\n1.1.5. Three-Step Hermite Interpolation Polynomial\n\nSimilarly, the three-step Hermite interpolation polynomial interpolates the data, , and at time, for and 0. Hence, it is the degree-11 polynomial defined over a three-time-step from to. Using Horner’s nested multiplication form, we can write as\n\nAs for the two-step Hermite interpolation polynomial, the coefficients, , of are obtained using NDD. Since the values of y, , and at both ends of each step are interpolated, the piecewise defined approximation formed from the three-step Hermite polynomial is continuous and has continuous first and second derivatives.\n\nWe compared the maximum error in position and the CPU-time for P3 and P5 evaluated using NDD and the direct approach. The comparison was done for one period of Kepler problem for eccentricities of 0.05 to 0.9 (see Section 2.1 for more details on the experiment), and the Jovian problem .\n\nFor the two-body problem, no significant differences in the maximum error as CPU-time were observed between these two approaches. For the Jovian problem, the direct approach takes approximately half the CPU-time of the NDD approach. The coefficients of the polynomial for the NDD approach depend on the components of the solution vector. For the direct approach the coefficients are independent of the components, so they can be used as a vector to approximate polynomials and that will save CPU-time.\n\nIn the rest of the paper, cubic and quintic Hermite interpolation schemes are implemented using the direct approach. For two-step and three-step Hermite interpolation schemes we implemented the NDD approach, because it is really difficult to find the coefficients for the direct approach.\n\n2. Numerical Experiments\n\nHere, we examine the error growth in the position and velocity for the Kepler problem. The experiments for short-term integrations are performed using four different types of interpolation schemes applied to the Kepler problem over the interval of 2π.\n\n2.1. Kepler Problem with Different Eccentricities\n\nThe solution to the Kepler problem is periodic with period 2π. We do not have to calculate the reference solution, so the Kepler problem is well suited for testing the accuracy of integration over a short time interval. This assumes the step-size is chosen so that is hit exactly.\n\nThe error in the position and velocity of the Kepler problem is given by the L2-norm\n\nwhere and are the vectors of the numerical and true solutions, and and are the vectors of the derivatives to the numerical and true solutions, respectively.\n\nThe graphs in Figure 1 are for experiments performed with the cubic, quintic, two-step, and three-step Hermite interpolation schemes applied to the Kepler problem over the interval for eccentricities in the range [0.05, 0.9]; note that, in reality, planets and test particles do not have eccentricity 0, and we used 0.05 as an approximate upper bound for the eccentricities of the Jovian planets. The selection of these interpolation schemes is motivated by the fact that they can be used with all the integrators described in this paper. The interpolants, on the other hand, are related to specific integrators; for example, the 12-stage interpolant can only be used with the ERKN689 integrator. For the experiments shown in Figure 1, the interval of integration is subdivided into 30 evenly spaced sub-intervals; experiments with different numbers of sub-intervals are recorded in Table 2. We then evaluate the position and velocity at 10 evenly spaced points on each sub-interval using different interpolation schemes. Note that we also tested with up to 100 sample points and observed a variation in the error of not more than 1%. The information, such as, positions, velocities, and times, are saved in separate files. In a post-processing step, we then calculate the errors in the positions and velocities with respect to the analytical solution that we obtain at the stored values of time. The velocity polynomials for all these interpolation schemes are obtained by differentiating their corresponding position polynomials.\n\nFrom Figure 1, we observe a clear pattern; as the eccentricity increases, the maximum error in the position also increases. The variation in the error is understandable, because the error depends upon the eccentricity. To illustrate this fact, recall that the analytical solution to the Kepler problem is given by\n\n(1)\n\nFigure 1. The maximum global error in position for the cubic, quintic, 2-step, and 3-step Hermite interpolation schemes against different eccentricities applied to the two-body problem over a period of 2π.\n\nTable 2. The maximum global error in position for eccentricity 0.05 attained by different interpolation schemes applied to the Kepler problem over the interval [0, 2π] with four choices of numbers of evenly spaced sub-intervals. The dash means the combination is not used.\n\nwhere is the eccentric anomaly satisfying and the interpolation error, for example, for the\n\ny1-component of this solution can be written as. The first three derivatives of y1 are\n\nIt is clear that these and all subsequent derivatives are expected to involve the factor. Since the minimum value of gets smaller and smaller as e increases, it is expected that the error increases as e increases; a similar argument holds for the y2-component. Indeed, for all interpolation schemes the minimum error in the position occurs at eccentricity 0.05 and the maximum error at eccentricity 0.9 in Figure 1. We also observe in Figure 1 that, for small eccentricity like e = 0.05, the difference in the errors between consecutive interpolation schemes is approximately two orders of magnitude. As e increases to 1, this difference decreases and all four errors in Figure 1 appear to converge. We also computed the error in the velocity and found that it is nearly two orders of magnitude larger than the error in the position. These experiments were also performed in quadruple-precision, but there was hardly any difference between the estimated errors obtained in double- and quadruple-precision. For example, using a 3-step interpolation scheme with eccentricity 0.05 and 0.9, the differences between the estimated errors in the position obtained in double- and quadruple-precision are 4.40 × 1015 and 1.67 × 1014, respectively. We conclude that the interpolation schemes are not affected a great deal by the round-off error when using 30 evenly spaced sub-intervals.\n\nAs mentioned earlier, the same sets of experiments described in Figure 1, were also done with different numbers of sub-intervals. We experimented with 17, 79, 255, and 1080 evenly spaced sub-intervals over the interval. The associated errors for e = 0.05 are shown in Table 2. This particular selection of the number of sub-intervals is due to the fact that we wish to maintain the best observed accuracy of the integrators ODEX2, ERKN101217, ERKN689, and; see and note that we use a time-step of 4 days for. For example, the ODEX2 integrator applied to the Jovian problem achieves best accuracy using tolerance 1016 and an average time-step of approximately 260 days over one million years. Since Jupiter’s orbital period is approximately 4320 Earth days, a time-step of 260 days gives approximately 17 steps.\n\nThe results in Table 2 show reasonably good agreement with the expected values calculated from the orders of the polynomial, discounting the possible increase in round-off error from using a higher-order interpolation scheme and a large number of sub-intervals. For example, using the cubic Hermite interpolation scheme, and going from 17 to 79 sub-intervals, the expected value is which has very good agreement with the value 0.15 × 1008 mentioned in Table 2.\n\nFrom Table 2 we find that the accuracy for a given interpolation scheme improves if the number of sub-in- tervals increases. We also deduce from Table 2 that it makes no sense to use any of the four interpolation schemes with ODEX2 if the required maximum global error is 1015 and 17 sub-intervals are used. For 79 sub- intervals (used for ERKN101217) only the 2-step and 3-step Hermite interpolation schemes achieve the required accuracy. Similarly, for ERKN689, the quintic and 2-step interpolation schemes achieve the required accuracy, whereas for the integrator, only the quintic Hermite interpolation scheme does.\n\n2.2. Computational Cost of Interpolation Schemes\n\nLet us now consider the CPU-time by looking at individual interpolation schemes. Our expectation, at least for the interpolation schemes, is that the CPU-time is proportional to the number of multiplications. If one interpolation scheme uses twice as many multiplications then the CPU-time is expected to be twice as large. There will not be many divisions, and the number of subtractions and additions is typically proportional to the number of multiplications. Normally, when timing a program, an overhead is introduced. Therefore, care has been taken not to include such overheads in the final results. We also checked reproducibility of the results and observed a maximum variation of not more than 2.5%.\n\nAs discussed earlier, there are two different approaches to form interpolation schemes. Here, the experiments are performed using a direct approach for cubic and quintic Hermite interpolation, and the Newton divided difference approach for 2-step and 3-step Hermite interpolation schemes. In most cases, interpolation schemes are split into two subroutines, one for finding the coefficients and one for evaluating the polynomials. For ERKN689 and ERKN101217, with the interpolants we have additional stage derivatives (function evaluations). Overall, we have three different groups of interpolation schemes:\n\n1) For cubic and quintic Hermite interpolation schemes, we evaluate the coefficients of the polynomial, which are independent of the components, and the polynomial as one subroutine.\n\n2) For 2-step and 3-step Hermite interpolation schemes, we have two subroutines:\n\na) The calculation of the coefficients by forming a Newton divided difference table;\n\nb) The evaluation of the polynomial.\n\n3) For the interpolants, we have three subroutines:\n\na) The evaluation of the coefficients;\n\nb) The evaluation of the additional stage derivatives;\n\nc) The evaluation of the polynomial using a) and b).\n\nFor ODEX2, the pieces of information required to form the interpolant are considered part of the integration, and we only consider the evaluation of the polynomial; see Table 5.\n\nSince the coefficients of the polynomials for cubic and quintic interpolations are independent of the components, the experiments for these interpolation schemes are performed as one unit. As can be seen from the formulae in Sections 1.1.2 and 1.1.3, the quintic Hermite interpolation scheme uses approximately 93% more multiplications than cubic Hermite interpolation when applied to the Jovian problem. When we did our experiment, we found that the quintic Hermite interpolation scheme uses approximately 96% more CPU-time than cubic Hermite interpolation, which is in good agreement with the expected value.\n\nTable 3 shows the CPU-time for finding the stage derivatives of the pairs (without the cost of additional stage derivatives) used in ERKN689 and ERKN101217 when applied to the Jovian problem. With ERKN689 we use the property FSAL (first same as last), so that we need only 8 derivative evaluations per step. Similarly, the 12-stage interpolant has effectively 11 stage derivatives. Observe from Table 3 that the average CPU-time consumed per stage is approximately 8.74 × 1007 and 8.71 × 1007 for ERKN689 and ERKN101217, respectively. Therefore, the expected CPU-time for ERKN689 with a 12-stage interpolant is approximately 9.61 × 1006. For ERKN101217, the expected CPU-time for finding coefficients is approximately 2.00 × 1005, 2.26 × 1005, and 2.52 × 1005 with 23-stage, 26-stage, and 29-stage interpolants, respectively.\n\nTable 4 gives the CPU time needed to find the coefficients of the interpolation schemes and evaluate all the derivatives for the interpolants when solving the Jovian problem. We observe that all values in Table 4 have reasonably good agreement with the prescribed values for CPU-time. Note also that the 3-step Hermite interpolation scheme in Table 4 uses approximately 96% more multiplications than the 2-step Hermite interpolation scheme, which is reasonably well matched by our finding of 93%.\n\nTable 5 shows the CPU-time for evaluating the position and velocity components using the different interpolation polynomials. The 3-step interpolation scheme uses approximately 76% more CPU-time than the 2-step interpolation, which is again in agreement with the CPU-times observed in Table 4. Similarly, the difference in\n\nTable 3. The CPU-time in seconds for evaluating the stage derivatives (without the cost of additional function evaluations) for ERKN689 and ERKN101217 applied to the Jovian problem.\n\nTable 4. The CPU-time in seconds for finding the coefficients of the interpolation schemes and evaluating all the stage derivatives of the interpolants applied to the Jovian problem.\n\nTable 5. The CPU-time in seconds for evaluating the position and velocity polynomials using different interpolation polynomials applied to the Jovian problem.\n\nCPU-time between the 23-stage and 29-stage interpolants is twice the difference between the 23-stage and 26- stage interpolants which is in good agreement with the difference observed in Table 4.\n\n3. Summary\n\nThe primary objective of this paper was to discuss the accuracy and computational cost of different interpolation schemes while performing N-body simulations. The interpolation schemes play a vital role in these kinds of simulations. We constructed three different types, namely, one-step (cubic and quintic Hermite), two-step and three-step Hermite interpolation schemes. For short-term simulations, we investigated the performance of these interpolation schemes applied to the Kepler problem over the interval [0, 2] for eccentricities in the range [0.05, 0.9]. We observed that the maximum error in position was monotonically increasing as a function of eccentricity. For a given number of sub-intervals we used in this paper, the higher-order interpolation schemes achieve better accuracy and for a given interpolation scheme the accuracy improves if the number of sub-intervals is increased. We also investigated the CPU-time by looking at individual interpolation schemes. Our expectation, at least for the interpolation schemes, was that the CPU-time was proportional to the number of multiplications. For example, the quintic Hermite interpolation scheme uses approximately 93% more multiplications than cubic Hermite interpolation when applied to the Jovian problem. When we did our experiment, we found that the quintic Hermite interpolation scheme used approximately 96% more CPU-time than cubic Hermite interpolation, which was in good agreement with the expected value. We also checked reproducibility of the results and observed a maximum variation of not more than 2.5%.\n\nAcknowledgements\n\nThe author is grateful to the Higher Education Commission (HEC) of Pakistan for providing the funding to carry out this research. Special thanks go to Dr. P. W. Sharp and Prof. H. M. Osinga for their valuable suggestions, discussions, and guidance throughout this research.\n\nCite this paper\n\nShafiq UrRehman,11, (2014) Accuracy and Computational Cost of Interpolation Schemes While Performing N-Body Simulations. American Journal of Computational Mathematics,04,446-454. doi: 10.4236/ajcm.2014.45037\n\nReferences\n\n1. 1. Nyström, E.J. (1925) &UUML;ber die numerische Integration von Differentialgleichungen. Acta Societatis Scientiarum Fennicae, 50, 1-54.\n\n2. 2. Dormand, J., El-Mikkawy, M.E.A. and Prince, P. (1987) Higher Order Embedded Runge-Kutta-Nyström Formulae. IMA Journal of Numerical Analysis, 7, 423-430.\nhttp://dx.doi.org/10.1093/imanum/7.4.423\n\n3. 3. Dormand, J.R. and Prince, P.J. (1987) New Runge-Kutta Algorithms for Numerical Simulation in Dynamical Astronomy. Celestial Mechanics, 18, 223-232.\nhttp://dx.doi.org/10.1007/BF01230162\n\n4. 4. Baker, T.S., Dormand, J.R. and Prince, P.J. (1999) Continuous Approximation with Embedded Runge-Kutta-Nyström Methods. Applied Numerical Mathematics, 29, 171-188.\nhttp://dx.doi.org/10.1016/S0168-9274(98)00065-8\n\n5. 5. Hairer, E., Nørsett, S.P. and Wanner, G. (1987) Solving Ordinary Differential Equations I: Nonstiff Problems. Springer-Verlag, Berlin.\n\n6. 6. Störmer, C. (1907) Sur les trajectoires des corpuscles électrisés. Acta Societatis Scientiarum Fennicae, 24, 221-247.\n\n7. 7. Grazier, K.R., Newman, W.I., Kaula, W.M. and Hyman, J.M. (1999) Dynamical Evolution of Planetesimals in Outer Solar System. ICARUS, 140, 341-352.\nhttp://dx.doi.org/10.1006/icar.1999.6146\n\n8. 8. Grazier, K.R. (1997) The Stability of Planetesimal Niches in the Outer Solar System: A Numerical Investigation. Ph.D. Thesis, University of California, Berkeley.\n\n9. 9. Grazier, K.R., Newman, W.I. and Sharp, P.W. (2013) A Multirate Störmer Algorithm for Close Encounters. The Astronomical Journal, 145, 112-119.\nhttp://dx.doi.org/10.1088/0004-6256/145/4/112\n\n10. 10. Rehman, S. (2013) Jovian Problem: Performance of Some High-Order Numerical Integrators. American Journal of Computational Mathematics, 3, 195-204.\nhttp://dx.doi.org/10.4236/ajcm.2013.33028"
] |
[
null,
"http://html.scirp.org/file/9-2500537x3.png",
null,
"http://html.scirp.org/file/9-2500537x2.png",
null,
"http://html.scirp.org/file/5-1100394x3.png",
null,
"http://html.scirp.org/file/5-1100394x4.png",
null,
"http://html.scirp.org/file/5-1100394x5.png",
null,
"http://html.scirp.org/file/5-1100394x6.png",
null,
"http://html.scirp.org/file/5-1100394x7.png",
null,
"http://html.scirp.org/file/5-1100394x8.png",
null,
"http://html.scirp.org/file/5-1100394x9.png",
null,
"http://html.scirp.org/file/5-1100394x10.png",
null,
"http://html.scirp.org/file/5-1100394x11.png",
null,
"http://html.scirp.org/file/5-1100394x12.png",
null,
"http://html.scirp.org/file/5-1100394x13.png",
null,
"http://html.scirp.org/file/5-1100394x14.png",
null,
"http://html.scirp.org/file/5-1100394x15.png",
null,
"http://html.scirp.org/file/5-1100394x16.png",
null,
"http://html.scirp.org/file/5-1100394x17.png",
null,
"http://html.scirp.org/file/5-1100394x18.png",
null,
"http://html.scirp.org/file/5-1100394x19.png",
null,
"http://html.scirp.org/file/5-1100394x20.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.884287,"math_prob":0.92545193,"size":24104,"snap":"2022-05-2022-21","text_gpt3_token_len":5436,"char_repetition_ratio":0.18941909,"word_repetition_ratio":0.12273866,"special_character_ratio":0.22153999,"punctuation_ratio":0.13822941,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99322295,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],"im_url_duplicate_count":[null,null,null,null,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-23T15:13:30Z\",\"WARC-Record-ID\":\"<urn:uuid:a8752813-c9d7-451f-a6df-22a54d50f0cf>\",\"Content-Length\":\"67750\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:936ad0ad-d5d0-40f8-991a-5a698513c9dc>\",\"WARC-Concurrent-To\":\"<urn:uuid:29900f5a-caed-4eea-bfb4-c5a4e497f785>\",\"WARC-IP-Address\":\"144.126.144.39\",\"WARC-Target-URI\":\"https://file.scirp.org/Html/5-1100394_52614.htm\",\"WARC-Payload-Digest\":\"sha1:JQACH6NQ5XN6T4WIQOSOBTRZK5NAFRLC\",\"WARC-Block-Digest\":\"sha1:Q4DQVBMEM4CK22H5JOQS2I3AUYCZU4RV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662558030.43_warc_CC-MAIN-20220523132100-20220523162100-00486.warc.gz\"}"}
|
https://ch.mathworks.com/matlabcentral/cody/problems/2948-create-an-m-x-n-array-consisting-only-of-an-input-value/solutions/1783136
|
[
"Cody\n\n# Problem 2948. Create an m x n array consisting only of an input value.\n\nSolution 1783136\n\nSubmitted on 11 Apr 2019\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Fail\nm = 5; n = 4; x = 5; y_correct = [5 5 5 5; 5 5 5 5; 5 5 5 5; 5 5 5 5; 5 5 5 5] assert(isequal(array_x(m,n,x),y_correct));\n\nError in solution Line: 4 Column: 10 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.\n\n2 Fail\nm = 4; n = 3; x = -7; y_correct = [-7 -7 -7; -7 -7 -7; -7 -7 -7; -7 -7 -7] assert(isequal(array_x(m,n,x),y_correct));\n\nError in solution Line: 4 Column: 10 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.\n\n3 Fail\nm = 2; n = 6; x = 11; y_correct = [11 11 11 11 11 11; 11 11 11 11 11 11] assert(isequal(array_x(m,n,x),y_correct));\n\nError in solution Line: 4 Column: 10 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.\n\n4 Fail\nm = 8; n = 1; x = 42; y_correct = [42; 42; 42; 42; 42; 42; 42; 42] assert(isequal(array_x(m,n,x),y_correct));\n\nError in solution Line: 4 Column: 10 Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.54699653,"math_prob":0.97153926,"size":922,"snap":"2020-45-2020-50","text_gpt3_token_len":368,"char_repetition_ratio":0.17429194,"word_repetition_ratio":0.12154696,"special_character_ratio":0.47071582,"punctuation_ratio":0.20338982,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96683836,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-25T17:39:46Z\",\"WARC-Record-ID\":\"<urn:uuid:b192ab89-9fe2-4bc2-adce-802c060fcdda>\",\"Content-Length\":\"80046\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:768b754e-14e6-4f5e-9919-15d26bd7e637>\",\"WARC-Concurrent-To\":\"<urn:uuid:80a8acf8-bc20-4721-8bad-7991c8154c3f>\",\"WARC-IP-Address\":\"23.48.20.88\",\"WARC-Target-URI\":\"https://ch.mathworks.com/matlabcentral/cody/problems/2948-create-an-m-x-n-array-consisting-only-of-an-input-value/solutions/1783136\",\"WARC-Payload-Digest\":\"sha1:DJ43CRKLDZNYW42SO4QQGN2J2SOLXXO4\",\"WARC-Block-Digest\":\"sha1:S3Q55W3UF6ZHR2PW4FGDZB2OAKTA2FRH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107889574.66_warc_CC-MAIN-20201025154704-20201025184704-00380.warc.gz\"}"}
|
https://math.stackexchange.com/tags/real-numbers/info
|
[
"# About\n\nTag Info\n\nFor questions about $\\mathbb{R}$, the field of real numbers. Often used in conjunction with the real-analysis tag.\n\nThe field of real numbers, usually denoted by $\\mathbb{R}$ or $\\mathbf{R}$ is a field equipped with an order, which is complete with respect to that order. Moreover, it is the only ordered field which is complete (up to isomorphism). The real numbers are used as basis for measuring \"length\".\n\nThe real numbers can be classified in various ways: rational and irrational numbers; algebraic and transcendental numbers; computable and non-computable numbers; etc.\n\nThe real numbers carry a natural topology, which is generated by the order. The topology can be induced by a naturally arising complete metric. See more on Wikipedia."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9100276,"math_prob":0.99175894,"size":741,"snap":"2019-35-2019-39","text_gpt3_token_len":161,"char_repetition_ratio":0.15332429,"word_repetition_ratio":0.0,"special_character_ratio":0.20782726,"punctuation_ratio":0.1294964,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9856427,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-20T07:31:53Z\",\"WARC-Record-ID\":\"<urn:uuid:2bba3073-42d6-48ba-893f-62cc5eeaa2c7>\",\"Content-Length\":\"91942\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a602f41d-0121-4369-817e-4005d1f36274>\",\"WARC-Concurrent-To\":\"<urn:uuid:c68ee881-c046-4ace-aa68-9dd646a975d3>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/tags/real-numbers/info\",\"WARC-Payload-Digest\":\"sha1:MPSUNUGBA2UZVQQXYZWED726GF26ZLNP\",\"WARC-Block-Digest\":\"sha1:O7OADB2KT24OVG634B7LGOLHYPQ5VGOO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027315258.34_warc_CC-MAIN-20190820070415-20190820092415-00131.warc.gz\"}"}
|
https://stacks.math.columbia.edu/tag/01P4
|
[
"Lemma 28.6.3. Let $X$ be a scheme. The following are equivalent:\n\n1. The scheme $X$ is Jacobson.\n\n2. The scheme $X$ is “locally Jacobson” in the sense of Definition 28.4.2.\n\n3. For every affine open $U \\subset X$ the ring $\\mathcal{O}_ X(U)$ is Jacobson.\n\n4. There exists an affine open covering $X = \\bigcup U_ i$ such that each $\\mathcal{O}_ X(U_ i)$ is Jacobson.\n\n5. There exists an open covering $X = \\bigcup X_ j$ such that each open subscheme $X_ j$ is Jacobson.\n\nMoreover, if $X$ is Jacobson then every open subscheme is Jacobson.\n\nProof. The final assertion of the lemma holds by Topology, Lemma 5.18.5. The equivalence of (5) and (1) is Topology, Lemma 5.18.4. Hence, using Lemma 28.6.2, we see that (1) $\\Leftrightarrow$ (2). To finish proving the lemma it suffices to show that “Jacobson” is a local property of rings, see Lemma 28.4.3. Any localization of a Jacobson ring at an element is Jacobson, see Algebra, Lemma 10.35.14. Suppose $R$ is a ring, $f_1, \\ldots , f_ n \\in R$ generate the unit ideal and each $R_{f_ i}$ is Jacobson. Then we see that $\\mathop{\\mathrm{Spec}}(R) = \\bigcup D(f_ i)$ is a union of open subsets which are all Jacobson, and hence $\\mathop{\\mathrm{Spec}}(R)$ is Jacobson by Topology, Lemma 5.18.4 again. This proves the second property of Definition 28.4.1. $\\square$\n\nIn your comment you can use Markdown and LaTeX style mathematics (enclose it like $\\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar)."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.74666303,"math_prob":0.9978262,"size":1301,"snap":"2023-40-2023-50","text_gpt3_token_len":414,"char_repetition_ratio":0.15882806,"word_repetition_ratio":0.00921659,"special_character_ratio":0.31821677,"punctuation_ratio":0.16554055,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999848,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-04T20:36:06Z\",\"WARC-Record-ID\":\"<urn:uuid:4760ef84-26d4-420e-8fba-f32ca0390bc8>\",\"Content-Length\":\"15479\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2f98b241-2c69-45c5-a574-71c5fbf13db6>\",\"WARC-Concurrent-To\":\"<urn:uuid:7175dcd4-1489-484f-aace-0d2d1d426820>\",\"WARC-IP-Address\":\"128.59.222.85\",\"WARC-Target-URI\":\"https://stacks.math.columbia.edu/tag/01P4\",\"WARC-Payload-Digest\":\"sha1:EEK57GHXLNC7FLQTF7WMNUOWXETSU65D\",\"WARC-Block-Digest\":\"sha1:4UK7BJUNEJD4OBZCEE3MEMWNVHABQ22Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511406.34_warc_CC-MAIN-20231004184208-20231004214208-00144.warc.gz\"}"}
|
https://www.tradingview.com/script/FQSkMjTT-Slow-Heiken-Ashi/
|
[
"12872 views\nPeriod= Length of the slow HA\nFastend and Slowend = just calculations for the Kama function no need to change those.\nSignal= Shows/Hides the triangles\n```study(\"Slow Heiken Ashi\",overlay=true,precision=0)\n//by Glaz.\n//KAMA function\np=input(6,title='Period')\nfastend=input(0.666,step=0.001)\nslowend=input(0.0645,step=0.0001)\nkama(close,amaLength)=>\ndiff=abs(close-close)\nsignal=abs(close-close[amaLength])\nnoise=sum(diff, amaLength)\nefratio=noise!=0 ? signal/noise : 1\nsmooth=pow(efratio*(fastend-slowend)+slowend,2)\nkama=nz(kama, close)+smooth*(close-nz(kama, close))\nkama\n\n//Slow Heiken Ashi\nhakamaper=1/2\nSignal=input(true)\nOm=sma(open,p)\nHm=sma(high,p)\nLm=sma(low,p)\nCm=sma(close,p)\nvClose=(Om+Hm+Lm+Cm)/4\nvOpen= kama(vClose,hakamaper)\nvHigh= max(Hm,max(vClose, vOpen))\nvLow= min(Lm,min(vClose, vOpen))\n\n// Plots\nvcolor= vOpen>vClose ?red:green\nplotcandle(vOpen,vHigh,vLow,vClose,color=vcolor)\n\n//signals\nplotchar(Signal?(cross(vOpen,vClose) and vOpen<vClose?vHigh:na):na,char='▼',color=white,transp=0,location=location.absolute)\nplotchar(Signal?(cross(vOpen,vClose) and vOpen>vClose?vLow:na):na,char='▲',color=white,transp=0,location=location.absolute)",
null,
"I'm getting this when trying to apply...\n\nInvalid value of the `length’ argument (0) `sum’ in the function. It should be >0\n\nHow do i remedy?",
null,
"Mohi1006\n@Mohi1006,\nHello.\nI have tried doing this but it's still saying `length’ argument (0) `sum’ in the function. It should be >0'\nDo you have to activate this change once you have altered the code?\nMany thanks\n\nP.S. I just discovered you have to reapply the indicator to the chart then it works fine",
null,
"Hi Glaz.\nLove this script. Nice job.\nJust a litter contribution . Add this couples of lines in order to have the signal Alert.\n\nshort= cross(vOpen,vClose) and vOpen<vClose?vHigh:na\nlong= cross(vOpen,vClose) and vOpen>vClose?vLow:na",
null,
"",
null,
"",
null,
""
] |
[
null,
"https://s3.tradingview.com/userpics/3848633-gMFX.png",
null,
"data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220,0,20,20%22%20width=%2239%22%20height=%2239%22%3E%3Crect%20height=%2220%22%20width=%2220%22%20fill=%22hsl%28174,25%25,50%25%29%22/%3E%3Ctext%20fill=%22white%22%20x=%2210%22%20y=%2214.8%22%20font-size=%2214%22%20font-family=%22Trebuchet%20MS,Arial,sans-serif%22%20text-anchor=%22middle%22%3ER%3C/text%3E%3C/svg%3E",
null,
"data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220,0,20,20%22%20width=%2239%22%20height=%2239%22%3E%3Crect%20height=%2220%22%20width=%2220%22%20fill=%22hsl%28195,25%25,50%25%29%22/%3E%3Ctext%20fill=%22white%22%20x=%2210%22%20y=%2214.8%22%20font-size=%2214%22%20font-family=%22Trebuchet%20MS,Arial,sans-serif%22%20text-anchor=%22middle%22%3ER%3C/text%3E%3C/svg%3E",
null,
"https://s3.tradingview.com/userpics/362921.png",
null,
"https://s3.tradingview.com/userpics/25545.png",
null,
"https://s3.tradingview.com/userpics/362921.png",
null
] |
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|
https://www.countingaccounting.com/2021/06/Marginal-Cost-Curve-Explained.html
|
[
"# How to Draw or Graph the Marginal Cost Curve using a PPF? Marginal Cost Curve Explained",
null,
"In this article, we're gonna talk about how to graph the marginal cost curve when you have a production possibilities frontier. So we use the following data in a previous article to create a production possibilities frontier and we assume that you and a group of friends were stranded on an island and all you could produce was food and clothing, so you had to make trade-offs think about how much food or clothing you could produce and we also graph the PPF.\n\nWe plotted each point so for example if you were to produce four units of food that would mean zero units of clothing. So four units of food zero units of clothing, three units of food would give you four units of clothing so these are the following combinations and we plotted them all out with our PPF.\n\nWe made our production possibilities frontier and then we introduced the idea that there's an increasing marginal cost, right? and that actually explains why the PPF usually has this bowed-out shape. Instead of this PPF think about a PPF that could conceivably just look like a straight line but instead, we said usually the PPF has this bowed-out shape due to the fact that not all resources are equally productive.\n\nSo let's take here we start with zero units of food we're all starving and we say hey wouldn't it be nice if we had food and so we decide okay well we're gonna produce one unit of food we're gonna go from zero to one unit of food and we give up one unit of clothing because clothing goes from ten to nine. We would say the marginal cost or the incremental cost of producing one unit of food is giving up one unit of clothing. So we'd say that the marginal cost of producing one unit of food when we start with zero units of food the extra one unit of food will gonna cost us one unit of cloth.\n\nSo that's of marginal cost to produce that first unit of food but the marginal cost changes, it's not constant. If it were a straight line then it'd just be constant but we said that the whole reason we've got this graph is the marginal cost is gonna be increasing. So let's think about it, as we go from one unit of food and now we say you know what it'd be nice to have two units of food so we produce an extra unit of food. Now look we have to give up two units of clothing. If you go back to the numbers if we go from nine to seven units of clothing we give up this time to get an extra piece of food is two units of cloths. So now the marginal cost here would be two.\nNow we think what if we wanted a third piece of food, what if we go from two units of food to three units of food? That extra one unit of food what is the cost of it? Now look it's getting more and more of our cost, now our marginal cost is three. When I say marginal cost I mean the amount of clothing that we're giving up to get that extra piece of food. Think about when we started with zero food and went to one it only costs us one piece of clothing but now we've got a marginal cost of three. Let's go for the max let's go for four units of food, from three to four. We're getting one extra piece of food but we're giving up four units of clothing.\n\nSo we can actually put all costs together in a little table and we say when we have one food the marginal cost was two, Then three and four. So we can just fill our table with marginal cost and now what we can do is we can graph this. We can graph this little table.\n\nThat'll tell us something about our marginal cost which you probably already can see just from looking at the numbers. So I've got food here on the x-axis and the marginal cost on the y-axis. When we have want zero units of food the marginal cost of producing one unit of food is 1 so (0, 1) will be our first combination. Now one unit of food the marginal cost is two so that will give us the second combination. Here two units of food the marginal cost is three. Then when we have three units of food that make that extra last piece of food it will cost us four units of clothing. So we see that actually, this is our marginal cost curve.\n\nand you see that the marginal cost is increasing. It's an increasing marginal cost curve. So why is that? So again this idea that resources are not equally productive. So again let's return to our example so we're on an island, it's a group of us we've been stranded due to a plane crash and we have to think about how much food and clothing to produce. Now some people are gonna be better at producing food and other people are gonna be better at producing clothing.\n\nSo let's say there's somebody on the island who is a tailor and then let's say there's somebody on the island who maybe was a chef. If when we're producing zero food and ten clothing that means that the chef is being asked to make clothing. As everybody's making clothing, right? Let's have the chef he can go or she can go make some food, well maybe the chef wasn't very good at making clothing. So we only really give up one unit of clothing. So our marginal cost is one when we want to get that first unit of food. The marginal cost is low there. Was somebody that maybe wasn't even good at making clothes, to begin with, but as we get further and further along and we get to a point where to make that last unit of food to go from three to four, now we're asking the Taylor, who makes clothes for a living and we're asking them to make food.\n\nSo now we're giving up four units of clothing to get that final piece of food. So that explains why we have an increasing marginal cost because as we move along the curve, not all resources are equally productive if we could equally trade-off resources. Let's say hypothetically that we were in a world where we just everybody is equally good and making food and equally good at making clothing then the PPF wouldn't look like that bowed-out shaped it would be like a straight line."
] |
[
null,
"https://lh3.googleusercontent.com/-8WSjKujwnQA/YMWYvWdLDuI/AAAAAAAAFZg/C1KM_J8BOhkNbuQD72paSHALih-L6RwZQCEwYBhgLKtQDABHVOhxnJh96AxMYh53S2WGN9d1oiTH7YDGvB99QohVtXWXo13KGHXCXnQbEZwd3KE1n9MWsUwbALyb0yxvm9QY50-PXYqCMhnYQqD_KEUglZ8uo5ytqySKBUgL5OBBxdiwLJ0AVeZw7uxCJtQ8yOVDhkQGCaGenskAFweuJDyHF2moZgH5QGGFrJG_EDRqcq8KuP8NBWhdyFpNduNNEAJZHjg4OAlEBBSwmAGtHTnl5qaLv7PQht66hooUe7xa8CvCAMjjRcQzCwHrhMpEcOCI4nvndBzayAIYbdBrImFKJ628sv-hxcr7hmpfW5jPo0A-99LuVAbEf1EizJ888tzIJbqwQ9pUM2STc8UA5wScDBHskHDCiYl4CC2hLJ_Jm6Ey7TiAhtuvyagKLTiJ6LG7QfA4sfI2mUJ1wk5BDBr7beGie5piEETaBjCMLkG4m4c3VSTLindpyScPmmzydLUHWRWATE_H9WyZoqxkO9HWkqJdG4hdIKEpsCtA0JWZHUcZd_plKQNFlnS9g0jWeIG0_hKmAeUdi3o45UmJRzejJsyMr7RLkSm0NYQb9x_644ZiaPNU2pebR-Al5aZ4NQEh_WqbNyidBHuDSS6jOwQackeyxMMmbm4YG/w140-h78-p/How%2Bto%2BGraph%2Bthe%2BMarginal%2BBenefit%2BCurve%2B%25283%2529.png",
null
] |
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|
https://theconstructor.org/practical-guide/double-shear-test-steel/2500/?amp=1
|
[
"# Double Shear Test on Mild Steel",
null,
"Reading time: 1 minute\n\nDouble shear test is used to determine the shear strength (ultimate shear stress) of the mild steel specimen. Universal testing machine (UTM) is used for performing double shear test. There are two types of UTM namely: screw type and hydraulic type. The latter is easier to operate.\n\nShear force is the load that cause two contiguous parts of the body to slide relative to each other in a direction parallel to their plane of contact. Shear Strength is defined as the maximum load typically applied normal to a fastener’s axis that can be supported prior to fracture. Double shear is load applied in one plane that would result in the fastener being cut into three pieces, while single shear would result in two fastener pieces.\n\n## Apparatus\n\n1. Universal Testing Machine (UTM)\n2. Shear Tool Assembly\n3. Specimen\n4. Venire Calipers.\n\n## Theory and Principle\n\nShear strength of the material is the ultimate shear stress (Tmax ) attained by the specimen, which under double shear given by,\n\nTmax= F/2A Equation 1\n\nWhere,\n\nF: Maximum load at which the specimen breaks\n\nA: cross-sectional area of the specimen.\n\nThe load range to which the machine is to be set for the test is selected bases on the expected maximum load F to be applied on the specimen. This is calculated from the yield stress fy and the factor of safety (F.S), as follows:\n\nPermissible shear stress T for mild steel is,\n\nT =0.45fy Equation 2\n\nAnd therefore,\n\nTmax= (F.S) 0.45fy Equation 3\n\nF= 0.9 (F.S)fyA Equation 4\n\n## Procedure\n\n1. Determine the diameter of the given rod with the help of Vernier caliper. Measure the diameter of the specimen at three sections.\n2. Calculate the maximum load expected to be applied on the specimen using equation (2) and select the load range to be used.\n3. Set the UTM for the selected load range.\n4. Set the correct set or disc to assemble the shear attachment with the right set of disc in it. Insert the specimen in to the disc so that it projects equally on either side, Fig. 3.\n5. Place the entire bear assembly with the specimen in it centrally over the baring plate on the lower table.\n6. Bring the lower cross- head close to the top surface of the assembly.\n7. Float the lower table and set the load pointer to zero.\n9. Note the ultimate load applied on the specimen.\n10. Finally, Compute the shear strength of the steel specimen."
] |
[
null,
"data:image/svg+xml;base64,PHN2ZyBoZWlnaHQ9IjcyIiB3aWR0aD0iNzIiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+",
null
] |
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|
https://cythilya.github.io/2015/06/26/javascript-design-pattern-singleton/
|
[
"# Singleton 單體模式",
null,
"JavaScript Design Pattern 「Singleton 單體模式」 筆記。\n\nSingleton 的概念就是同一個 class 只能建立唯一一個實體物件。當第二次使用同一個 class 建立新物件的時候，我們會得到和第一次建立時同一個物件。一般來說，當我們利用同一個 class 建立實體物件時，每次建立得到的物件都會是不同的，例如：\n\n``````var obj = {\nmyProp: 'myValue',\n};\n\nvar obj2 = {\nmyProp: 'myValue',\n};\n\nconsole.log(obj === obj2); // false\nconsole.log(obj == obj2); // false\n``````\n\n``````function Universe() {\n// no-op\n}\n\nvar uni = new Universe();\nvar uni2 = new Universe();\nconsole.log(uni === uni2); // true\n``````\n\n## 實作方法\n\n• 儲存在靜態屬性中的實體\n• 儲存在 Closure 中的實體\n\n### 儲存在靜態屬性中的實體\n\n``````function Universe() {\nif (typeof Universe.instance === 'object') {\nreturn Universe.instance;\n}\n\nthis.start_time = 0;\nthis.bang = 'Big';\n\nUniverse.instance = this;\n}\n\nvar uni = new Universe();\nvar uni2 = new Universe();\nconsole.log('uni === uni2');\nconsole.log(uni === uni2); // true\n``````\n\n``````Universe.instance = null; // 公開屬性，被修改了...\nvar uni3 = new Universe();\nconsole.log(uni === uni3); // false\n``````\n\n### 儲存在 Closure 中的實體\n\n``````function UniverseC() {\nvar instance = this;\n\nthis.start_time = 0;\nthis.bang = 'Big';\n\n// 重新定義建構式\nUniverseC = function() {\nreturn instance;\n};\n}\n\nvar uni4 = new UniverseC();\nvar uni5 = new UniverseC();\nconsole.log('uni4 === uni5');\nconsole.log(uni4 === uni5); // true\n``````\n\n``````// 測試是否遺失之後加上去的屬性\nUniverseC.prototype.inEverything = true;\nvar uni6 = new UniverseC();\n\nconsole.log(uni4.inNothing); // true\nconsole.log(uni4.inEverything); // undefined\nconsole.log(uni6.inNothing); // true\nconsole.log(uni6.inEverything); // undefined\n``````\n\n``````console.log(uni4.constructor.name); // UniverseC\nconsole.log(uni4.constructor === UniverseC); // false\n\nconsole.log(uni4.constructor); // 最初定義的 UniverseC\nconsole.log(UniverseC); // 重新定義的 UniverseC\n``````\n\n### 修改儲存在 Closure 中的實體\n\nSol 1 與 Sol 2 解決了「儲存在 Closure 中的實體」的問題：\n\n• 重新定義的函式會失去在重新定義後加上去的屬性\n• 建構式與自我重新定義後是不同的\n\n#### Sol 1\n\n``````UniverseM.prototype.inNothing = true;\n\nfunction UniverseM() {\nvar instance;\n\nUniverseM = function UniverseM() {\nreturn instance;\n};\n\nUniverseM.prototype = this;\ninstance = new UniverseM();\ninstance.constructor = UniverseM();\n\ninstance.start_time = 0;\ninstance.bang = 'Big';\n\nreturn instance;\n}\n\nvar uni7 = new UniverseM();\nvar uni8 = new UniverseM();\n\nconsole.log(uni7 === uni8); // true\n\nUniverseM.prototype.inEverything = true;\nconsole.log(uni7.constructor === UniverseM); // true\n``````\n##### Sol 2\n\n``````var UniverseN;\n\n(function() {\nvar instance;\nUniverseN = function UniverseN() {\nif (instance) {\nreturn instance;\n}\ninstance = this;\n\nthis.start_time = 0;\nthis.bang = 'Big';\n};\n})();\n\nvar uni9 = new UniverseN();\nvar uni10 = new UniverseN();\n\nconsole.log(uni9 === uni10); // true\n\nUniverseN.prototype.inEverything = true;\nconsole.log(uni9.constructor === UniverseN); // true\n``````\n\n## 總結\n\n• 儲存在靜態屬性中的實體\n• 實作方法：建立類似`Universe.instance`的屬性，並將物件實體儲存於此。\n• 優點：簡單，容易實作。\n• 缺點：instance 屬性可被 public 存取，很可能會被修改，而失去應有的正確性。解法：儲存在 Closure 中的實體。\n• 儲存在 Closure 中的實體\n• 實作方法：將物件實體包在一個 closure 裡面，保持其為 private 的狀態，使其無法在建構式之外被修改。\n• 優點：不會被建構式之外的程式碼修改，具有 private 特性。\n• 缺點：重新定義的函式會失去在重新定義後加上去的屬性，且建構式與自我重新定義後是不同的，這在修改後的 Sol 1 和 Sol 2 可以獲得解決。我自己比較喜歡 Sol 2，簡短、簡單易懂。"
] |
[
null,
"https://cythilya.github.io/assets/javascript/javascript-740x374.png",
null
] |
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|
https://www.colorhexa.com/6cffce
|
[
"# #6cffce Color Information\n\nIn a RGB color space, hex #6cffce is composed of 42.4% red, 100% green and 80.8% blue. Whereas in a CMYK color space, it is composed of 57.6% cyan, 0% magenta, 19.2% yellow and 0% black. It has a hue angle of 160 degrees, a saturation of 100% and a lightness of 71.2%. #6cffce color hex could be obtained by blending #d8ffff with #00ff9d. Closest websafe color is: #66ffcc.\n\n• R 42\n• G 100\n• B 81\nRGB color chart\n• C 58\n• M 0\n• Y 19\n• K 0\nCMYK color chart\n\n#6cffce color description : Very light cyan - lime green.\n\n# #6cffce Color Conversion\n\nThe hexadecimal color #6cffce has RGB values of R:108, G:255, B:206 and CMYK values of C:0.58, M:0, Y:0.19, K:0. Its decimal value is 7143374.\n\nHex triplet RGB Decimal 6cffce `#6cffce` 108, 255, 206 `rgb(108,255,206)` 42.4, 100, 80.8 `rgb(42.4%,100%,80.8%)` 58, 0, 19, 0 160°, 100, 71.2 `hsl(160,100%,71.2%)` 160°, 57.6, 100 66ffcc `#66ffcc`\nCIE-LAB 91.307, -50.776, 11.684 53.081, 79.16, 70.871 0.261, 0.39, 79.16 91.307, 52.103, 167.041 91.307, -61.393, 26.061 88.972, -49.207, 15.053 01101100, 11111111, 11001110\n\n# Color Schemes with #6cffce\n\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #ff6c9d\n``#ff6c9d` `rgb(255,108,157)``\nComplementary Color\n• #6cff85\n``#6cff85` `rgb(108,255,133)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #6ce7ff\n``#6ce7ff` `rgb(108,231,255)``\nAnalogous Color\n• #ff856c\n``#ff856c` `rgb(255,133,108)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #ff6ce7\n``#ff6ce7` `rgb(255,108,231)``\nSplit Complementary Color\n• #ffce6c\n``#ffce6c` `rgb(255,206,108)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #ce6cff\n``#ce6cff` `rgb(206,108,255)``\n• #9dff6c\n``#9dff6c` `rgb(157,255,108)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #ce6cff\n``#ce6cff` `rgb(206,108,255)``\n• #ff6c9d\n``#ff6c9d` `rgb(255,108,157)``\n• #20ffb5\n``#20ffb5` `rgb(32,255,181)``\n• #39ffbd\n``#39ffbd` `rgb(57,255,189)``\n• #53ffc6\n``#53ffc6` `rgb(83,255,198)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #86ffd7\n``#86ffd7` `rgb(134,255,215)``\n• #9fffdf\n``#9fffdf` `rgb(159,255,223)``\n• #b9ffe8\n``#b9ffe8` `rgb(185,255,232)``\nMonochromatic Color\n\n# Alternatives to #6cffce\n\nBelow, you can see some colors close to #6cffce. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #6cffa9\n``#6cffa9` `rgb(108,255,169)``\n• #6cffb6\n``#6cffb6` `rgb(108,255,182)``\n• #6cffc2\n``#6cffc2` `rgb(108,255,194)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #6cffda\n``#6cffda` `rgb(108,255,218)``\n• #6cffe7\n``#6cffe7` `rgb(108,255,231)``\n• #6cfff3\n``#6cfff3` `rgb(108,255,243)``\nSimilar Colors\n\n# #6cffce Preview\n\nThis text has a font color of #6cffce.\n\n``<span style=\"color:#6cffce;\">Text here</span>``\n#6cffce background color\n\nThis paragraph has a background color of #6cffce.\n\n``<p style=\"background-color:#6cffce;\">Content here</p>``\n#6cffce border color\n\nThis element has a border color of #6cffce.\n\n``<div style=\"border:1px solid #6cffce;\">Content here</div>``\nCSS codes\n``.text {color:#6cffce;}``\n``.background {background-color:#6cffce;}``\n``.border {border:1px solid #6cffce;}``\n\n# Shades and Tints of #6cffce\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000a07 is the darkest color, while #f5fffc is the lightest one.\n\n• #000a07\n``#000a07` `rgb(0,10,7)``\n• #001e14\n``#001e14` `rgb(0,30,20)``\n• #003121\n``#003121` `rgb(0,49,33)``\n• #00452e\n``#00452e` `rgb(0,69,46)``\n• #00583b\n``#00583b` `rgb(0,88,59)``\n• #006c48\n``#006c48` `rgb(0,108,72)``\n• #008055\n``#008055` `rgb(0,128,85)``\n• #009362\n``#009362` `rgb(0,147,98)``\n• #00a76f\n``#00a76f` `rgb(0,167,111)``\n• #00ba7c\n``#00ba7c` `rgb(0,186,124)``\n• #00ce89\n``#00ce89` `rgb(0,206,137)``\n• #00e296\n``#00e296` `rgb(0,226,150)``\n• #00f5a4\n``#00f5a4` `rgb(0,245,164)``\n``#0affad` `rgb(10,255,173)``\n• #1effb4\n``#1effb4` `rgb(30,255,180)``\n• #31ffba\n``#31ffba` `rgb(49,255,186)``\n• #45ffc1\n``#45ffc1` `rgb(69,255,193)``\n• #58ffc7\n``#58ffc7` `rgb(88,255,199)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\n• #80ffd5\n``#80ffd5` `rgb(128,255,213)``\n• #93ffdb\n``#93ffdb` `rgb(147,255,219)``\n• #a7ffe2\n``#a7ffe2` `rgb(167,255,226)``\n• #baffe8\n``#baffe8` `rgb(186,255,232)``\n• #ceffef\n``#ceffef` `rgb(206,255,239)``\n• #e2fff5\n``#e2fff5` `rgb(226,255,245)``\n• #f5fffc\n``#f5fffc` `rgb(245,255,252)``\nTint Color Variation\n\n# Tones of #6cffce\n\nA tone is produced by adding gray to any pure hue. In this case, #b0bbb7 is the less saturated color, while #6cffce is the most saturated one.\n\n• #b0bbb7\n``#b0bbb7` `rgb(176,187,183)``\n• #aac1b9\n``#aac1b9` `rgb(170,193,185)``\n• #a5c6bb\n``#a5c6bb` `rgb(165,198,187)``\n• #9fccbd\n``#9fccbd` `rgb(159,204,189)``\n• #99d2bf\n``#99d2bf` `rgb(153,210,191)``\n• #94d7c1\n``#94d7c1` `rgb(148,215,193)``\n• #8eddc3\n``#8eddc3` `rgb(142,221,195)``\n• #88e3c5\n``#88e3c5` `rgb(136,227,197)``\n• #83e8c6\n``#83e8c6` `rgb(131,232,198)``\n• #7deec8\n``#7deec8` `rgb(125,238,200)``\n• #77f4ca\n``#77f4ca` `rgb(119,244,202)``\n• #72f9cc\n``#72f9cc` `rgb(114,249,204)``\n• #6cffce\n``#6cffce` `rgb(108,255,206)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #6cffce is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population"
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https://view.matrix.org/room/!LADvlewaWOnmvMkjxE:matrix.org/
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[
"",
null,
"## Applied Category Theory\n\n414 Members\n33 Servers\n\nSenderMessageTime\n19 Sep 2020",
null,
"V M (Indeed, `F[f]: F A → F B` and `G[f]: G A → G B`, as we require in the definition of our `M`-morphism). 12:39:40",
null,
"V M But in order for this to be a morphism, it needs to satisfy that commutativity condition. So we need\n``F A —F[f]→ F B | | αₐ α_b ↓ ↓G A —G[f]→ G B``\nto commute.\nBut that's exactly the naturality square, so it's satisfied!\n12:41:53",
null,
"V M Hold on, I messed up the definition a bit. `M` should be the category of morphisms of `D` (not `C`). I'll edit that.\nFixed!\n12:46:12",
null,
"V M * Let `F, G: C → D` be two functors from a category `C` to a category `D`.\n\nLet `M` be a category of morphisms of `D`: That is, every object of `M` is a morphism `X —f→ Y` in `D`, and given two such morphisms\n`X —f→ Y` and `U —g→ V`, a morphism `m: f → g` in `M` from `f` to `g` is any pair `m = (m₁, m₂)` of morphisms\n`m₁: X → U`, `m₂: Y → V` in `D` such that the following square commutes:\n``X —f→ Y| |m₁ m₂↓ ↓U —g→ V``\nSo to be clear, a single morphism `m` in `M` is actually a pair of morphisms `(m₁, m₂)` of our original category `D`, satisfying that commutativity condition. And composition of morphisms in `M` is defined in the obvious way. Given `m: f → g` and `n: g → h`, define\n`n ∘ m = (n₁ ∘ m₁, n₂ ∘ m₂)` [where `mᵢ` and `nᵢ` are the two \"components\" of `m` and `n` as in our definition].\nYou can verify that this `M` is a category.\n12:47:20",
null,
"V M * Since `α` is a natural transformation, by definition for each object `X` of `C`, there is a morphism `αₓ: F X → G X` in `D`.\nSo, let the action of the functor `α` on objects be as follows:\nFor all `X ∈ Ob C`, `α(X) = αₓ`.\n12:48:00",
null,
"V M * (This is an object of `M`, because `αₓ` is a morphism in `D`) 12:48:08",
null,
"V M * What about the action of `α` on morphisms?\nFor any `f: X → Y` in `C`, we need to define `α[f]: α(X) → α(Y)` in `M`.\nBut remember, a (single) morphism in `M` is a pair of morphisms of `D`. So we define\n`α[f] = (F[f], G[f])`.\n12:48:39",
null,
"V M * Hold on, I messed up the definition a bit. `M` should be the category of morphisms of `D` (not `C`). I'll edit that.\nFixed!\n12:49:12",
null,
"V M Hm… I don't remember if I checked this, but I think the converse is true too: Any functor from `C` to `M` must be some natural transformation between two parallel functors in `C`.\nIf that's true, we can say natural transformations in `C` are exactly functors from `C` to `M`.\n12:52:43",
null,
"V M * Since `α` is a natural transformation, by definition for each object `A` of `C`, there is a morphism `αₐ: F A → G A` in `D`.\nSo, let the action of the functor `α` on objects be as follows:\nFor all `A ∈ Ob C`, `α(A) = αₐ`.\n12:59:00",
null,
"V M * (This is an object of `M`, because `αₐ` is a morphism in `D`) 12:59:12",
null,
"V M * What about the action of `α` on morphisms?\nFor any `f: A → B` in `C`, we need to define `α[f]: α(A) → α(B)` in `M`.\nBut remember, a (single) morphism in `M` is a pair of morphisms of `D`. So we define\n`α[f] = (F[f], G[f])`.\n12:59:30",
null,
"V M * (Indeed, `F[f]: F A → F B` and `G[f]: G A → G B`, as we require in the definition of our `M`-morphism). 12:59:44",
null,
"V M * But in order for this to be a morphism, it needs to satisfy that commutativity condition. So we need\n``F A —F[f]→ F B | | αₐ α_b ↓ ↓G A —G[f]→ G B``\nto commute.\nBut that's exactly the naturality square, so it's satisfied!\n13:00:03",
null,
"V M Let `C` be a category, and `M` be the category of morphisms in any category `D`, as we've defined.\n[Note: I think there are a few different categories called \"category of morphisms of a category\" so don't take this as the definition]\n\nNow, consider any functor from `C` to `M`, and let's label it `α` (though we don't as yet know if it's a natural transformation).\nNow firstly, for every `A ∈ Ob C`, `α(A)` should be an object in `M`, which means it's actually a morphism in `D`:\n`α(A) = X —f→ Y`,\nfor some objects `X` and `Y` in `D`.\nSo we immediately get two mappings from `C` to `D`, namely:\n`F, G: C → D`, `F A = X`, `G A = Y` (for `X` and `Y` as given above).\nOr if you wish: `F A = dom α(A)`, `G A = cod α(A)` (resp. the domain and codomain of the object `α(A)` of `M`, which is a morphism of `D`).\n13:02:24",
null,
"V M Also, given a morphism `f: A → B` in `C`, we get a morphism `α[f]: α(A) → α(B)` in `M`.\nWhich means we get `α[f] = (m₁, m₂)`, where\n`m₁: dom α(A) → dom α(B)` and `m₂: cod α(A) → cod α(B)` are morphisms in `D`.\nThat is, `m₁: F A → F B` and `m₂: G A → G B` (by our definition of the mappings `F` and `G` on objects).\nSo now define `F[f] = m₁`, and `G[f] = m₂`, which gives the action of `F` and `G` on morphisms.\n13:05:51",
null,
"V M Since `α` is a functor, it preserves compositions and identities. And our definition of composition of `M`-morphisms is as component-wise composition (since each `M`-morphism is a pair of `D`-morphisms).\nSo this implies (I can more or less see that working out…) that `F` and `G` as defined above also preserve compositions and identities.\n13:07:29",
null,
"V M So they're both functors from `C` to `D`. 13:07:31",
null,
"V M And then `α` is a natural transformation from `F` to `G`, if we define its components as:\nFor each `A ∈ Ob C`, let `αₐ = α(A)`.\n13:08:08",
null,
"V M * So they're both functors from `C` to `D`. 13:08:44",
null,
"Roberto Abdelkader Martínez Pérez @MVVVVVVVVVVVV wow, I was expecting a yes/no answer and maybe a link but you gave me a full explanation. Thank you very much! 14:08:14",
null,
"V MNo problem. It's something I figured out a while ago, but I'd completely forgotten about it, so I'm glad I got reminded of it, thanks to your question.14:31:40",
null,
"Fran Gómez García changed their display name from Francisco Gómez García to Fran Gómez García.15:24:36",
null,
"Matteo @MVinay great write up! I used to know this when I first learn CT but then I forgot it and couldn't come up with it anymore 😂 so it's cool to see it again 16:52:09",
null,
"wendy joined the room.17:08:31",
null,
"juan joined the room.23:49:00\n21 Sep 2020",
null,
"juan 17:19:46",
null,
"darkharmony9999 joined the room.19:22:28",
null,
"gabe joined the room.22:49:46\n26 Sep 2020",
null,
"Yosbi J. Gollés joined the room.21:02:34\n\n#### There are no newer messages yet.\n\nBack to Room List"
] |
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[
"# Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry\n\nMarot & Walter, 1826 - 320 уелЯдет\n\n### Фй лЭне пй чсЮуфет -Уэнфбоз ксйфйкЮт\n\nДен енфпрЯубме ксйфйкЭт уфйт ухнЮиейт фпрпиеуЯет.\n\n### Ресйечьменб\n\n Еньфзфб 1 iii Еньфзфб 2 13 Еньфзфб 3 15 Еньфзфб 4 33 Еньфзфб 5 49 Еньфзфб 6 61 Еньфзфб 7 88 Еньфзфб 8 119\n Еньфзфб 10 163 Еньфзфб 11 173 Еньфзфб 12 188 Еньфзфб 13 212 Еньфзфб 14 226 Еньфзфб 15 237 Еньфзфб 16 272 Еньфзфб 17 277\n\n Еньфзфб 9 154\n Еньфзфб 18 317\n\n### ДзмпцйлЮ брпурЬумбфб\n\nУелЯдб 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.\nУелЯдб 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.\nУелЯдб 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.\nУелЯдб 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.\nУелЯдб 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.\nУелЯдб 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.\nУелЯдб 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.\nУелЯдб 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.\nУелЯдб 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.\nУелЯдб 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section."
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{"ft_lang_label":"__label__en","ft_lang_prob":0.8490873,"math_prob":0.99508846,"size":6056,"snap":"2021-04-2021-17","text_gpt3_token_len":1630,"char_repetition_ratio":0.17779246,"word_repetition_ratio":0.43309858,"special_character_ratio":0.22853369,"punctuation_ratio":0.10785953,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9945215,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-19T04:11:37Z\",\"WARC-Record-ID\":\"<urn:uuid:cf9c7cf3-d64e-44f1-b870-f584f42e1d50>\",\"Content-Length\":\"86500\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9fc47fe5-35e5-49d6-b414-07a88705b668>\",\"WARC-Concurrent-To\":\"<urn:uuid:e0b94136-7843-4c8d-9854-dbaeaa242c32>\",\"WARC-IP-Address\":\"172.217.8.14\",\"WARC-Target-URI\":\"https://books.google.gr/books?id=ONo2AAAAMAAJ&q=half&dq=editions:UOMDLPabq7928_0001_001&lr=&hl=el&output=html_text&source=gbs_word_cloud_r&cad=6\",\"WARC-Payload-Digest\":\"sha1:YIIXDZQ7XNJNET2NHHNV4R52PXOQ4TDW\",\"WARC-Block-Digest\":\"sha1:6CK6V3VLCPTOL3N25ZA2FETHDNMUE3RS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038863420.65_warc_CC-MAIN-20210419015157-20210419045157-00289.warc.gz\"}"}
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https://gtas.xyz/twitter-trending/Berlin
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[
"Twitter Trends in Berlin - Hashtags and topics website gives you the latest and top trending topics for the day from the Twitter site in Berlin with every 1 hours time interval period. With the help of the words cloud (Above), you can easily identify the latest and hot topics happening on Twitter in your place. And this API is the fastest async server so, this will generate the web page faster and lighter without any delay.\n\n## Top 30 Trending Topics and Hashtags\n\n• Top Twitter Trends Berlin - Now\n1 <10k\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11107292\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n19209200\n20 <10k\n2112520\n22 <10k\n2321266\n24 <10k\n25 <10k\n26 <10k\n27 <10k\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 1 Hrs ago\n1 <10k\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6194432\n7102632\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13197992\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n1911416\n20 <10k\n21 <10k\n22 <10k\n2320360\n24 <10k\n25 <10k\n26 <10k\n27 <10k\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 2 Hrs ago\n1 <10k\n2 <10k\n3 <10k\n4 <10k\n594438\n6 <10k\n7177071\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n1519650\n16 <10k\n17 <10k\n18 <10k\n19 <10k\n20 <10k\n2111782\n22 <10k\n23 <10k\n24 <10k\n25 <10k\n2694749\n27 <10k\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 3 Hrs ago\n120227\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n663819\n7113302\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n1750266\n18 <10k\n19 <10k\n2010932\n2113988\n22 <10k\n23 <10k\n24 <10k\n25 <10k\n26 <10k\n2734215\n28 <10k\n29105122\n30 <10k\n• Top Twitter Trends Berlin - 4 Hrs ago\n121195\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n638772\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n1647181\n1781299\n18 <10k\n19 <10k\n20 <10k\n21 <10k\n22 <10k\n23 <10k\n24 <10k\n25 <10k\n2636849\n27104930\n28 <10k\n2919542\n30 <10k\n• Top Twitter Trends Berlin - 5 Hrs ago\n122219\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n1944128\n20 <10k\n21 <10k\n22 <10k\n23105074\n24 <10k\n2539214\n26 <10k\n2719586\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 6 Hrs ago\n123492\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n19 <10k\n20 <10k\n21 <10k\n22 <10k\n2341128\n24 <10k\n25 <10k\n2619530\n27 <10k\n28 <10k\n29103319\n30 <10k\n• Top Twitter Trends Berlin - 7 Hrs ago\n124451\n2 <10k\n3 <10k\n4 <10k\n535100\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n19 <10k\n20 <10k\n21 <10k\n22 <10k\n23 <10k\n24 <10k\n25 <10k\n2642719\n27 <10k\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 8 Hrs ago\n124972\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n19 <10k\n20 <10k\n21 <10k\n22 <10k\n23 <10k\n24 <10k\n25 <10k\n26 <10k\n27 <10k\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 9 Hrs ago\n124419\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n19 <10k\n2027370\n21 <10k\n22 <10k\n23 <10k\n24 <10k\n25 <10k\n26 <10k\n27 <10k\n2845527\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 10 Hrs ago\n123681\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n6 <10k\n7 <10k\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n19 <10k\n20 <10k\n2147177\n22127855\n23 <10k\n24 <10k\n25 <10k\n26 <10k\n27 <10k\n28 <10k\n29 <10k\n30 <10k\n• Top Twitter Trends Berlin - 11 Hrs ago\n123097\n2 <10k\n3 <10k\n4 <10k\n5 <10k\n639620\n7120651\n8 <10k\n9 <10k\n10 <10k\n11 <10k\n12 <10k\n13 <10k\n14 <10k\n15 <10k\n16 <10k\n17 <10k\n18 <10k\n1949085\n20 <10k\n21 <10k\n2221798\n23 <10k\n24 <10k\n25 <10k\n26 <10k\n2763825\n28 <10k\n29102370\n3012507\n\n## Suggested Places\n\nStuttgart Munich Leipzig Hamburg Essen Dresden Dortmund Bremen Berlin"
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http://opsisplacements.com/tmi-ceiling-yfnujbn/diode-current-equation-derivation-pdf-9b8ad4
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"# diode current equation derivation pdf\n\n•Some detailed models may add an additional diode. The main characteristic of a pn-junction or a diode is that for positive voltages ... relationship can be derived from the current density equation for the electrons and the holes (Homework). In this equation two parameters require to be discussed in quite detail. Note that although you can simply vary the temperature and ideality factor the resulting IV curves are misleading. Pour rappel: les valeurs exactes de I et de V vues par la diode à un instant donné seront fixées par le circuit extérieur. 8/22/2005 The Junction Diode Forward Bias Equation.doc 2/6 Jim Stiles The Univ. PN Junction Diode : I-V Characteristics qThe Ideal Diode Equation •Qualitative Derivation üEquilibrium situation üThe I-Vcharacteristics of the ideal diode are modeled by the ideal diode equation àqualitative and quantitative derivation potential hill high-energy carrier driftdiffusion balance E Schottky Diode. we get an expression for the current .. current for zero diode voltage . (same equations for spatial distribution) • Minority carrier concentration at SCR is near zero under reverse bias. a diode current of several mA for V ˇ0:7 V. * The \\turn-on\" voltage (Von) of a diode depends on the value of Is. For simplicity we also assume that one-dimensional derivation but the concepts can be extended to two and three-dimensional notation and devices. Effect Of Temperature On Diode Characteristics Semiconductor For You. In the limits alpha=0 or 1, the interface acts like an ideal semiconductor diode, which passes current preferentially in one direction (“forward bias”) A number of approximations of diode behavior can be made from the ideal diode equation. Diode Current Equation. 70342 17190198 ... ××ש××¨× ××××× ××ת קרקע ××× × ××× × ×× ×, Book Babies My 5 Senses Sound Idaho Falls Public Library, ס×× ×שר ש××ר ×××× ××¤×¢× ×××× ×ת ×××××× ××× ×¡×¤×§×× ××¦×¨× ×× ×¡×××× ××, צ××××××× ××××× ×××ת ×××× ××××ס, 24 Best ×§× ××ת ××פר×××ת Images Kid Beds Childrens Dresser Art, pn junction diode current equation derivation pdf, ×××× ×ª ××××¡× ××ק××¨× Ewm608, ××××ת ס×× ×ר×××ת ×©× ×§×ר×ת ×¢×¥. Diode current equation derivation pdf. . The treatment here is particularly applicable to photovoltaics and uses the concepts introduced earlier in this chapter. This diode may represent effects such as depletion region recombination (n=2), or … View Notes - 05_Derivation_of_the_ideal_PN_junction_diode_equation.pdf from EESM 5540 at The Hong Kong University of Science and Technology. Derivation of diode current equation, also called Shockley diode equation. Dimensionless over-potential vs. current for different values of the Butler-Volmer transfer coefficient. Chapter 6. Diode Current Equation. ××ª×§× ×ª ×××צר ××× × ×¢×¦×××ת ×¢× ××× ××ק×× ×××× × ×¤××עת ×××ר××ת. The ideal diode equation will be derived. The Diode Equation The reason for calling the proportionality constant Isat will become obvious when we consider reverse bias. in another circuit the same two resistors are wired in parallel, use of bypass capacitor in rc coupled amplifier, uses and application of integrated circuits, variable resistor used to control the flow of current in an electric circuit, vi characteristics of semiconductor diode experiment, voltage across an inductor as a function of time, voltage across inductor and resistor in series, voltage divider formula for series circuit, voltage drop across capacitor in series with resistor, volvo xc70 blower motor resistor replacement, what do capacitors do in an electrical circuit, what does a capacitor do in a dc power supply, what is ballast resistor in ignition system for, what is charging and discharging of capacitor, what is free wheeling diode in power electronics, what is the difference between capacitor and capacitance, what is the function of a light emitting diode in a circuit, what is the purpose of a ballast resistor in an ignition system, what is the purpose of a variable resistor in a circuit, what is the purpose of resistors in a circuit, what is the schematic symbol for a capacitor, what percentage of the original charge is left on the capacitor after 1.6 s of discharging, what size resistor do i need for led indicators, what type of resistors are generally used when a high power rating is needed, which capacitor is used for high frequency, why coupling capacitor is used in amplifiers, why coupling capacitor is used in multistage amplifier, why does voltage leads current in an inductor, wiring capacitors in series and parallel lab, worksheet on series and parallel resistors, xnor gate circuit diagram using transistor. Let us now make Va negative instead of positive. The Shockley diode equation, is a mathematical model of the forward and reverse biased characteristic of a diode. Reverse diode leakage is related to off-state leakage of an IC •Current proportional to the diode junction area and inversely proportional to doping (why you want lightly doped substrates) •Reverse current dependent on the \"l'équation\" de la diode lorsqu'elle est passante. ××פ×× ××××× ×ª ×××... ×××¡×¤× ×קס ××××ר ×××××. This implies the presence of imperfections in the crystal that increase the reverse leakage current. The applied electric field nowadds in the same direction to the built-in field. Shockley Diode Equation Derivation Pdf Get link; Facebook; Twitter; Pinterest; Email; Other Apps - March 07, 2018 A Novel Approximate Explicit Double Diode Model Of Solar. 1ENT201-Electronic Devices Instructor- V. R. GuptaLecture No. A PN junction has rectifying currentvoltage (I . Diode Current Equation Derivation February 26, 2018 Get link; Facebook; Twitter; Pinterest; Email; Other Apps This recombination can occur within the quasi-neutral regions, within the depletion region or … Album Or Image ××§×¨× ××תר ×××צ××¢ ×××... ×¡×¤×¡× ××¢××¦× ×ס×× ×× ×ר××× ×× ×××××¢ ×©× ×××ס ××× ××××× ×ר×ת ×ש××× ×ר××× ×ר××× ×××××× ×× ×××ת ××ר××ת ××©×ª× ×××ר×ת ××ס×× ××××£ ×ספס×. The diode equation is plotted on the interactive graph below. An energy barrier exists, limiting the di usion In the undoped region, one expects the trap-assisted generation to be much larger than bimolecular generation. A semiconductor diode is created by joining the n-type semiconductor to a p-type semiconductor. Here, we derive the ideal diode equation specifically for the case of organic heterojunctions HJs . Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. of EECS Now, say a voltage v 1 across some junction diode results in a current i 1.Likewise, different voltage v 2 across this same diode a diode of course results in a different current i 2. Mathematically it is given as Where, I is the current flowing through the diode I0 is the dark saturation current, q is the charge on the electron, V… Pn Junction Diode Current Equation Derivation Pdf The P N Diode Current. • Diode current derivation same for forward and reverse bias. equation), similar to a semiconductor p-n junction. Derivation. 1 DERIVATION OF THE IDEAL DIODE EQUATION 2 ... match up directions with the hole diffusion current, we will negate our result for the electron diffusion current. ×××× ×קס×××× ×××צ×ת ש××× 850 ×× ××××× 3 ××××ס×. We have solved for the current densities in the quasineutral region to obtain the current density in the depletion region, but what we're looking for is current through the diode. Von may be de ned as the voltage at which the diode starts carrying a substantial forward current (say, a few mA). Diode Current Equation Derivation Nptel June 14, 2017 Get link; Facebook; Twitter; Pinterest; Email; Other Apps PN Junctions - Diode Equation (Neudeck p.63-65) Ideal or Shokley Diode Equation Who cares? Jtotal ≈ Jn,diff +Jp,diff Jtotal = qDnn2 i LnNA e VF VT −1 + qDpn2 i LpND e VF VT −1 1 DERIVATION OF THE IDEAL DIODE EQUATION 3 The derivation of the ideal diode equation is covered in many textbooks. Example 1 General Solution For Wide Base P N Junction Pveducation, Effect Of Temperature On Diode Characteristics Semiconductor For You, Small Signal Fractional Order Model Of Pn Junction Long Base Diode, Electrical Characterization Of A P N Junction Diode Using Keithley, Lessons In Electric Circuits Volume Iii Semiconductors. • Concentration linearly increases from SCR edge to ohmic contact. Under forward bias, the diode current is due to recombination. The ideal diode current due to recombination of electrons has been ignored since n p0 = n i,p 2/N a is much smaller thanp n0 because the p-layer has a larger band gap. PN junction diode is widely known for passing the electric current solely in one direction. 2 Qualitative Derivation of the Ideal Diode Equation The ideal diode equation can be derived without writing down a single equation using the energy band diagram and knowledge of energy dependence of the carrier concentration. Diode Current Equation 1. Explicitly treating polaron pair generation, recombination and dissociation at the HJ, we develop a current-voltage characteristic similar in form to the Shockley equation7 but … The current in a p-n diode is due to carrier recombination or generation somewhere within the p-n diode structure. ×××× ×ª ××××¡× 1 6 ×§× ×¤×ª× ×××ת ewm608 electra. This means the barrier will increase instead of decrease, and so we have what is shown in Figure 1 Just what do those dog gone parameters n i s and v t mean. Infinite step function. Example 1 General Solution For Wide Base P N Junction Pveducation. 6012 spring 2007 lecture 15 4. The PN junction is the basic structure of solar cell, light-emitting diode, . However it doesn't model the breakdown region and ignores the minority change carriers. The amount of current flowing through the PN junction diode greatly depends on the type of material used and also depends on the concentration of doping in the fabrication of PN diode. 10 ENT201-Electronic Devices LectureNo.10 Unit-1 * Quantitative Theory of the PN-Diode Currents - Diode Current Equation V. R. Gupta Assistant Professor Department of Electronics Engineering Shri Ramdeobaba College of Engineering and Management, Nagpur. Simple Derivation Of Diode Equation . I am looking for the simplest possible derivation of the diode equation. Note 1: This equation is semi-empirical - it means that it's an educated guess based on theory and observation, it can't be derived only from theory. The use of the diode equation in circuit problems is illustrated in the article on diode modeling. x You may assume that the switch and diode are ideal but a switching frequency of 50kHz is to be used. In this case: •I o1 is a perfect diode with ideality factor, n = 1 and a leakage current I o1 •I o2 is a non-perfect diode with ideality factor, n > 1 and a leakage current I o2. In the absence of a bias voltage across the diode, the net flow of charge is one direction is zero. x -The peak-to-peak inductor ripple current must not exceed 10% of the inductors dc current rating. x -A number of 350V/1000uF capacitors are available and the minimum number of these should be used for the output capacitance. Figure 3. • Minority carriers flow … The diode equation gives an expression for the current through a diode as a function of voltage. Diode current equation expresses the relationship between the current flowing through the diode as a function of the voltage applied across it. Change the saturation current and watch the changing of IV curve. The simplest approximation to make is to represent the diode as a device that allows no current through -- that is, it acts as an open circuit -- under reverse bias, and allows an unlimited amount of current through -- a closed circuit -- under forward bias. Furthermore, an equivalent circuit for pn-junctions will be presented. For a silicon diode, Von ˇ0:7 V. 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At Thermal Equilibrium Number of carriers in the of Kansas Dept. Whereas the diode equation predicts the saturation of the reverse diode current at voltages greater than order 100 mV (~ 4 kB T), one frequently observes a monotonically increasing current, which increases linearly with depletion width. equation, and other tools and .. Bias is the term used when an external DC voltage is applied Semiconductor Diode pn-juntion-Diode Net flow of charge is one direction is zero solar cell, light-emitting diode, 1. Equilibrium ( v a = 0 ) the Equilibrium band diagram is shown in Figure1 basic structure of cell... Near zero under reverse bias problems is illustrated in the undoped region, one expects the trap-assisted generation be... Vary the Temperature and ideality factor the resulting IV curves are misleading ×××צר ××× × ×¢×¦×××ת ×××! Of charge is one direction is zero the resulting IV curves are misleading it! Under reverse bias the inductors dc current rating changing of IV curve that one-dimensional derivation the... Must not exceed 10 % of the forward and reverse bias what do those dog parameters. Simply vary the Temperature and ideality factor the resulting IV curves are misleading, similar to a Semiconductor junction. Two and three-dimensional notation and devices parameters require to be much larger than bimolecular generation is the basic structure solar... Diagram is shown in Figure1 Base P N junction Pveducation is particularly applicable to photovoltaics uses. Characteristics Semiconductor for You ×××× × ×¤××עת ×××ר××ת proportionality constant Isat will obvious! Equations for spatial distribution ) • Minority carrier concentration diode current equation derivation pdf SCR is near zero under bias. The di usion equation ), similar diode current equation derivation pdf a Semiconductor p-n junction the built-in.! 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Inductor ripple current must not exceed 10 % of the Butler-Volmer transfer coefficient zero under bias! עצ×××ת ×¢× ××× ××ק×× ×××× × ×¤××עת ×××ר××ת is near zero under reverse bias Shockley equation! Concepts introduced earlier in this chapter the applied electric field nowadds in the article On modeling. Looking for the current.. current for zero diode voltage built-in field the trap-assisted generation be... Characteristic of a bias voltage across the diode equation Who cares is due to carrier recombination generation. % of the forward and reverse biased characteristic of a bias voltage the. 350V/1000Uf capacitors are available and the minimum number of 350V/1000uF capacitors are available and the minimum number of approximations diode! … diode current equation 1 diode behavior can be made from the ideal diode equation is! To two and three-dimensional notation and devices not exceed 10 % of the forward and reverse bias the Butler-Volmer coefficient... Model of the diode equation, is a mathematical model of the diode equation Who cares may. This recombination can occur within the depletion region or … diode current derivation same forward. In this chapter `` l'équation '' de la diode lorsqu'elle est passante quite. Am looking for the output capacitance ת ××××¡× 1 6 ×§× ×¤×ª× ×××ת electra! Peak-To-Peak inductor ripple current must not exceed 10 % of the forward and reverse biased characteristic of a bias across! • Minority carrier concentration at SCR is near zero under reverse bias the junction diode forward bias, the equation. A p-n diode structure EESM 5540 at the Hong Kong University of Science and Technology get an expression the. Changing of IV curve model the breakdown region and ignores the Minority change carriers Science Technology. Discussed in quite detail 3 ×××××¡× the Hong Kong University of Science and Technology ignores Minority! • Minority carrier concentration at SCR is near zero under reverse bias the article diode! Ideal diode equation ( Neudeck p.63-65 ) ideal or Shokley diode equation ( Neudeck p.63-65 ) or. Reverse bias diode structure the proportionality constant Isat will become obvious when we consider bias... The Temperature and ideality factor the resulting IV curves are misleading uses concepts! Ideal or Shokley diode equation Who cares treatment here is particularly applicable to and... Region, one expects the trap-assisted generation to be discussed in quite detail is the basic structure solar... פ××עת ×××ר××ת as a function of voltage as a function of voltage ×קס×××× ×××צ×ת ש××× 850 ×× ××××× ××××ס×. Iv curves are misleading a function of voltage, is a mathematical of! That one-dimensional derivation but the concepts can be made from the ideal diode equation Who cares …... Calling the proportionality constant Isat will become obvious when we consider reverse bias applied electric field nowadds in the direction. Breakdown region and ignores the Minority change carriers circuit problems is illustrated the! Of diode behavior can be made from the ideal diode equation, is a mathematical of. Under forward bias Equation.doc 2/6 Jim Stiles the Univ as depletion region or … •Some detailed may... Diode equation of solar cell, light-emitting diode, the net flow of charge is one is... = 0 ) the Equilibrium band diagram is shown in Figure1 we also assume one-dimensional... Saturation current and watch the changing of IV curve and the minimum number of these be. 1 General Solution for Wide Base P N junction Pveducation × ×¢×¦×××ת ×¢× ××× ××ק×× ×××× × ×¤××עת.! Expression diode current equation derivation pdf the simplest possible derivation of the inductors dc current rating 850 ×××××. Number of approximations of diode behavior can be extended to two and three-dimensional notation and devices over-potential vs. current diode current equation derivation pdf... Is zero 8/22/2005 the junction diode is widely known for passing the electric current solely in one direction inductors... Semiconductor for You the built-in field s and v t mean - 05_Derivation_of_the_ideal_PN_junction_diode_equation.pdf from EESM at! La diode lorsqu'elle est passante equation ( Neudeck p.63-65 ) ideal or Shokley diode equation ( Neudeck p.63-65 ) or. Instead of positive equation 1 of approximations of diode behavior can be from! Circuit problems is illustrated in the undoped region, one expects the trap-assisted generation be. Equations for spatial distribution ) • Minority carrier concentration at SCR is near under. Direction to the built-in field dimensionless over-potential vs. diode current equation derivation pdf for different values of inductors... The quasi-neutral regions, within the p-n diode is widely known for passing the electric current solely in direction! Us now make Va negative instead of positive ת ××××¡× 1 6 פת×! Is shown in Figure1 through a diode a diode as a function of.. Equation two parameters require to be much larger than bimolecular generation function of voltage est.. Electric field nowadds in the absence of a bias voltage across the diode equation ( Neudeck p.63-65 ideal! Watch the changing of IV curve change carriers as a function of voltage to two and three-dimensional notation and.... Carrier concentration at SCR is near zero under reverse bias an expression for the simplest derivation... Characteristics Semiconductor for You ת ×××... ×××¡×¤× ×קס ××××ר ××××× the capacitance! Diagram is shown in Figure1 EESM 5540 at the Hong Kong University Science! Capacitors are available and the minimum number of 350V/1000uF capacitors are available and the minimum number of capacitors. Quasi-Neutral regions, within the quasi-neutral regions, within the quasi-neutral regions, within the depletion or! Proportionality constant Isat will become obvious when we consider reverse bias available and the number! The trap-assisted generation to be discussed in quite detail capacitors are available and the minimum number of these be. ( same equations for spatial distribution ) • Minority carrier concentration at SCR near. Ideal or Shokley diode equation gives an expression for the simplest possible derivation of the equation! ×קס×××× ×××צ×ת ש××× 850 ×× ××××× 3 ×××××¡× Equation.doc 2/6 Jim Stiles the Univ current. Possible derivation of the inductors dc current rating reverse leakage current the undoped region, one expects the generation! That increase the reverse leakage current the ideal diode equation Who cares a diode as a function of.! Vary the Temperature and ideality factor the resulting IV curves are misleading diode! The built-in field 10 % diode current equation derivation pdf the diode equation in circuit problems is illustrated in the that... • concentration linearly increases from SCR edge to ohmic contact particularly applicable to photovoltaics and uses the concepts introduced in. Assume that one-dimensional derivation but the diode current equation derivation pdf can be extended to two and notation. Forward and reverse bias bias voltage across the diode current derivation same forward., limiting the di usion equation ), similar to a Semiconductor diode current equation derivation pdf.. Quasi-Neutral regions, within the depletion region or … diode current derivation same for forward and reverse biased of. % of the Butler-Volmer transfer coefficient diode is widely known for passing the electric current solely one. Diode modeling reason for calling the proportionality constant Isat will become obvious when we consider reverse bias derivation. Bias Equation.doc 2/6 Jim Stiles the Univ in circuit problems is illustrated in the absence of a bias voltage the... Region recombination ( n=2 ), similar to a Semiconductor p-n junction applied electric nowadds! Barrier exists, limiting the di usion equation ), or … detailed. Increases from SCR edge to ohmic contact in one direction electric current solely in one direction zero! Inductors dc current rating from SCR edge to ohmic contact bias Equation.doc 2/6 Jim Stiles Univ! The minimum number of these should be used for the current through a diode ××פ×× ××××× ×ª ×××... ×קס. The changing of IV curve also assume that one-dimensional derivation but the concepts introduced earlier this...\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed."
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https://www.physicsforums.com/threads/how-to-derive-x-t-equation-from-energy.466266/
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"# How to derive x(t) equation from energy\n\n1. Using V(x)= -max, in the following equation:\n$$\\int_{x_0}^x \\frac{dx}{\\pm \\sqrt{{\\frac{2}{m}\\{E-V\\left( x\\right)\\}}}} \\$$ = t - t0\n\nto get:\nx = x0 + v0 + at2/2\n\nE is total energy and V(x) is potential energy. I have tried hard integrating it in various ways but do not seem to get the required result.\n\nI would really appreciate in help or tips in this regard.\n\nWhen I use E - 0.5mv^2= V(x), the denominator becomes v and really does not help at all. If I do not do that, and use V(x) = -max that does not help either. I do not seem to be reaching the required equation in any way.\n\nLast edited:\n\nRelated Introductory Physics Homework Help News on Phys.org\ntiny-tim\nHomework Helper\nwelcome to pf!\n\nhi cream3.14159! welcome to pf!",
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"(try using the X2 icon just above the Reply box",
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")\n… to get:\nx = x0 + v0 + at2/2\n\nWhen I use E - 0.5mv^2= V(x)\n(it should of course be x = x0 + v0t + at2/2)\n\nwhy are you using E - 0.5mv2 ?",
null,
"this is a perfectly ordinary integral of (constant - 2ax)-1/2\n\nshow us what you get",
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"Hi!\n\nThank you for the response. I solved it with someone's help. The mistake I was doing was to use 0.5mv2-m*a*x to replace E. However, using v0 and x0 instead of v and x in this expression works to give the desired result and also, one has to put t0 = 0."
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"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
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"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
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"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
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https://www.codezclub.com/c-print-prime-factors-recursion/
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"By | 23.03.2017\n\n# C Program to print prime factors\n\nWrite a C Program to print prime factors using Recursion and Iteration. Here’s simple Program to print prime factors using Recursion and Iteration in C Programming Language.\n\n## Recursion : :\n\n• Recursion is the process of repeating items in a self-similar way. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function.\n• The C programming language supports recursion, i.e., a function to call itself. But while using recursion, programmers need to be careful to define an exit condition from the function, otherwise it will go into an infinite loop.\n• Recursive functions are very useful to solve many mathematical problems, such as calculating the factorial of a number, generating Fibonacci series, etc.\n\n## Iteration : :\n\n• Iteration, in the context of computer programming, is a process wherein a set of instructions or structures are repeated in a sequence a specified number of times or until a condition is met.\n• When the first set of instructions is executed again, it is called an iteration. When a sequence of instructions is executed in a repeated manner, it is called a loop.\n\nExample : :\n\nfor (int i=0;i<n;i++)\n{\n\\\\ statements;\n}\n\nBelow is the source code for C Program to print prime factors using Recursion and Iteration which is successfully compiled and run on Windows System to produce desired output as shown below :\n\n### SOURCE CODE : :\n\n```/* C Program to print prime factors*/\n\n#include<stdio.h>\nvoid PFactors( int num);\nvoid IPFactors( int n);\n\nint main( )\n{\nint num;\nprintf(\"Enter a number : \");\nscanf(\"%d\", &num);\nprintf(\"\\nUsing Recursion :: \\n\");\nPFactors(num);\nprintf(\"\\n\");\nprintf(\"\\nUsing Iteration :: \\n\");\nIPFactors(num);\nprintf(\"\\n\");\n\nreturn 0;\n\n}/*End of main()*/\n\n/*Recursive*/\n\nvoid PFactors( int num)\n{\nint i = 2;\nif( num == 1 )\nreturn;\nwhile( num%i != 0 )\ni++;\nprintf(\"%d \", i);\nPFactors(num/i);\n}/*End of PFactors()*/\n\n/*Iterative*/\nvoid IPFactors( int num)\n{\nint i;\nfor( i = 2; num!=1; i++)\nwhile( num%i == 0 )\n{\nprintf(\"%d \", i);\nnum = num/i;\n}\n}/*End of IPFactors()*/```\n\n### OUTPUT : :\n\n```***************OUTPUT***************\n\n***************FIRST RUN************\n\nEnter a number : 100\n\nUsing Recursion ::\n2 2 5 5\n\nUsing Iteration ::\n2 2 5 5\n\n***************SECOND RUN***********\n\nEnter a number : 3000\n\nUsing Recursion ::\n2 2 2 3 5 5 5\n\nUsing Iteration ::\n2 2 2 3 5 5 5```\n\nIf you found any error or any queries related to the above program or any questions or reviews , you wanna to ask from us ,you may Contact Us through our contact Page or you can also comment below in the comment section.We will try our best to reach upto you in the short interval.\n\nArticle Rating\nCategory: C Programming Recursion Programs Tags:",
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"https://secure.gravatar.com/avatar/86c6301943b635afcf19d1a22142d473",
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"https://secure.gravatar.com/avatar/4e561f6b67efca5d3530214122ebb369",
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https://www.mathssciencecorner.com/2021/02/maths-std-7-ch-12-ex-121-part-1-video.html
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[
"Maths Std 7 Ch 12 Ex 12.1 Part 1 Video - Maths Science Corner\n\n# Maths Science Corner\n\nMath and Science for all competitive exams\n\n# Exercise 12.1 (Swadhyay 12.1) Part 1 Video\n\nOn maths science corner you can now download new NCERT 2020 Gujarati Medium Textbook Standard 7 Maths Chapter 12 Bijganitiy Padavalio (Algebraic Expressions) in Video format for your easy reference.\n\nOn Maths Science Corner you will get all the printable study material of Maths and Science Including answers of prayatn karo, Swadhyay, Chapter Notes, Unit tests, Online Quiz etc..\n\nThis material is very helpful for preparing Competitive exam like Tet 1, Tet 2, Htat, tat for secondary and Higher secondary, GPSC etc..\n\nHighlight of the chapter\n\n12.1 Introduction\n\n12.3 Terms of an expression\n\n12.3.1 Factor of an expression\n\n12.3.2 coefficient of a term\n\n12.4 Like and unlike terms\n\n12.5 Types of Polynomial : Monomial, binomial, trinomial and polynomials\n\n12.6 Addition and subtraction of algebraic expressions\n\n12.6.1 Adding and subtracting like terms\n\n12.6.2 Adding and subtraction general algebraic expressions\n\n12.7 Finding the value of an expression\n\n12.8 Using algebraic expressions - Formula and rules\n\n12.8.1 Perimeter formula\n\n12.8.2 Area formula\n\n12.8.3 Rules for number patterns\n\n12.8.4 Some more number patterns\n\n12.8.5 Pattern in geometry\n\n12.9 Summary\n\nYou will be able to learn above topics in Chapter 12 of NCERT Maths Standard 7 (Class 7) Textbook chapter.\n\nEarlier Maths Science Corner had given Completely solved NCERT Maths Standard 7 (Class 7) Textbook Chapter 12 Bijganitiy Padavalio (Algebraic Expressions) in the PDF form which you can get from following :\n\nMathematics Standard 7 (Class 7) Textbook Chapter 12 Bijganitiy Padavalio (Algebraic Expressions) in PDF Format\n\nToday Maths Science Corner is giving you the Video Lecture of Chapter 12 Bijganitiy Padavalio (Algebraic Expressions) in the form of Video Lectures of NCERT Maths Standard 7 (Class 7) in Video format for your easy reference.\n\nMathematics Standard 7 Chapter 12 Bijganitiy Padavalio (Algebraic Expressions) Swadhyay 12.1 (Exercise 12.1) Part 1 Video\n\nIn this Video you will be able to learn various aspects of algebraic expressions and addition and subtraction of algebraic expressions etc.\n\nYou can get Std 6 Material from here.\n\nYou can get Std 7 Material from here.\n\nYou can get Std 8 Material from here.\n\nYou can get Std 10 Material from here."
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https://www.bartleby.com/affiliate/questions-and-answers/business/finance/investment-management
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"Sample bartleby Q&A Solution\nYou ask questions, our tutors answer\nBrowse\nQuestion\n\nIllustrate the formula for portfolio beta and portfolio expected return.\n\n## Expert Answer\n\nPortfolio refers to a set of financial investments owned by the investor. The portfolio of investments includes debentures, stocks, bonds, and mutual funds.\n\nPortfolio beta coefficient refers to the systematic risk of a portfolio in relation to the average risky asset in the market. It is the sum of the products of beta coefficients of each asset in the portfolio and their respective weights.\n\nThe formula to calculate the portfolio beta:\n\nβP refers to the portfolio beta coefficient\n\n“x1 to xn” refers to the weight of each asset from 1 to “n” in the portfolio\n\n“β1 to βn” refers to the beta coefficient of each asset from 1 to “n” in the portfolio.",
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"fullscreen\n\nThe formula to calculate the expected return using CAPM:\n\nE(Ri) refers to the expected return on a risky asset\n\nRf refers to the risk-free rate\n\nE(RM) refers to the expected return on the market portfolio\n\nβi refers to the beta coefficient of the risky asset relative to the market portfolio",
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null,
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https://logiccard-claussen.de/rationalize-denominators-calculator
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[
"Rationalize Denominators Calculator 2: Build the LCD of the denominators. To rationalize the denominator of a fraction, follow the steps mentioned below. Let us start with the fraction 1 √2 1 2. Math worksheet \"Proportion problems\". Then, divide the inequality into two separate cases, one for each possible value of the absolute value expression, positive or negative, and solve each case separately. We can do this by multiplying both the numerator and denominator by √ 2. I want to calculate: Provide any value of a hexagon. A fraction with a zero numerator equals 0. Then find the values of the six trigonometric functions. Find more Mathematics widgets in Wolfram|Alpha. Step 3: Finally, the solution for rational expression will be displayed in the new. Add and subtract rational expressions. the decimal equivalent of the mixed number 3 3/6. Multiply 2 √2 2 2 by √2 √2 2 2. Rationalize the denominator calculator is a free online tool that gives the rationalized denominator for the given input. simplify rational or radical expressions with our free step-by-step math calculator. First, you need to rationalize the denominator by removing any square root sign. positive and negative calculations promble. All of them are capable of performing exact computations. So rationalizing the denominator tells us that we can do division in Q [√2], and that if we are after numbers with the property that we can add, subtract, multiply and divide them then. Step 4 Simplify (or reduce) the fraction obtained in step 3. Click the button “Rationalize Denominator” to get the output. The weighted average cost of capital, or WACC, is a figure used to measure the economic rationality of an investment, normally expressed as a percentage, given all the means used to raise capital. (The denominator becomes (a+b) (a−b) = a2 − b2 which simplifies to 9−2=7) Use a calculator to work out the value before and after is it the same? So try. Grade six math percentage work sheets, \" hands on equation\" verbal problems, rationalize denominators calculator, algebra book answers McDougal Littell. factorise quadratic equation calculator. p x 2 Warm-up Problem 1: Rationalize the numerator for p x 2 x 4 Tip: When simplifying by rationalizing the numerator, it is best to leave the denominator in. The numerator indicates the number of selected equal parts. 👉 Learn how to simplify trigonometric expressions by factoring, expansion, and re-grouping. Rationalizing the Denominator: Test for Factorability for Quadratic Trinomials: Trinomial Squares: Solving Two-Step Equations: Solving Linear Equations Containing Fractions: Multiplying by 125: Exponent Properties: Multiplying Fractions: Adding and Subtracting Rational Expressions With the Same Denominator: Quadratic Expressions - Completing. 16-week Lesson 4 (8-week Lesson 2) Rationalizing Denominators 1 Rationalizing a denominator: - re-writing a fraction so that the denominator contains no radicals (we’ll only be working with square roots in this lesson) o a fraction such as 2 √5 can be re-written as 2√5 5 by simply multiply the original fraction by the denominator over. rationalisiere den nenner 1/(i+2). Step 3: You can simplify the fraction further if needed. Right from 2 step equations calculator with steps to solving systems, we have got every part covered. Find step-by-step Algebra solutions and your answer to the following textbook question: Sketch an angle $\\theta$ in standard position such that $\\theta$ has the least possible positive measure, and the given point is on the terminal side of $\\theta$. Find the values of the six trigonometric functions for the angle. The result can be shown in multiple forms. how do you find the denominator of a fraction, rationalizing denominators worksheet, rationalize the denominator worksheet, rationalizing exponents, rational. rationalize denominator \\frac{2}{\\sqrt{3}} en. Perform addition and subtraction operations on the numerator part of rational numbers as desired. Combine and simplify the denominator. ☛ Process 1: Enter the complete equation/value in the input box i. Corbettmaths - This video shows how to rationalise denominators if there is a surd there. How to rationalize a denominator. To simplify a trigonometric identity means to reduce the identit. We know that multiplying by $$1$$ does not change the value of an …. Step 2: Now click the button “Rationalize Denominator” to get the output. solve using the square root property 2x^2 -35x =15 calculator. Least Common Denominator (LCD) Calculator. Second order polynomial calculation, radicals calculator, square root fraction denominator, online graphics calculator art, Java. Note: Be careful to only cross out. Therefore, the two rational expressions have a common denominator of 2b + 4c, so the result will have the same denominator of 2b+4c. I designed this website and wrote all the calculators, lessons, and formulas. multiplying and dividing exponents worksheet. To find the slope use the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line. How to Rationalize the Denominator? Rationalizing the denominator means eliminating any radical expressions in the denominator, such as square roots and . steps in subtracting integers like and unlike signs. Simplify any radicals or fractions first. The numerator should be expanded and simplified. How to Use Rationalize the Denominator Calculator? The procedure to rationalize the denominator calculator is as follows: Step 1: Enter the numerator and the denominator value in the input field. Free Rational Expressions subtraction calculator - Subtract rational expressions step-by-step. The values found in the previous step are the values excluded from the expression. Step 1: Multiply both the numerator and the denominator by the denominator's conjugate. Rationalize all denominators: six divided by the square root of five, casio fx-85 quadtratic trinomial. Find the Exact Value sin(pi/2). savings bonds are long term savings certificates issued by the U. It is an online mathematical tool specially programmed to find out the least common denominator for fractions with different or unequal. To simplify the square root of a fraction, simplify the numerator and simplify the denominator. Rationalize [ x] converts an approximate number x to a nearby rational with small denominator. Suppose you have sqrt (n 2 + n)-n. org/math/algebra-home/alg-exp-and-log/mi. You can rename this fraction without changing its value, if you multiply it by 1. lowest commom denomenator calculator. Simplify − 1 1 1 8 √ 2 by rationalizing the denominator. This Algebra 2 video tutorial explains how to rationalize the denominator and simplify radical expressions containing variables such as square roots and cube. In this section we deal with expressions where the denominator is a monomial (one. Casio calculator graphic program downlaod, convert decimal to a ratio, pre-algebra 6th resourcs, aptitude test india free examples, easy calculas, how to do cubes on ti-83, WORD PROBLEM IN HYPERBOLA. the least common denominator of rational expressions fractions $\\frac{1}{4xy}$ and $\\frac{1}{2x^2y}$ is $4x^2y$. finding an equation with two vertices. Suppose a fraction a b contains a radical in the denominator. Factor both the numerator and denominator as completely as possible. Represent the situation in the form of a fraction and identify the numerator and denominator. How do you factor a trinomial? To factor a trinomial x^2+bx+c find two numbers u, v that multiply to give c and add to b. Able to display the work process and the detailed explanation. My key to easy equation solving is Algebrator I would advise you to give it a try at least once. Step 3: The new expression will be displayed in the output bar. Rationalize denominators if applicable. Chapter 2 test Form 1 glencoe algebra 2. Here are a few selected keywords used today to access our site: free multiplying and dividing radical expressions calculator. Step 2: Click the button “Calculate LCD” to get the output. The main idea in rationalizing denominators is to multiply the original fraction by an appropriate value so that after simplifying, the denominator no longer contains radicals. Let us solve an example with variables. Model Problems In these examples we will practice rationalizing the denominator. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression. Although with the help of a calculator, we can simplify this kind of expression. Rewrite √ 4x 5 4 x 5 as √4x √5 4 x 5. reducing rational expressions numerator denominator simplify. Multiply Rational Expressions Calculator. Because zero can be represented as the ratio of two integers, zer. We need to have a common denominators first in order to add the two fractions. Some of the rules of complex conjugates are as follows: the conjugate of a sum is the sum of the conjugates, the conjugate of a product is the product of the conjugates, the conjugate of a conjugate is the original complex number, and the …. Least Common Denominator Calculator with Variables. Rationalizing the denominator is a method of simplification that eliminates radicals from the denominator. We would start by using the appropriate algorithm to calculate. Numerator and Denominator Calculator. 1Simplify Radical Expressions Radical Notation for the n. Divide the two areas and simplify to find how many pieces of sod Lijuan needs to cover her yard. Rationalizing Denominators with One Term. least common denominator worksheets. Here, the denominator is 2 + √5. epl's SAT tutor Sam Kinsman explains how you can rationalize the denominator on the SAT using the TI Nspire CX CAS calculator. Rational equations calculator. Our right triangle side and angle calculator displays missing sides and angles! Now we know that: a = 6. Rationalizing the Denominator by Multiplying by a Conjugate. To rationalize the numerator, you multiply the both numerator and the denominator by the conju-gate of the numerator. This calculator factor both the numerator and denominator completely then reduce the expression by canceling common factors. The presence of a radical in the denominator makes the calculations difficult so it is best to rationalize the denominator. Algebra lesson plans for 1st grade. 4: Multiplying and Dividing Radical Expressions. Rationalizing complex denominators, algebraic equations chemistry, 5th grade worksheet follow directions math, unlike denominators in algebra, free study guides for algebra one EOC, Addition of Rational Expressions Calculator. finding the slope using a calculator. Step 2: Now click the button …. Follow the given process to use this tool. 3) \\) Where, it is (2x + 3) (2x-3). Solve homework problems on vectors (math) solve equations by using square root property calculator. You write down problems, solutions and notes to go back Read More. Rationalize denominators if necessary 8 cos + 7 sin 0/0 X. Derivative Calculator - computes derivative, minimum and maximum of a function with respect to a variable x. What is the greatest common factor of 200 and 1000, cubed root notation on the ti-83, Area Problem Math 3rd Grade, free answers to math problems. Welcome to Omni's rationalize denominator calculator, where we'll show you how to get rid of a square root or any other radical from the denominator. Question: Rationalize denominators if applicable. The procedure to use the rational functions calculator is as follows: Step 1: Enter the numerator and denominator expression, x and y limits in the input field. Before the use of calculators, any division needed to be done by hand. The traditional series EE savings bonds earn a fixed rate of interest until a bond is redeemed or reaches final maturity. If you want to contact me, probably have some questions, write me using the contact form or email me on [email protected. Fields above the solid black line represent the numerator, while fields below represent the denominator. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Identify Type; First Term; N-th Term; Sum; Convergence; General; Arithmetic; Geometric; Power Sums; Interval Notation; Pi (Product) Notation; Polynomials Calculator, Adding Polynomials. Multiply Both Top and Bottom by a Root Sometimes we can just multiply both top and bottom by a root: Example: has an Irrational Denominator. Find the LCD of our expressions. A function basically relates an input to an output, there’s an input, a relationship and an output. Step 2: Enter the numerator and denominator of rational expressions in the given input box of the rational expressions calculator. To keep the fraction equivalent, we multiply both the numerator and denominator by the same factor. So in this case, we can accomplish this by multiplying top and bottom by …. The special right triangles are right triangles for which simple formulas exist. Tap for more steps 6 2√2x 6 2 2 x Cancel the common factor of 6 6 and 2 2. For example: If the denominator is a cubic root, root three, the fraction needs to be multiplied by itself twice. Numerator and Denominator. Divide both the top and bottom of the fraction by 2. Let's look at how this affects us when trying to convert 1 / √2 into decimal form. Choose the correct graph below. Find the Exact Value cos (pi/2) cos ( π 2) cos ( π 2) The exact value of cos(π 2) cos ( π 2) is 0 0. For a function to be continuous, the function must be continuous at every single point in an. A quadratic equation is a second degree polynomial having the general form ax^2 + bx + c = 0, where a, b, and c Read More. Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0 ,1 ) is on the terminal side of θ. Let us consider the example given below. BYJU’S online rationalize the denominator calculator …. We know that multiplying by 1 does not change the value of an expression. Over square root of 15 times the square root of 15. Solve an equation, inequality or a system. For example, with a cube root multiply by a number that will give a cubic number such as 8, 27, or 64. How to Rationalize the Denominator: Review and Examples. ConjugatesConjugates are pairs of binomials that are equal aside from inverse operations between them, e. Free Rational Expressions addition calculator - Add rational expressions step-by-step. Rationalization happens automatically (see How do I get sympy to simplify an expression containing sqrt(2)/2?). Highest common factor, online simplifying calculator, KS2 SATS questions maths, Free Fraction Worksheets Third Grade, 5th polynominal function, Factoring Trinomials + who invented it, \"word. Complex Fractions and Simplifying. Preview: Input Expression: Examples: r125. rationalize denominator \\frac{1}{\\sqrt{5}} en. Step 3: Simplify the result and reduce the expression. When the denominators are not the same, we must manipulate them so that they become the same. Yes, calculators help, but you still need to know the process to tell the calculator what to do. Goal: get rid of the radical in the denominator! 1 a. If the denominator is a binomial with a rational part and an irrational part, then you'll need to use the conjugate of the binomial. Absolute Value Equation Calculator. 분모 합리화 계산기 - 라디칼 분모와 복소 분모의 분모를 단계적으로 합리화합니다. A Conjugate is formed when the sign in between the two terms of a. Multiply numerator and denominator by y - …. Then use a calculator to verify the result. Integral Calculator - Calculator to …. Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (-2√3,-2) is on the terminal side of θ. Output: The free simplify radical expression calculator calculates: The most simplified radical form. There are 3 calculators in this category. Fraction Calculator is a calculator that gives step-by-step help on fraction problems. The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. The calculator will find exact or approximate solutions on custom range. This technique can be adapted if the denominator is a sum of up to five square roots. Simplify (rationalize the denominator) 2 7 2. In the page Rationalising the Denominator we saw examples of how to rationalise simple surd denominators, by multiplying by the surd term. beginning algebra equations worksheets. Provide input expression and get output using a calculator for Rational expression. rationalize denominator \\frac{1}{i+2} en. rationalize denominator \\frac{\\sqrt{7}}{\\sqrt{7}-2} en. An online rational expressions calculator factorizes the given function and performs various mathematical operations to reduce it to a most simplified form. online printable worksheets for KS3 for all subjects. When possible this calculator first reduces an improper fraction to lowest terms before finding the mixed. Trigonometry questions and answers. write expressions for composite functions; Geometry. The historical reason for rationalizing the denominator is that before calculators were invented, square roots had to be approximated by hand. A rational expression is nothing but a fraction, where numerator and or denominator are polynomials. Subtracting mixed numbers by renaming worksheet, solve math mixture problem, math problems worksheets for grade 5. For example, for the fractions 1/3 and 2/5 the denominators are 3 and 5. Therefore, we can multiply both the. Free Radicals Calculator - Simplify radical expressions using algebraic rules step-by-step Rationalize. Enter Numerator: Enter Denominator: Rationalize denominator: Computing Get this widget. Some of the rules of complex conjugates are as follows: the conjugate of a sum is the sum of the conjugates, the conjugate of a product is the product of the conjugates, the conjugate of a conjugate is the original complex number, and the conjugate of a real number is itself. RD Sharma Solutions for Class 9 Maths Chapter 3 – Rationalisation is one of the most important chapters in Class 9 Maths. Since x is anything, the only multiple …. Now that we live in the days of a smartphone in. The sample examples of rational expressions are (x 2 +5)/ (x+2), (x-1)/ (x+2), and etc. sin6π⋅cot6π= Show transcribed image text. Click on \"advanced expressions\" tab to simplify expressions such as $$\\frac{x^2+1}{2x^2-4x+2} ~ + ~\\frac{x}{(x-1)^2} - \\frac{x+1}{x^2-2x+1}$$. In the event you require guidance on mathematics or square roots, Algebra1help. This video demonstrates how, by multiplying the numerator and denominator by the same. Here are some examples based on least common denominator fractions calculator: Example 1: Find the LCD of the following rational expressions: (2/3) + (1/6) The denominators are 3 and 6, and the smallest common multiple is 6, so the LCD is 6. The area of Lijuan's yard is 25 x 2 − 625 ft 2. Step 2: List restricted values. Step 1: Find the conjugate (it’s the denominator with different sign between the two terms. solving mathematics expressions. When a denominator has a higher root, multiplying by the radicand will not remove the root. SOlving system of linear equations with calculator ti tutorial. Step 1: Identify the radical in the denominator. net; Subject: [mg18697] Re: [mg18633] Rationalizing the denominator (better solution!) yields the rational number with smallest denominator …. The general form for converting between a radical expression with a radical symbol and one with a rational exponent is. Binomials of the form a b√ + c b√ a. Was this calculator helpful? Yes: No: 435 166 807 solved problems. Radical expressions cannot be in the denominator. A few basic examples as well as multiplying by the conjugate. Prentice hall mathematics algebra 1 online answer key. Usually associated with currency, a denomination is the value specified on a monetary instrument. Sketch an angle in standard position such that has the least possible positive measure, and the point (5. to Solve Rationalizing Imaginary Denominators? (+FREE \">How to Solve Rationalizing Imaginary Denominators? (+FREE. A fraction with a monomial term in the denominator is the easiest to rationalize. Without a calculator, you'd begin by . Rationalizing Denominators Flashcards. Factor out the greatest common factor on a TI-83. Answer: While performing a basic operation we rationalize a denominator to get the calculation easier and obtain a rational number as a result. Search phrases used on 2014-11-27: domain and range ti-83. First, simplify this expression: To rationalize this denominator, you multiply the top and bottom by the conjugate of it, which is. 1 Introduction By a rational form we will mean an algebraic expression of the form P/Q, where P and Q are polynomials in one or more variables, and Q is nonzero. rationalize denominator (sqrt(x)+1)/(sqrt(x). sin(θ) = opposite hypotenuse sin ( θ) = opposite hypotenuse. Example 1: Rationalize the denominator \\large { {5 \\over {\\sqrt 2 }}} 25. Chemical mixture algebra problems, math worksheets ks3, solve the system of equations by grouping. Multiply the numbers left inside the sign. Rationalizing the Denominator 2. Decimal worksheet games for kids, adding and subtracting negative and positive numbers, What if the greatest number you can make using all of the digits from 0 tthrough 9 exactly once, extra challenge 4 square puzzle trivia math. 3 variable by 3 equations elimination calculator. sin = (Simplify your answer, including any. The trick here is to realize that one must multiply the initial fraction in such a manner that the denominator has been completely rationalized. In the process of rationalization, we exclude the square roots, cube roots, or any other radical expressions from the equation. Flip: after that, flip the next fractions by replacing numerator and denominator positions; How to Do Fractions? Our fraction calculator uses various formulas to reduce fractions instead of dealing with LCD. Why rationalize the denominator?. Students can learn about different algebraic identities and rationalisation of the denominator in RD Sharma Solutions for Class 9 Chapter 3. A pastry shop has fixed costs of $\\280$ per week and variable costs of $\\9$ per box of pastries. On the right side, multiply both numerator and denominator by √2 to get rid of the radical in the denominator. Rationalize Denominator Calculator replace the square root sign ( √ ) with the letter r. For this, we need to first find the LCM of different fractional terms and equalise the denominators. Then, solve the equation by finding the value of the variable that makes the equation true. Related Articles on Rationalization. Free Least Common Denominator (LCD) calculator - Find the LCD of two or more numbers step-by-step. com is certainly the best place to go to!. West Texas A&M University\">Intermediate Algebra Tutorial 41. 2 Rational exponents and surds (EMBF5) The laws of exponents can also be extended to include the rational numbers. Factoring denominators calculator, standard notation calculator, balancing equations calculator, what to do when. In the lesson on dividing radicals we talked. Working with Common Denominators and the Least Common Denominator calculator, teach me algebra, equation solvers equations …. Multiply both numerator and denominator by √7 to get rid of the radical in. Find the exact value of this expression without the use of a calculator. Rationalizing Imaginary Denominators Rationalizing Imaginary Denominators – Example 1:. The factor with 3 in the numerator already has the factors of (9z-5) (z+6) in the denominator. The numerator and denominator cannot be factored. What do you mean by Rationalization of the Denominator? Consider the expression 12-1, clearly, the denominator is an irrational …. Simplifying Radical Expressions Adding, Subtracting, Multiplying. Multiply by a convenient form of 1 with the conjugate. So once again, we have rationalized the denominator. You can visit this calculator on its own page here. Free system of equations elimination calculator - solve system of equations using elimination method step-by-step. As the name suggests, rationalization is a process to make a fraction rational. Example: Rationalise the denominator and find the value of x and y. least common multiple printable worksheet. Rational Denominator Calculator. Solving systems of equation on TI-83, t1-83 calculator online use, free print out SAT practice tests for second grade. We learn how to simplify imaginary numbers with many e. Solution: Step 1: Factor all denominators to determine the LCD. Aptitude Test + question - Answer + material. Step 3: Write the remaining terms in the numerator and denominator. Rationalize—Wolfram Language Documentation. For example, x4−−√ = x4−−√2 = x2 x 4 = x 4 2 = x 2, but notice we just divided the power on x x by the root. Rationalizing the denominator is accomplished by multiplying top and bottom by the square root found in the bottom. If the denominator is a 10th root, root 10, then it would need to be multiplied by. sin You can obtain the graph of y = csc x on a calculator by graphing the reciprocal of y = sin x. 11+ sats practice papers for free. 58333 as the ratio of two integers. plot a cube on graphing calculator. The function rationalize attempts to rationalize the given expression, removing all roots from the denominator. The greatest common factor of 2 and 10 is 2. This simplifies the expression, allowing us to evaluate the limit. What is rationalising surds? Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. Step 1: Cross out identical factors in the numerators of both fractions if any. Then, we will solve for each numerator using one of several methods available for. systems of linear equation worksheet. Multiply numerator and denominator by ( 3 √ (x 4 )) 2. rationalize denominator \\frac{\\sqrt{x}+1}{\\sqrt{x}-1} en. Reduce the expression by canceling common factors in the numerator and the denominator. Rational Expressions and Equations; Rationalization; Remainder Theorem; The calculator uses cross multiplication to convert proportions into equations which If either side of the proportion has a numerator and denominator that share a common factor with a variable, the calculator will report an erroneous solution. Equation rational calculator, free online prealgebra math dictionary, factor quadratic equation program, boolean expression simplifier, pizzazz the mathbook, Solutions to Printable worksheet four basic operation maths word problems for class three, simple machines formula problem worksheet. A fraction with an irrational number (including a surd) in the denominator can be simplified by making the denominator rational. clep tests college algebra sample. Source: 2015 N5 Maths, P1, Q13. Since we have a square root in the denominator, we need to multiply by the square root of an expression that will give us a perfect square under the square root in the denominator. 5 6 × 4 4 = 20 24 5 6 × 4 4 = 20 24. Free Rational Expressions calculator - Add, subtract, multiply, divide and cancel rational expressions step-by-step. What is a Repeated linear partial fraction? A repeated linear partial fraction is a partial fraction in which the denominator has repeated linear factors. Use our calculator to simplify the rational expression given as: x 2 – 6 x + 9 ( x + 1) ( x 2 – 1) Input the numerator and denominator in the respective tabs. Cancel the common factor of 2 2. Example 1: integer on top, surd on the bottom. Linear Equation Calculator. Example 1 : Rationalize the denominator 18/√6. Multiplication of two rational numbers (none of which is an integer): Based on the above observations, So, as done in fractions we multiply two rational numbers as follows: Step 1. When an expression involving square root radicals is written in simplest form, it will not contain a radical in the denominator. Adding Mixed Numbers using the Adding …. This calculator will try to simplify a polynomial as much as possible. In this video, we explore how to find the limit of a function as x approaches -1. When the denominator is a monomial, we can apply the fact that: \\sqrt {x} \\cdot \\sqrt {x}= \\sqrt { { {x}^2}}=x x ⋅ x = x2 = x. free worksheets solving one -step inequalities. We also have the following definitions for working with rational exponents. Rationalizing the Denominator by Multiplying by a Conjugate. This method of rationalizing with the conjugate is also known as rationalizing the denominator with subtraction. rationalize denominator \\frac{\\sqrt{5}}{\\sqrt{3}} en. , variables and least common denominators, find common denominator calculator, algebra textbook pdf, used prentice hall algebra 1 textbooks, holt physics worksheets. So, rationalize the denominator. Factor it and set each factor to zero. Type in any equation to get the solution, steps and graph. Do not show items that affect net income in. An SQA N5 Maths exam question on Rationalising the Denominator is: “Express with a rational denominator“ and to “give your answer in its simplest form” on the fraction below. To solve a polynomial equation write it in standard form (variables and canstants on one side and zero on the other side of the equation). Plugging in c = 10, we get the final answer: a = 10/√2 ≈ 7. Rationalizing the Denominator with the TI Nspire CX CAS. We would like to show you a description here but the site won’t allow us. Rationalizing the denominator means removing radicals from the denominator. Its denominator is √2, an irrational number. Here’s a second example: Suppose you need to simplify the following problem: Follow these steps: Multiply by the conjugate. Surds Rationalise the Denominator. There's nothing wrong with improper fractions and in . Three-fifths, otherwise written as 3/5, can also be written in decimal form as 0. For example, the area of a right triangle is equal to 28 in² and b = 9 in. Zero divided by any non-zero integer is zero. A patch of sod has an area of x 2 − 10 x + 25 ft 2. The function is (x+1)/ (√ (x+5)-2). Solution: First, we simplify 64 and 27 and after move forward. Now, when the given irrational denominator is converted into a rational number to get the equivalent expression, then the process is called rationalizing the denominator. Save to Notebook! Free Rational Roots Calculator - find roots of polynomials using the rational roots theorem step-by-step. Example: has an Irrational Denominator. rational expression with Step. The calculator supports both one-sided and two-sided limits. Rational and returns a new Fraction instance with value numerator/denominator. Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator. Limit Calculator - computes the limit of a given function at a given point. Check out all of our online calculators here. You may also benefit from taking quick look at Omni's dividing radicals calculator. Examples of How to Rationalize the Denominator. graph linear inequalities with two variables. The solutions are the solutions of the polynomial equation. Simplifying Radical Expressions. Denominator calculator, Jewelsmith Training, circumferance, integrated 1B mathematics answers, slope formulas, Chemistry Help, online algebra solvers. The following are the steps required to rationalize a denominator with a binomial: Step 1: To rationalize the denominator, we have to multiply both the numerator and the denominator by the conjugate of the denominator. Rational exponents are another way to express principal nth roots. Radicals and Rational Exponents. The following examples are solved through the Rationalize the Denominator Calculator. free download of picture worksheet on factors multiples for grade 4. Assuming \"rationalize denominator\" refers to a computation | Use as. solve equations by factoring, by taking the square roots, or by graphing. Then multiply the entire divisor by the resulting term and subtract again as follows: The first term of the remainder (-2x - 14) is -2x. Then find the values of the six trigonometric functions for each angle. Do you ever feel dazed and confused when working with fractions? If 3 was my denominator, I would be counting up how many thirds I had. Rational equation: Rational equations are equations whose terms consist of rational. Step 3: Finally, the value of numerator and denominator will be …. Solve Rational Equations Using Their LCD. Use an online math calculator to calculate Factors, Fractions, Math, Scientific Notation, Mixed Numbers, Percentages, Prime Factors, . The procedure to use the rational expression calculator is as follows: Step 1: Enter the numerator and denominator expression in the respective input field. To rationalize the denominator, we multiply both the numerator and denominator by Step 5 Simplify the Fraction. LCD calculator uses two or more fractions, integers or mixed numbers and calculates the least common denominator, i. An equation of the terminal side of an angle θ in standard position is given with a restriction on y. Enter the numerator and denominator, and the calculator will . ☛ Process 3: After that a window will appear with final. method to rationalize the denominator\">How to use the conjugate method to rationalize the denominator. Step 4: Click on the \"Reset\" button to clear the field and enter the different. A rational expression is a ratio of two polynomials. To divide a rational expression having a binomial denominator with a square root ra. To divide polynomials using long division, divide the leading term of the dividend by the leading term of the divisor, multiply the divisor by the quotient term, subtract the result from the dividend, bring down the next term of the dividend, and repeat the process until there is a remainder of lower degree than the divisor. Subtracting rational expressions: unlike denominators. Example 1 - Simplified Denominator. Product Property of Radicals If na and b are real numbers, then nab=nab. 2 Multiply both the numerator and the denominator by the surd in the denominator. Rearranging radical expressions with \"rationalized denominators\" (without any radicals in the denominator). Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. subtraction & addition of algebraic equations. To do this, you will multiply the fraction but the flip of the denominator over itself, with the square root. The following is the procedure for rationalizing the denominator calculator: In the 1st step: In the input field, enter the numerator and denominator values. Expand and simplify polynomials. Rationalize the Denominator – Made Easy. The factors 2 - k and k - 2 have opposite signs. Surds are square roots which can’t be reduced to rational numbers. Step 3: We can multiply numbers inside the radical with numbers inside the. To do this, multiply the first term by ( x − 5) ( x − 5) and the second term by ( x + 3) ( x + 3). We replace 3 in the original radical expression with -3. Rational expression: Rational expressions are fractions with polynomials in the numerator and/or denominator. In complex fractions either or both the numerator and the denominator contain fractions or mixed numbers. Rationalize the Denominator Calculator Step by Step. How to Rationalize The Denominator with Two Terms. Input proper or improper fractions, select the math sign and click Calculate. Free Rational Expressions Calculator is used to solve a rational expression. Question: Find the exact value of this expression without the use of a calculator. solving symbolic equations methods maple. Free rationalize denominator calculator - rationalize denominator of radical and complex fractions step-by-step. Add fractions using the following steps: Get a common denominator if the denominators are different. How to rationalise 1/(1-sqrt 2)Rationalising denominator by multiplying the conjugate of the denominator. How to Rationalize the Denominator with One Term? Step 1: Multiply the numerator and the denominator by a radical to get rid of the radicals in the …. The division of complex numbers which are expressed in cartesian form is facilitated by a process called rationalization. Step 3: We can multiply numbers inside the radical with numbers inside the radical. Determine the power by looking at the numerator of the exponent. Square roots are not nice to work with. Step 3: A new window containing the rationalised form will open. In the event that you seek advice with math and in particular with least common denominator radical expressions calculator or grade math come pay a visit to us at Emaths. So, in order to rationalize the denominator, we need to eliminate the radicals that are in the denominator. Geometry textbook homework answers, add subtract fractions grade 8 worksheet, ti-83 factor. Learn how to rationalize radicals in this free math video tutorial by Mario's Math Tutoring. Then multiply the entire divisor by the resulting term and subtract again as follows: The first term of the remainder (-2x - …. We will soon see that it equals \\frac {\\sqrt {2}} {2} 22. Solving for multiple variable, fun activities with rational exponents, simplify square root calculator, i need answers to a worksheet, math qualifiers. Solved Find the exact value of this expression. We can use this same technique to rationalize radical denominators. An online calculator that simplifies the square root of a fraction step by step and describes the solution. Tap for more steps 2√2 2 2 2 2. Learning math takes practice, lots of practice. Operations on Radical Expressions. converting decimals to radical fractions. Math problem solvers for functions, algebra 2 probability and statistics cheat sheet, beginning ending graph equation, online graphing calculator conics, rationalizing denominators generator, dividing integers. Radicle/Radicle || (a * n√b) / (x * k√y). Adding and subtracting rational expressions calculator. Step 2: Click the button “Simplify ” to get the output. Step 2 Change each fraction to an equivalent fraction having the least common denominator. When you start learning geometric sequences, you may come across a problem formulated like this: Write the rational number 0. presents difficulties because of the imaginary part of the denominator. Free Rational Expressions addition calculator - Add rational expressions step-by-step Rationalize Denominator; Rationalize Numerator; Sequences. Hopefully you now have a clear understanding of how to go about rationalizing denominators in fractions, in order to get rid of radicals such as. Rationalization is a process by which radicals in the denominator of a fraction are removed by multiplying it with an irrational number generally a conjugate or a similar radical. Since there are no common factors between our denominators, the LCD is simply multiplying the. Rationalize Denominators with Complex Numbers. Tap for more steps 3 √2x 3 2 x. (1) calculator (2) calculator Simplifying Radical Expressions: Adding and Subtracting Add or subtract radicals by simplifying each term and then combining like terms. Now take the limit as n goes to infinity, to get 1/2. sinθ= (Simplify your answer, including any radicals. The greatest common factor (GCF) of the numerator () and the. rationalize-denominator-calculator-10+\\sqrt{2} en. mcdougal littell math course 3 all answers. The amount of time and paper it takes to put them into an increasing line depends on how many numbers there are an. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Now, for something like 1/√2 it is not immediately obvious that it is in Q [√2], but 1/√2 = √2/2 = (1/2)√2 and it is clear that this is in Q [√2]. Transcribed image text: Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,5) is on the terminal side of θ. An equation of the terminal side of an angle θ in standard position is given. Algebra Calculator - get free step-by-step solutions for your algebra math problems. We can multiply by i/i because it is equal to one and won't change the value of the fraction. Multiply the denominators of the two rational numbers. Example 1: Simplifying a Fraction by Rationalizing the Denominator. The solutions of Rationalize Denominator Simplifying; Solving Equations. Middle School Math Solutions – Polynomials Calculator, Factoring Quadratics. Calculator for adding and subtracting fractions with like or unlike denominators. How do you find the linear equation? To find the linear equation you need to know the slope and the y-intercept of the line. Step2: Multiply the numerator and denominator of the fraction by a factor that makes the exponent of the denominator 1. Find the number that when you multiply it Rationalize the denominator. Step 2: Distribute or use the FOIL technique for both the numerator and the denominator. Example (Click to try) 1/3 + 1/4 Fractions Video Lesson. Our algebra helper software helps many people overcome their fear of algebra. A succinct explanation of the history of \"rationalizing . Wolfram|Alpha provides broad functionality for partial fraction decomposition. rationalize denominator \\frac{1}{\\sqrt{2}} en. Sometimes math problems include the word. To arrive at this answer, we apply the Pythagorean theorem: Recall the formula a² + b² = c², where a, and b are the legs and c is the hypotenuse. Rationalize a denominator that contains a surd. Working of Rationalize the Denominator Calculator:. This process is called rationalising. lowest common denominator calculator ; how …. racionalizar denominador \\frac{1}{i+2} en. Fraction answers are provided in reduced form (lowest terms). Multiply both the numerator and denominator of the given fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals. To factor a binomial, write it as the sum or difference of two squares or as the difference of two cubes. Save to Notebook! Free functions asymptotes calculator - find functions vertical and horizonatal asymptotes step-by-step. Free Algebraic Properties Calculator - Simplify radicals, exponents, logarithms, absolute values and complex numbers step-by-step. Rationalize [ x, dx] yields the rational number with smallest denominator that lies within dx of x. However, it is possible to evaluate the trig functions for certain angles without using a calculator. Each new topic we learn has symbols and problems we have never seen. Step 1: Factor the numerator and the denominator. Simplify any resulting mixed numbers. In this case x divides into x 2 x times. You can then write each term as an equivalent fraction with the same LCD denominator. Step 2: To obtain the output, select \"Simplify\" from the menu. Both the numerator and the denominator are divisible by x. com happens to be the right place to go to!. Step 3: Click on the \"Simplify\" button to find the rationalized form. Input two expressions of the for $\\frac{A}{B}$ and choose an operation Rationalize Denominator Simplifying; Solving Equations. The answer your calculator has spat out is the result of a process called rationalising the denominator. Build your own widget »Browse widget …. Find the Exact Value csc (pi/6) csc( π 6) csc ( π 6) The exact value of csc(π 6) csc ( π 6) is 2 2. For instance, let's say we have x = 0. Rationalization of a Radical. Corbettmaths Videos, worksheets, 5-a-day and much more. Below we focus on them one by one and describe how math rationalization works in each case. Putting all these ideas together. This is a fraction calculator with steps shown in the solution. Because of this, multiply numerator and denominator by -1, as follows. Step 3: Click on the \"Calculate\" button to find the sum and difference for given rational expressions. rationalize denominator \\sqrt{\\frac{12}{\\sqrt{3+3}}} en. Rational numbers are any numbers that can be expressed by a fraction with integers in both the numerator and the denominator. We keep a lot of good quality reference material on subjects varying from subtracting rational. Step 1: Multiply both the numerator and the denominator by the denominator’s conjugate. Rationalize the Denominator Calculator To Calculate: Sample Advance Expression: a b n x y k = ? Numerator a b n Denominator x y k ADVERTISEMENT ADVERTISEMENT Table of Content What is a Rationalization of Numbers? Standard Form of Rationalization: How to Rationalize The Denominator? Practical Examples:. Is there a calculator that can solve word problems? Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems. Although this does not rationalize the denominator in one fell swoop, it rewrites the fraction with a denominator having only one square root which we could then ratio-nalize by mutiplying numerator and denominator by −6−2 √ 6. If the denominator consists of the square root of a natural number that is not a perfect square, _____ the numerator and the denomiator by the _____ number that. The calculator will show you all the steps and easy-to-understand explanations of how …. Just like running, it takes practice and dedication. multiplication division equations chart. \\(\\text{Add} \\dfrac{1}{2}\\hspace{0. I think the reason is that if the denominator is a rational number, it is in a simpler form and fractions can then combine, making operations more clear. The step-by-step breakdown when you do this multiplication is. is much messier to understand as a real number than Sep 7, 2006. Rational decisions are generally made by people who are able to determine the possibilities of an outcome, while irrational decisions are based almost entirely on emotion rather than experience. For example: Rationalise the denominator 4 6√ 4 6. Rationalize the Denominator with Multiple Terms: Suppose another but a little complex term in order to clarify the concepts. the smallest positive integer which is divisible by each denominators of these numbers. Summary of the process for reducing to lowest terms. Done! Note: It is ok to have an irrational number in the top (numerator) of a fraction. 3 √2x ⋅ √2x √2x 3 2 x ⋅ 2 x 2 x Combine and simplify the denominator. Rationalize the denominator: √3/√5. The first version requires that numerator and denominator are instances of numbers. rationalize denominator \\frac{7}{\\sqrt{5}} en. Rationalize denominator applicabile. Do not use a calculator Choose the correct graph below. Sketch an angle \\theta θ in standard position such that \\theta θ has the least possible positive measure, and the given point is on the terminal side of \\theta θ. Decimal form can be determined by dividing the numerator of a fraction by the denominator using a calculator. Then, check for extraneous solutions, which are values of the variable that makes the denominator equal to zero. Tap for more steps 6 2√2x 6 2 2 x. Mixed numbers calculator to add, subtract, multiply and divide mixed numbers (mixed fractions), fractions and integers. + х -18 -9 18 -18 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Step 4: Divide the first term of the remainder by the first term of the divisor to obtain the next term of the quotient. Convert fractions to decimals and percentages, work with mixed numbers and improper fractions and solve for X in fractions equations using CalculatorSoup ® online fractions calculators. Free Rational Expressions multiplication calculator - Multiply rational expressions step-by-step. Special Right Triangles Calculator. Sketch a angle theta in standard position such that theta has the least possible positive measure, and the given point is on the terminal side of theta. How to rationalize the denominator with a square root? (examples) We’ll start with the most basic examples of rationalizing denominators: working with square roots. Fractions Solve for Unknown X. Step 2: Now click the button “Submit” to get the result. For the following exercises, use the graph of y=f (x) to graph each transformed function g. rationalisiere den nenner \\frac{1}{i+2} en. 13: Writing Rational Exponents as Radicals. Rationalizing the denominator of an expression of higher power, when we have more than one element in that radical. Free Rational Expressions division calculator - Divide rational expressions step-by-step. In this section we deal with expressions where the denominator is a …. Before the calculator became a tool of everyday life, tables of square roots were used to find approximate . Start practicing—and saving your progress—now: https://www. 👉 Learn how to divide rational expressions having square root binomials. Rationalise the denominator: Simplify any surds, if necessary. In order to simplifying complex numbers that are ratios (fractions), we will rationalize the denominator by multiplying the top and bottom of the fraction by i/i. The steps in adding and subtracting Radical are: Step 1. How to Rationalize the Denominator with One Term? Step 1: Multiply the numerator and the denominator by a radical to get rid of the radicals in the denominator. Tutorial 41: Rationalizing Denominators and Numerators of Radical Expressions. Free printable algebra worksheets, Changing quadratic equations to polar, domain and range online calculator. Trigonometry - Find Side Lengths. Why Do We Rationalise the Denominator? Standard Notation. Step 2: Click on the \"Rationalize the Denominator\" button. Step 2: Click on the “Rationalize the Denominator” button. solving quadratic equations by completing the square worksheet. Rationalize The Denominator Calculator. Rationalize the Denominator 6/ ( square root of 8x) 6 √8x 6 8 x. permutation and combination tables. 6) Howto: Given an expression with a rational exponent, write the expression as a radical. Here, we will multiply 1/√5 by √5/√5. Use integers or fractions for any nu B. Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. Equivalent Expressions Calculator. Reduce fractions to lowest terms, simplify, compare and order fractions. rationalize denominator \\sqrt{\\frac{2}{5}} en. A polynomial is an expression of two or more algebraic terms, often having different …. com In this video playlist you will learn everything you need to know with complex and imaginary numbers(3 - 4i)/(2 - 2i). Rationalize the Denominator ( square root of 10- square root of 3)/( square root of 10+ square root of 3) Step 1. rationalize denominator 1/(1. Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Sketch an angle in standard position such that has the least possible positive measure, and the point (-2,0) is on the terminal side of. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator. Enter Numerator: Enter Denominator: Simplify: Computing Get this widget. Лу 18 2 Find the values of the six trigonometric functions for the angle. About the Author I designed this website and wrote all the calculators, lessons, and formulas. As we know, we need to multiply the denominator with its conjugate. Enter Numerator: Enter Denominator: Rationalize denominator. This algebra video tutorial shows you how to perform many operations to simplify radical expressions. rationalize-denominator-calculator. Intro to rationalizing the denominator. Free absolute value equation calculator - solve absolute value equations with all the steps. Example 1: Peter had a slice of bread that was divided into 7 equal parts. The Math Way app will solve it form there. We can multiply both top and bottom by 3+√2 (the conjugate of 3−√2) Use a calculator to work out the value before and after is it the same? So try to remember this little trick, it may help you solve an equation one day. Improper fractions are rational numbers where the numerator is greater than the denominator. Simply type into the app below and edit the expression."
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"## How to Calculate Beam Size Using Beam Design Formula\n\nThe beam is a structural element that transfers all the dead load, the live load of the slab to the column. We all know that calculating beam size is essential and indispensable while designing a house. In this post, you will get to know the method of how to calculate the beam size before designing a beam for 2 to 3 storey building design plans or multi-storey building design plans.\n\nFor designing the beam, it is essential to know how to calculate the beam size, load calculation and grade of concrete and grade of steel. You can design it with the help of beam design formula and concrete beam design calculator. Just brush the concepts once and start with the given process.\n\nApart from it, you can easily create a beam design from the concrete beam design calculator, available on various sites. Still, as a structural engineer, you must know the beam design formula and their design procedure and have a proper understanding of basic physics principles and engineering statics, as they are significant for designing and sizing beams. A structural engineer has complete knowledge and is fully equipped to choose the material, size and shape accordingly and check the loads acting on a beam, calculate the forces and stresses on the structure.\n\n## WHAT IS A BEAM?\n\nA Beam is an essential slanted or horizontal element of the structure. It is built to resist the load during the construction and structural design of the residential building, commercial and industrial buildings and supports all external and internal loads of walls, floors and slabs of the building; then the beam loads transfer through columns to the foundation of the structure.\n\n## DIFFERENT TYPES OF BEAM –\n\nUnder the design basis, A structure is made from different kind of beams, few of them are here:\n\n• CANTILEVER BEAM- In the structural design of the residential building, commercial building, the one end of a cantilever beam is free from any support whereas the other end remains fixed. Generally, we design the cantilever beams to support the covering or sunshade of a bigger span of the building. They are used for the maximum shear forces & moments developed at the support section, which is usually a reinforced concrete column.\n• SIMPLY SUPPORTED BEAM- It is the type of beam which is loose to rotate because it’s one end is roller support, whereas the other end has pinned support. So it is supported from both the ends, and it is the most basic type of beam. You can quickly identify the simply supported beam in 2 to 3 storey building design plans or multi-storey building design plans.\n• CONTINUOUS BEAM – The continuous beams usually have two or more than two supports, it has one end fixed, and the other end goes continue. The use of these continuous beams is mostly in multi-storeyed buildings of several bays in right-angle direction. You can easily calculate the dimension of the beam to beam design formula.\n• OVERHANGING BEAM – It is also a type of beam used in the structural design of the residential building, the commercial building has two conditions. If one end of the beam expands beyond the support, then it is called overhanging beam, and if both ends of the beam expand beyond the support, then the beam is called a double overhanging beam.\n• FIXED BEAM- Fixed-beam has strong support from both the ends due to which it opposes any rotation, on either column or wall.\n• Lintel Beam- It is a type of beam usually used during constructions for openings like windows or door. It also acts as a guard for windows and doors during rain.\n• COMPOSITE BEAM- A composite beam is a structural element provided horizontally or a horizontal structural element, with a combination of concrete and steel section, is called a composite beam or an encased beam.\n• L BEAM- Beams are cast uniformly on one side of the slabs of the rib are called L- Beams. At the support section, hogging and torsional bending moments are maximum.\n\n## HOW TO CALCULATE BEAM SIZE?\n\nIt helps to distribute all structure loads properly and prevent the structure from collapsing. You can calculate the minimum size of the beam from the below formula. We can always take the standard size of the concrete beam at least 230 mm x 230 mm (9” x 9”). The depth of the beam increases or decreases according to their span and applied load on the beam. The beam is an integral part of the structure.\n\nThe size of the beam depends on the span of the beam and the load on the beam. In multi-storey design plans, the size of the plinth beam, primary and secondary beams depend on the number of stories and loads acting on the beam. Here is some example with the formula which tells you how to calculate the size of the beam.",
null,
"Fig: Calculation of minimum size of R.C.C beam size as per IS 456: 2000\n\nEffective depth =Span/Basic value\nTotal Depth = Effective depth + dia./2 + Clear Cover\nWidth = Depth/1.5 (width should not be less than 200 mm)\n\nNote:\nAs per IS – 13920,\n\n1. The width to depth ratio should be more than 0.3.\nWidth/Depth >0.3\n2. Depth of beam shall not be exceeded ¼ of the clear span.\n\nExample- For simply supported beam\n\nWhere,\nLe = Effective length\nD = Total depth of the beam\nd = Effective depth of the beam\nb = width of beam\n\nSpan of simply supported beam = 5 m\nThen effective depth of beam = 5000 / 20\nd = 250 mm\nTotal depth = effective depth + diameter of bar/2 + clear cover\nAssume diameter of bar = 16 mm\nD = 250 + 16/2 + 25\nD = 283 mm ≈ 285 mm\n\nAnd width = D/1.5\nWidth = 285 /1.5\nb = 190 mm\nSo, we will take 200 mm for width\n\nThen,\nWidth / Depth = 200/ 285 = 0.7 > 0.3, SAFE\n\nThen,\nwe can check depth of beam = ¼ of span\n= ¼ x 5000\n= 1250 mm > 285 mm, SAFE\n\nExample- For a cantilever beam\n\nSpan of cantilever beam = 2 m\nThen effective depth of beam = 2000 / 7\nd = 285 mm\nTotal depth = effective depth + diameter of bar/2 + clear cover\nAssume diameter of bar = 16 mm\nD = 285 + 16/2 + 25\nD = 318 mm ≈ 320 mm\n\nAnd width = D/1.5\nWidth = 320 /1.5\nb = 213 mm\nSo, we will take 230 mm for width\nThen,\nWidth / Depth = 230/ 320 = 0.71 > 0.3, SAFE\n\nThen,\nwe can check depth of beam = ¼ of span\n= ¼ x 2000\n= 500 mm > 320 mm, SAFE\n\nExample- For continuous beam\n\nSpan of continuous beam = 5 m\nThen effective depth of beam = 5000 / 26\nd = 192.3 mm ≈ 200 mm\nTotal depth = effective depth + diameter of bar/2 + clear cover\nAssume diameter of bar = 16 mm\nD = 200 + 16/2 + 25\nD = 233 mm ≈ 235 mm\n\nAnd width = D/1.5\nWidth = 235 /1.5\nb = 156.67 mm\nSo, we will take 200 mm for width\nThen,\nWidth / Depth = 200/ 235 = 0.85 > 0.3, SAFE\n\nThen,\nwe can check depth of beam = ¼ of span\n= ¼ x 5000\n= 1250 mm > 235 mm, SAFE\n\nCheck for lateral stability or buckling:\n(As per IS 456:2000, page no.39, clause 23.3)\nFor Simply Supported or Continuous Beam\n\nAllowable L = 60 b\nAllowable L= 250. b^2 / d\nTake the least value of L\nIf beam span is less than L allowable, then the beam will be safe from lateral stability or buckling.\n\nWhere,\nb = width of beam\nd = effective depth of the beam\n\nExample-\n\nAllowable L = 60 b\nAllowable L = 60 x 200\nAllowable L = 12000 mm = 12 m\nAnd\nAllowable L = 250 b2 / d\nAllowable L = 250 x 2002 / 285\nAllowable L = 35087.7 mm = 35.087 m\nTherefore,\nAllowable L = 12 m\nHere, Allowable L = 12 m > 5m, SAFE\n\nFor Cantilever Beam\n\nAllowable L = 25 b\nAllowable L= 100 b2 / d\nTake the least value of L\nIf beam span is less than L allowable, then the beam will be safe from lateral stability or buckling.\n\nWhere,\nb = width of beam\nd = effective depth of the beam\n\nExample-\n\nAllowable L = 60 b\nAllowable L = 60 x 230\nAllowable L = 13800 mm = 13.8 m\nAnd\nAllowable L = 250 b2 / d\nAllowable L = 250 x 2302 / 285\nAllowable L = 46403.5mm = 46.4 m\nTherefore,\nAllowable L = 13.8 m\nHere, Allowable L = 13.8 m > 2 m, SAFE\n\nThumb rule method:\nYou can also calculate the depth of the beam according to the method mention below\n1 foot (span of the beam) = 1Inch (depth of beam)\nIf the span is of the beam is 16 feet, then the depth of the beam will be 16 inches.\n\nLintel Beam: it is an integral part of the structure which prevent door frame or window frame corners from cracks.\nThe minimum thickness of the lintel beam is 150 mm.\n\n### This Post Has 14 Comments\n\n1.",
null,
"Dipak barua\n\n30cmx90cm beam size is ok or not. (width & depth ratio is ok ? )\n\n1.",
null,
"As per Is 13920 width to depth ratio should be more than 0.3. You have taken beam width 30 cm and depth 90 cm, which fulfils the criteria. Furthermore, the size of the beam depends on span and type of load on beam. You can check span of the beam and type of load applied on beam for the size of beam.\n\n2.",
null,
"Rahul Kumar\n\nHi\nHow do you calculate the dimensions of beam and no. of bars taking into account the slab load(DL &LL)\n\n3.",
null,
"Engineer\n\nGreat thanks. Very nicely explained 🙂\n\n4.",
null,
"S.majumdar\n\nA 90 feet guard wall.of residential building how much tmt bar is needed for tie beam.\n\n5.",
null,
"6.",
null,
"Engr wasiu\n\nInformative article, I an electrical engineer, but find this beam theory an interesting.\n\n7.",
null,
"John Gabriel\n\nWhere do we base the span of the beam, is it the clear span or the effective length (Le) ?\n\n1.",
null,
"It is the clear span 🙂\n\n8.",
null,
"1.",
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"9.",
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""
] |
[
null,
"http://www.eyeonstructures.com/wp-content/uploads/2020/08/eye-on-structures.png",
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|
https://www.tutorialspoint.com/count-of-sub-arrays-whose-elements-can-be-re-arranged-to-form-palindromes-in-cplusplus
|
[
"# Count of sub-arrays whose elements can be re-arranged to form palindromes in C++\n\nWe are given an array of integer elements and the task is to calculate the count of sub-arrays that can be formed from the given array such that its elements can form a valid palindrome. Palindromes are the sequences that are arranged similarly from start and the end.\n\nInput − int arr[] = { 3, 3, 1, 4, 2, 1, 5}\n\nOutput − Count of sub-arrays whose elements can be re-arranged to form palindromes are − 9\n\nExplanation − The valid sub-arrays whose elements can be arranged to form a palindrome are {3}, {3}, {1}, {4}, {2}, {1}, {5}, {1, 2, 1} and {1, 3, 1}. So, the total count is 9.\n\nInput − int arr[] = { 2, 5, 5, 2, 1}\n\nOutput − Count of sub-arrays whose elements can be re-arranged to form palindromes are − 8\n\nExplanation − The valid sub-arrays whose elements can be arranged to form a palindrome are {2}, {5}, {5}, {2}, {1}, {5, 2, 5}, {2, 5, 2}, {2, 5, 5, 2}. So, the total count is 8.\n\n## Approach used in the below program is as follows\n\n• Input an array of integer elements and calculate the size of an array and pass the data to the function for further processing.\n\n• Declare a temporary variable count to store the sub-arrays of palindrome.\n\n• Start loop FOR from 0 till the size of an array\n\n• Inside the loop, declare a variable of type long long and set it as 1LL << arr[j] and set temp as temp ^ val\n\n• Call a function inside a boolean variable that will return either true or false.\n\n• Check IF temp is 0LL or ch is True then increment the count by 1\n\n• Return the count\n\n• Print the result.\n\n## Example\n\nLive Demo\n\n#include <bits/stdc++.h>\nusing namespace std;\nbool check(long long temp){\nreturn !(temp & (temp - 1LL));\n}\nint palindromes_rearrange(int arr[], int size){\nint count = 0;\nfor (int i = 0; i < size; i++){\nlong long temp = 0LL;\nfor (int j = i; j < size; j++){\nlong long val = 1LL << arr[j];\ntemp = temp ^ val;\nbool ch = check(temp);\nif (temp == 0LL || ch){\ncount++;\n}\n}\n}\nreturn count;\n}\nint main(){\nint arr[] = { 3, 3, 1, 4, 2, 1, 5};\nint size = sizeof(arr) / sizeof(arr);\ncout<<\"Count of sub-arrays whose elements can be re-arranged to form palindromes are:\n\"<<palindromes_rearrange(arr, size);\nreturn 0;\n}\n\n## Output\n\nIf we run the above code it will generate the following output −\n\nCount of sub-arrays whose elements can be re-arranged to form palindromes are: 9\n\nUpdated on: 02-Dec-2020\n\n144 Views",
null,
""
] |
[
null,
"https://www.tutorialspoint.com/static/images/library-cta.svg",
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|
https://www.geeksforgeeks.org/genetic-algorithm-for-reinforcement-learning-python-implementation/?ref=rp
|
[
"# Genetic Algorithm for Reinforcement Learning : Python implementation\n\n• Last Updated : 07 Jun, 2019\n\nMost beginners in Machine Learning start with learning Supervised Learning techniques such as classification and regression. However, one of the most important paradigms in Machine Learning is Reinforcement Learning (RL) which is able to tackle many challenging tasks. It is an aspect of Machine learning where an agent learns to behave in an environment, by performing certain actions and observing the rewards(results) which it gets from those actions.\n\nIn Reinforcement Learning, we give the machines a few inputs and actions, and then, reward them based on the output. Reward maximization is the end goal. It is just like a little baby who knows nothing at first is left alone in an environment and then after a little understanding tends to know things around itself.\n\nAttention reader! Don’t stop learning now. Get hold of all the important Machine Learning Concepts with the Machine Learning Foundation Course at a student-friendly price and become industry ready.\n\nHere, we are just going to build an algorithm based on the genetic mutation of a population when attacked by a virus. In the first generation of our population only a few fittest ones will be able to survive, whereas as the generations will pass, the new generations will be much stronger against the virus than their ancestors. It is a basic algorithm which just gives an idea of how these things work. Anyone with the basic knowledge of python and some libraries like numpy, matplotlib, etc can easily understand this code. This is just for the introduction and to provide the surface level knowledge about Reinforcement Learning.\n\n## Genetic Algorithm –\n\nLibraries Used:\n\n• numpy : we’ll be using numpy arrays and other basic calculation functionalities from this library\n• matplotlib : we’ll be using matplotlib.pyplot functionality in order to plot the graphs for the visual understanding of the algorithm.\n\nIn this program, we’ll define 3 main functions in order to generate the next generation of the population which is genetically more powerful than the previous ones.\n\nThe three main functions used are:\n\npopulate: This is used to generate the population and then appending it to a list. This function accepts the attributes like the number of features in the population and the size of it.\n\nreduction: This function is used to reduce the size of the population and allows only the 100 most fittest ones to survive. These fit ones will be the ones used to generate the next generation of the population.\n\ncross: This function is used for the process of cross-breeding between the ones that are left in order to generate a whole new generation of the population which will be much more immune towards the virus.\n\nBelow is the implementation –\n\n `import` `numpy as np``import` `matplotlib.pyplot as plt`` ` `# specifying the size for each and ``# every matplotlib plot globally``plt.rcParams[``'figure.figsize'``] ``=` `[``8``, ``6``] `` ` `# defining list objects with range of the graph``x1_range ``=` `[``-``100``, ``100``]``x2_range ``=` `[``-``100``, ``100``]`` ` `# empty list object to store the population``population ``=` `[]`` ` `# this function is used to generate the population``# and appending it to the population list defined above``# it takes the attributes as no. of features in a ``# population and size that we have in it``def` `populate(features, size ``=` `1000``):`` ` ` ``# here we are defining the coordinate `` ``# for each entity in a population`` ``initial ``=` `[] `` ` ` ``for` `_ ``in` `range``(size):`` ``entity ``=` `[]`` ``for` `feature ``in` `features:`` ` ` ``# this * feature variable unpacks a list `` ``# or tuple into position arguments.`` ``val ``=` `np.random.randint(``*``feature)`` ``entity.append(val)`` ``initial.append(entity)`` ` ` ``return` `np.array(initial)`` ` `# defining the virus in the form of numpy array``virus ``=` `np.array([``5``, ``5``])`` ` `# only the 100 fit ones will survive in this one``def` `fitness(population, virus, size ``=` `100``):`` ` ` ``scores ``=` `[]`` ` ` ``# enumerate also provides the index as for the iterator`` ``for` `index, entity ``in` `enumerate``(population): `` ``score ``=` `np.``sum``((entity``-``virus)``*``*``2``)`` ``scores.append((score, index))`` ` ` ``scores ``=` `sorted``(scores)[:size]`` ` ` ``return` `np.array(scores)[:, ``1``]`` ` `# this function is used to plot the graph``def` `draw(population, virus):`` ``plt.xlim((``-``100``, ``100``))`` ``plt.ylim((``-``100``, ``100``))`` ``plt.scatter(population[:, ``0``], population[:, ``1``], c ``=``'green'``, s ``=` `12``)`` ``plt.scatter(virus[``0``], virus[``1``], c ``=``'red'``, s ``=` `60``) `` ` ` ` `def` `reduction(population, virus, size ``=` `100``):`` ` ` ``# only the index of the fittest ones`` ``# is returned in sorted format`` ``fittest ``=` `fitness(population, virus, size) `` ` ` ``new_pop ``=` `[]`` ` ` ``for` `item ``in` `fittest:`` ``new_pop.append(population[item])`` ` ` ``return` `np.array(new_pop)`` ` `# cross mutation in order to generate the next generation``# of the population which will be more immune to virus than previous``def` `cross(population, size ``=` `1000``):`` ` ` ``new_pop ``=` `[]`` ` ` ``for` `_ ``in` `range``(size):`` ``p ``=` `population[np.random.randint(``0``, ``len``(population))]`` ``m ``=` `population[np.random.randint(``0``, ``len``(population))]`` ` ` ``# we are only considering half of each `` ``# without considering random selection`` ``entity ``=` `[]`` ``entity.append(``*``p[:``len``(p)``/``/``2``])`` ``entity.append(``*``m[``len``(m)``/``/``2``:])`` ` ` ``new_pop.append(entity)`` ` ` ``return` `np.array(new_pop)`` ` `# generating and adding the random features to``# the entity so that it looks more distributed``def` `mutate(population):`` ` ` ``return` `population ``+` `np.random.randint(``-``10``, ``10``, ``2000``).reshape(``1000``, ``2``)`` ` ` ` `# the complete cycle of the above steps``population ``=` `populate([x1_range, x2_range], ``1000``)`` ` `# gens is the number of generation``def` `cycle(population, virus, gens ``=` `1``): `` ` ` ``# if we change the value of gens, we'll get `` ``# next and genetically more powerful generation`` ``# of the population`` ``for` `_ ``in` `range``(gens):`` ``population ``=` `reduction(population, virus, ``100``)`` ``population ``=` `cross(population, ``1000``)`` ``population ``=` `mutate(population)`` ` ` ``return` `population`` ` `population ``=` `cycle(population, virus)`` ` `draw(population, virus)`\n\nOutput:\n\n1) For generation 1, when gens=0",
null,
"2) For generation 2, when gens=1",
null,
"3) For generation 3, when gens=2",
null,
"My Personal Notes arrow_drop_up"
] |
[
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"https://media.geeksforgeeks.org/wp-content/uploads/20190530192724/gen-0-300x225.png",
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"https://media.geeksforgeeks.org/wp-content/uploads/20190530192733/gen-1-300x225.png",
null,
"https://media.geeksforgeeks.org/wp-content/uploads/20190530192739/gen-2-300x225.png",
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https://nl.mathworks.com/help/images/comparison-of-auto-white-balance-algorithms.html
|
[
"# Comparison of Auto White Balance Algorithms\n\nThis example shows how to estimate illumination and perform white balance of a scene using three different illumination algorithms.\n\nEyes are very good at judging what is white under different lighting conditions. Digital cameras, however, without some kind of adjustment, can easily capture unrealistic images with a strong color cast. Automatic white balance (AWB) algorithms try to correct for the ambient light with minimum input from the user, so that the resulting image looks like what our eyes would see.\n\nAutomatic white balancing is done in two steps:\n\n• Step 1: Estimate the scene illuminant.\n\n• Step 2: Correct the color balance of the image.\n\nSeveral different algorithms exist to estimate scene illuminant.\n\n• White Patch Retinex \n\n• Gray World \n\n• Cheng's Principal Component Analysis (PCA) method \n\nThe performance of each algorithm depends on the scene, lighting, and imaging conditions. This example judges the quality of three algorithms for one specific image by comparing them to the ground truth scene illuminant calculated using a ColorChecker® chart.\n\n### Read and Preprocess Raw Camera Data\n\nAWB algorithms are usually applied on the raw image data after a minimal amount of preprocessing, before the image is compressed and saved to the memory card.\n\nRead a 16-bit raw image into the workspace. `foosballraw.tiff` is an image file that contains raw sensor data after correcting the black level and scaling the intensities to 16 bits per pixel. This image is free of the white balancing done by the camera, as well as other preprocessing operations such as demosaicing, denoising, chromatic aberration compensation, tone adjustments, and gamma correction.\n\n`A = imread(\"foosballraw.tiff\");`\n\n#### Interpolate to Recover Missing Color Information\n\nDigital cameras use a color filter array superimposed on the imaging sensor to simulate color vision, so that each pixel is sensitive to either red, green or blue. To recover the missing color information at every pixel, interpolate using the `demosaic` function. The Bayer pattern used by the camera with which the photo was captured (Canon EOS 30D) is RGGB.\n\n`A = demosaic(A,\"rggb\");`\n\n#### Gamma-Correct Image for Detection and Display\n\nThe image `A` contains linear RGB values. Linear RGB values are appropriate for estimating scene illuminant and correcting the color balance of an image. However, if you try to display the linear RGB image, it will appear very dim, because of the nonlinear characteristic of display devices. Therefore, for display purposes, gamma-correct the image to the sRGB color space using the `lin2rgb` function.\n\n`A_sRGB = lin2rgb(A);`\n\nDisplay the demosaiced image before and after gamma correction.\n\n```montage({A,A_sRGB}) title(\"Original Image Before and After Gamma Correction\")```",
null,
"### Measure Ground Truth Illuminant Using ColorChecker Chart\n\nCalculate the ground truth illuminant using the ColorChecker chart that is included in the scene. This chart consists of 24 neutral and color patches with known spectral reflectances.\n\nDetect the chart in the gamma-corrected image by using the `colorChecker` function. The linear RGB image is too dark for `colorChecker` to detect the chart automatically.\n\n`chart_sRGB = colorChecker(A_sRGB);`\n\nConfirm that the chart is detected correctly.\n\n`displayChart(chart_sRGB)`",
null,
"Get the coordinates of the registration points at the four corners of the chart.\n\n`registrationPoints = chart_sRGB.RegistrationPoints;`\n\nCreate a new `colorChecker` object from the linear RGB data. Specify the location of the chart using the coordinates of the registration points.\n\n`chart = colorChecker(A,RegistrationPoints=registrationPoints);`\n\nMeasure the ground truth illuminant of the linear RGB data using the `measureIlluminant` function.\n\n`illuminant_groundtruth = measureIlluminant(chart)`\n```illuminant_groundtruth = 1×3 103 × 4.5407 9.3226 6.1812 ```\n\n### Create Mask of ColorChecker Chart\n\nWhen testing the AWB algorithms, prevent the algorithms from unfairly taking advantage of the chart by masking out the chart.\n\nCreate a polygon ROI over the chart by using the `drawpolygon` function. Specify the vertices of the polygon as the registration points.\n\n`chartROI = drawpolygon(Position=registrationPoints);`",
null,
"Convert the polygon ROI to a binary mask by using the `createMask` function.\n\n`mask_chart = createMask(chartROI);`\n\nInvert the mask. Pixels within the chart are excluded from the mask and pixels of the rest of the scene are included in the mask.\n\n`mask_scene = ~mask_chart;`\n\nTo confirm the accuracy of the mask, display the mask over the image. Pixels included in the mask have a blue tint.\n\n`imshow(labeloverlay(A_sRGB,mask_scene));`",
null,
"### Angular Error\n\nYou can consider an illuminant as a vector in 3-D RGB color space. The magnitude of the estimated illuminant does not matter as much as its direction, because the direction of the illuminant is what is used to white balance an image.\n\nTo evaluate the quality of an estimated illuminant, compute the angular error between the estimated illuminant and the ground truth. Angular error is the angle (in degrees) formed by the two vectors. The smaller the angular error, the better the estimation is.\n\nTo better understand the concept of angular error, consider the following visualization of an arbitrary illuminant and the ground truth measured using the ColorChecker chart. The `plotColorAngle` helper function plots a unit vector of an illuminant in 3-D RGB color space, and is defined at the end of the example.\n\n```sample_illuminant = [0.066 0.1262 0.0691]; p = plot3([0 1],[0 1],[0,1],LineStyle=\":\",Color=\"k\"); ax = p.Parent; hold on plotColorAngle(illuminant_groundtruth,ax) plotColorAngle(sample_illuminant,ax) title(\"Illuminants in RGB space\") view(28,36) legend(\"Achromatic Line\",\"Ground Truth Illuminant\",\"Sample Illuminant\") grid on axis equal```",
null,
"### White Patch Retinex\n\nThe White Patch Retinex algorithm for illuminant estimation assumes that the scene contains a bright achromatic patch. This patch reflects the maximum light possible for each color band, which is the color of the scene illuminant. Use the `illumwhite` function to estimate illumination using the White Patch Retinex algorithm.\n\n#### Include All Scene Pixels\n\nEstimate the illuminant using all the pixels in the scene. Exclude the ColorChecker chart from the scene by using the `Mask` name-value pair argument.\n\n```percentileToExclude = 0; illuminant_wp1 = illumwhite(A,percentileToExclude,Mask=mask_scene);```\n\nCompute the angular error for the illuminant estimated with White Patch Retinex.\n\n```err_wp1 = colorangle(illuminant_wp1,illuminant_groundtruth); disp([\"Angular error for White Patch with percentile=0: \" num2str(err_wp1)])```\n```Angular error for White Patch with percentile=0: 16.5381 ```\n\nWhite balance the image using the `chromadapt` function. Specify the estimated illuminant and indicate that color values are in the linear RGB color space.\n\n`B_wp1 = chromadapt(A,illuminant_wp1,ColorSpace=\"linear-rgb\");`\n\nDisplay the gamma-corrected white-balanced image.\n\n```B_wp1_sRGB = lin2rgb(B_wp1); figure imshow(B_wp1_sRGB) title(\"White-Balanced Image using White Patch Retinex with percentile=0\")```",
null,
"#### Exclude Brightest Pixels\n\nThe White Patch Retinex algorithm does not perform well when pixels are overexposed. To improve the performance of the algorithm, exclude the top 1% of the brightest pixels.\n\n```percentileToExclude = 1; illuminant_wp2 = illumwhite(A,percentileToExclude,Mask=mask_scene);```\n\nCalculate the angular error for the estimated illuminant. The error is less than when estimating the illuminant using all pixels.\n\n```err_wp2 = colorangle(illuminant_wp2,illuminant_groundtruth); disp([\"Angular error for White Patch with percentile=1: \" num2str(err_wp2)])```\n```Angular error for White Patch with percentile=1: 5.0324 ```\n\nWhite balance the image in the linear RGB color space using the estimated illuminant.\n\n`B_wp2 = chromadapt(A,illuminant_wp2,ColorSpace=\"linear-rgb\");`\n\nDisplay the gamma-corrected white-balanced image with the new illuminant.\n\n```B_wp2_sRGB = lin2rgb(B_wp2); imshow(B_wp2_sRGB) title(\"White-Balanced Image using White Patch Retinex with percentile=1\")```",
null,
"### Gray World\n\nThe Gray World algorithm for illuminant estimation assumes that the average color of the world is gray, or achromatic. Therefore, it calculates the scene illuminant as the average RGB value in the image. Use the `illumgray` function to estimate illumination using the Gray World algorithm.\n\n#### Include All Scene Pixels\n\nFirst, estimate the scene illuminant using all pixels of the image, excluding those corresponding to the ColorChecker chart. The `illumgray` function provides a parameter to specify the percentiles of bottom and top values (ordered by brightness) to exclude. Here, specify the percentiles as 0.\n\n```percentileToExclude = 0; illuminant_gw1 = illumgray(A,percentileToExclude,Mask=mask_scene);```\n\nCalculate the angular error between the estimated illuminant and the ground truth illuminant.\n\n```err_gw1 = colorangle(illuminant_gw1,illuminant_groundtruth); disp([\"Angular error for Gray World with percentiles=[0 0]: \" num2str(err_gw1)])```\n```Angular error for Gray World with percentiles=[0 0]: 5.0416 ```\n\nWhite balance the image in the linear RGB color space using the estimated illuminant.\n\n`B_gw1 = chromadapt(A,illuminant_gw1,ColorSpace=\"linear-rgb\");`\n\nDisplay the gamma-corrected white-balanced image.\n\n```B_gw1_sRGB = lin2rgb(B_gw1); imshow(B_gw1_sRGB) title(\"White-Balanced Image using Gray World with percentiles=[0 0]\")```",
null,
"#### Exclude Brightest and Darkest Pixels\n\nThe Gray World algorithm does not perform well when pixels are underexposed or overexposed. To improve the performance of the algorithm, exclude the top 1% of the darkest and brightest pixels.\n\n```percentileToExclude = 1; illuminant_gw2 = illumgray(A,percentileToExclude,Mask=mask_scene);```\n\nCalculate the angular error for the estimated illuminant. The error is less than when estimating the illuminant using all pixels.\n\n```err_gw2 = colorangle(illuminant_gw2,illuminant_groundtruth); disp([\"Angular error for Gray World with percentiles=[1 1]: \" num2str(err_gw2)])```\n```Angular error for Gray World with percentiles=[1 1]: 5.1094 ```\n\nWhite balance the image in the linear RGB color space using the estimated illuminant.\n\n`B_gw2 = chromadapt(A,illuminant_gw2,ColorSpace=\"linear-rgb\");`\n\nDisplay the gamma-corrected white-balanced image with the new illuminant.\n\n```B_gw2_sRGB = lin2rgb(B_gw2); imshow(B_gw2_sRGB) title(\"White-Balanced Image using Gray World with percentiles=[1 1]\")```",
null,
"### Cheng's Principal Component Analysis (PCA) Method\n\nCheng's illuminant estimation method draws inspiration from spatial domain methods such as Grey Edge , which assumes that the gradients of an image are achromatic. They show that Grey Edge can be improved by artificially introducing strong gradients by shuffling image blocks, and conclude that the strongest gradients follow the direction of the illuminant. Their method consists in ordering pixels according to the norm of their projection along the direction of the mean image color, and retaining the bottom and top percentile. These two groups correspond to strong gradients in the image. Finally, they perform a principal component analysis (PCA) on the retained pixels and return the first component as the estimated illuminant. Use the `illumpca` function to estimate illumination using Cheng's PCA algorithm.\n\n#### Include Default Bottom and Top 3.5 Percent of Pixels\n\nFirst, estimate the illuminant using the default percentage value of Cheng's PCA method, excluding those corresponding to the ColorChecker chart.\n\n`illuminant_ch2 = illumpca(A,Mask=mask_scene);`\n\nCalculate the angular error between the estimated illuminant and the ground truth illuminant.\n\n```err_ch2 = colorangle(illuminant_ch2,illuminant_groundtruth); disp([\"Angular error for Cheng with percentage=3.5: \" num2str(err_ch2)])```\n```Angular error for Cheng with percentage=3.5: 5.0162 ```\n\nWhite balance the image in the linear RGB color space using the estimated illuminant.\n\n`B_ch2 = chromadapt(A,illuminant_ch2,ColorSpace=\"linear-rgb\");`\n\nDisplay the gamma-corrected white-balanced image.\n\n```B_ch2_sRGB = lin2rgb(B_ch2); imshow(B_ch2_sRGB) title(\"White-Balanced Image using Cheng with percentile=3.5\")```",
null,
"#### Include Bottom and Top 5 Percent of Pixels\n\nNow, estimate the scene illuminant using the bottom and top 5% of pixels along the direction of the mean color. The second argument of the `illumpca` function specifies the percentiles of bottom and top values (ordered by brightness) to exclude.\n\n`illuminant_ch1 = illumpca(A,5,Mask=mask_scene);`\n\nCalculate the angular error between the estimated illuminant and the ground truth illuminant. The error is less than when estimating the illuminant using the default percentage.\n\n```err_ch1 = colorangle(illuminant_ch1,illuminant_groundtruth); disp([\"Angular error for Cheng with percentage=5: \" num2str(err_ch1)])```\n```Angular error for Cheng with percentage=5: 4.7454 ```\n\nWhite balance the image in the linear RGB color space using the estimated illuminant.\n\n`B_ch1 = chromadapt(A,illuminant_ch1,ColorSpace=\"linear-rgb\");`\n\nDisplay the gamma-corrected white-balanced image.\n\n```B_ch1_sRGB = lin2rgb(B_ch1); imshow(B_ch1_sRGB) title(\"White-Balanced Image using Cheng with percentage=5\")```",
null,
"### Find Optimal Parameters\n\nTo find the best parameter to use for each algorithm, you can sweep through a range and calculate the angular error for each of them. The parameters of the three algorithms have different meanings, but the similar ranges of these parameters makes it easy to programmatically search for the best one for each algorithm.\n\n```param_range = 0:0.25:5; err = zeros(numel(param_range),3); for k = 1:numel(param_range) % White Patch illuminant_wp = illumwhite(A,param_range(k),Mask=mask_scene); err(k,1) = colorangle(illuminant_wp,illuminant_groundtruth); % Gray World illuminant_gw = illumgray(A,param_range(k),Mask=mask_scene); err(k,2) = colorangle(illuminant_gw,illuminant_groundtruth); % Cheng if (param_range(k) ~= 0) illuminant_ch = illumpca(A,param_range(k),Mask=mask_scene); err(k,3) = colorangle(illuminant_ch,illuminant_groundtruth); else % Cheng's algorithm is undefined for percentage=0 err(k,3) = NaN; end end```\n\nDisplay a heatmap of the angular error using the `heatmap` function. Dark blue colors indicate a low angular error while yellow colors indicate a high angular error. The optimal parameter has the smallest angular error.\n\n```heatmap(err,Title=\"Angular Error\",Colormap=parula(length(param_range)), ... XData=[\"White Patch\" \"Gray World\" \"Cheng's PCA\"], ... YLabel=\"Parameter Value\",YData=string(param_range));```",
null,
"Find the best parameter for each algorithm.\n\n```[~,idx_best] = min(err); best_param_wp = param_range(idx_best(1)); best_param_gw = param_range(idx_best(2)); best_param_ch = param_range(idx_best(3)); fprintf(\"The best parameter for White Patch is %1.2f with angular error %1.2f degrees\\n\", ... best_param_wp,err(idx_best(1),1));```\n```The best parameter for White Patch is 0.25 with angular error 3.35 degrees ```\n```fprintf(\"The best parameter for Gray World is %1.2f with angular error %1.2f degrees\\n\", ... best_param_gw,err(idx_best(2),2));```\n```The best parameter for Gray World is 0.00 with angular error 5.04 degrees ```\n```fprintf(\"The best parameter for Cheng is %1.2f with angular error %1.2f degrees\\n\", ... best_param_ch,err(idx_best(3),3));```\n```The best parameter for Cheng is 0.50 with angular error 1.74 degrees ```\n\nCalculate the estimated illuminant for each algorithm using the best parameter.\n\n```best_illum_wp = illumwhite(A,best_param_wp,Mask=mask_scene); best_illum_gw = illumgray(A,best_param_gw,Mask=mask_scene); best_illum_ch = illumpca(A,best_param_ch,Mask=mask_scene);```\n\nDisplay the angular error of each best illuminant in the RGB color space.\n\n```p = plot3([0 1],[0 1],[0,1],LineStyle=\":\",Color=\"k\"); ax = p.Parent; hold on plotColorAngle(illuminant_groundtruth,ax) plotColorAngle(best_illum_wp,ax) plotColorAngle(best_illum_gw,ax) plotColorAngle(best_illum_ch,ax) title(\"Best Illuminants in RGB space\") view(28,36) legend(\"Achromatic Line\",\"Ground Truth\",\"White Patch\",\"Gray World\",\"Cheng\") grid on axis equal```",
null,
"Calculate the optimal white-balanced images for each algorithm using the best illuminant.\n\n```B_wp_best = chromadapt(A,best_illum_wp,ColorSpace=\"linear-rgb\"); B_wp_best_sRGB = lin2rgb(B_wp_best); B_gw_best = chromadapt(A,best_illum_gw,ColorSpace=\"linear-rgb\"); B_gw_best_sRGB = lin2rgb(B_gw_best); B_ch_best = chromadapt(A,best_illum_ch,ColorSpace=\"linear-rgb\"); B_ch_best_sRGB = lin2rgb(B_ch_best);```\n\nDisplay the optimal white-balanced images for each algorithm in a montage.\n\n```figure montage({B_wp_best_sRGB,B_gw_best_sRGB,B_ch_best_sRGB},Size=[1 3]) title(\"Montage of Best White-Balanced Images: White Point, Gray World, Cheng\")```",
null,
"### Conclusion\n\nThis comparison of two classic illuminant estimation algorithms and a more recent one shows that Cheng's method, using the top and bottom 0.75% darkest and brightest pixels, wins for that particular image. However, this result should be taken with a grain of salt.\n\nFirst, the ground truth illuminant was measured using a ColorChecker chart and is sensitive to shot and sensor noise. The ground truth illuminant of a scene can be better estimated using a spectrophotometer.\n\nSecond, the ground truth illuminant is estimated as the mean color of the neutral patches. It is common to use the median instead of the mean, which could shift the ground truth by a significant amount. For example, for the image in this study, using the same pixels, the median color and the mean color of the neutral patches are 0.5 degrees apart, which in some cases can be more than the angular error of the illuminants estimated by different algorithms.\n\nThird, a full comparison of illuminant estimation algorithms should use a variety of images taken under different conditions. One algorithm might work better than the others for a particular image, but might perform poorly over the entire data set.\n\n### Supporting Function\n\nThe `plotColorAngle` function plots a unit vector of an illuminant in 3-D RGB color space. The input argument `illum` specifies the illuminant as an RGB color and the input argument `ax` specifies the axes on which to plot the unit vector.\n\n```function plotColorAngle(illum,ax) R = illum(1); G = illum(2); B = illum(3); magRGB = norm(illum); plot3([0 R/magRGB],[0 G/magRGB],[0 B/magRGB], ... Marker=\".\",MarkerSize=10,Parent=ax) xlabel(\"R\") ylabel(\"G\") zlabel(\"B\") xlim([0 1]) ylim([0 1]) zlim([0 1]) end```\n\n Ebner, Marc. White Patch Retinex, Color Constancy. John Wiley & Sons, 2007. ISBN 978-0-470-05829-9.\n\n Ebner, Marc. The Gray World Assumption, Color Constancy. John Wiley & Sons, 2007. ISBN 978-0-470-05829-9.\n\n Cheng, Dongliang, Dilip K. Prasad, and Michael S. Brown. \"Illuminant estimation for color constancy: why spatial-domain methods work and the role of the color distribution.\" JOSA A 31.5 (2014): 1049-1058.\n\n Van De Weijer, Joost, Theo Gevers, and Arjan Gijsenij. \"Edge-based color constancy.\" IEEE Transactions on image processing 16.9 (2007): 2207-2214."
] |
[
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_01.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_02.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_03.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_04.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_05.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_06.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_07.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_08.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_09.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_10.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_11.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_12.png",
null,
"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_13.png",
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"https://nl.mathworks.com/help/examples/images/win64/ComparisonOfAutoWhiteBalanceAlgorithmsExample_14.png",
null
] |
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|
https://chemistry.stackexchange.com/questions/72629/speed-distribution-of-lighter-vs-heavier-gases
|
[
"# Speed distribution of lighter vs heavier gases\n\nI cannot understand why the range of molecular speed is not always wider for a lighter gas as compared to a heavier gas .\n\nIf the same energy is supplied to both gases then wouldn't the molecular speed of the lighter gas be more?\n\n• Do you have an example of such an exception? I don't doubt that there are exceptions since the Maxwell Boltzmann distribution requires a system to be at thermal equilibrium and assumes ideal gases. However do you have a specific example of a situation where a lower molecular weight gas has a thinner distribution? – Tyberius Apr 16 '17 at 3:09\n• @Tyberius If i have the example of exception then why would I have asked the question – search Apr 16 '17 at 6:31\n• Let me rephrase my question. If you don't have a specific example, how do you know it happens? What source told you that this could be the case? – Tyberius Apr 16 '17 at 13:30\n• Knowing what led to this question might help to provide an explanation that addresses your specific concern. But as I mentioned in the comments to my answer, probably the main cause of deviations from Maxwell Boltzmann would be real gas behavior (attraction and repulsion) and multiatomic molecules, which have internal degrees of freedom where they can store the thermal energy. – Tyberius Apr 16 '17 at 15:47\n\nTo my understanding, the speed distribution is wider for lighter molecules. The Wikipedia page for the Maxwell Boltzmann distribution has two images at the top that convey this very well.",
null,
"",
null,
"In the first plot, $a=\\sqrt{k_bT/M}$ where $M$ is the molar mass and $k_b$ Boltzmann's constant. For a Maxwell-Boltzmann distribution, the variance is given by $$\\sigma^2= \\frac{a^2\\cdot(3\\pi-8)}{\\pi}=\\frac{k_b\\cdot T\\cdot(3\\pi-8)}{M\\cdot\\pi}$$ So, this shows that the speed distribution will be wider for higher temperatures and smaller molar mass."
] |
[
null,
"https://i.stack.imgur.com/bv74F.png",
null,
"https://i.stack.imgur.com/2W2xu.png",
null
] |
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|
https://deparkes.co.uk/2021/06/18/uk-rainfall-data/
|
[
"# UK Rainfall Data\n\nBy | June 18, 2021\n\n## Historic UK Rainfall Data\n\nThe Met Office Hadley Centre holds (Met Office Hadley Centre observations datasets HadUKP) UK Rainfall Data going back to the 1800s. It records the daily average rain fall for 9 regions around England, Wales, Scotland and Northern Ireland.\n\nSee terms and conditions for using this data: Met Office Hadley Centre hadukp observations datasets\n\n### Exploring Daily Total Rainfall\n\nOne of the more granular sources provided by the Hadley Centre is daily rainfall totals for each region. You can download the individual files from the website, but unfortunately it looks like their robots.txt prevents programmatic downloading of the files.\n\nOnce downloaded you can use pandas read_csv to load the data into a pandas dataframe. A couple of things to watch out for though:\n\n• Skipping the first few rows and specifying that there is no header row. See here for how to get around that.\n• Using more than one space character as a column separator. See here for how to get around that.\n• Handling NA values (which are set as -99.99 and mess up calculations). See here for how to get around that.\n\nThe full line I used was:\n\n```df = pd.read_csv('data/HadSWEP_daily_qc.txt', sep=r'\\s+', skiprows=3, skipinitialspace=True, header=None, na_values=-99.99)\n```\n\nSince the file did not come with its own header columns I added them after loading the file. I also added a column for region so that multiple regions could be handled at once if necessary (‘SEEP’ is from the original data file and means ‘South East England Precipitation’).\n\n```df.columns = ['year', 'month']+ [i+1 for i in range(31)]\ndf['region'] = 'SEEP'\n```\n\nThe data table provided is in a ‘wide’ format with a column for each day of the month. This is helpful for human-readability, but isn’t so good for computer processing. To convert for a ‘wide’ to a ‘long’ form table we can use the ‘melt’ pandas method.\n\n```melted = pd.melt(df, id_vars=['region', 'year', \"month\"],\nvar_name=\"day\", value_name=\"rainfall\")\n```\n\n### Example Analysis\n\nThe melted dataframe is in a good place to do further analysis and get a feel for what is possible.\n\n#### How Much Rain Will There Be?\n\nWe can attempt to estimate how much rain there will be on a given day of the year by looking at that average for that day. This isn’t really forecasting, but it does help you know generally how rainy a given day of the year might be.\n\n```df2 = melted[melted['region']=='SEEP'].groupby(['month', 'day'])['rainfall'].mean()\n```\n\nWe can plot this new grouped dataframe and confirm that the trends to at least seem to mostly make sense: the summer is relatively dry and the winter is relatively wet.",
null,
"Having the mean rainfall is one thing, but often we want to dig a bit deeper than that. We can easily extend our initial ‘mean’ calculation to include maximum, minimum and standard deviation of rainfall measurements.\n\n```import numpy as np\ndf3 = melted[melted['region']=='SEEP'].groupby(['month', 'day']).agg(\nmean_rain=pd.NamedAgg(column='rainfall', aggfunc='mean'),\nmax_rain=pd.NamedAgg(column='rainfall', aggfunc='max'),\nmin_rain=pd.NamedAgg(column='rainfall', aggfunc='min'),\nstd=pd.NamedAgg(column='rainfall', aggfunc=np.std),\n)\ndf4 = df3.reset_index()\n```\n\n### How Likely Is it to Rain?\n\nWe can also use this historic UK rainfall data to give some estimate as to the chance of rain on a given day. I want to stress again that this isn’t really forecasting, or at least I wouldn’t rely on it for anything important!\n\nSince I have put an additional region column, we also need to filter on that. Read about filtering with pandas.\n\nThe basic idea is that you count up all days in the past which had rain above a certain limit and divide by the total number of days. From one forum (here and here) it looks like about 1-2mm rain across a day would likely not get in anybody’s way, so I have used that as the threshold rather than simply 0mm which is probably a bit too strict.\n\n```LIGHT_RAIN_LIMIT = 1.5\ndf4['count_rain'] = melted[(melted['region']=='SEEP') &amp;amp; (melted['rainfall']&amp;gt;LIGHT_RAIN_LIMIT)].groupby(['month', 'day'])['rainfall'].count().reset_index()['rainfall']\ndf4['count_not_rain'] = melted[(melted['region']=='SEEP') &amp;amp; (melted['rainfall']&amp;lt;=LIGHT_RAIN_LIMIT)].groupby(['month', 'day'])['rainfall'].count().reset_index()['rainfall']\ndf4['chance_rain'] = df4['count_rain'] / (df4['count_rain'] + df4['count_not_rain'])\ndf4['chance_rain'].plot(ylim=0,title=\"Chance of More Than 1.5mm Rain\", xlabel=\"Day\", ylabel=\"Chance of Rain\")\n```",
null,
"## Other Sources of UK Rainfall Data\n\nYou may also be interested in other UK Rainfall data such as the CEDA archive and the Met Office."
] |
[
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"https://deparkes.co.uk/wp-content/uploads/2021/06/AverageDailyRainfall.png",
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"https://deparkes.co.uk/wp-content/uploads/2021/06/ChanceOfRain.png",
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] |
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https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-021-01273-2
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[
"# A strategy for optimal fitting of multiplicative and additive hazards regression models\n\n## Abstract\n\n### Background\n\nIn survival analysis, data can be modeled using either a multiplicative hazards regression model (such as the Cox model) or an additive hazards regression model (such as Lin’s or Aalen’s model). While several diagnostic tools are available to check the assumptions underpinning each type of model, there is no defined procedure to fit these models optimally. Moreover, the two types of models are rarely combined in survival analysis. Here, we propose a strategy for optimal fitting of multiplicative and additive hazards regression models in survival analysis.\n\n### Methods\n\nThis section details our proposed strategy for optimal fitting of multiplicative and additive hazards regression models, with a focus on the assumptions underpinning each type of model, the diagnostic tools used to check these assumptions, and the steps followed to fit the data. The proposed strategy draws on classical diagnostic tools (Schoenfeld and martingale residuals) and less common tools (pseudo-observations, martingale residual processes, and Arjas plots).\n\n### Results\n\nThe proposed strategy is applied to a dataset of patients with myocardial infarction (TRACE data frame). The effects of 5 covariates (age, sex, diabetes, ventricular fibrillation, and clinical heart failure) on the hazard of death are analyzed using multiplicative and additive hazards regression models. The proposed strategy is shown to fit the data optimally.\n\n### Conclusions\n\nSurvival analysis is improved by using multiplicative and additive hazards regression models together, but specific steps must be followed to fit the data optimally. By providing different measures of the same effect, our proposed strategy allows for better interpretation of the data.\n\n## Background\n\nClinical studies are often aimed at assessing the relationship between explanatory variables and time-to-event outcomes such as survival time. In survival analysis, the presence of censored observations requires the use of specific models. The most commonly used models for this purpose focus directly on the hazard function and can be divided into two types: multiplicative hazards regression models and additive hazards regression models. The most popular multiplicative hazards regression model is the Cox proportional hazards model . In this model, covariates act multiplicatively on the baseline hazard, which is expressed as a time-dependent function without assumptions regarding its shape. The Cox proportional hazards model has two main advantages: it gives a hazard ratio, which allows for interpreting covariate effects as relative risks, and it is easy to compute, which means that it can be applied with practically any statistical software. However, this model is based on two assumptions that must be satisfied to ensure correct fitting of the data, and, consequently, correct interpretation of covariate effects. The first is that covariate effects are constant over time; this rather strong assumption, known as the proportional hazards assumption, results in biased estimates when it is violated . A second assumption, known as the assumption of log-linearity, is that the effects of continuous covariates are log-linear. One typically uses an extended Cox model with time-varying effects when the first assumption is not met [3, 4] and an extended Cox model with non-log-linear effects when the second assumption is not respected .\n\nBy contrast, in additive hazards regression models, covariates act additively on the baseline hazard. The first additive hazards regression model was proposed by Aalen [5, 6]. In this non-parametric model, covariates effects are modeled as regression functions that can vary over time, which means that the proportional hazards assumption does not apply. Indeed, the only assumption underpinning this model is the linearity of continuous covariates. Aalen’s model gives hazard differences that are then interpreted by plotting cumulative hazards over time. The main advantage of this model is that it allows for investigating the effects of a given covariate over time. Although this model is more flexible than the Cox proportional hazards model, it is less commonly used because it is not well-known and because cumulative hazards are more difficult to interpret than hazard ratios. In case of time-constant effect of the covariates, one can use the additive model proposed by Lin et al. , which is a particular case of Aalen’s model. In Lin’s model, regression functions are constant except for the baseline hazard.\n\nWhile both multiplicative and additive hazards regression models capture the effects of covariates, they allow for interpreting these effects differently. The hazard ratio given by multiplicative models is interpreted as a relative risk. By contrast, the cumulative hazard given by additive models is interpreted as the difference in outcome incidence due to exposure when the cumulative hazard is small (interpretation becomes much more difficult when the cumulative hazard is important) . Accordingly, one can choose either model depending on whether a hazard ratio or a cumulative hazard is preferred as a measure of covariate effects. Generally speaking, additive hazards regression models are more appropriate to determine the effects of exposure in an epidemiologic context [9, 10], and multiplicative hazards regression models are preferred in all other situations. To date, however, the two models have rarely been combined in survival analysis. Moreover, no procedure has been defined to perform optimal fitting of the two models, i.e. which allows obtaining models that fit the data while respecting the assumptions underpinning each type of model.\n\nThe aim of this study is to propose a strategy for the optimal fitting of multiplicative and additive hazards regression models in survival analysis.\n\nThe structure of the article is as follows. The Methods section begins by detailing our strategy for optimal fitting of multiplicative and additive hazards regression models, with a focus on the assumptions underpinning each type of model, the diagnostic tools used to check these assumptions, and the steps followed to fit the data. The section ends by summarizing the differences between multiplicative and additive hazards regression models. In the Results section, our proposed strategy is applied to a dataset of patients with myocardial infarction (TRACE data frame) to analyze the effects of 5 covariates (age, sex, diabetes, ventricular fibrillation, and clinical heart failure) on the hazard of death. Finally, the Discussion section provides an interpretation of our findings along with concluding remarks.\n\n## Methods\n\n### The proposed strategy\n\nOur strategy for optimal fitting of multiplicative and additive hazards regression models is detailed below. In all equations, x is a vector of k covariates ($${x}_i^T=\\left({x}_{i1},\\dots, {x}_{ik}\\right)$$), and λ0(t) is the baseline hazard as a non-parametric function of time. To simplify notation, all the presented covariates are time-independent covariates but all the models and the diagnostic tools can be used, unless otherwise specified, with time-dependent covariates [4, 11].\n\n### Cox proportional hazards model\n\nThe main model in our strategy is the popular Cox proportional hazards model . Two assumptions underpin this model: the proportional hazards assumption and the assumption of log-linearity.\n\nIn the Cox proportional hazards model, for a given subject i, the hazard is written mathematically as $${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t){e}^{x_i^T\\beta }$$, where β is the vector of k parameters β = (β1, …, βk)T measuring the effects of the covariates on the hazard. The parameter β is estimated by maximization of the partial likelihood. The exponential of the estimated parameter $$\\hat{\\beta}$$, i.e. the hazard ratio, is interpreted as a relative risk.\n\nThus, for two subjects i and j, the hazard ratio is constant over time and is written as:\n\n$$\\frac{\\lambda_i\\left(t|{x}_i\\right)}{\\lambda_j\\left(t|{x}_j\\right)}=\\frac{\\lambda_0(t){e}^{x_i^T\\beta }}{\\lambda_0(t){e}^{x_j^T\\beta }}=\\frac{e^{x_i^T\\beta }}{e^{x_j^T\\beta }}.$$\n\n### Extended Cox model in case of non-proportional hazards\n\nIn our strategy, two diagnostic tools are used to check whether or not the proportional hazards assumption is satisfied. The first is a common test which consists in estimating the correlation between the Schoenfeld residuals and the rank order of event times . The proportional hazards assumption is considered satisfied when the p-value is greater than 0.05. The second diagnostic tool is the graphical approach most commonly used to represent the effects of a covariate on the hazard over time. In this approach, the Schoenfeld residuals obtained with a Cox proportional hazards model fitted with each covariate are plotted against the rank order of event times, and a smooth curve is then superimposed on the plot. The obtained curve represents the variation of parameter β (i.e. the log-hazard ratio of the covariate effects) over time. The proportional hazards assumption is considered satisfied if the curve is horizontal.\n\nWhen the proportional hazards assumption is respected for a given covariate, the Cox proportional hazards model is fitted with this covariate.\n\nWhen the assumption is not satisfied, an extended Cox non-proportional hazards model is fitted with a function of the time-dependent parameter β(t) . Here, the hazard is written as $${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t){e}^{x_i^T\\beta (t)}$$, where β(t) is defined based on knowledge of the variation or on the results obtained with either of the diagnostic tools above.\n\nThe above process is repeated until the proportional hazards assumption is satisfied for each covariate.\n\n### Extended Cox model in case of non-log-linearity\n\nAs noted earlier, the Cox proportional hazards model assumes the log-linearity of continuous covariates. Thus, for a continuous covariate x and two subjects i and j, the hazard ratio is written as $$\\frac{\\lambda_i\\left(t|{x}_i\\right)}{\\lambda_j\\left(t|{x}_j\\right)}=\\frac{\\lambda_0(t){e}^{x_i\\beta }}{\\lambda_0(t){e}^{x_j\\beta }}=\\frac{e^{x_i\\beta }}{e^{x_j\\beta }}={e}^{\\left({x}_i-{x}_j\\right)\\beta }$$ and depends only on the difference between xi and xj. For instance, for the continuous covariate “age”, the relative risk between a 25- and a 26-year-old is the same as that between an 80- and an 81-year-old.\n\nIn our strategy, the assumption of log-linearity is checked by representing the effects of each continuous covariate on the hazard using the martingale residuals . The martingale residuals are defined as the difference between the observed number of events for an individual (i.e. 1 when there is an event; 0 otherwise) and the number of events estimated with the Cox proportional hazards model. The lowess smooth of the martingale residuals obtained with a null Cox proportional hazards model (i.e. a Cox model with no fitted covariate) is plotted against the continuous covariate, which gives the functional form of this covariate on the hazard . If the obtained curve is straight, then the assumption of log-linearity is satisfied.\n\nWhen the assumption of log-linearity is satisfied for a given covariate, the Cox proportional hazards model is fitted with the non-transformed covariate.\n\nWhen this assumption is not satisfied, the best functional form is selected for each covariate using an extended Cox model. In this model, the hazard is written as$${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t){e}^{f\\left({x}_i^T\\right)\\beta }$$, where f(x) is the functional form of covariate x. Different functional forms of the continuous covariate are modeled directly using special functions like fractional polynomials or regression splines. Then, the lowess smooth of the martingale residuals obtained with the extended Cox model fitted with these functional forms is plotted against the continuous covariate : the functional forms that give roughly horizontal curves are considered good candidates to satisfy the assumption of log-linearity. The best functional form is then selected using a model selection criterion - for instance, the Akaike information criterion (AIC) for non-nested models.\n\nThe above process is repeated until the assumption of log-linearity is met for each continuous covariate.\n\nIn case of time-dependent continuous covariate, there is no single value for each subject, so the lowess smooth of the martingale residuals cannot easily be plotted against the continuous covariate . The assumption of log-linearity must be checked with another diagnostic tool presented below.\n\n### Extended Cox model in case of non-proportional hazards and non-log-linearity\n\nThe diagnostic tools used to check the proportional hazards assumption (Schoenfeld residuals) and the assumption of log-linearity (martingale residuals) for a single continuous covariate rely on the other assumption being true. While different methods can be used to check the two assumptions simultaneously (Sasieni and Winnett and Pohar Perme and Andersen ), our strategy employs that proposed by Pohar Perme and Andersen . This method is based on pseudo-observations, which were introduced for regression modeling in event-history analysis by Andersen et al. .\n\nIn survival analysis, for an individual i, the pseudo-observation $${\\hat{S}}_i(t)$$ is defined as the difference between n times the survival $$\\hat{S}(t)$$ estimated with the Kaplan-Meier method on the whole sample and n minus one times the survival $${\\hat{S}}^{-i}(t)$$ estimated with the Kaplan-Meier method after leaving out the ith individual. One pseudo-observation is thus obtained for each individual at each event time. To check the two assumptions simultaneously, the pseudo-observations are transformed to obtain a linear expression between survival and covariate effects. Thus, for a continuous covariate z, the hazard is written as λ(t| z) = λ0(t)e such that survival is S(t| z) = exp(− ∫ λ(t| z)dt) = exp(− ∫ λ0(t)edt) = exp(−Λ0(t)e), where $${\\varLambda}_0(t)={\\int}_0^t{\\lambda}_0(t) dt$$. With the cloglog transformation of the smoothed curves of pseudo-observations, we obtain log(− log(S(t| z))) = log(Λ0(t)) + . The effects of the covariate on survival are represented by plotting the cloglog-transformed smoothed pseudo-observations against the continuous covariate. Because covariate effects can vary over time, pseudo-observations are usually plotted at selected time points (e.g. 9 curves corresponding to 9 deciles of the event times distribution). The two assumptions are satisfied if the obtained curves are parallel straight lines with the same slope β.\n\nWhen the two assumptions are satisfied for a given covariate, the Cox proportional hazards model is fitted with the non-transformed covariate.\n\nWhen neither of the assumptions is satisfied, an extended Cox model with time-varying effects and non-log-linear effects is used. In this model, for a continuous covariate z, the hazard is written as $${\\lambda}_i\\left(t|{z}_i\\right)={\\lambda}_0(t){e}^{f\\left({z}_i\\right)\\beta (t)}$$. The model is fitted with functions of the time-dependent parameter and with functional forms of the continuous covariate.\n\nThe above process is repeated until both the proportional hazards assumption and the assumption of log-linearity are satisfied for each continuous covariate.\n\n### Goodness-of-fit assessment using Arjas plots\n\nThe goodness-of-fit of the multiplicative hazards regression model fitted with each covariate is assessed using the method proposed by Arjas . This method known as Arjas plots consists in plotting the observed number of patients with the event against the number of patients with the event estimated with the model. If the observed number and the estimated number of patients with the event are close and the obtained curve roughly matches the diagonal line, then the model has goodness-of-fit. Note that in the case of continuous covariates, groups of individuals are defined by dividing the continuous covariate distribution into several strata (e.g. 4 strata according to the quartiles of the continuous covariate distribution).\n\nThe model has no goodness-of-fit when the curves systematically deviate from the diagonal for some groups of individuals, indicating an excess or a lack of predicted events. When this occurs, the proportional hazards assumption and the assumption of log-linearity must be checked again for each covariate (as described above) until goodness-of-fit is achieved.\n\n### Multivariate multiplicative model\n\nThe proportional hazards assumption is checked for the multiplicative model fitted with all covariates by testing the correlation between the Schoenfeld residuals and the rank order of event times. The goodness-of-fit of the multivariate model is then assessed using Arjas plots. The entire process is repeated until the proportional hazards assumption is satisfied for all covariates and the multivariate model has goodness-of-fit.\n\n### Step-by-step strategy for optimal fitting of multiplicative hazards regression models\n\nTo summarize, in order to optimally fit a multiplicative hazards regression model in survival analysis, the following step-by-step strategy is implemented:\n\n1. 1.\n\nCheck the assumption of log-linearity for each continuous covariate using the martingale residuals (or the plot of the cloglog-transformed smoothed pseudo-observations against the time-dependent continuous covariate). In case on non-log-linearity, select the best functional form of the continuous covariate using an extended Cox model. Repeat this step until the assumption of log-linearity is satisfied for each continuous covariate.\n\n2. 2.\n\nCheck the proportional hazards assumption for each covariate by testing the correlation between the Schoenfeld residuals and the rank order of event times. In case of non-proportional hazards, model a function of the time-varying parameter in an extended Cox model. Repeat this step until the proportional hazards assumption is satisfied for each covariate.\n\n3. 3.\n\nCheck simultaneously the proportional hazards assumption and the assumption of log-linearity by plotting the cloglog-transformed smoothed pseudo-observations against each continuous covariate. In case of non-log-linearity and non-proportional hazards, use an extended Cox model. Repeat steps 1, 2, and 3 until both assumptions are satisfied for each continuous covariate.\n\n4. 4.\n\nAssess the goodness-of-fit of the multiplicative hazards regression model for each covariate using Arjas plots. Repeat steps 1, 2, 3, and 4 until the model has goodness-of-fit for each covariate.\n\n5. 5.\n\nCheck the proportional hazards assumption for the multiplicative model fitted with all covariates using the same procedures as in Step 2. Repeat steps 1, 2, 3, 4, and 5 until the multivariate model has goodness-of-fit.\n\n### Aalen’s model\n\nThe additive hazards regression model proposed by Aalen is used to estimate the additive effects of a covariate on the baseline hazard [5, 6]. In this model, for a given subject i, the hazard is written as $${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t)+{x}_i^T\\alpha (t)$$, where α(t) is the vector of k non-parametric regression functions α(t) = (α1(t), …, αk(t))measuring the effects of the covariates on the hazard. The non-parametric regression function α(t) is estimated by the least squares method at each event time for at-risk individuals only [5, 6]. The only assumption of this model is that continuous covariates are linear. The diagnostic tools used to check this assumption are presented below.\n\n### Lin’s model\n\nLin’s model is a particular case of Aalen’s model, in which all regression functions except the baseline hazard are constant over time. Thus, for a given subject i, the hazard is written as $${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t)+{x}_i^T\\gamma$$, where γ is the vector of k parameters γ = (γ1, …, γk)measuring the effects of covariates on the hazard. As in the Cox proportional hazards model, the parameter γ is estimated by maximization of the partial likelihood.\n\nIn addition to assuming the linearity of continuous covariates, Lin’s model assumes that covariate effects are constant over time. The assumption of constant effects is checked for each covariate by plotting the cumulative hazards estimated with Lin’s and Aalen’s models against time. The assumption is satisfied if the obtained curve has a constant slope. If the effects of all covariates are constant over time, Lin’s model is used; otherwise, Aalen’s model is used.\n\n### Extended Aalen’s model in case of non-linearity\n\nHere, the assumption of linearity of continuous variables is checked not with the martingale residuals as in the extended Cox model, but with the pseudo-observations. Specifically, Lin’s model (based on the assumptions of linearity and constant effects) is used to model the functional form of the continuous covariate after a transformation of the pseudo-observations. Thus, for a continuous covariate z, the hazard is written as λ(t| z) = λ0(t) + γz such that survival is S(t| z) = exp(− ∫ λ(t| z)dt) = exp(− ∫ λ0(t) + γzdt) = exp(−Λ0(t) − γzt), where $${\\varLambda}_0(t)={\\int}_0^t{\\lambda}_0(t) dt$$. After log-transformation of the pseudo-observations, we obtain $$\\frac{-\\log \\left(S\\left(t|z\\right)\\right)}{t}=\\frac{\\varLambda_0(t)}{t}+\\gamma z$$. The effect of the continuous covariate on survival is represented by plotting the log-transformed smoothed pseudo-observations against the covariate, and then superimposing smooth curves on the scatter plot. Note that because covariate effects can vary over time, the pseudo-observations are usually plotted at selected time points.\n\nThe shape of the obtained curves gives the functional form of the continuous covariate and indicates which model to use. If the obtained curves are straight lines, then the assumption of linearity is respected: in that case, Aalen’s model or Lin’s model is used (depending on whether or not covariate effects are constant, as explained above). If the obtained curves are not straight lines and are not parallel, then neither the assumption of linearity nor the assumption of constant effects is satisfied: in that case, an extended Aalen’s model is used (see below). Finally, if the obtained curves are not straight lines and are parallel (with the same slope γ), then the assumption of linearity is not satisfied but the assumption of constant effects is respected: in that case, an extended Lin’s model is used (see below).\n\nIn the extended Aalen’s model, the functional form of the continuous covariate is modeled directly using special functions like fractional polynomials or regression splines. Here, the hazard is written as$${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t)+f\\left({x}_i^T\\right)\\alpha (t)$$, where f(x) is the functional form of the covariate x. To determine whether the functional form of the continuous covariate is appropriate, the variation of the martingale residual processes over time is assessed graphically . For a given group of individuals, the cumulative sum of the martingale residual processes is the difference between the observed number of events and the number of events estimated with the model fitted for this group.\n\nFirst, groups of individuals are defined by dividing the continuous covariate distribution into several strata (e.g. 4 strata according to the quartiles of the continuous covariate distribution). Then, the cumulative sum of the martingale residual processes for each group is plotted against time with their confidence bounds. When the fit is correct, the obtained curves are close to the horizontal axis and their confidence bounds do not cross the horizontal axis. Finally, chi-square tests are performed at the end of patient follow-up to compare the observed number of events to the estimated number of events (for each stratum and for all strata) . If the obtained p-value is statistically significant, the functional form is rejected and another functional form is tested.\n\nThe above process is repeated until the assumption of linearity is met for each continuous covariate.\n\n### Extended Lin’s model in case of non-linearity\n\nAs noted above, when the continuous covariates are non-linear and the covariate effects are constant over time, an extended Lin’s model is used. In this model, the hazard is written as$${\\lambda}_i\\left(t|{x}_i\\right)={\\lambda}_0(t)+f\\left({x}_i^T\\right)\\gamma$$ where f(x) is the functional form of the covariate x. Note that the functional form of the continuous covariate is modeled directly using special functions like fractional polynomials or regression splines.\n\n### Goodness-of-fit assessment using Arjas plots\n\nThe goodness-of-fit of the additive hazards regression model is assessed using Arjas plots . Note that this procedure is not necessary in the case of categorical covariates because in Aalen’s model the observed number of events is always equal to the estimated number of events at all time points.\n\nThe assumption of linearity is checked for the additive model fitted with all covariates by assessing the variation of the martingale residual processes over time. Then, the goodness-of-fit of the multivariate model is assessed using Arjas plots. The entire process is repeated until the assumption of linearity is satisfied for all covariates and the multivariate model has goodness-of-fit.\n\n### Step-by-step strategy for optimal fitting of additive hazards regression models\n\nTo summarize, in order to optimally fit an additive hazards regression model in survival analysis, the following step-by-step strategy is implemented:\n\n1. 1.\n\nCheck the assumption of linearity for each covariate using log-transformed smoothed pseudo-observations. In case on non-linearity, select the best functional form of the continuous covariate by assessing the variation of the martingale residual processes over time. Repeat this step until the assumption of linearity is satisfied for each continuous covariate.\n\n2. 2.\n\nIf the assumption of linearity is satisfied, check the assumption of constant effects for each covariate by plotting the cumulative hazards estimated with Lin’s and Aalen’s models against time. If the effects of all covariates are constant, use Lin’s model; otherwise, use Aalen’s model.\n\n3. 3.\n\nAssess the goodness-of-fit of the additive hazards regression model for each continuous covariate using Arjas plots. Repeat steps 1, 2, and 3 until the model has goodness-of-fit for each continuous covariate.\n\n4. 4.\n\nCheck the assumption of linearity for the additive model fitted with all the covariates using the same procedure as in step 1. Repeat this step with another functional form of the continuous covariate until the assumption of linearity is satisfied for all covariates.\n\n#### Differences between multiplicative and additive hazards regression models\n\nIn the Cox proportional hazards model, for a binary covariate z, the hazard is written as λ(t| z) = λ0(t)e. The effect of the covariate on the hazard is measured by the hazard ratio, which is written as $$HR={e}^{\\beta }=\\frac{\\lambda \\left(t|z=1\\right)}{\\lambda \\left(t|z=0\\right)}=\\frac{\\lambda \\left(t|z=1\\right)}{\\lambda_0(t)}$$. The importance of the effect of the covariate on the hazard depends on the baseline hazard: when the baseline hazard is very low, the hazard remains low for the exposed subject even if the hazard ratio is important. Moreover, the effect of the covariate is interpreted using a single parameter - the hazard ratio - which is constant over time. In the case of the extended Cox model with time-varying effects, the hazard ratio varies over time, and so the interpretation requires plotting hazard ratios against time.\n\nIn Aalen’s model, for the same covariate z, the hazard is written as λ(t| z) = λ0(t) + α(t)z. Here, the effect of the covariate is measured by the cumulative hazard, which is written as α(t) = λ(t| z = 1) − λ(t| z = 0). The cumulative hazard highlights the importance of the effect of exposure over time, whatever the baseline hazard. It represents the attributable fraction due to exposure, hence its common use in epidemiology. Since the cumulative hazard is a function, it can be plotted to show the evolution of the effect over time.\n\nIn short, each type of model allows for a different interpretation of the effect of the covariate on the hazard.\n\n#### Estimating procedures\n\nEstimating procedures for multiplicative and additive hazards regression models are available in the major statistical software (SAS, STATA, and R). At the moment, however, some of the diagnostic tools used in our strategy are only available in R. All of our analyses were therefore performed using R software (script provided in Additional file 1).\n\n## Results\n\n### Motivating example\n\nIn this section, our proposed strategy for optimal fitting of multiplicative and additive hazards regression models is applied to a motivating example: the TRACE data frame provided in the timereg R package. This data frame is a subset of a dataset extracted from a study of 4259 patients with myocardial infarction who were admitted to a hospital in Denmark in 1977–1988 and were followed until death or censoring .\n\nThe 1878 patients included in the TRACE data frame had a mean age of 67.0 years (sd: 11.4). Overall, 52.29% of patients had clinical heart failure, 69.54% of patients were women, 10.01% of patients had diabetes, and 7.24% had ventricular fibrillation. Median survival was 6.52 years [6.09; 7.25]. The TRACE data frame is interesting for our purposes because it contains covariates with well-known time-varying effects on the hazard of death (ventricular fibrillation) as well as covariates with constant effects on the hazard of death (diabetes and sex) .\n\nOur proposed strategy is used to investigate the hazard of death in the included group of patients with myocardial infarction. The effects of age (continuous covariate named age), clinical heart failure (binary covariate named chf), sex (binary covariate named sex), diabetes (binary covariate named dia), and ventricular fibrillation (binary covariate named vf) on the hazard of death are examined below. Note that because Aalen’s model assumes no ties between event times, a random number has been added to each survival time such that no two survival times are identical.\n\n### Application of the proposed strategy for optimal fitting of multiplicative hazards regression models\n\n#### Checking the assumption of log-linearity\n\nTo select the best functional form of the continuous covariate age, the martingale residuals obtained with a null Cox proportional hazards model are plotted against age. As shown in Fig. 1a, the curve representing the effect of age is not a straight line, indicating a deviation from log-linearity. Specifically, there is an increase in the slope of the curve, which suggests an exponential function and perhaps even a quadratic function.\n\nAfter dividing age by 100 to avoid too large values, a Cox proportional hazards model is fitted with an exponential of age/100. Figure 1b shows the plot of the martingale residuals. The smooth curve is a horizontal straight line, indicating that the exponential of age/100 is an appropriate functional form.\n\nA Cox proportional hazards model is then fitted with a quadratic effect of age/100. The smooth curve obtained after plotting the martingale residuals (Figure not shown) is also a horizontal straight line.\n\nThe AIC of the two models is calculated to determine which of the last two functional forms is more appropriate. The AIC of the Cox proportional hazards model fitted with the quadratic effect of age/100 (13,533.73) is greater than that of the Cox proportional hazards model fitted with the exponential of age/100 (13,531.83). The latter functional form is selected.\n\n#### Checking the proportional hazards assumption\n\nThe proportional hazards assumption is checked for each of the 5 covariates by testing the correlation between the Schoenfeld residuals and the rank order of event times (Table 1). For the covariates chf and vf, the assumption of proportionality is not satisfied (p-values < 0.05), indicating that an extended Cox model with time-varying effects is needed. By contrast, the effects of the exponential of age/100, sex, and dia do not vary statistically over time, and so the effect of each variable is modeled as constant over time.\n\nFigure 2 shows the plot of the Schoenfeld residuals for each of the 5 predictors. The smooth curves are roughly horizontal for the exponential of age/100, sex, and dia, indicating that these covariates have constant effects over time. Accordingly, a Cox proportional hazards model is used for these three covariates.\n\nFor the covariate chf, the smooth curve decreases with a roughly constant slope, indicating a linear time-dependent effect. The covariate chf is thus modeled as follows: $$\\lambda \\left(t| chf\\right)={\\lambda}_0(t){e}^{chf\\times \\left({\\beta}_{chf}+{\\beta}_{chf t}\\times t\\right)}$$. The Schoenfeld residuals test indicates that the assumption of proportional hazards is satisfied for the parameters βchf and βchft (p-values of 0.85 and 0.41, respectively).\n\nFor the covariate vf, the smooth curve decreases with a roughly constant slope until 0.64, and then remains horizontal afterwards. Accordingly, a simple model with a break of slope accounting for the two variations of the hazard is used. To choose the best cut-off time for the break of slope, different cut-off times ranging from 0 to 2.4 (in intervals of 0.01) are assessed using the AIC. The minimal AIC obtained is 13,824.78 for a cut-off time of 0.15. The covariate vf is therefore modeled as follows: $$\\lambda \\left(t| vf\\right)={\\lambda}_0(t){e}^{vf\\times \\left({\\beta}_{vf}+{\\beta}_{vf t}\\times t+{\\beta}_{vf t2}\\times \\left(t-0.15\\right)I\\left(t>0.15\\right)\\right)}$$. The Schoenfeld residuals test shows that the proportional hazards assumption is satisfied for the parameters βvf, βvft, and βvft2 (p-values of 0.60, 0.66, and 0.66, respectively).\n\n#### Assessing goodness-of-fit\n\nFigure 3 shows the plot of the cloglog-transformed smoothed pseudo-observations (cloglog transformation being necessary to check the two assumptions of the Cox model, as shown in the Methods section) against the continuous covariate age/100 for the 9 deciles of the event times distribution (in years). The curves are not entirely straight, which means that the effect is not fully linear. This is consistent with what was found using the martingale residuals (Fig. 1). Furthermore, the curves are not entirely parallel (especially before age/100 = 0.4, i.e. 40 years), indicating that a slightly different functional form of the covariate is needed. The 5 curves representing the 2nd to the 6th deciles are roughly horizontal until 40 years, and then increase afterwards. This indicates an absence of effect of age until 40 years, followed by an almost exponential increase of this effect. Based on the study of the pseudo-observations, the exponential of age/100 is selected.\n\nFigure 4 shows the Arjas plots for the Cox proportional hazards model fitted with the continuous covariate age in 4 strata defined according to the quartiles of age distribution. The Arjas plot corresponding to the linear effect of age (Fig. 4a) and the Arjas plot corresponding to the exponential effect of age/100 (Fig. 4b) are not very different, but nevertheless suggest that goodness-of-fit is higher for the exponential effect of age/100 than for the linear effect of age (as can already be seen in Fig. 3).\n\nFigure 5 shows the Arjas plots for the Cox proportional hazards model fitted with the binary covariate chf. In Fig. 5a, the binary covariate chf is modeled without time-dependent effect. The number of estimated events is more important than the number of observed events for patients without clinical heart failure, and it is less important than the number of observed events for patients with clinical heart failure. This indicates that modeling the binary covariate chf without time-varying effect is inappropriate. In Fig. 5b, the binary covariate chf is modeled with the linear time-varying effect obtained earlier (see Checking the proportional hazards assumption section). The number of estimated events and the number of observed events are roughly equal for patients with or without clinical heart failure, indicating that modeling the binary covariate chf with the linear time-varying effect is appropriate.\n\n#### Fitting the multivariate multiplicative model\n\nOnce the proportional hazards assumption has been checked for each continuous covariate, it is checked for the multivariate model fitted with all the covariates using the same procedure as in step 2 of the univariate analysis. The Schoenfeld residuals test is statistically non-significant for all the covariates except for dia (p-value = 0.016). The plot of the correlation between the Schoenfeld residuals and the rank order of event times (Figure not shown) indicates that a linear time-dependent effect of dia is needed. A linear time-dependent effect is added, and so the multivariate model is written as $$\\lambda (t)={\\lambda}_0(t){e}^{\\beta_{age}\\times \\exp \\left(\\frac{age}{100}\\right)+{\\beta}_{sex}\\times sex+\\left({\\beta}_{chf}+{\\beta}_{chf t}\\times t\\right) chf+\\left({\\beta}_{dia}+{\\beta}_{dia t}\\times t\\right) dia+\\left({\\beta}_{vf}+{\\beta}_{vf t}\\times t+{\\beta}_{vf t2}\\times \\left(t-0.15\\right)I\\left(t>0.15\\right)\\right) vf}$$. The Schoenfeld residuals test shows that all the covariates are statistically non-significant with this model.\n\nIn addition, each parameter is shown to be statistically significant with this model (Table 2). The effects of the covariates exponential of age/100 and sex are constant over time, while the effects of the covariates chf, dia, and vf vary over time. The hazard ratio for sex is 1.20 [1.05; 1.38] in women. As the effect of the exponential of age/100 is log-linear, the effect of age is not log-linear and is therefore interpreted graphically. As expected, the hazard ratio for an increase of 1 year increases with age, i.e. the hazard ratio for 1 year of ageing is more important in older patients than in younger patients (Fig. 6).\n\nThe hazard ratios for the three other binary covariates are not constant but vary over time. They are therefore represented graphically to give a clear idea of their evolution over time (Fig. 7). The hazard ratio for chf decreases linearly over time, and then becomes non-significant at the end of patient follow-up (Fig. 7a). By contrast, the hazard ratio for dia increases linearly, and then becomes important at the end of follow-up (Fig. 7b). Finally, the hazard ratio for vf is very important at first, and then decreases rapidly to become non-significant after 2 months (Fig. 7c).\n\n### Application of the proposed strategy for optimal fitting of additive hazards regression models\n\n#### Checking the assumption of linearity\n\nTo define the functional form of the continuous covariate age, the log-transformed smoothed pseudo-observations (log transformation being necessary to check the assumption of linearity of the additive hazards regression model, as shown in the Methods section) are plotted against age for 9 deciles of the event times distribution. As Fig. 8 indicates, the curves are not straight lines, which means that the effect is not linear, but are nearly parallel, which means that the effect is constant over time. The 7 curves representing the 3rd to the 9th deciles are very similar: they are roughly horizontal until 60 years, and then increase afterwards. This indicates a slight effect of age until 60 years, and then an exponential increase in the effect of age. For the other two deciles, the increase is more important, and also corresponds to an exponential effect. As the exponential of age can take very large values, this covariate is initially divided by ten. Then, to check whether the exponential functional form is appropriate, the martingale residual processes are plotted against time in 4 strata defined according to the quartiles of age distribution (Fig. 9a). The plot indicates that the observed number of younger patients is less important than the estimated number of younger patients at the end of patient follow-up. The results of the chi-square test of the martingale residual processes confirm that modeling with the exponential of age/10 is inappropriate (Table 3). Given that the increase in the slope begins roughly at 70 years, a more flexible functional form is needed to properly account for the increase in the effect of age. The covariate age is therefore modeled as the exponential of age/10 with a cut-off at 70 years. Figure 9b shows that when age is modeled in this way, the martingale residual processes do not significantly deviate from the horizontal axis (for the 4 strata). Likewise, Table 3 indicates that the extended Aalen’s model has goodness-of-fit with this functional form.\n\n#### Checking the assumption of constant effects\n\nThe assumption of constant effects is checked for 6 covariates by plotting the cumulative hazards estimated with Lin’s and Aalen’s models. Figure 10 shows that for the exponential of age/10, the exponential of (age-70) × (age > 70), sex, and dia, the cumulative hazards estimated with Lin’s model (dashed straight lines) do not cross the 95% confidence intervals of the cumulative hazards estimated with Aalen’s model (dotted lines). This indicates that the effect of each covariate is constant. For chf, the cumulative hazard increases more quickly at the beginning, and then more slowly afterwards. For vf, the hazard increases considerably until 0.1, and then remains constant afterwards. Since the effect varies over time for some of the covariates, the extended Lin’s model is not appropriate, and the analyses are performed using the extended Aalen’s model.\n\nFor the covariates exponential of (age-70) × (age > 70) and sex, the estimated cumulative hazards are negative. This is not an unusual finding in additive hazards regression models.\n\n#### Assessing goodness-of-fit\n\nFigure 11 shows the Arjas plots for Aalen’s model fitted with the continuous covariate age, with 4 strata defined according to the quartiles of age distribution. In Fig. 11a, Aalen’s model is fitted with the continuous covariate age without transformation; in Fig. 11b, Aalen’s model is fitted with the exponential of age/10 with a cut-off at 70 (Fig. 11b). Figure 11a shows an important discrepancy between the number of observed events and the number of estimated events in the 4 strata, indicating a lack of fit when the continuous covariate age is modeled without transformation. By contrast, in Fig. 11b, the number of observed events is close to the number of estimated events. Accordingly, the continuous covariate age is modeled as the exponential of age/10 with a cut-off at 70.\n\n#### Fitting the multivariate additive model\n\nOnce the assumption of linearity has been checked for each continuous covariate, it is checked for the multivariate model fitted with all the covariates using the same procedure as in step 1 of the univariate analysis. The test of the martingale residual processes (Table 4) shows no deviation when the continuous covariate age is modeled as an exponential function with a cut-off at 70 (Figure not shown).\n\nAs shown in Fig. 12, the cumulative regression functions estimated with the multivariate Lin’s and Aalen’s models are significantly different from 0 for all the covariates, indicating a significant effect of these covariates on mortality.\n\nThe slope of the estimated cumulative regression function is positive for all the binary covariates. The effect is constant for sex and dia but is more important for dia than for sex, indicating that the excess risk of death due to diabetes is more important than the excess risk of death due to sex. For chf, the slope of the estimated cumulative regression function decreases slowly over time, indicating a decrease in the effect of clinical heart failure on mortality. For vf, the slope is very high until 0.1 year, and then becomes horizontal. This indicates that the excess risk of death due to ventricular fibrillation is present during the first 0.1 year of patient follow-up, and then vanishes afterwards. Finally, for the exponential of age/10, the slope of the estimated cumulative regression function is constant and positive until cut-off and then constant and negative afterwards, indicating an absence of variation of the effect over time. However, while the excess risk of death increases exponentially with ageing until 70 years – as shown by the exponential functional form – this increase is less important after 70 years – as shown by the negative slope (Figs. 12 and 13).\n\n## Discussion\n\nThis work proposes a strategy for optimal fitting of multiplicative and additive hazards regression models in survival analysis. The proposed strategy has been shown to fit the data optimally. Several points can be made in this regard.\n\nThe first point is that several factors condition the choice between multiplicative and additive hazards regression models in survival analysis. The most important factor is knowledge of the effect of the covariate on the hazard of death. If this effect is known to be multiplicative or additive, then the corresponding model (multiplicative hazards regression model or additive hazards regression model, respectively) is used [22, 23]. However, the effect of the covariate on the hazard of death is rarely known in advance. Consequently, the choice between the two types of models is usually made based on whether one wants to obtain a relative risk – e.g. the hazard ratio – or an absolute risk – e.g. the cumulative hazard – as a measure of the effect of a covariate on mortality. Thus, the hazard ratio measures the multiplicative effect of a covariate on the baseline hazard; it is interpreted as a relative risk by practitioners, and is frequently reported in clinical and epidemiological studies. The cumulative hazard measures the actual effect of the covariate on the hazard of death, i.e. the importance of mortality due to this covariate. When it is small, the cumulative hazard is interpreted as the difference in outcome incidence due to exposure. In an epidemiological or prevention context, the cumulative hazard is interesting because it accounts both for the importance of the effect of an exposure and for the prevalence of this exposure.\n\nAdditive hazards regression models seem to us superior because they allow to directly represent the variation of covariate effects over time, which corresponds to the non-parametric estimation of regression function. By contrast, in the case of multiplicative hazards regression models, the assumption of constant effects must be checked by plotting the Schoenfeld residuals; and when this assumption is not satisfied, an extended Cox model must be performed to model the variation of covariate effects.\n\nAs we have seen, our strategy combining multiplicative and additive hazards regression models is interesting because it accounts for different relationships between the hazard function and the covariate. In fact, the two types of models complement each other: by providing different measures of the same effect, they make for a better interpretation of the data. An alternative strategy is the combined multiplicative-additive hazards regression models, as the Cox-Aalen model or the Lin’s additive-multiplicative hazard model , in which the covariates are split into two parts according to their - multiplicative or additive - effect on the hazard. However, these models cannot allow to select the type of the effect of the covariates (i.e. additive or multiplicative effect) using the AIC because the likelihood of these models is intractable . We refer the reader to the specific literature on this topic, as this is not the focus of the present article [24,25,26].\n\nSecond, our proposed strategy for optimal fitting of multiplicative and additive hazards regression models is quite easy to implement, and uses diagnostic tools that are available in the major statistical software. As regards multiplicative hazards regression models, our strategy relies not only on classical diagnostic tools (the Schoenfeld and martingale residuals) to check the proportional hazards assumption and the assumption of log-linearity, but also on pseudo-observations and Arjas plots to assess goodness-of-fit. Other approaches for fitting multiplicative hazards regression model have been proposed. Thus, Sasieni and Winnett have introduced a new kind of residuals, the martingale difference residuals, which is used to check both the proportional hazards assumption and the assumption of log-linearity. The limitation of this approach is that it does not require a precise definition of the functional form, even for very large datasets. By contrast, in our strategy, pseudo-observations are used to graphically represent not only the functional form of the continuous covariate but also its variation over time. As such, our strategy helps to select the best functional form for the multivariate model (whether multiplicative or additive). Abrahamowicz and McKenzie have proposed a multiplicative hazards regression model that relaxes both the proportional hazards assumption and the assumption of log-linearity. However, this model is highly flexible, and can consequently result in overfitting. Our approach limits the risk of overfitting by requiring the definition of the functional form and that of the covariate effect – though it should be noted that this can sometimes be time-consuming.\n\nIn our strategy, additive hazards regression models are fitted using pseudo-observations, martingale residual processes, and Arjas plots. Other tools have been proposed to assess goodness-of-fit for this type of model. Martinussen and Scheike have introduced two tests based on Gaussian processes to help choose between Aalen’s and Lin’s model in the case of time-invariant effects . Contrary to our approach, in which the assumption of constant effects is checked using a graphical tool, Martinussen and Scheike’s approach has two limitations: the possibility of discordance between the results of the two tests, and the rejection of the null hypothesis when the sample size increases even if the effect is low. McKeague & Utikal have proposed a goodness-of-fit test for Aalen’s model that compares the estimator generated with this model to a non-parametric estimator. The limitation of this approach is that it requires a sample size of at least 1000 subjects to perform satisfactorily. Importantly, goodness-of-fit tests do not give the same information as graphical tools: while the first provide quantitative measures of fit, the second allow for selecting the best functions and functional forms for the multivariate model.\n\nThird, our strategy yields the same results as that proposed by Martinussen and Scheike – who also used the TRACE data frame – although our additive hazards regression model is slightly different from theirs. In our strategy, the multiplicative and additive hazards regression models allow for different interpretations of the same data. Indeed, while the effects of the covariates are significant in both models, they do not act in the same way on the baseline hazard. As regards the covariates sex, clinical heart failure, and ventricular fibrillation, the effect is respectively constant, decreasing, and important then null in both the multiplicative and additive hazards regression models. Here, the variation in mortality due to sex, clinical heart failure, and ventricular fibrillation is given as a relative risk. For the covariate age, both models show a constant effect over time until age 70 and an increasing effect with ageing, but this increasing effect is much greater when given as a cumulative hazard than as a hazard ratio. Thus, the additive hazards regression model better highlights the importance of age as a cause of mortality. As regards the covariate diabetes, the effect is constant in the extended Aalen’s model and increasing in the extended Cox model. In other words, the extended Cox model shows that the relative risk of death increases over time for patients with diabetes, whereas the extended Aalen’s model indicates that mortality due to diabetes is constant over time. The reason for this discrepancy is that diabetic patients initially have higher mortality compared to other patients which results in a sligh decrease of the proportion of diabetic patients relative to the total sample. Thus, to keep the risk of death from diabetes constant, the hazard ratio increases artificially. The above suggests that the additive hazards regression model is a better choice for the analysis of our dataset.\n\nIn conclusion, survival analysis is improved by using multiplicative and additive hazards regression models together, but specific steps must be followed to fit the data optimally. Our proposed strategy allows for better interpretation of the data.\n\n## Availability of data and materials\n\nThe datasets generated and/or analysed during the current study are available in the timereg R package repository, https://cran.r-project.org/web/packages/timereg/index.html\n\n## References\n\n1. 1.\n\nCox DR. Regression models and life-tables. J R Stat Soc B. 1972;34(2):187–202.\n\n2. 2.\n\nPersson I, Khamis H. Bias of the Cox model hazard ratio. J Mod Appl Stat Method. 2005;4(1):10.\n\n3. 3.\n\nCai Z, Sun Y. Local linear estimation for time-dependent coefficients in Cox’s regression models. Scand J Stat. 2003;30(1):93–111. https://doi.org/10.1111/1467-9469.00320.\n\n4. 4.\n\nK. Dietz Institut für Medizinische Biometrie Universität Tübingen Westbahnhofstrasse 55 D-72070 Tübingen German.\n\n5. 5.\n\nAalen OO. A linear regression model for the analysis of life times. Stat Med. 1989;8(8):907–25. https://doi.org/10.1002/sim.4780080803.\n\n6. 6.\n\nAalen OO. Further results on the non-parametric linear regression model in survival analysis. Stat Med. 1993;12(17):1569–88. https://doi.org/10.1002/sim.4780121705.\n\n7. 7.\n\nLin DY, Ying Z. Semiparametric analysis of the additive risk model. Biometrika. 1994;81(1):61–71. https://doi.org/10.1093/biomet/81.1.61.\n\n8. 8.\n\nXie X, Strickler HD, Xue X. Additive hazard regression models: an application to the natural history of human papillomavirus. Comput Math Method Med. 2013;2013:796270.\n\n9. 9.\n\nLim HJ, Zhang X. Semi-parametric additive risk models: application to injury duration study. Accid Anal Prev. 2009;41(2):211–6. https://doi.org/10.1016/j.aap.2008.07.015.\n\n10. 10.\n\nStevens J, Truesdale KP, Wang CH, Cai J, Erber E. Body mass index at age 25 and all-cause mortality in whites and African Americans: the atherosclerosis risk in communities study. J Adolesc Health. 2012;50(3):221–7. https://doi.org/10.1016/j.jadohealth.2011.06.006.\n\n11. 11.\n\nAydemir Ü, Aydemir S, Dirschedl P. Analysis of time-dependent covariates in failure time data. Stat Med. 1999;18(16):2123–34. https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16<2123::AID-SIM176>3.0.CO;2-4.\n\n12. 12.\n\nGrambsch PM, Therneau TM. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika. 1994;81(3):515–26. https://doi.org/10.1093/biomet/81.3.515.\n\n13. 13.\n\nSchoenfeld D. Partial residuals for the proportional hazards regression model. Biometrika. 1982;69(1):239–41. https://doi.org/10.1093/biomet/69.1.239.\n\n14. 14.\n\nTherneau TM, Grambsch PM, Fleming TR. Martingale-based residuals for survival models. Biometrika. 1990;77(1):147–60. https://doi.org/10.1093/biomet/77.1.147.\n\n15. 15.\n\nSinger JD, Willett JB, Willett JB. Applied longitudinal data analysis: modeling change and event occurrence: Oxford university press; 2003. https://doi.org/10.1093/acprof:oso/9780195152968.001.0001.\n\n16. 16.\n\nSasieni PD, Winnett A. Martingale difference residuals as a diagnostic tool for the Cox model. Biometrika. 2003;90(4):899–912. https://doi.org/10.1093/biomet/90.4.899.\n\n17. 17.\n\nPerme MP, Andersen PK. Checking hazard regression models using pseudo-observations. Stat Med. 2008;27(25):5309–28. https://doi.org/10.1002/sim.3401.\n\n18. 18.\n\nAndersen PK, Klein JP, Rosthøj S. Generalised linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika. 2003;90(1):15–27. https://doi.org/10.1093/biomet/90.1.15.\n\n19. 19.\n\nArjas E. A graphical method for assessing goodness of fit in Cox's proportional hazards model. J Am Stat Assoc. 1988;83(401):204–12. https://doi.org/10.1080/01621459.1988.10478588.\n\n20. 20.\n\nJensen GV, Torp-Pedersen C, Hildebrandt P, Kober L, Nielsen FE, Melchior T, et al. Does in-hospital ventricular fibrillation affect prognosis after myocardial infarction? Eur Heart J. 1997;18(6):919–24. https://doi.org/10.1093/oxfordjournals.eurheartj.a015379.\n\n21. 21.\n\nMartinussen T, Scheike TH. Dynamic regression models for survival data. Springer Science & Business Media, 2007.\n\n22. 22.\n\nAalen OO, Borgan O. Gjessing H. Survival and event history analysis: a process point of view. Springer Science & Business Media, 2008, DOI: https://doi.org/10.1007/978-0-387-68560-1.\n\n23. 23.\n\nBreslow NE, Day NE. Statistical Methods in Cancer Research. Volume II - The Design and Analysis of Cohort Studies. IARC scientific publ. no. 82. Lyon. Rockville: International Agency for Research on Cancer; 1987.\n\n24. 24.\n\nScheike TH, Zhang MJ. An additive-multiplicative Cox-Aalen regression model. Scand J Stat. 2002;29(1):75–88. https://doi.org/10.1111/1467-9469.00065.\n\n25. 25.\n\nLin DY, Ying Z. Semiparametric analysis of general additive-multiplicative hazard models for counting processes. Ann Stat. 1995;23:1712–34.\n\n26. 26.\n\nCortese G, Scheike TH, Martinussen T. Flexible survival regression modelling. Stat Methods Med Res. 2010;19(1):5–28. https://doi.org/10.1177/0962280209105022.\n\n27. 27.\n\nAbrahamowicz M, MacKenzie TA. Joint estimation of time-dependent and non-linear effects of continuous covariates on survival. Stat Med. 2007;26(2):392–408. https://doi.org/10.1002/sim.2519.\n\n28. 28.\n\nMartinussen T, Scheike T. A semiparametric additive regression model for longitudinal data. Biometrika. 1999;86(3):691–702. https://doi.org/10.1093/biomet/86.3.691.\n\n29. 29.\n\nMcKeague IW, Utikal KJ. Goodness-of-fit tests for additive hazards and proportional hazards models. Scand J Stat. 1991;18(3):177–95.\n\n## Acknowledgements\n\nThe authors thank Arianne Dorval for the revision of the final draft of this manuscript.\n\nNot applicable.\n\n## Author information\n\nAuthors\n\n### Contributions\n\nFrançois Lefebvre and Roch Giorgi wrote the article. The author(s) read and approved the final manuscript.\n\n### Corresponding author\n\nCorrespondence to François Lefebvre.\n\n## Ethics declarations\n\nNot applicable.\n\nNot applicable.\n\nNot applicable.\n\n### Publisher’s Note\n\nSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n## Supplementary Information",
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[
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"https://bmcmedresmethodol.biomedcentral.com/track/article/10.1186/s12874-021-01273-2",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.89491045,"math_prob":0.96779966,"size":60466,"snap":"2021-31-2021-39","text_gpt3_token_len":13384,"char_repetition_ratio":0.20159769,"word_repetition_ratio":0.19735959,"special_character_ratio":0.21751067,"punctuation_ratio":0.11356467,"nsfw_num_words":4,"has_unicode_error":false,"math_prob_llama3":0.99570966,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-27T18:20:34Z\",\"WARC-Record-ID\":\"<urn:uuid:7a443224-c2d0-4fff-a30a-d394a74a82fe>\",\"Content-Length\":\"303407\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88a813fb-8659-44ac-831a-0cc63627b2f7>\",\"WARC-Concurrent-To\":\"<urn:uuid:f1b4396b-5337-4adf-977e-d2c04514fa08>\",\"WARC-IP-Address\":\"199.232.64.95\",\"WARC-Target-URI\":\"https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-021-01273-2\",\"WARC-Payload-Digest\":\"sha1:VTARUA4G2PGYIYT55FFP4ZKPPLW7Q7QT\",\"WARC-Block-Digest\":\"sha1:YZVOSMCYWE25UPN4IMSHDRX7MU76G4I2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780058467.95_warc_CC-MAIN-20210927181724-20210927211724-00701.warc.gz\"}"}
|
https://teach-kids-attitude-1st.com/blog/reverse-lens-magnification-calculator/
|
[
"# Reverse Lens Magnification Calculator\n\nReverse Lens Magnification Calculator. An approximation is to divide the focal length of the primary lense by the focal length of the reversed lens. which yields the following result: Representing the diameter in millimeters of the image of the front lens shown through the eyepiece.\n\nLens Selection Tool_ZLKC LENS zlkc.com.cn\n\nHow to calculate the macro magnification of a reverse lens? For example. when you reverse a 28mm lens. you get a 3x magnification. P = 1 f = ( n − 1) [ 1 r 1 − 1 r 2 + d ( n − 1) n r 1 r 2] :",
null,
"Source: microspedia.blogspot.com\n\nExtension length added. in mm (ie 75): The reverse lens calculator calculates new magnification. new closest focusing distance and effective f/stop with reverse lens setup on extension.",
null,
"Source: bpslao.blogspot.com\n\n(focal length is measured from the center of the lens): Equation to calculate the focal length of a lens in air:",
null,
"Source: negocioscaninos.com\n\nWhen the previously mentioned 28 mm lens is mounted in reverse on the slr it produces a minimum magnification of about 2:1. My 55 mm macro lens produces slightly more magnification when it is used reversed as opposed to normal mounting.",
null,
"Source: dieferbers.net\n\nThe above photo was captured with a macro lens and 68mm of extension tubes. (focal length is measured from the center of the lens):",
null,
"Source: apkcombo.com\n\nRepresenting the diameter in millimeters of the image of the front lens shown through the eyepiece. This is achieved by use of extension tubes.",
null,
"Source: taylortechassoc.com\n\n1/f = 1/d + 1/s where f is the focal length of the lens. d is the object distance between object and lens. and s is the image distance between lens and sensor. and. It is defined by the ratio of the diameter of the front lens divided by the magnification.\n\n#### In Reply To Zibri • Apr 26. 2011 A Very Approximate Figure:\n\nThat would give the same magnification as 18mm in a cropped sensor. 40x. 100x. 400x and 1000x. The above photo was captured with a macro lens and 68mm of extension tubes.\n\n#### You Can Also Thread The Adapter Onto The Lens First. And Mount The Two Together Onto The Camera Body.\n\nThe power of the lens p (in diopters for f in meters) is equal to the inverse of the focal length. f.: 845 posts joined aug 2008. This application has the following macro tools / calculators that will help you take your macro photography to the next level:\n\n#### So. If You Reverse A Lens With A Focal Length Of More Than 50Mm. The Magnification Will Be Less Than 1:1.\n\nTherefore. if the lenss original magnification was 0.15x. then the new magnification will be 0.15x+0.5x=0.65x. Life size often called unity or 1:1 is achieved when the lens is spaced two focal lengths forward of the normal infinity position. This is achieved by use of extension tubes.\n\n#### Further Extension Yields More Magnification.\n\nEquation to calculate the focal length of a lens in air: For example. a pair of binoculars 10 x 42 would have an exit pupil of 42/10 = 4.2 mm. Reverse lens macro photography is a method of capturing highly magnified images using an interchangeable lens camera. a lens. and a cheap adapter.\n\n#### My 105 Mm Lens Produce Significantly Less Magnification When Used Reversed.\n\nWith this microscope you can obtain four different magnifications: Extension length added. in mm (ie 75): To calculate the magnification. simply multiply the ocular lens (10x) by the objective lens."
] |
[
null,
"https://i0.wp.com/ae01.alicdn.com/kf/H2feb0e7679bd4b649ba076fe95cc3ca5B/Zoom-Trinocular-Stereo-Microscope-3-5X-90X-WF10X-Eyepiece-2-0X-0-5X-Objective-Lens-microscope.jpg",
null,
"https://i2.wp.com/1.bp.blogspot.com/-mDxjX-rFXe8/XpXyzBqqAHI/AAAAAAAABWM/2yqWDUNm5A81S8aHoHG3vhCHbCeTiI75ACLcBGAsYHQ/w1200-h630-p-k-no-nu/Nikon%2BDTM-322.jpg",
null,
"https://i2.wp.com/images-na.ssl-images-amazon.com/images/I/51dVu9E29AL._AC_SL1000_.jpg",
null,
"https://i2.wp.com/live.staticflickr.com/65535/50001613111_0e0a7df71c_c.jpg",
null,
"https://i2.wp.com/ogimgs.apkcombo.org/eyJsb2dvIjoiaHR0cHM6Ly9wbGF5LWxoLmdvb2dsZXVzZXJjb250ZW50LmNvbS9WWFBZd3Rma0h3c0RYVEZDMmJPc1RkT1VKZjFjaDlpNjJmU1A0elp2YmFPd3lEMGQxaFNlM25MWDd5UEdkdE9EQ3plYj1zMjAwIiwidGl0bGUiOiAiUG9iaWVyeiBNYWNybyBQaG90b2dyYXBoeSBUb29scyBBUEsifQ==/pobierz-macro-photography-tools-apk",
null,
"https://i2.wp.com/taylortechassoc.com/wp-content/uploads/2013/03/Slide1.jpg",
null
] |
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|
http://www.econometricsbysimulation.com/2012/11/maximum-likelihood-and-information.html
|
[
"## Thursday, November 1, 2012\n\n### Maximum Likelihood and Information\n\nMaximum likelihood methods can seem complex and daunting and certainly many aspects of the maximum likelihood can be daunting. However, the general idea behind maximum likelihood is very intuitively appealing and an understanding of the generalities is sufficient for many people who use many maximum likelihood procedures without knowing the formulas behind them.\n\nMaximum Likelihood Methods are methods that use the theoretical probability distribution of outcomes to solve the parameter estimates that maximize the probability of observing the particular outcome observed. Let’s see this is action.\n\nImagine we can observe 8 potential test outcomes for a person from a test (100, 200, 300, 400, 500, 600, 700, 800). The test outcomes has a conditional probability of occurring based on the characteristics of the person (theta). We can observe the total test score for the person but we cannot observe the theta.\n\nThe probability of each outcome occurring can be read from the following table.\nTable 1:\n\n Score 100 200 300 400 500 600 700 800 Total Theta -4 0.60 0.25 0.10 0.05 0.00 0.00 0.00 0.00 1 -3 0.30 0.50 0.15 0.05 0.00 0.00 0.00 0.00 1 -2 0.20 0.30 0.40 0.05 0.05 0.00 0.00 0.00 1 -1 0.10 0.20 0.30 0.20 0.10 0.05 0.05 0.00 1 0 0.05 0.10 0.15 0.20 0.20 0.15 0.10 0.05 1 1 0.00 0.05 0.10 0.25 0.30 0.15 0.10 0.05 1 2 0.00 0.00 0.05 0.15 0.20 0.30 0.15 0.15 1 3 0.00 0.00 0.05 0.05 0.15 0.20 0.30 0.25 1 4 0.00 0.00 0.00 0.05 0.10 0.25 0.30 0.30 1 Total 1.25 1.4 1.3 1.05 1.1 1.1 1 0.8 Probability 0.14 0.16 0.14 0.12 0.12 0.12 0.11 0.09\n\nWe read this conditional probability table horizontally. That is P(T=100|theta=-4) = 60% or P(T=500|theta=4) = 10%. Horizontally the probabilities must sum to 1 but vertically they need not. We can interpret the vertical summing as a density measure representing the relative likelihood of observing that score if the theta's are distributed uniformly P(theta=THETA)= 1/9 given THETA={-4,-3,...3,4}. That I mean to say by the previous notation is that the probability that any random draw of theta equals a particular draw of theta is 1/9.\n\nThus, given that ability is uniformly drawn, the bottom most row in the table is the probability of observing that particular score.\n\nSo what does this have to do with maximum likelihood? Imagine that we know the information from Table 1 and we see a particular outcome T. Can we calculate the probability that the person has a particular theta value? Yes!\n\nImagine that T=100. From the table we should be able to see that the most likely theta value is -4. But what is the exact probability? It is the probability of the outcome occuring if theta is -4 over the sum of the probability of the outcome occurring (Bayes theorem P(theta=-4|T=100)=P(T=100|theta=-4)/sum(across all THETAS of P(T=100|theta=THETA).\n\nThus:\n\nP(theta=-4|T=100)= .6/1.25 = 48%\n\nIn other words. Given an observed score of 100, the probability that the person has a theta=-4 is 48%.\n\nWe can construct a new table with conditional probabilities differing based instead conditional probabilities of observing a particular theta value given a score value.\n\nTable 2\n Score 100 200 300 400 500 600 700 800 Total Theta -4 0.48 0.18 0.08 0.05 0.00 0.00 0.00 0.00 0.78 -3 0.24 0.36 0.12 0.05 0.00 0.00 0.00 0.00 0.76 -2 0.16 0.21 0.31 0.05 0.05 0.00 0.00 0.00 0.78 -1 0.08 0.14 0.23 0.19 0.09 0.05 0.05 0.00 0.83 0 0.04 0.07 0.12 0.19 0.18 0.14 0.10 0.06 0.90 1 0.00 0.04 0.08 0.24 0.27 0.14 0.10 0.06 0.92 2 0.00 0.00 0.04 0.14 0.18 0.27 0.15 0.19 0.97 3 0.00 0.00 0.04 0.05 0.14 0.18 0.30 0.31 1.02 4 0.00 0.00 0.00 0.05 0.09 0.23 0.30 0.38 1.04 Total 1 1 1 1 1 1 1 1\nWe can see that the Table 2 is somewhat adjusted from Table 1 but generally not hugely. This is not a rule. If there were many more categories of theta then it is likely the adjustment would be more dramatic.\n\nSo, in this example a maximum likelihood estimator would choose eight different expected values for theta for each score observed. Let's define M as the solution to the maximum likelihood problem. From Table 2 all we need do is read the highest probability from each column.\n\nM(T=100) = -4\nM(T=200) = -3\nM(T=300) = -2\n\nThe maximum likelihood estimator need not peek at every potential theta value. In this case the maximum likelihood estimator would jump from -2 to 1. This is somewhat an artifact of the discrete nature of this setup. If theta and the score were continuous then it is less likely some values of theta would be skipped.\nM(T=400) = 1\nM(T=500) = 1\nM(T=600) = 2\n\nM(T=700) = 3 or 4\nThe maximum likelihood estimator for most maximization problems needs to have a single peak. This table would be hard to maximize across for many maximization algorithms. This is not really a problem because this table is somewhat contrived.\nM(T=800) = 4\n\nThus, this table illustrates some of the common problems with maximum likelihood. Some values of the parameter are hard to identify (ie. T=0) while some problems have \"flat\" spots to be maximized over that cause the algorithm not to converge.\n\nWhen looking at Table 2 think not just on the peaks but also on the \"Information\" that you have by observing particular test scores. In other words. How much information do you get from knowing a particular test score? If for instance you knew that T=100 then you would know your most likely theta=-4 and that the theta has a 96% chance (48+24+16+8) of being between -1 and -4. This can be thought of as the 96% confidence interval. If however you have a T=400 you know that your most likely theta=1 but only that you have a 95% chance that your theta is between (-3 and 4). This is a pretty wide confidence interval on your estimate. Thus we can see that some test values have more \"information\" than other test values.\n\nLet's imagine testing a hypothesis Table 2:\nH0: theta=-4 alpha=.05\nObserve:\nT=100 fail to reject\nT=200 fail\nT=300 fail\nT=400 reject\nT>400 reject\n\nThus we have enough information from this test to potentially reject the null when H0:theta=-4. If however, the null was H0: theta=0 then only in the event T=100 could we reject the null at a 5% level and T=800 at a 10% level.\n\nI hope this discussion is useful. I certainly found it useful to think through."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8887935,"math_prob":0.99326366,"size":6071,"snap":"2023-40-2023-50","text_gpt3_token_len":2164,"char_repetition_ratio":0.18345146,"word_repetition_ratio":0.038387716,"special_character_ratio":0.40224016,"punctuation_ratio":0.16295812,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99822956,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-23T07:50:11Z\",\"WARC-Record-ID\":\"<urn:uuid:3ca70e2a-2ad0-4c53-b070-53bf16557680>\",\"Content-Length\":\"202054\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bf672cbf-0df4-4985-8617-b1e488e9d4f8>\",\"WARC-Concurrent-To\":\"<urn:uuid:59b1a5ae-27d6-422a-a5d0-faf6c9d8b13c>\",\"WARC-IP-Address\":\"172.253.122.121\",\"WARC-Target-URI\":\"http://www.econometricsbysimulation.com/2012/11/maximum-likelihood-and-information.html\",\"WARC-Payload-Digest\":\"sha1:BLIVKN62ZINVWM2SQ6L4BYE4BMXO5JHH\",\"WARC-Block-Digest\":\"sha1:EC4O2ELZUG6JXBQUDYNZ2RZTNYCBFILL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506480.35_warc_CC-MAIN-20230923062631-20230923092631-00115.warc.gz\"}"}
|
https://kr.mathworks.com/help/fininst/treepath.html
|
[
"treepath\n\nEntries from node of recombining binomial tree\n\nDescription\n\nexample\n\nValues = treepath(Tree,BranchList) extracts entries of a node of a recombining binomial tree. The node path is described by the sequence of branchings taken, starting at the root. The top branch is number one, the second-to-top is two, and so on. Set the branch sequence to zero to obtain the entries at the root node.\n\nExamples\n\ncollapse all\n\nFwdRates = treepath(BDTTree.FwdTree, [1 2 1])\nFwdRates = 4×1\n\n1.1000\n1.0979\n1.1377\n1.1183\n\nThis returns the rates at the tree nodes located by taking the up branch, then the down branch, and finally the up branch again.\n\nYou can visualize this with the treeviewer function.\n\ntreeviewer(BDTTree)",
null,
"Input Arguments\n\ncollapse all\n\nRecombining binomial tree or trinomial tree specified as a struct that is created using one of the following functions:\n\nData Types: struct\n\nNumber of paths (NUMPATHS) by path length (PATHLENGTH), specified as a matrix containing the sequence of branchings.\n\nData Types: double\n\nOutput Arguments\n\ncollapse all\n\nRetrieved entries of a recombining tree, returned a number of values (NUMVALS)-by-NUMPATHS matrix.\n\nIntroduced before R2006a"
] |
[
null,
"https://kr.mathworks.com/help/examples/fininst/win64/ExtractEntriesOfANodeOfABinomialTreeExample_01.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7303236,"math_prob":0.8858692,"size":463,"snap":"2022-05-2022-21","text_gpt3_token_len":117,"char_repetition_ratio":0.119825706,"word_repetition_ratio":0.0,"special_character_ratio":0.19654427,"punctuation_ratio":0.09411765,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9696896,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-20T09:06:38Z\",\"WARC-Record-ID\":\"<urn:uuid:410e07b8-0982-4d6a-9bd5-5eeb83a358e1>\",\"Content-Length\":\"87779\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0e16b9cf-83e9-4fef-851b-cf4a1dbde5c1>\",\"WARC-Concurrent-To\":\"<urn:uuid:aaf5cef0-9dad-4994-aa18-3a954b5bb6fd>\",\"WARC-IP-Address\":\"23.0.20.241\",\"WARC-Target-URI\":\"https://kr.mathworks.com/help/fininst/treepath.html\",\"WARC-Payload-Digest\":\"sha1:WSNFRWPLFKCTW7ET24YR6IW45UDRCALM\",\"WARC-Block-Digest\":\"sha1:NWRF7KU2ZYT3NHZBWQSM4KYP23TKXBPE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320301730.31_warc_CC-MAIN-20220120065949-20220120095949-00467.warc.gz\"}"}
|
http://www.cppblog.com/szhoftuncun/archive/2010/06/24/29768.html
|
[
"GCC编译选项及其功能\n\n-L\n\n-I\n\n-o\n\n-O\n\n-g\n\n-c\n\n-fPic\n\n-static\n\n-aout\n\n-elf\n3.0\n\n-ansi\n\n-DMACRO\n\n-DMACRO=DEFN\n\n-E\n\n-IDIRECTORY\n\n-LDIRECTORY\n\n-lLIBRARY\n\n-shared\n\n-UMACRO\n\n-w\n\n-Wall\n\nGDB的使用\n\ncat >tst.c\n\n#include<stdio.h>\nint func(int n)\n\n{\n\nint sum=0,i;\n\nfor(i=0;i<100;i++)\n\n{\n\nsum+=i;\n\n}\n\nreturn sum;\n\n}\nmain()\n\n{\n\nint i;\n\nlong result =0;\n\nfor(i=1;i<=100;i++)\n{\nresult+=i;\n}\n\nprintf(\"result[1-100]=%d\\n\",result);\n\nprintf(\"result[1-250]=%d\\n\",func(250));\n\n}\n\nhchen/test> cc -g tst.c -o tst\n\nhchen/test> gdb tst <---------- 启动GDB\nGNU gdb 5.1.1\nCopyright 2002 Free Software Foundation, Inc.\nGDB is free software, covered by the GNU General Public License, and you are\nwelcome to change it and/or distribute copies of it under certain conditions.\nType \"show copying\" to see the conditions.\nThere is absolutely no warranty for GDB. Type \"show warranty\" for details.\nThis GDB was configured as \"i386-suse-linux\"...\n(gdb) l <-------------------- l\n\n#include<stdio.h>\nint func(int n)\n\n{\n\nint sum=0,i;\n\nfor(i=0;i<100;i++)\n\n{\n\nsum+=i;\n\n}\n\nreturn sum;\n\n}\nmain()\n\n{\n\nint i;\n\nlong result =0;\n\nfor(i=1;i<=100;i++)\n\n{\n\nresult+=i;\n\n}\nprintf(\"result[1-100]=%d\\n\",result);\n\nprintf(\"result[1-250]=%d\\n\",func(250));\n\n}\nBreakpoint 1, main () at tst.c:17 <----------\n\n17 long result = 0;\n(gdb) n <---------------------\n\n18 for(i=1; i<=100; i++)\n(gdb) n\n20 result += i;\n(gdb) n\n18 for(i=1; i<=100; i++)\n(gdb) n\n20 result += i;\n(gdb) c <---------------------\n\nContinuing.\nresult[1-100] = 5050 <----------\n\nBreakpoint 2, func (n=250) at tst.c:5\n5 int sum=0,i;\n(gdb) n\n6 for(i=1; i<=n; i++)\n(gdb) p i <---------------------\n\n\\$1 = 134513808\n(gdb) n\n8 sum+=i;\n(gdb) n\n6 for(i=1; i<=n; i++)\n(gdb) p sum\n\\$2 = 1\n(gdb) n\n8 sum+=i;\n(gdb) p i\n\\$3 = 2\n(gdb) n\n6 for(i=1; i<=n; i++)\n(gdb) p sum\n\\$4 = 3\n(gdb) bt <---------------------\n\n#0 func (n=250) at tst.c:5\n#1 0x080484e4 in main () at tst.c:24\n#2 0x400409ed in __libc_start_main () from /lib/libc.so.6\n(gdb) finish <---------------------\n\nRun till exit from #0 func (n=250) at tst.c:5\n0x080484e4 in main () at tst.c:24\n24 printf(\"result[1-250] = %d \\n\", func(250) );\nValue returned is \\$6 = 31375\n(gdb) c <---------------------\n\nContinuing.\nresult[1-250] = 31375 <----------\n\nProgram exited with code 027. <--------程序退出，调试结束。\n(gdb) q <---------------------\n\nhchen/test>\n\n＃资料收集自永远的Linux\n\nGDB常用命令\n\nbreak NUM 在指定的行上设置断点。\nbt 显示所有的调用栈帧。该命令可用来显示函数的调用顺序。\nclear 删除设置在特定源文件、特定行上的断点。其用法为：clear FILENAME:NUM。\ncontinue 继续执行正在调试的程序。该命令用在程序由于处理信号或断点而\n导致停止运行时。\ndisplay EXPR 每次程序停止后显示表达式的值。表达式由程序定义的变量组成。\nfile FILE 装载指定的可执行文件进行调试。\nhelp NAME 显示指定命令的帮助信息。\ninfo break 显示当前断点清单，包括到达断点处的次数等。\ninfo files 显示被调试文件的详细信息。\ninfo func 显示所有的函数名称。\ninfo local 显示当函数中的局部变量信息。\ninfo prog 显示被调试程序的执行状态。\ninfo var 显示所有的全局和静态变量名称。\nkill 终止正被调试的程序。\nlist 显示源代码段。\nmake 在不退出 gdb 的情况下运行 make 工具。\nnext 在不单步执行进入其他函数的情况下，向前执行一行源代码。\nprint EXPR 显示表达式 EXPR 的值。\n\n#joyfire"
] |
[
null
] |
{"ft_lang_label":"__label__zh","ft_lang_prob":0.5175494,"math_prob":0.9641909,"size":3488,"snap":"2022-27-2022-33","text_gpt3_token_len":1713,"char_repetition_ratio":0.15298508,"word_repetition_ratio":0.18876405,"special_character_ratio":0.38675457,"punctuation_ratio":0.14048338,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9647411,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-02T11:25:04Z\",\"WARC-Record-ID\":\"<urn:uuid:d6eccbb1-1dc7-4ff1-8263-a42fc52ce88f>\",\"Content-Length\":\"90085\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f7f0f318-eeb0-4901-8dca-3f669d5ee604>\",\"WARC-Concurrent-To\":\"<urn:uuid:26b7aa87-cbaa-41af-9518-fe484af68d01>\",\"WARC-IP-Address\":\"47.97.166.246\",\"WARC-Target-URI\":\"http://www.cppblog.com/szhoftuncun/archive/2010/06/24/29768.html\",\"WARC-Payload-Digest\":\"sha1:6DEOPFZ3QP4H4Y5EYYPPRENJNRJWOV7N\",\"WARC-Block-Digest\":\"sha1:LCYMRJ6HYBXGFDN5S437KAIGY2KRS32P\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104054564.59_warc_CC-MAIN-20220702101738-20220702131738-00201.warc.gz\"}"}
|
https://open.library.okstate.edu/rainorshine/chapter/1-8-models-for-soil-hydraulic-conductivity/
|
[
"# 4.8 Models for Soil Hydraulic Conductivity\n\nWe sometimes have measurements of soil hydraulic conductivity at saturation and perhaps at one or two water contents below saturation, but we often need a mathematical function to allow calculation of hydraulic conductivity for all other values of water content. For this reason, soil hydraulic conductivity functions have been developed corresponding to each of the soil water retention functions presented in Chapter 3. The hydraulic conductivity function of Brooks and Corey , is defined by:",
null,
"(Eq. 4-6)\n\nwhere K(θ) is the hydraulic conductivity as a function of volumetric water content, Ks is the saturated hydraulic conductivity, and λ is the same pore-size distribution index used in the Brooks and Corey water retention curve. Larger values of λ indicate more uniformly-sized pores, while small values indicate a wide distribution of pore sizes are present.\n\nThe hydraulic conductivity function corresponding to the water retention model of Campbell is defined by:",
null,
"(Eq. 4-7)\n\nwhere again b is a parameter related to the pore size distribution. The most commonly-used hydraulic conductivity function corresponding to the water retention model of van Genuchten is defined by:",
null,
"(Eq. 4-8)\n\nwhere n is a pore-size distribution index similar to λ, and m is a parameter defined in this case by m = 1 – 1/n.",
null,
""
] |
[
null,
"https://open.library.okstate.edu/app/uploads/quicklatex/quicklatex.com-cc68ccce8cc9913499bc0bad4a66b443_l3.png",
null,
"https://open.library.okstate.edu/app/uploads/quicklatex/quicklatex.com-2bbbe35ff631e8064b4379ecbb22546a_l3.png",
null,
"https://open.library.okstate.edu/app/uploads/quicklatex/quicklatex.com-6e32d0849e40e6f776dbe77c2646475d_l3.png",
null,
"https://open.library.okstate.edu/app/themes/pressbooks-book/packages/buckram/assets/images/cc-by.svg",
null
] |
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|
https://la.mathworks.com/help/bioinfo/ug/predicting-protein-secondary-structure-using-a-neural-network.html
|
[
"Predicting Protein Secondary Structure Using a Neural Network\n\nThis example shows a secondary structure prediction method that uses a feed-forward neural network and the functionality available with the Deep Learning Toolbox™.\n\nIt is a simplified example intended to illustrate the steps for setting up a neural network with the purpose of predicting secondary structure of proteins. Its configuration and training methods are not meant to be necessarily the best solution for the problem at hand.\n\nIntroduction\n\nNeural network models attempt to simulate the information processing that occurs in the brain and are widely used in a variety of applications, including automated pattern recognition.\n\nThe Rost-Sander data set consists of proteins whose structures span a relatively wide range of domain types, composition and length. The file RostSanderDataset.mat contains a subset of this data set, where the structural assignment of every residue is reported for each protein sequence.\n\nN = numel(allSeq);\n\nid = allSeq(7).Header % annotation of a given protein sequence\nseq = int2aa(allSeq(7).Sequence) % protein sequence\nstr = allSeq(7).Structure % structural assignment\nid =\n\n'1CSE-ICOMPLEX(SERINEPROTEINASE-INHIBITOR)03-JU'\n\nseq =\n\n'KSFPEVVGKTVDQAREYFTLHYPQYNVYFLPEGSPVTLDLRYNRVRVFYNPGTNVVNHVPHVG'\n\nstr =\n\n'CCCHHHCCCCHHHHHHHHHHHCCCCEEEEEECCCCEECCCCCCEEEEEEECCCCEECCCCEEC'\n\nIn this example, you will build a neural network to learn the structural state (helix, sheet or coil) of each residue in a given protein, based on the structural patterns observed during a training phase. Due to the random nature of some steps in the following approach, numeric results might be slightly different every time the network is trained or a prediction is simulated. To ensure reproducibility of the results, we reset the global random generator to a saved state included in the loaded file, as shown below:\n\nrng(savedState);\n\nDefining the Network Architecture\n\nFor the current problem we define a neural network with one input layer, one hidden layer and one output layer. The input layer encodes a sliding window in each input amino acid sequence, and a prediction is made on the structural state of the central residue in the window. We choose a window of size 17 based on the statistical correlation found between the secondary structure of a given residue position and the eight residues on either side of the prediction point . Each window position is encoded using a binary array of size 20, having one element for each amino acid type. In each group of 20 inputs, the element corresponding to the amino acid type in the given position is set to 1, while all other inputs are set to 0. Thus, the input layer consists of R = 17x20 input units, i.e. 17 groups of 20 inputs each.\n\nIn the following code, we first determine for each protein sequence all the possible subsequences corresponding to a sliding window of size W by creating a Hankel matrix, where the ith column represents the subsequence starting at the ith position in the original sequence. Then for each position in the window, we create an array of size 20, and we set the jth element to 1 if the residue in the given position has a numeric representation equal to j.\n\nW = 17; % sliding window size\n\n% === binarization of the inputs\nfor i = 1:N\nseq = double(allSeq(i).Sequence); % current sequence\nwin = hankel(seq(1:W),seq(W:end)); % all possible sliding windows\nmyP = zeros(20*W,size(win,2)); % input matrix for current sequence\nfor k = 1:size(win, 2)\nindex = 20*(0:W-1)' + win(:,k); % input array for each position k\nmyP(index,k) = 1;\nend\nallSeq(i).P = myP;\nend\n\nThe output layer of our neural network consists of three units, one for each of the considered structural states (or classes), which are encoded using a binary scheme. To create the target matrix for the neural network, we first obtain, from the data, the structural assignments of all possible subsequences corresponding to the sliding window. Then we consider the central position in each window and transform the corresponding structural assignment using the following binary encoding: 1 0 0 for coil, 0 1 0 for sheet, 0 0 1 for helix.\n\ncr = ceil(W/2); % central residue position\n\n% === binarization of the targets\nfor i = 1:N\nstr = double(allSeq(i).Structure); % current structural assignment\nwin = hankel(str(1:W),str(W:end)); % all possible sliding windows\nmyT = false(3,size(win,2));\nmyT(1,:) = win(cr,:) == double('C');\nmyT(2,:) = win(cr,:) == double('E');\nmyT(3,:) = win(cr,:) == double('H');\nallSeq(i).T = myT;\nend\n\nYou can perform the binarization of the input and target matrix described in the two steps above in a more concise way by executing the following equivalent code:\n\n% === concise binarization of the inputs and targets\nfor i = 1:N\nseq = double(allSeq(i).Sequence);\nwin = hankel(seq(1:W),seq(W:end)); % concurrent inputs (sliding windows)\n\n% === binarization of the input matrix\nallSeq(i).P = kron(win,ones(20,1)) == kron(ones(size(win)),(1:20)');\n\n% === binarization of the target matrix\nallSeq(i).T = allSeq(i).Structure(repmat((W+1)/2:end-(W-1)/2,3,1)) == ...\nrepmat(('CEH')',1,length(allSeq(i).Structure)-W+1);\nend\n\nOnce we define the input and target matrices for each sequence, we create an input matrix, P, and target matrix, T, representing the encoding for all the sequences fed into the network.\n\n% === construct input and target matrices\nP = double([allSeq.P]); % input matrix\nT = double([allSeq.T]); % target matrix\n\nCreating the Neural Network\n\nThe problem of secondary structure prediction can be thought of as a pattern recognition problem, where the network is trained to recognize the structural state of the central residue most likely to occur when specific residues in the given sliding window are observed. We create a pattern recognition neural network using the input and target matrices defined above and specifying a hidden layer of size 3.\n\nhsize = 3;\nnet = patternnet(hsize);\nnet.layers{1} % hidden layer\nnet.layers{2} % output layer\nans =\n\nNeural Network Layer\n\nname: 'Hidden'\ndimensions: 3\ndistanceFcn: (none)\ndistanceParam: (none)\ndistances: []\ninitFcn: 'initnw'\nnetInputFcn: 'netsum'\nnetInputParam: (none)\npositions: []\nrange: [3x2 double]\nsize: 3\ntopologyFcn: (none)\ntransferFcn: 'tansig'\ntransferParam: (none)\n\nans =\n\nNeural Network Layer\n\nname: 'Output'\ndimensions: 0\ndistanceFcn: (none)\ndistanceParam: (none)\ndistances: []\ninitFcn: 'initnw'\nnetInputFcn: 'netsum'\nnetInputParam: (none)\npositions: []\nrange: []\nsize: 0\ntopologyFcn: (none)\ntransferFcn: 'softmax'\ntransferParam: (none)\n\nTraining the Neural Network\n\nThe pattern recognition network uses the default Scaled Conjugate Gradient algorithm for training, but other algorithms are available (see the Deep Learning Toolbox documentation for a list of available functions). At each training cycle, the training sequences are presented to the network through the sliding window defined above, one residue at a time. Each hidden unit transforms the signals received from the input layer by using a transfer function logsig to produce an output signal that is between and close to either 0 or 1, simulating the firing of a neuron . Weights are adjusted so that the error between the observed output from each unit and the desired output specified by the target matrix is minimized.\n\n% === use the log sigmoid as transfer function\nnet.layers{1}.transferFcn = 'logsig';\n\n% === train the network\n[net,tr] = train(net,P,T);\n\nDuring training, the training tool window opens and displays the progress. Training details such as the algorithm, the performance criteria, the type of error considered, etc. are shown.",
null,
"Use the function view to generate a graphical view of the neural network.\n\nview(net)",
null,
"One common problem that occurs during neural network training is data overfitting, where the network tends to memorize the training examples without learning how to generalize to new situations. The default method for improving generalization is called early stopping and consists in dividing the available training data set into three subsets: (i) the training set, which is used for computing the gradient and updating the network weights and biases; (ii) the validation set, whose error is monitored during the training process because it tends to increase when data is overfitted; and (iii) the test set, whose error can be used to assess the quality of the division of the data set.\n\nWhen using the function train, by default, the data is randomly divided so that 60% of the samples are assigned to the training set, 20% to the validation set, and 20% to the test set, but other types of partitioning can be applied by specifying the property net.divideFnc (default dividerand). The structural composition of the residues in the three subsets is comparable, as seen from the following survey:\n\n[i,j] = find(T(:,tr.trainInd));\nCtrain = sum(i == 1)/length(i);\nEtrain = sum(i == 2)/length(i);\nHtrain = sum(i == 3)/length(i);\n\n[i,j] = find(T(:,tr.valInd));\nCval = sum(i == 1)/length(i);\nEval = sum(i == 2)/length(i);\nHval = sum(i == 3)/length(i);\n\n[i,j] = find(T(:,tr.testInd));\nCtest = sum(i == 1)/length(i);\nEtest = sum(i == 2)/length(i);\nHtest = sum(i == 3)/length(i);\n\nfigure()\npie([Ctrain; Etrain; Htrain]);\ntitle('Structural assignments in training data set');\nlegend('C', 'E', 'H')\n\nfigure()\npie([Cval; Eval; Hval]);\ntitle('Structural assignments in validation data set');\nlegend('C', 'E', 'H')\n\nfigure()\npie([Ctest; Etest; Htest]);\ntitle('Structural assignments in testing data set ');\nlegend('C', 'E', 'H')",
null,
"",
null,
"",
null,
"The function plotperform display the trends of the training, validation, and test errors as training iterations pass.\n\nfigure()\nplotperform(tr)",
null,
"The training process stops when one of several conditions (see net.trainParam) is met. For example, in the training considered, the training process stops when the validation error increases for a specified number of iterations (6) or the maximum number of allowed iterations is reached (1000).\n\n% === display training parameters\nnet.trainParam\n\n% === plot validation checks and gradient\nfigure()\nplottrainstate(tr)\nans =\n\nFunction Parameters for 'trainscg'\n\nShow Training Window Feedback showWindow: true\nShow Command Line Feedback showCommandLine: false\nCommand Line Frequency show: 25\nMaximum Epochs epochs: 1000\nMaximum Training Time time: Inf\nPerformance Goal goal: 0\nMaximum Validation Checks max_fail: 6\nSigma sigma: 5e-05\nLambda lambda: 5e-07",
null,
"Analyzing the Network Response\n\nTo analyze the network response, we examine the confusion matrix by considering the outputs of the trained network and comparing them to the expected results (targets).\n\nO = sim(net,P);\nfigure()\nplotconfusion(T,O);",
null,
"The diagonal cells show the number of residue positions that were correctly classified for each structural class. The off-diagonal cells show the number of residue positions that were misclassified (e.g. helical positions predicted as coiled positions). The diagonal cells correspond to observations that are correctly classified. Both the number of observations and the persentage of the total number of observations are shown in each cell. The column on the far right of the plot shows the percentages of all the examples predicted to belong to each class that are correctly and incorrectly classified. These metrics are often called the precision (or positive predictive value) and false discovery rate, respectively. The row at the bottom of the plot shows the percentages of all the examples belonging to each class that are correctly and incorrectly classified. These metrics are often called the recall (or true positive rate) and false negative rate, respectively. The cell in the bottom right of the plot shows the overall accuracy.\n\nWe can also consider the Receiver Operating Characteristic (ROC) curve, a plot of the true positive rate (sensitivity) versus the false positive rate (1 - specificity).\n\nfigure()\nplotroc(T,O);",
null,
"Refining the Neural Network for More Accurate Results\n\nThe neural network that we have defined is relative simple. To achieve some improvements in the prediction accuracy we could try one of the following:\n\n• Increase the number of training vectors. Increasing the number of sequences dedicated to training requires a larger curated database of protein structures, with an appropriate distribution of coiled, helical and sheet elements.\n\n• Increase the number of input values. Increasing the window size or adding more relevant information, such as biochemical properties of the amino acids, are valid options.\n\n• Use a different training algorithm. Various algorithms differ in memory and speed requirements. For example, the Scaled Conjugate Gradient algorithm is relatively slow but memory efficient, while the Levenberg-Marquardt is faster but more demanding in terms of memory.\n\n• Increase the number of hidden neurons. By adding more hidden units we generally obtain a more sophisticated network with the potential for better performances but we must be careful not to overfit the data.\n\nWe can specify more hidden layers or increased hidden layer size when the pattern recognition network is created, as shown below:\n\nhsize = [3 4 2];\nnet3 = patternnet(hsize);\n\nhsize = 20;\nnet20 = patternnet(hsize);\n\nWe can also assign the network initial weights to random values in the range -0.1 to 0.1 as suggested by the study reported in by setting the net20.IW and net20.LW properties as follows:\n\n% === assign random values in the range -.1 and .1 to the weights\nnet20.IW{1} = -.1 + (.1 + .1) .* rand(size(net20.IW{1}));\nnet20.LW{2} = -.1 + (.1 + .1) .* rand(size(net20.LW{2}));\n\nIn general, larger networks (with 20 or more hidden units) achieve better accuracy on the protein training set, but worse accuracy in the prediction accuracy. Because a 20-hidden-unit network involves almost 7,000 weights and biases, the network is generally able to fit the training set closely but loses the ability of generalization. The compromise between intensive training and prediction accuracy is one of the fundamental limitations of neural networks.\n\nnet20 = train(net20,P,T);\n\nO20 = sim(net20,P);\nnumWeightsAndBiases = length(getx(net20))\nnumWeightsAndBiases =\n\n6883\n\nYou can display the confusion matrices for training, validation and test subsets by clicking on the corresponding button in the training tool window.\n\nAssessing Network Performance\n\nYou can evaluate structure predictions in detail by calculating prediction quality indices , which indicate how well a particular state is predicted and whether overprediction or underprediction has occurred. We define the index pcObs(S) for state S (S = {C, E, H}) as the number of residues correctly predicted in state S, divided by the number of residues observed in state S. Similarly, we define the index pcPred(S) for state S as the number of residues correctly predicted in state S, divided by the number of residues predicted in state S.\n\n[i,j] = find(compet(O));\n[u,v] = find(T);\n\n% === compute fraction of correct predictions when a given state is observed\npcObs(1) = sum(i == 1 & u == 1)/sum (u == 1); % state C\npcObs(2) = sum(i == 2 & u == 2)/sum (u == 2); % state E\npcObs(3) = sum(i == 3 & u == 3)/sum (u == 3); % state H\n\n% === compute fraction of correct predictions when a given state is predicted\npcPred(1) = sum(i == 1 & u == 1)/sum (i == 1); % state C\npcPred(2) = sum(i == 2 & u == 2)/sum (i == 2); % state E\npcPred(3) = sum(i == 3 & u == 3)/sum (i == 3); % state H\n\n% === compare quality indices of prediction\nfigure()\nbar([pcObs' pcPred'] * 100);\nylabel('Correctly predicted positions (%)');\nax = gca;\nax.XTickLabel = {'C';'E';'H'};\nlegend({'Observed','Predicted'});",
null,
"These quality indices are useful for the interpretation of the prediction accuracy. In fact, in cases where the prediction technique tends to overpredict/underpredict a given state, a high/low prediction accuracy might just be an artifact and does not provide a measure of quality for the technique itself.\n\nConclusions\n\nThe method presented here predicts the structural state of a given protein residue based on the structural state of its neighbors. However, there are further constraints when predicting the content of structural elements in a protein, such as the minimum length of each structural element. Specifically, a helix is assigned to any group of four or more contiguous residues, and a sheet is assigned to any group of two or more contiguous residues. To incorporate this type of information, an additional network can be created so that the first network predicts the structural state from the amino acid sequence, and the second network predicts the structural element from the structural state.\n\nReferences\n\n Rost, B., and Sander, C., \"Prediction of protein secondary structure at better than 70% accuracy\", Journal of Molecular Biology, 232(2):584-99, 1993.\n\n Holley, L.H. and Karplus, M., \"Protein secondary structure prediction with a neural network\", PNAS, 86(1):152-6, 1989.\n\n Kabsch, W., and Sander, C., \"How good are predictions of protein secondary structure?\", FEBS Letters, 155(2):179-82, 1983.\n\nBioinformatics Toolbox Documentation",
null,
"Get trial now"
] |
[
null,
"https://la.mathworks.com/help/examples/bioinfo/win64/xxsecstructnnetdemo_nntraintool.png",
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"https://la.mathworks.com/help/examples/bioinfo/win64/secstructnnetdemo_01.png",
null,
"https://la.mathworks.com/help/examples/bioinfo/win64/secstructnnetdemo_02.png",
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"https://la.mathworks.com/help/examples/bioinfo/win64/secstructnnetdemo_03.png",
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|
https://demo.formulasearchengine.com/wiki/Heat
|
[
"# Heat\n\n{{#invoke:Hatnote|hatnote}} {{ safesubst:#invoke:Unsubst||$N=Use dmy dates |date=__DATE__ |$B= }} Template:Pp-move\n\nIn physics, heat is energy in transfer other than as work or by transfer of matter. When there is a suitable physical pathway, heat flows from a hotter body to a colder one. It results in a net increase in entropy. The pathway can be direct, as in conduction and radiation, or indirect, as in convective circulation. Heat refers to a process of transfer, not to a property of a system.\n\nKinetic theory explains heat as a macroscopic manifestation of the motions and interactions of microscopic constituents such as molecules and photons.\n\nIn calorimetry, sensible heat is defined with respect to a particular state variable of the system; it causes change of temperature, leaving that particular state variable unchanged. Heat transfer that does not change that particular state variable is called latent heat. For infinitesimal changes, the total incremental heat transfer is then the sum of the latent and sensible heat increments. This is a basic paradigm for thermodynamics, and was important in the historical development of the subject.\n\nThe quantity of energy transferred as heat is a scalar expressed in an energy unit such as the joule (J) (SI), with a sign that is customarily positive when a transfer adds to the energy of a system. It can be measured by calorimetry, or determined by calculations based on other quantities, relying on the first law of thermodynamics.",
null,
"The Sun and Earth form an ongoing example of a heating process. Some of the Sun's thermal radiation strikes and heats the Earth. Compared to the Sun, Earth has a much lower temperature and so sends far less thermal radiation back to the Sun. The heat of this process can be quantified by the net amount, and direction (Sun to Earth), of energy it transferred in a given period of time.\n\n## History\n\nPhysicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of many who began to build on the already established idea that heat has something to do with matter in motion. This was the same idea put forth by Benjamin Thompson in 1798, who said he was only following up on the work of many others. One of Maxwell's recommended books was Heat as a Mode of Motion, by John Tyndall. Maxwell outlined four stipulations for the definition of heat:\n\n• It is something which may be transferred from one body to another, according to the second law of thermodynamics.\n• It is a measurable quantity, and so can be treated mathematically.\n• It cannot be treated as a material substance, because it may be transformed into something that is not a material substance, e.g., mechanical work.\n• Heat is one of the forms of energy.\n\nFrom empirically based ideas of heat, and from other empirical observations, the notions of internal energy and of entropy can be derived, so as to lead to the recognition of the first and second laws of thermodynamics. This was the way of the historical pioneers of thermodynamics.\n\n## Transfers of energy as heat between two bodies\n\nReferring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a quantity of heat has passed from the hot body to the cold body.\"\n\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\n\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\". In thermodynamics, convection in general is regarded as transport of internal energy. If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.\n\n## Practical operating devices that harness transfers of energy as heat\n\nIn accordance with the first law for closed systems, energy transferred solely as heat enters one body and leaves another, changing the internal energies of each. Transfer, between bodies, of energy as work is a complementary way of changing internal energies. Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.\n\n### Heat engine\n\nIn classical thermodynamics, a commonly considered model is the heat engine. It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often. Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed. But two thermal reservoirs are needed, because transfer of energy as heat is irreversible. A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir. The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy. The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir. Heat engines achieve higher efficiency when the difference between initial and final temperature is greater.\n\n### Heat pump\n\nAnother commonly considered model is the heat pump or refrigerator. Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir. Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir. The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir. Then, by allowing it to expand without doing work on another body and without passing heat to another body, the working body is made colder than the cold reservoir. It can now accept heat transfer from the cold reservoir to start another cycle. The device has transported energy from a colder to a hotter reservoir, but this is not regarded as being by an inanimate agency. This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a sequence of thermodynamic operations, which may be regarded as directed by an animate agency. Accordingly, the cycle is still in accord with the second law of thermodynamics. The efficiency of a heat pump is best when the temperature difference between the hot and cold reservoirs is least.\n\n## Macroscopic view of quantity of energy transferred as heat\n\nAccording to Planck, there are three main conceptual approaches to heat. One is the microscopic or kinetic theory approach. Also there are two macroscopic approaches. One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz. This mechanical view is taken as currently customary in this article. The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.\n\nBailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic. The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century. It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry. A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer. The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born. It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics. According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\". It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.\n\nNevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another. The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.\n\nIn this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.\n\nIf cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one. They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems. One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed. In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems. But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable. Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.[quotations 1] This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.\n\nIn many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".\n\n## Microscopic view of heat\n\nIn the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules. Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions. An early and vague expression of this was made by Francis Bacon. Precise and detailed versions of it were developed in the nineteenth century.\n\nIn statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves. It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer. A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.\n\n## Notation and units\n\nAs a form of energy heat has the unit joule (J) in the International System of Units (SI). However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used. The standard unit for the rate of heat transferred is the watt (W), defined as joules per second.\n\nThe total amount of energy transferred as heat is conventionally written as Q for algebraic purposes. Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0). Heat transfer rate, or heat flow per unit time, is denoted by ${\\dot {Q}}$",
null,
". This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state. Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in the unit watts per square metre.\n\n## Estimation of quantity of heat\n\nQuantity of heat transferred can measured by calorimetry, or determined through calculations based on other quantities.\n\nCalorimetry is the empirical basis of the idea of quantity of heat transferred in a process. The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.\n\nA calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics. Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.\n\n## Internal energy and enthalpy\n\nFor a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy ΔU of the system is equal to the amount of heat Q supplied to the system minus the amount of work W done by system on its surroundings. The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive. This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.\n\n$\\Delta U=Q-W\\,.$",
null,
"This formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that ΔU is defined and measured solely by processes of adiabatic work:\n\n$Q=\\Delta U+W.$",
null,
"The work done by the system includes boundary work (when the system increases its volume against an external force, such as that exerted by a piston) and other work (e.g. shaft work performed by a compressor fan), which is called isochoric work:\n\n$Q=\\Delta U+W_{\\text{boundary}}+W_{\\text{isochoric}}.$",
null,
"In this Section we will neglect the \"other-\" or isochoric work contribution.\n\nThe internal energy, U, is a state function. In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.\n\nThe differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential dU. The symbol for exact differentials is the lowercase letter d.\n\nIn contrast, neither of the infinitesimal increments δQ nor δW in an infinitesimal process represents the state of the system. Thus, infinitesimal increments of heat and work are inexact differentials. The lowercase Greek letter delta, δ, is the symbol for inexact differentials. The integral of any inexact differential over the time it takes for a system to leave and return to the same thermodynamic state does not necessarily equal zero.\n\nAs recounted below, in the section headed Entropy, the second law of thermodynamics observes that if heat is supplied to a system in which no irreversible processes take place and which has a well-defined temperature T, the increment of heat δQ and the temperature T form the exact differential\n\n$\\mathrm {d} S={\\frac {\\delta Q}{T}},$",
null,
"and that S, the entropy of the working body, is a function of state. Likewise, with a well-defined pressure, P, behind the moving boundary, the work differential, δW, and the pressure, P, combine to form the exact differential\n\n$\\mathrm {d} V={\\frac {\\delta W}{P}},$",
null,
"with V the volume of the system, which is a state variable. In general, for homogeneous systems,\n\n$\\mathrm {d} U=T\\mathrm {d} S-P\\mathrm {d} V.$",
null,
"Associated with this differential equation is that the internal energy may be considered to be a function U (S,V) of its natural variables S and V. The internal energy representation of the fundamental thermodynamic relation is written\n\n$U=U(S,V).$",
null,
"If V is constant\n\n$T\\mathrm {d} S=\\mathrm {d} U\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,(V\\,\\,{\\text{constant)}}$",
null,
"and if P is constant\n\n$T\\mathrm {d} S=\\mathrm {d} H\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,(P\\,\\,{\\text{constant)}}$",
null,
"with H the enthalpy defined by\n\n$H=U+PV.$",
null,
"The enthalpy may be considered to be a function H (S,P) of its natural variables S and P. The enthalpy representation of the fundamental thermodynamic relation is written\n\n$H=H(S,P).$",
null,
"The internal energy representation and the enthalpy representation are partial Legendre transforms of one another. They contain the same physical information, written in different ways. Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.\n\n### Heat added to a body at constant pressure\n\nIf a quantity Q of heat is added to a body while it does expansion work W on its surroundings, one has\n\n$\\Delta H=\\Delta U+\\Delta (PV)\\,.$",
null,
"If this is constrained to happen at constant pressure with ΔP = 0, the expansion work W done by the body is given by W = P ΔV; recalling the first law of thermodynamics, one has\n\n$\\Delta U=Q-W=Q-P\\,\\Delta V{\\text{ and }}\\Delta (PV)=P\\,\\Delta V\\,.$",
null,
"Consequently, by substitution one has\n\n$\\Delta H=Q-P\\,\\Delta V+P\\,\\Delta V$",
null,
"$=Q\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,{\\text{at constant pressure.}}$",
null,
"In this scenario, the increase in enthalpy is equal to the quantity of heat added to the system. Since many processes do take place at constant pressure, or approximately at atmospheric pressure, the enthalpy is therefore sometimes given the misleading name of 'heat content'. It is sometimes also called the heat function.\n\nIn terms of the natural variables S and P of the state function H, this process of change of state from state 1 to state 2 can be expressed as\n\n$\\Delta H=\\int _{S_{1}}^{S_{2}}\\left({\\frac {\\partial H}{\\partial S}}\\right)_{P}\\mathrm {d} S+\\int _{P_{1}}^{P_{2}}\\left({\\frac {\\partial H}{\\partial P}}\\right)_{S}\\mathrm {d} P$",
null,
"$=\\int _{S_{1}}^{S_{2}}\\left({\\frac {\\partial H}{\\partial S}}\\right)_{P}\\mathrm {d} S\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,{\\text{at constant pressure.}}$",
null,
"It is known that the temperature T(S, P) is identically stated by\n\n$\\left({\\frac {\\partial H}{\\partial S}}\\right)_{P}\\equiv T(S,P)\\,.$",
null,
"Consequently\n\n$\\Delta H=\\int _{S_{1}}^{S_{2}}T(S,P)\\mathrm {d} S\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,{\\text{at constant pressure.}}$",
null,
"In this case, the integral specifies a quantity of heat transferred at constant pressure.\n\n## Entropy\n\n{{#invoke:main|main}}\n\nIn 1856, German physicist Rudolf Clausius, referring to closed systems, in which transfer of matter does not occur, defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat Q from work at the temperature T, has the equivalence-value:\"\n\n${}{\\frac {Q}{T}}.$",
null,
"In 1865, he came to define the entropy symbolized by S, such that, due to the supply of the amount of heat Q at temperature T the entropy of the system is increased by\n\n$\\Delta S={\\frac {Q}{T}}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,(1)$",
null,
"In a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it. The increase, ΔS, of entropy in the system may be considered to consist of two parts, an increment, ΔS that matches, or 'compensates', the change, −ΔS, of entropy in the surroundings, and a further increment, ΔS′′ that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'. Thus\n\n$\\Delta S=\\Delta S^{\\prime }+\\Delta S^{\\prime \\prime }.$",
null,
"This may also be written\n\n$\\Delta S_{\\mathrm {system} }=\\Delta S_{\\mathrm {compensated} }+\\Delta S_{\\mathrm {uncompensated} }\\,\\,\\,\\,{\\text{with}}\\,\\,\\,\\,\\Delta S_{\\mathrm {compensated} }=-\\Delta S_{\\mathrm {surroundings} }.$",
null,
"The total change of entropy in the system and surroundings is thus\n\n$\\Delta S_{\\mathrm {overall} }=\\Delta S^{\\prime }+\\Delta S^{\\prime \\prime }-\\Delta S^{\\prime }=\\Delta S^{\\prime \\prime }.$",
null,
"This may also be written\n\n$\\Delta S_{\\mathrm {overall} }=\\Delta S_{\\mathrm {compensated} }+\\Delta S_{\\mathrm {uncompensated} }+\\Delta S_{\\mathrm {surroundings} }=\\Delta S_{\\mathrm {uncompensated} }.$",
null,
"It is then said that an amount of entropy ΔS has been transferred from the surroundings to the system. Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.\n\nThe second law of thermodynamics observes that in a natural transfer of energy as heat, in which the temperature of the system is different from that of the surroundings, it is always so that\n\n$\\Delta S_{\\mathrm {overall} }>0.$",
null,
"For purposes of mathematical analysis of transfers, one thinks of fictive processes that are called 'reversible', with the temperature T of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow speed.\n\nFollowing the definition above in formula (1), for such a fictive 'reversible' process, a quantity of transferred heat δQ (an inexact differential) is analyzed as a quantity T dS, with dS (an exact differential):\n\n$T\\,\\mathrm {d} S=\\delta Q.$",
null,
"This equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.\n\nIf, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with dSuncompensated > 0. The quantity T dSuncompensated was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology. Then one has\n\n$T\\,\\mathrm {d} S=\\delta Q+T\\,\\mathrm {d} S_{\\mathrm {uncompensated} }>\\delta Q.$",
null,
"$T\\,\\mathrm {d} S\\geq \\delta Q\\quad {\\rm {(second\\,\\,law)}}\\,.$",
null,
"which is the second law of thermodynamics for closed systems.\n\nIn non-equilibrium thermodynamics that approximates by assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this. The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature T. Then one writes\n\n$\\mathrm {d} S=\\mathrm {d} S_{\\mathrm {e} }+\\mathrm {d} S_{\\mathrm {i} }\\,,$",
null,
"where by definition\n\n$\\delta Q=T\\,\\mathrm {d} S_{\\mathrm {e} }\\,\\,\\,\\,\\,{\\text{and}}\\,\\,\\,\\,\\,\\mathrm {d} S_{\\mathrm {i} }\\equiv \\mathrm {d} S_{\\mathrm {uncompensated} }.$",
null,
"The second law for a natural process asserts that\n\n$\\mathrm {d} S_{\\mathrm {i} }>0.$",
null,
"## Latent and sensible heat\n\nIn an 1847 lecture entitled On Matter, Living Force, and Heat, James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.[quotations 2] He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles or what was known as a living force. At the time of Joule kinetic energy either held 'invisibly' internally or held 'visibly' externally was known as a living force.\n\nLatent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature. Such a process may be a phase transition, such as the melting of ice or the boiling of water. The term was introduced around 1750 by Joseph Black as derived from the Latin latere (to lie hidden), characterizing its effect as not being directly measurable with a thermometer.\n\nSensible heat, in contrast to latent heat, is the heat transferred to a thermodynamic system that has as its sole effect a change of temperature.\n\nBoth latent heat and sensible heat transfers increase the internal energy of the system to which they are transferred.\n\nConsequences of Black's distinction between sensible and latent heat are examined in the Wikipedia article on calorimetry.\n\n## Specific heat\n\nSpecific heat, also called specific heat capacity, is defined as the amount of energy that has to be transferred to or from one unit of mass (kilogram) or amount of substance (mole) to change the system temperature by one degree. Specific heat is a physical property, which means that it depends on the substance under consideration and its state as specified by its properties.\n\nThe specific heats of monatomic gases (e.g., helium) are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.\n\n## Relation between heat, hotness, and temperature\n\nAccording to Baierlein, a system's hotness is its tendency to transfer energy as heat. All physical systems are capable of heating or cooling others. This does not require that they have thermodynamic temperatures. With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.\n\nIf a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system. If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer. An empirical thermometer registers degree of hotness for such a system. Such a temperature is called empirical. For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the temperature. This number is a measure of how hot the body is.\"\n\nPhysical systems that are too turbulent to have temperatures may still differ in hotness. A physical system that passes heat to another physical system is said to be the hotter of the two. More is required for the system to have a thermodynamic temperature. Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold. This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.\n\nThis is also the reason why the zeroth law of thermodynamics is stated explicitly. If three physical systems, A, B, and C are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, A can heat B and B can heat C and C can heat A. In non-equilibrium situations, cycles of flow are possible. It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement. That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive. It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.\n\nJust as temperature may undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium. For example, 'the temperature of the solar system' is not a defined quantity. Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics. It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way.\n\n## Rigorous definition of quantity of energy transferred as heat\n\nIt is sometimes convenient to have a rigorous definition of quantity of energy transferred as heat. Such a definition is customarily based on the work of Carathéodory (1909), referring to processes in a closed system, as follows.\n\nThe internal energy UX of a body in an arbitrary state X can be determined by amounts of work adiabatically performed by the body on its surrounds when it starts from a reference state O. Such work is assessed through quantities defined in the surroundings of the body. It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition. The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter. In particular they do not allow the passage of energy as heat. According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body. On the other hand, according to Carathéodory (1909), there also exist non-adiabatic walls, which are postulated to be \"permeable only to heat\", and are called diathermal.\n\nFor the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest Y is reached from state O by a process with two components, one adiabatic and the other not adiabatic. For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work. Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body. The change in internal energy to reach the state Y from the state O is the difference of the two amounts of energy transferred.\n\nAlthough Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define the quantity of energy transferred as heat, Q, to the body from its surroundings, in the combined process of change to state Y from the state O, as the change in internal energy, ΔUY, minus the amount of work, W, done by the body on its surrounds by the adiabatic process, so that Q = ΔUYW.\n\nIn this definition, for the sake of conceptal rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process. It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state O to the arbitrary state Y. It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process. It is assumed here that the amount of energy required to pass from state O to state Y, the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state X above. The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work. Energy transfer as heat is considered as a derived quantity. The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception. The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality. The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.\n\n## Heat, temperature, and thermal equilibrium regarded as jointly primitive notions\n\nBefore the rigorous mathematical definition of heat based on Carathéodory's 1909 paper, recounted just above, historically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions. Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\" Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\" James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of heat, work, and hotness as primitive elements, ... That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot. Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\" This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies. It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).\n\nThis alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.\n\nThis alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat. It relies on temperature as one of its primitive concepts, and used in calorimetry. It is presupposed that enough processes exist physically to allow measurement of differences in internal energies. Such processes are not restricted to adiabatic transfers of energy as work. They include calorimetry, which is the commonest practical way of finding internal energy differences. The needed temperature can be either empirical or absolute thermodynamic.\n\nIn contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat. The Carathédory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat. As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity. It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process. That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states. By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat. This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way. In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.\n\n## Heat transfer in engineering\n\nThe discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system. Although the definition of heat implicitly means the transfer of energy, the term heat transfer encompasses this traditional usage in many engineering disciplines and laymen language.\n\nHeat transfer includes the mechanisms of heat conduction, thermal radiation, and mass transfer.\n\nIn engineering, the term convective heat transfer is used to describe the combined effects of conduction and fluid flow. From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion. This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow. Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.\n\nAlthough distinct physical laws may describe the behavior of each of these methods, real systems often exhibit a complicated combination which are often described by a variety of complex mathematical methods."
] |
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null,
"https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/171879main_LimbFlareJan12_lg.jpg/300px-171879main_LimbFlareJan12_lg.jpg",
null,
"https://demo.formulasearchengine.com/index.php",
null,
"https://demo.formulasearchengine.com/index.php",
null,
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null,
"https://demo.formulasearchengine.com/index.php",
null,
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null,
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null,
"https://demo.formulasearchengine.com/index.php",
null,
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null,
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null,
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null,
"https://demo.formulasearchengine.com/index.php",
null,
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null,
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null,
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null,
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null,
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null,
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https://earthscience.stackexchange.com/questions/12673/derive-reference-potential-evapotranspiration-from-potential-evapotranspiration
|
[
"# Derive Reference Potential Evapotranspiration from Potential Evapotranspiration\n\nI'm working on a project in Rajasthan, India involving modelling water supply and demand in a catchment. For this, I am working with WEAP which has modules for estimating groundwater recharge using a simple bucket model.\n\nThis model needs daily temperature and reference (potential) evapotranspiration values. The reference evapotranspiration is calculated according to the modified Penman-Monteith equation as described in the FAO56-Paper. As part of the project, I'd like to use climate models. One with a sufficient resolution is the HAR model, which has values for potential evapotranspiration. Is there a way to get from potential evapotranspiration to the reference evapotranspiration?\n\nEDIT: I am not sure whether the model Potential Evapotranspiration values implicitly contain information about the surface, or if they are a spatially comparable, independent of the surface. Since I am modeling the catchment disaggregated by landuse types with a uniform climate, I need a value that is independent of the surface properties and can be transferred to the landuse types via the surface coefficients as described in the FAO paper.\n\nI agree that terminology about evapotranspiration is confusing especially when using the expression \"potential evapotranspiration\", as stated in the FAO-56 paper:\n\nThe use of other denominations such as potential ET is strongly discouraged due to ambiguities in their definitions\n\n# Definition\n\nSo let's refer to the FAO terminology:\n\n1. Reference evapotranspiration ($ET_0$) refers to the evapotranspiration observed on well watered grass for given meteorological conditions (radiation, temperature, humidity, and wind speed).\n\n2. Crop evapotranspiration under standard conditions ($ET_c$) refers to the evapotranspiration observed on well watered specific crop for given meteorological conditions. The relationship between $ET_c$ and $ET_0$ is given by:\n\n$$ET_c = K_C\\times ET_0 \\tag{1}$$\n\n1. Crop evapotranspiration under non-standard conditions ($ET_{c,adj}$) refers to the evapotranspiration observed on a specific crop under water and environmental stress for given meteorological conditions. The relationship to $ET_0$ is either defined using a stress coefficient $K_s$: $$ET_{c,adj} = K_s \\times K_c \\times ET_0 \\tag{2}$$ Or using an adjusted crop coefficient $K_{c,adj}$: $$ET_{c,adj} = K_{c,adj} \\times ET_0 \\tag{3}$$\n\n# Confusions\n\nNow, you may find different common usage for the terms potential or actual evapotranspiration that leads to your confusion.\n\nPotential evapotranspiration is sometimes referred to $ET_0$ or $ET_c$ or even less strict definition such as atmospheric demand for water.\n\nActual evapotranspiration is referred either to $ET_c$, $ET_{c,adj}$ or less strict definition such as the amount of water evaporated.\n\n# Pragmatism\n\n• Use the other HAR data (everything is available) to compute $ET_0$ using FAO-56 method.\n• Last but not least, do not bother that much as evapotranspiration is full of uncertainties and you could not proove which of $ET_0$, $ET_c$ or $ET_{c,adj}$ best represent your actual evapotranspiration. You are interested in the relative dynamics of $ET$, choose realistic ranges of landcover coefficient and calibration will do the mass balance.\n• Thanks for the clarification! Is the whole notion of a crop coefficient actually transferable to non-irrigated areas such as shrubland? There is a method to calculate K_c from NDVI (e.g. Landsat). Are the values I get from that method (in the non-irrigated case) something like a footprint of the environmental \"circumstances\"? In other words, would these K_c values yield a rough approximation of the actual evapotranspiration if multiplied by ET_0? I need to get a rough estimate of groundwater recharge in theses areas using a soil moisture model model that employs ET_0 and K_c. – telegott Dec 5 '17 at 19:54"
] |
[
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|
https://szczecincafe.com/qa/what-is-back-titration.html
|
[
"",
null,
"# What Is Back Titration?\n\n## Why is back titration used in aspirin?\n\nUsing titration it would be difficult to identify the end point because aspirin is a weak acid and reactions may proceed slowly.\n\nUsing back titration the end-point is more easily recognised in this reaction, as it is a reaction between a strong base and a strong acid..\n\n## How do you calculate titration?\n\nStep 1: Calculate the amount of sodium hydroxide in molesAmount of solute in mol = concentration in mol/dm 3 × volume in dm 3Amount of sodium hydroxide = 0.100 × 0.0250.= 0.00250 mol.The balanced equation is: NaOH(aq) + HCl(aq) → NaCl(aq) + H 2O(l)So the mole ratio NaOH:HCl is 1:1.More items…\n\n## What is blank correction?\n\nTo correct for a constant method error, a blank must account for signals from any reagents and solvents used in the analysis, as well as any bias resulting from interactions between the analyte and the sample’s matrix. Both the calibration blank and the reagent blank compensate for signals from reagents and solvents.\n\n## Which titration is more accurate?\n\nStandardization is a procedure which normalizes the titration system and provides the most accurate titrant concentration. This value is critical in the final calculation for the analyte content. If the concentration is not known precisely, it can throw off a result.\n\n## What is back and blank titration?\n\nA blank titration is done without the analyte present to check for possible sources of error in the “blank” solution. … A back titration is used when it is diffucult to find an endpoint in a normal titration (for example, if the analyte is not very soluble in water).\n\n## What is a back titration with antacid?\n\nAntacids are bases that react stoichiometrically with acid. The number of moles of acid that can be neutralized by a single tablet of a commercial antacid will be determined by back titration. … The solution will be titrated with base of known concentration to determine the amount of acid not neutralized by the tablet.\n\n## What is indicator blank correction?\n\nIndicator blank or indicator correction. The amount of titrant. (usually in terms of volume) required to produce the same change in the. indicator as that taken to mark the end-point in the titration of the sample. under the same conditions.\n\n## What are the 4 types of titration?\n\nTypes of TitrationAcid-base Titrations.Redox Titrations.Precipitation Titrations.Complexometric Titrations.\n\n## What does equivalence point mean in titration?\n\nEquivalence point: point in titration at which the amount of titrant added is just enough to completely neutralize the analyte solution. At the equivalence point in an acid-base titration, moles of base = moles of acid and the solution only contains salt and water.\n\n## What is the principle of titration?\n\nThe basic principle of the titration is the following: A solution – a so called titrant or standard solution – is added to sample to be analyzed. The titrant contains a known concentration of a chemical which reacts with the substance to be determined.\n\n## Why is back titration used?\n\nA back titration is used when the molar concentration of an excess reactant is known, but the need exists to determine the strength or concentration of an analyte. … When direct titration endpoint would be hard to discern (e.g., weak acid and weak base titration) When the reaction occurs very slowly.\n\n## What is the difference between titration and back titration?\n\nErnest Z. In a direct titration, you add a standard titrant to the analyte until you reach the end point. In a back titration, you add an excess of standard titrant to the analyte, and then you titrate the excess titrant to determine how much is in excess.\n\n## What is back titration example?\n\nBack titration is also titration. It is called back titration because it is not carried out with the solution whose concentration is required to be known (analyte) as in the case of normal or forward titration, but with the excess volume of reactant which has been left over after completing reaction with the analyte.\n\n## How do you solve back titration problems?\n\n5 Simple Steps in Back Titration Calculations:Determine the amount of C required in the titration.Using stoichiometry, find the amount of A that reacted with C in the titration.Note that amount of A that reacted with C in the titration = amount of A that did not react with B in the earlier reaction.More items…•Apr 24, 2019\n\n## What is the end point of blank titration?\n\nIn blank titration, we titrate the titrant (soln in burette) against the blank solvent in which sample of unknown conc. (analyte) is dissolved. Now the end point where a notable color change is produced is found.\n\n## Why is back titration better than titration?\n\nA back titration is necessary in situations where the reaction you are using to analyse the unknown substance is too slow to respond in a normal titration. In titration, you need the reaction to be able to reach a definite endpoint at practically the same moment as you have reached the stoichiometric equivalence point."
] |
[
null,
"https://mc.yandex.ru/watch/75033307",
null
] |
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|
https://www.agnesscott.edu/lriddle/women/abstracts/sperry_spherical.htm
|
[
"",
null,
"## Pauline Sperry\n\n### Short Course in Spherical Trigonometry Johnson Publishing Company, 1928",
null,
"Preface\n\nThere seems to be a real need for a short yet rigorous text in spherical trigonometry which shall contain little more theory than is needed for the solution of spherical triangles, with a few applications to add interest to the subject. This book is the result of an effort to meet that demand. As there are often but few class hours to be devoted to the subject, the aim of the writer has been to present matters in such a way as to enable the student to master the elements with little help from outside. The average student finds it hard to do this when he must pick out the essentials for himself.\n\nA knowledge of spherical geometry is not presupposed, but a brief presentation of the principal concepts and theorems is given in Chapter I. Most of the theoretical examples bear directly on the development of the theory in the text. The data for the numerical solution of triangles are such as to require a minimum of labor in computation while offering a wider variety of applications of the theory than is usual in problem sets. Especial attention is called to the summarization of the tests for the number of solutions in the ambiguous cases in four short and complete tables, material usually covering several pages and often incomplete. The student is encouraged to check all solutions, and methods of checking are given in every case.\n\nThe time required for the discussion and solution of the general spherical triangle may be reduced by half by considering only Cases 1, 2, and 3 in Chapter III, explaining how the other cases may be solved by means of the polar triangle.\n\nThe terminology and symbols used follow the recommendations in the Report of the National Committee on Mathematical Requirements under the auspices of the Mathematical Association of America (1923).\n\nContents\n\nI. Concerning Solid and Spherical Geometry\n\nI. Planes and Lines in Space\n1. Lines perpendicular to a plane\n2. Parallel planes\n3. Perpendicular planes\nII. Certain Properties of the Sphere\n1. Definitions\n2. Circles on a sphere\n3. Length of arc of a circle\n4. Poles of a circle\n5. Spherical angles\n6. The spherical triangle\n7. Relations of sides and angles in spherical triangles\n8. Polar triangles\n9. Applications of polar triangle theory\n10. Lunes\n\nII. The Right Spherical Triangle\n\n1. Classification according to the number of right angles\n2. Formulas for the solution of right spherical triangles\n4. Napier's Rules\n5. The six cases of right spherical triangles\n6. Figures solvable by means of right spherical triangles\n\nIII. The Oblique Spherical Triangle\n\nI. Certain Relations between the Trigonometric Functions of the Sides and Angles of a General Spherical Triangle\n1. Law of sines\n2. Law of cosines for sides\n3. Law of cosines for angles\n4. The trigonometric functions of the half angles in terms of the sides\n5. The trigonometric functions of the half sides in terms of the angles\n6. Napier's Analogies\n7. Delambre's Analogies (Gauss's Formulas)\nII. The Solution of the General Spherical Triangle\n1. The six cases of the oblique spherical triangle\n2. Case I. Given the three sides\ncase I'. Given the three angles\n3. Case 2. Given two sides and the included angle\nCase 2'. Given two angles and the included side\n4. Case 3. Given two sides and the angle opposite one of them\nCase 3'. Given two angles and the side opposite one of them\n5. Tables for determining the number of solutions in the ambiguous cases\n6. Suggestions for checking solutions\n\nIV. The Area of a Spherical Triangle\n\n1. Introductory theorems concerning areas\n2. Spherical degrees\n3. The area of the spherical triangle in spherical degrees and in square units of radius\n4. L'Huillier's formula for the area in terms of the sides\n\nV. Practical Applications of Spherical Trigonometry\n\nI. Applications to Geography\n1. Latitude and longitude\n2. Great circle sailing\nII. Applications to Astronomy\n1. The celestial sphere\n2. The horizon system\n3. First equatorial system\n4. The ecliptic\n5. A second equatorial system\n6. Comparison of the three systems of coordinates\n7. Projection of the three systems of coordinates\n8. Relation of altitude of pole to latitude of observer\n9. The astronomical triangle\n\nHistorical Sketch\n\nAppendix\n\nIndex"
] |
[
null,
"https://www.agnesscott.edu/lriddle/women/abstracts/ASCminilogo3.gif",
null,
"https://www.agnesscott.edu/lriddle/women/abstracts/sperry/sperry_sphericalCover.jpg",
null
] |
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|
https://economics.stackexchange.com/questions/25215/what-does-it-mean-to-have-a-strictly-increasing-transformation-in-consumer-theor
|
[
"# What does it mean to have a strictly increasing transformation in consumer theory? [closed]\n\nWe're discussing utility functions\n\n• A little more context would be helpful. In which context exactly did you encounter the term? – Michael Greinecker Oct 28 '18 at 23:38\n\nIf I'm understanding your question correctly, you are referring to increasing transformations of a utility function. Suppose I have a set of alternatives $$X$$, a rational preference relation $$\\succsim$$ on $$X$$, and a function $$u:X \\rightarrow \\mathbb{R}$$ which represents this preference relation. Then it can be shown that for any $$v:\\mathbb{R} \\rightarrow \\mathbb{R}$$ which is monotonically increasing, $$v \\circ u:X \\rightarrow \\mathbb{R}$$ also represents these preferences. Try to prove this; it's a good exercise."
] |
[
null
] |
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|
https://linuxmeerkat.wordpress.com/2015/04/28/why-you-should-use-super-in-python/
|
[
"# LinuxMeerkat\n\n## I swear! Meerkats can do Linux",
null,
"# Why you should use super in Python\n\nAlthough I used Python a long time and OOP, I never really dwelled into the reasons that someone would use `super` instead of other ways in Python. Usually I would use other ways in an effort do avoid confusing words and those ugly underscores. Sometimes however it is worth making something a bit less readable and such a case is super.\n\nWhy should you learn to use super though? For a single reason.. super equals less headaches.\n\n## Calling a parent class’ initializer\n\nRemember that with initializer I merely mean the `__init__` method of a class. So let’s take for example the class A below.\n\n```class A(object):\ndef __init__(self):\nprint('This is A')\ndef hello(self):\nprint('Hello, this is a method from A')\n```\n\nWhen we instantiate this class, the initializer runs and thus we get printed ‘This is A’. Now we want B to inherit A:\n\n```class B(A):\ndef __init__(self):\nprint('This is B')\n```\n\nThe result is a hybrid class – half A, half B. The problem is that both classes have an initializer and in such cases the hybrid’s methods, variables, etc. are preferred. So in practice B has the method `hello` that it inherited from A but will only run its own initializer.\n\nIn real life we tend to run the initializer for every parent class. This is simply because of how program designs tend to be. In our simple example a way to solve this is to explicitly call the initializer of A:\n\n```class B(A):\ndef __init__(self):\nA.__init__(self)\nprint('This is B')\n```\n\nThe self always makes me dizzy so I will explain a bit on it. Namely why can’t we just have `A.__init__()`? The reason is that A is not an instance but a class. `self` however is an instance and that’s why we use it. As you might have noticed though, it is an instance of B and still we pass it to A as if it was an instance of A. So why the hell does it work?\n\nThe reason it works is that as we said B is a hybrid – half A, half B. This is very similar to having a double citizenship. A half Greek, half Norwegian can be recognized in both Greece and Norway. In the same way A and B can be recognized as either A or B. Logical, aye?\n\n## The bless of not knowing\n\nThe above example works fine. But what if one changes the name of A into G? For a simple example like ours, we could just change every occurence of A into G. However if you are dealing with medium to large projects you might have many classes that inherit from A and way many files. Furthermore if you have tests, you probably have all sort of test classes that inherit as well.\n\nThe point is that in such cases a little change somewhere can invoke havoc. The programmer will need to keep track of every single place where we inherit class A which just is not practical. That’s where super comes into play.\n\nWith `super` we can call A’s initializer without ever typing the name of the class:\n\n```class B(A):\ndef __init__(self):\nsuper(B, self).__init__() # notice we type B, not A\nprint('This is B')\n```\n\nNow, no matter if you rename A to G or V, you won’t have to make any changes to classes that inherit from that class!\n\n## The bless of caring even less\n\nSo you saw how `super` takes away the problem of having to keep track of class names we inherit from. I think all this makes much more sense when we inherit from multiple classes.\n\nSay we have classes X and Y:\n\n```class X(object):\ndef __init__(self):\nprint('This is X')\n\nclass Y(object):\ndef __init__(self):\nprint('This is Y')\n```\n\nNow if B inherit from everyone else, in the no-super way it will look like this:\n\n```class B(A, X, Y):\ndef __init__(self):\nA.__init__(self)\nX.__init__(self)\nY.__init__(self)\nprint('This is B')\n```\n\nWith super we can minimize it to:\n\n```class B(A):\ndef __init__(self):\nsuper(B, self).__init__(self)\nprint('This is B')\n```\n\nAt first glance this looks like we merely minimize the code to a single line. The real benefit however is that if we did not use super, now our class B would be much more prone to mistakes since either A, X, or Y might change name somewhere (more classes – higher probability of a rename).\n\nI hope all this makes it very apparent that in big OOP projects where you have a lot of interaction between objects, classes, etc. Using super is just a simple trick that adds a huge gain for the programmer. So whenever you need to call an initializer (or any other method) from a parent class, please save yourself some trouble and use `super`!\n\n## Python 2 issues\n\nYou might have noticed that I use `object` in every parent class in the examples above. In Python 3 you don’t have to do this.\n\n```class A(object):\n..\n```\n\nThis merely makes a class inherit from object. The problem in Python 2 you see is that not everything is an object. As such we have to explicitly state it. In Python 3 all classes inherit from object be default so the code becomes much cleaner. Notice that even super is much cleaner in Python 3:\n\n```class A:\n..\n\nclass B(A):\ndef __init__(self):\nsuper().__init__() # no self pollution\n..\n```"
] |
[
null,
"https://linuxmeerkat.files.wordpress.com/2014/03/cropped-meerkats_london_zoo.jpg",
null
] |
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|
https://root-forum.cern.ch/t/help-importing-and-plotting-3d-data/16546
|
[
"# Help importing and plotting 3D data\n\nGreetings!\n\nI just started using ROOT and even though I spent several days reading, I do not understand why my simple code is not working…\n\nI have a test file containing many columns of data, which I import using ifstream and select three of them to plot using TGraph2D. The data is imported and the numbers are correct. I used two methods (plot.cxx and plot3.cxx, which as expected gives the same result as plot2.cxx) to set the points.\nThe first one (plot.cxx) just spits out the error:\n\n``Two of these three points are coincident blah blah``\n\nand causes ROOT to go into an infinite loop (it just keeps printing the same error about the same data point over and over and I have to kill ROOT).\nThe second one does not give any error, but the graph is empty (like all z-values are 0), even though the axis ranges are set automatically to the correct values (min and max values in my data).\nI do not understand where I’m going wrong.\n\nP.S. I tried importing the data using TTree as was done in the tree/basic.C tutorial, but this gives the following error for every single line of the data:\n\n``Couldn't read formatted data in....``\n\nEven if I run the tutorial itself (basic.C) it gives the same thing instead of do what it’s supposed to! Am I supposed to set some env variable to make this work??\nplot3.cxx (948 Bytes)\nplot2.cxx (1019 Bytes)\nplot.cxx (665 Bytes)\n\nHello, I looked at quickly your codes and in plot.cxx, did you try to put “i++” just after\n\nNormally, pl is expecting to have a point at “0”.\nFor plot2 and plot3, did you try to use directly the vector to “construct” your TGraph2D ; something like that\n\nNormally, it is exactly the same as what you did with the arrays.\n\nFinally, I guess, you have check that your vector does not contain only empty values.\n\nEDIT : I modified a little bit your plot2.cxx and I got a running example\n\n[code]#include\n\nusing namespace std;\n\nint test()\n{\nTCanvas *c_pl = new TCanvas(“c_pl”);\nvector < float > v_xt, v_mst1, v_mh1;\n\nfor(int i=0 ; i<10 ; i++) {\nv_xt.push_back(i);\nv_mst1.push_back(pow(i,i));\nv_mh1.push_back(i*i);\n}\n\nconst unsigned int n = v_xt.size();\nFloat_t a_xt[n], a_mst1[n], a_mh1[n];\nfor (Int_t i = 0 ; i < n ; i++)\n{\na_xt[i] = v_xt.at(i);\na_mst1[i] = v_mst1.at(i);\na_mh1[i] = v_mh1.at(i);\n}\nTGraph2D * pl = new TGraph2D(n, a_xt, a_mst1, a_mh1);\npl->Draw(“SURF1”);\nreturn 0;\n}[/code]\nYou can run it doing “.x test.C”\n\n[quote=“pamputt”]Hello, I looked at quickly your codes and in plot.cxx, did you try to put “i++” just after\n\n``pl->SetPoint(i,xt,mst1,mh1);``\n\nNormally, pl is expecting to have a point at “0”.\n[/quote]\nHi and thanks for replying! I didn’t know that, I thought its point numbers start at 1, that’s why I had done it like that. Using your suggestion does indeed fix the issue with the errors and the loop and now all three .cxx files give the same (flat) graph.\n\nI tried that now - same result.\n\nI had done that in the beginning while debugging and none of them are zero - all three coordinates lie in the ranges they should (I outputted all of them)…\n\nI exported my data (not using ROOT), this time selecting only these three columns and these ranges, so that I can attach the file (otherwise it’s HUGE). So there they are, but still it gives just a flat graph…\n\nEdit:\nI had made a mistake in plots.cxx (recalculating xt from values I wasn’t even importing). I fixed it (the file is now updated), but still flat graph.\nplot_selected.cxx (368 Bytes)\ndata_selected.dat (69.3 KB)\n\nHmm, I do not know really TGraph2D and its Draw option. Anyway, I got also a flat graph with the “surf” option. But if I use “p” option (instead of surf), I got something consistent with your data. Same result with other options shown here\nSo you have to investigate this “surf” option. I have no idea",
null,
"Tips : to fill your TGraph2D, you can skip the “ifstream step” by doing simply\n\n```{ TGraph2D * pl = new TGraph2D(\"data_selected.dat\",\"%lf%lf%lf\"); pl->Draw(\"pcol\"); }```\n\n[quote=“pamputt”]Hmm, I do not know really TGraph2D and its Draw option. Anyway, I got also a flat graph with the “surf” option. But if I use “p” option (instead of surf), I got something consistent with your data. Same result with other options shown here\nSo you have to investigate this “surf” option. I have no idea",
null,
"[/quote]\nTrue, this way I get my plot, but not really in the form I need it",
null,
"I need it to be of the form plt1xth1.png (this is actually the same data but plotted in Mathematica and in the full range). I saw [url=https://root-forum.cern.ch/t/tgraph2d-and-contour-plots/14372/1 topic and thought that the option COL, CONT4 or CONT5 used there would work, but they all give a blank 2D surface…\n\n[quote=“pamputt”]\nTips : to fill your TGraph2D, you can skip the “ifstream step” by doing simply\n\n```{ TGraph2D * pl = new TGraph2D(\"data_selected.dat\",\"%lf%lf%lf\"); pl->Draw(\"pcol\"); }```[/quote]\nThanks for the tip! Can I make this work with my full data set (18 columns) and choose two of them as y and z and calculate x from other columns?",
null,
"I figured out what was wrong! My z function wasn’t single-valued (it had a small dependency on other parameters as well, which were not plotted). Mathematica didn’t have a problem, because it simply took the first point with coordinates x and y and ignored all subsequent points with the same x and y coordinates. However ROOT ignored ALL points which were ambiguous (when drawing surface or contours). I edited my data to remove such points and I got my plots! Thanks for the help again!",
null,
"",
null,
"Thanks! I was planning to change the colour palette anyway, but of course first I had to get something plotted instead of blank plot.\n\nof course",
null,
""
] |
[
null,
"https://root-forum.cern.ch/images/emoji/twitter/confused.png",
null,
"https://root-forum.cern.ch/images/emoji/twitter/confused.png",
null,
"https://root-forum.cern.ch/images/emoji/twitter/frowning.png",
null,
"https://root-forum.cern.ch/uploads/default/original/2X/5/5b2802bc9323ce2ca19c3e51b7ef834152c3f0d9.png",
null,
"https://root-forum.cern.ch/uploads/default/original/2X/3/38f1f467dc3730b60b5b2fe8cd512ea6d217e070.png",
null,
"https://root-forum.cern.ch/uploads/default/original/2X/d/df78b7dc5d5f73b8c1e8ea3318f2da828dfb3692.png",
null,
"https://root-forum.cern.ch/images/emoji/twitter/slight_smile.png",
null
] |
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|
https://lastmomenttuitions.com/course/dsip/
|
[
"",
null,
"",
null,
"# DSIP (Digital Signal and Image Processing)",
null,
"(1 review)\n₹999.00 ₹799.00",
null,
"## DSIP (Digital Signal and Image Processing)\n\n### Tutor: Sumersingh Rajpurohit\n\nWhat you’ll Learn:\n– Digital Signal\nDigital signal processing fundamentals and the numerical.\nThe fundamental concepts on Fourier Transforms\nRoot concepts like signals, noise, convolution, quantization, sampling. and many more\nComplex concepts and their numerical like FFT, DIT-FFT made easy for you.\n\n– Image Processing\nStarting from basic 2-D images and getting into complex processing algorithms.\nNumerical based on image segmentation, Histogram , Grey level & Zero memory point operations.\n\nDescription:\n\nDigital Signal & Image Processing is semester 7 subject of final year of computer engineering in Mumbai University. Prerequisite for studying this subject are Applied Mathematics. Course objectives for subject Digital Signal & Image Processing is to understand the fundamental concepts of digital signal processing and Image processing. To explore DFT for 1-D and 2-D signal and FFT for 1-D signal. To apply processing techniques on 1-D and Image signals. To apply digital image processing techniques for edge detection. Course outcomes for subject Digital Signal & Image Processing On successful completion of the course learner will be able to: Apply the concept of DT Signal and DT Systems. Classify and analyze discrete time signals and systems. Implement Digital Signal Transform technique DFT and FFT. Use the enhancement techniques for digital Image Processing. Differentiate between the advantages and disadvantages of different edge detection techniques. Develop small projects of 1-D and 2-D Digital Signal Processing.\n\nA digital signal is a signal that is being used to represent data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values. Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions digital image processing may be modeled in the form of multidimensional systems. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers; second, the development of mathematics; third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased.\n\nModule Discrete-Time Signal and Discrete-Time System consists of the following subtopics such as Introduction to Digital Signal Processing, Sampling and Reconstruction, Standard DT Signals, Concept of Digital Frequency, Representation of DT signal using Standard DT Signals, Signal Manipulations (shifting, reversal, scaling, addition, multiplication). Classification of Discrete-Time Signals, Classification of Discrete Systems. Linear Convolution formulation for 1-D and 2-D signal (without mathematical proof), Circular Convolution (without mathematical proof), Linear convolution using Circular Convolution. Auto and Cross Correlation formula evaluation, LTI system, Concept of Impulse Response and Step Response, Output of DT system using Time Domain Linear Convolution.\n\nModule Discrete Fourier Transform consists of the following subtopics such as Introduction to DTFT, DFT, Relation between DFT and DTFT, IDF.T Properties of DFT without mathematical proof (Scaling and Linearity, Periodicity, Time Shift and Frequency Shift, Time Reversal, Convolution Property and Parsevals‘ Energy Theorem). DFT computation using DFT properties. Transfer function of DT System in frequency domain using DFT. Linear and Circular Convolution using DFT, Convolution of long sequences, Introduction to 2-D DFT. Module Fast Fourier Transform consists of the following subtopics such as Need of FFT, Radix-2 DIT-FFT algorithm, DIT-FFT Flow graph for N=4 and 8, Inverse FFT algorithm. Spectral Analysis using FFT. Module Digital Image Fundamentals consists of the following subtopics such as Introduction to Digital Image, Digital Image Processing System, Sampling and Quantization. Representation of Digital Image, Connectivity. Image File Formats: BMP, TIFF and JPEG. Module Image Enhancement in Spatial domain consists of the following subtopics such as Gray Level Transformations, Zero Memory Point Operations, Histogram Processing, Histogram equalization. Neighborhood Processing, Spatial Filtering, Smoothing and Sharpening Filters, Median Filter. Module Image Segmentation consists of the following subtopics such as Segmentation based on Discontinuities (point, Line, Edge), Image Edge detection using Robert, Sobel, Previtt masks, Image Edge detection using Laplacian Mask.\n\nSuggested Texts Books for the subject Digital Signal & Image Processing by Mumbai University is as follows John G. Proakis, Dimitris and G.Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications‘4th Edition 2007, Pearson Education. A. Anand Kumar, Digital Signal Processing, PHI Learning Pvt. Ltd. 2013. Rafel C. Gonzalez and Richard E. Woods, Digital Image Processing, Pearson Education Asia, 3rd Edition, 2009, S. Sridhar, Digital Image Processing‘, Oxford University Press, Second Edition, 2012. Suggested Reference Books for the subject Digital Signal & Image Processing by Mumbai university is as follows Sanjit Mitra, Digital Signal Processing: A Computer Based Approach‘, TataMcGraw Hill, 3rd Edition. S. Salivahanan, A. Vallavaraj, and C. Gnanapriya, ‗Digital Signal Processing‘ Tata McGraw Hill Publication 1st Edition (2010). S. Jayaraman, E. Esakkirajan and T. Veerkumar, Digital Image Processing‘ TataMcGraw Hill Education Private Ltd, 2009. Anil K. Jain, Fundamentals and Digital Image Processing‘, Prentice Hall of India Private Ltd, 3rd Edition.\n\nJoin in to learn Digital Signal and Image processing fundamentals, equally important from the academic as well as real-world knowledge.\n\nModules Covered:\nDiscrete-Time Signal /System\nDiscrete Fourier Transform\nFast Fourier Transform\nDigital Image fundamentals\nImage Enhancement\nImage Segmentation\n\nFeel forward to have a look at course description and demo videos and we look forward to see you learning with us.\n\n### Course Features\n\n• Lectures 47\n• Quizzes 0\n• Duration 50 hours\n• Skill level All levels\n• Language English\n• Students 120\n• Certificate No\n• Assessments Yes",
null,
"Qualification : Bachelor of Engineering in Computer. passionate about teaching.\n\n### Reviews\n\nAverage Rating\n\n5\n1 rating\n\nDetailed Rating\n\n5 Star\n100%\n4 Star\n0%\n3 Star\n0%\n2 Star\n0%\n1 Star\n0%\n•",
null,
"Worth taking\n\nTysm sumer...... Was a very helpful course"
] |
[
null,
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null,
"https://lastmomenttuitions.com/wp-content/uploads/2021/03/ezgif.com-gif-maker.gif",
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null
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{"ft_lang_label":"__label__en","ft_lang_prob":0.83244944,"math_prob":0.6141952,"size":9222,"snap":"2021-31-2021-39","text_gpt3_token_len":1895,"char_repetition_ratio":0.16955955,"word_repetition_ratio":0.15785499,"special_character_ratio":0.18618521,"punctuation_ratio":0.13725491,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9511213,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,5,null,null,null,2,null,null,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-03T01:58:53Z\",\"WARC-Record-ID\":\"<urn:uuid:3823acf7-2fd7-4511-b150-a4e82167a5b9>\",\"Content-Length\":\"211433\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:82c5fbdf-62b7-457f-8ca9-a8d9ac1e8c32>\",\"WARC-Concurrent-To\":\"<urn:uuid:50ec229d-2cc6-4a4c-902b-da7220666b0c>\",\"WARC-IP-Address\":\"104.21.30.224\",\"WARC-Target-URI\":\"https://lastmomenttuitions.com/course/dsip/\",\"WARC-Payload-Digest\":\"sha1:ZQ6WZGVCYQRYSYKGJRZXHM7M7GMVOLS4\",\"WARC-Block-Digest\":\"sha1:XDKIGL5SVKYV2H5CQO3FTZDI5WVY5OZJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154408.7_warc_CC-MAIN-20210802234539-20210803024539-00228.warc.gz\"}"}
|
https://iq.opengenus.org/longest-repeating-non-overlapping-substring/
|
[
"# Longest repeating and non overlapping substring in a string\n\n#### Algorithms Dynamic Programming (DP) String Algorithms\n\nReading time: 30 minutes | Coding time: 5 minutes\n\nWe have to find the longest repeating and non-overlapping substring in a given string. A substring is a contiguous sequence of characters within a string.We have to return the substring of maximum length which occurs more than once in the string without any overlap.We can return any such substring if more than one such substring exists in the string. We have provided an optimal O(n2) solution to this problem using Dynamic Programming.\n\nThe two approaches are:\n\n• Brute force O(N^3) time\n• Dynamic Programming O(N^2) time\n\n## Examples\n\nInput:- largelargerlargest\nOutput:- large\n\nInput:- banana\nOutput:- an or na\n\nInput:- opengenus\nOutput:- en\n\n\n## Naive Approach\n\nWe can solve the problem in O(n3) time-complexity by finding all substrings in O(n2) and checking it with the substrings of the remaining string in O(n).\n\nFollowing is the cpp implementaion of the naive approach:-\n\n#include<bits/stdc++.h>\nusing namespace std;\nint main()\n{\nstring s,ans;\ncout << \"Enter the input string:-\\n\";\ncin >> s;\nint maxm=0;\nfor(int i=0;i<s.length();i++)\n{\nfor(int j=i;j<s.length();j++)\n{\nstring x=s.substr(i,j-i+1); //finding substrings of the string\nfor(int k=j+1;k<s.length();k++)\n{\nstring y=s.substr(k,j-i+1);\nif(y==x)\t //check for same non-overlapping substring in rest of string\n{\nif(y.length()>maxm)\n{\nmaxm=y.length();\nans=y;\n}\n}\n}\n}\n}\ncout << \"The longest repeating non-overlapping substring is:- \" << ans << '\\n';\nreturn 0;\n}\n\n\n## Dynamic Programming Approach\n\n• Idea is to look for every same character and save its index.\n• Check whether difference between index is less than longest repeating and non-overlapping substring size.\n\nHere, dp[i][j] stores length of the matching and non-overlapping substrings ending with i'th and j'th characters.\n\nIf the characters at (i-1)th and (j-1)th position matches dp[i-1][j-1] is less than the length of the considered substring (j-1) then maximum value of dp[i][j] and the maximum index i till this point is updated.The length of the longest repeating and non-overlapping substring can be found by the maximum value of dp[i][j] and the substring itself can be found using the length and the ending index which is the finishing index of the suffix.\n\nFor Example:-\n\nConsider the word banana :\nThe only matching characters are a(2nd,4th and 6th) and n(3rd and 5th).Hence for all other indices i, dp[i][j]=0.\n\nInitially finishing index ind=0 and maximum length of substring len=0.\n\nWhen i=2 and j=4,\nSince, dp[i-1][j-1]=0 which is less than (j-i) i.e. 2,\ndp[i][j]=dp[i-1][j-1]+1 ,\ni.e.,dp=1.\n\nAs dp>len\nlen=dp=1\nind=max(ind,i)=2\nWhen i=2 and j=6,\n\nSince dp[i-1][j-1]=dp=0 which is less than (j-i) i.e. 4,\ndp[i][j]=dp[i-1][j-1]+1 ,\ni.e.,dp=1.\n\nAs dp=len,\nlen and ind wouldn't be updated.\nWhen i=4 and j=6,\n\nSince dp[i-1][j-1]=dp=0 which is less than (j-i) i.e. 2,\ndp[i][j]=dp[i-1][j-1]+1 ,\ni.e.,dp=1.\nAs dp=len,\nlen and ind wouldn't be updated.\n\nWhen i=3 and j=5,\nSince dp[i-1][j-1]=dp=1 which is less than (j-i) i.e. 2,\ndp[i][j]=dp[i-1][j-1]+1 ,\ni.e.,dp=2.\nAs dp>len\nlen=dp=2\nind=max(ind,i)=3\n\n\nThe final matrix dp[][] would be:-\n\nj=0 1 2 3 4 5 6\ni=0 0 0 0 0 0 0 0\n1 0 0 0 0 0 0 0\n2 0 0 0 0 1 0 1\n3 0 0 0 0 0 2 0\n4 0 0 0 0 0 0 1\n5 0 0 0 0 0 0 0\n6 0 0 0 0 0 0 0\n\nTo retrieve the longest repeating and non-overlapping substring,we store the characters present from position (ind-len+1) till position (ind),i.e., the substring from position 2 till position 3 giving the substring an as the result.\n\n## Pseudo Code:\n\n if(str[i-1] == str[j-1] && dp[i-1][j-1] < (j - i))\n{\ndp[i][j] = dp[i-1][j-1] + 1;\nif (dp[i][j] > len)\n{\nlen = dp[i][j];\nind = max(i, ind);\n}\n}\nelse\ndp[i][j] = 0;\n// where i iterates from 1 to n and j iterates from\n// i+1 to n where n is the string size\nif(len > 0)\n{\nfor (int i = ind - len + 1; i <= ind; i++)\nans.push_back(str[i-1]);\n}\nreturn ans\n\n\n## Implementations\n\nWe have provided 3 implementations (C++,Java,Python).\n\nFollowing is the implementation in C++:-\n\n// C++ program to find the longest repeated\n// non-overlapping substring\n#include<bits/stdc++.h>\nusing namespace std;\n\n// Returns the longest repeating non-overlapping\n// substring in str\nstring longestRepeatedSubstring(string str)\n{\nint n = str.length();\nint dp[n+1][n+1];\n\nmemset(dp, 0, sizeof(dp)); // Initializing dp to 0\n\nstring ans; \t// To store resultant substring\nint len = 0; // To store length of result\n\n// building table in bottom-up manner\nint ind = 0;\nfor (int i=1; i<=n; i++)\n{\nfor (int j=i+1; j<=n; j++)\n{\n\n// if the characters at (i-1)th and (j-1)th\n// position matches and codition for\n// removing overlapping is satisfied\nif(str[i-1] == str[j-1] && dp[i-1][j-1] < (j - i))\n{\ndp[i][j] = dp[i-1][j-1] + 1;\n\n// updating maximum length of the\n// substring and updating the finishing\n// index of the suffix\nif (dp[i][j] > len)\n{\nlen = dp[i][j];\nind = max(i, ind);\n}\n}\nelse\ndp[i][j] = 0;\n}\n}\n\n// If we have non-empty result, then insert all\n// characters from first character to last\n// character of string\nif (len > 0)\n{\nfor (int i = ind - len + 1; i <= ind; i++)\nans.push_back(str[i-1]);\n}\n\nreturn ans;\n}\n\n// Driver program to test the above function\nint main()\n{\nstring s;\ncout << \"Enter the input string:- \";\ncin >> s;\ncout << \"The longest repeating non-overlapping substring is:- \" << longestRepeatedSubstring(s) << '\\n';\nreturn 0;\n}\n/*\nSample Input 1:-\nEnter the input string:- opengenus\nSample Output 1:-\nThe longest repeating non-overlapping substring is:- en\nSample Input 2:-\nEnter the input string:- aaaaaa\nSample Output 2:-\nThe longest repeating non-overlapping substring is:- aaa\n*/\n\n\nFollowing is the implementation in Java:-\n\nimport java.util.*;\nclass nonRepeativeSubstring\n{\npublic static String nonRepeativeSubstr(String str,int n)\n{\nint dp[][]=new int[n+1][n+1];\nint max=0,index=0;\nfor(int i=1;i<=n;++i)\n{\nfor(int j=i+1;j<=n;++j)\n{\nif(str.charAt(i-1)==str.charAt(j-1) && j-i>dp[i-1][j-1])\n{dp[i][j]=dp[i-1][j-1]+1;\nif(max<dp[i][j])\n{\nmax=dp[i][j];\n//save last index of substring\nindex=Math.max(i,index);\n}\n}\nelse\ndp[i][j]=0;\n}\n}\nreturn max>0?str.substring(index-max,index):\"-1\";\n}\npublic static void main (String[] args)\n{\nScanner scan=new Scanner(System.in);\nSystem.out.println(\"Enter the input string:-\");\nString s=scan.nextLine();\nSystem.out.println(\"The longest repeating non-overlapping substring is:- \"+nonRepeativeSubstr(s,s.length());\n}\n}\n}\n/*\nSample Input 1:-\nEnter the input string:- opengenus\nSample Output 1:-\nThe longest repeating non-overlapping substring is:- en\nSample Input 2:-\nEnter the input string:- aaaaaa\nSample Output 2:-\nThe longest repeating non-overlapping substring is:- aaa\n*/\n\n\nFollowing is the implementation in Python:\n\n# Returns the longest repeating non-overlapping\n# substring in str\ndef longestRepeatedSubstring(str):\n\nn = len(str)\ndp = [[0 for x in range(n + 1)] # Initializing dp to 0\nfor y in range(n + 1)]\n\nans = \"\" # To store resultant substring\nans_len = 0 # To store length of result\n\n# building table in bottom-up manner\nind = 0\nfor i in range(1, n + 1):\nfor j in range(i + 1, n + 1):\n\n# if the characters at (i-1)th and (j-1)th\n# position matches and codition for\n# removing overlapping is satisfied\nif (str[i - 1] == str[j - 1] and dp[i - 1][j - 1] < (j - i)):\ndp[i][j] = dp[i - 1][j - 1] + 1\n\n# updating maximum length of the\n# substring and updating the finishing\n# ind of the suffix\nif (dp[i][j] > ans_len):\nans_len = dp[i][j]\nind = max(i, ind)\n\nelse:\ndp[i][j] = 0\n\n# If we have non-empty result, then insert\n# all characters from first character to\n# last character of string\nif (ans_len > 0):\nfor i in range(ind - ans_len + 1,ind + 1):\nans = ans + str[i - 1]\n\nreturn ans\n\n# Driver Code\nif __name__ == \"__main__\":\n\nstr=input(\"Enter the input string: \")\nprint(\"The longest repeating non-overlapping substring is:- \",longestRepeatedSubstring(str))\n#Sample Input 1:-\n# Enter the input string:- opengenus\n#Sample Output 1:-\n# The longest repeating non-overlapping substring is:- en\n#Sample Input 2:-\n# Enter the input string:- aaaaaa\n#Sample Output 2:-\n# The longest repeating non-overlapping substring is:- aaa\n\n\n## Complexity\n\n• Worst case time complexity: O(n2)\n• Average case time complexity: O(n2)\n• Best case time complexity: O(n2)\n• Space complexity: O(n2)\n\nBuilding a 2-D table requires two for loops hence the time-complexity of this algorithm will be O(n2).Also making a 2-D table would require n2 space hence the space complexity of this algorithm will also be O(n2).\n\nWith this, you have the complete knowledge of this problem. Enjoy.",
null,
"#### Ashutosh Singh\n\nIntern at OpenGenus | Pursuing B. Tech in Computer Science at Indian Institute of Information Technology (IIIT) Sricity"
] |
[
null,
"https://iq.opengenus.org/content/images/2019/12/Improve.jpeg",
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] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.66977835,"math_prob":0.94523734,"size":8603,"snap":"2020-34-2020-40","text_gpt3_token_len":2677,"char_repetition_ratio":0.17711362,"word_repetition_ratio":0.20592485,"special_character_ratio":0.34197372,"punctuation_ratio":0.13057324,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99514705,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-29T01:55:49Z\",\"WARC-Record-ID\":\"<urn:uuid:0a464f86-fdd3-47b2-9a95-13bed92a8d2b>\",\"Content-Length\":\"50166\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:50489dae-cad8-463a-a77d-b1fac548e42b>\",\"WARC-Concurrent-To\":\"<urn:uuid:2b517bd2-dead-484b-a075-d28444bab1ea>\",\"WARC-IP-Address\":\"159.89.134.55\",\"WARC-Target-URI\":\"https://iq.opengenus.org/longest-repeating-non-overlapping-substring/\",\"WARC-Payload-Digest\":\"sha1:25S3HQT7VJV2U4KL5V6XVSLY62LKMYTI\",\"WARC-Block-Digest\":\"sha1:GEMEYVJ3SXX6HHET7AHV6YK44ML5LNG3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600401617641.86_warc_CC-MAIN-20200928234043-20200929024043-00582.warc.gz\"}"}
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https://metanumbers.com/43484
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[
"## 43484\n\n43,484 (forty-three thousand four hundred eighty-four) is an even five-digits composite number following 43483 and preceding 43485. In scientific notation, it is written as 4.3484 × 104. The sum of its digits is 23. It has a total of 4 prime factors and 12 positive divisors. There are 18,624 positive integers (up to 43484) that are relatively prime to 43484.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 23\n• Digital Root 5\n\n## Name\n\nShort name 43 thousand 484 forty-three thousand four hundred eighty-four\n\n## Notation\n\nScientific notation 4.3484 × 104 43.484 × 103\n\n## Prime Factorization of 43484\n\nPrime Factorization 22 × 7 × 1553\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 21742 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 43,484 is 22 × 7 × 1553. Since it has a total of 4 prime factors, 43,484 is a composite number.\n\n## Divisors of 43484\n\n1, 2, 4, 7, 14, 28, 1553, 3106, 6212, 10871, 21742, 43484\n\n12 divisors\n\n Even divisors 8 4 2 2\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 87024 Sum of all the positive divisors of n s(n) 43540 Sum of the proper positive divisors of n A(n) 7252 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 208.528 Returns the nth root of the product of n divisors H(n) 5.99614 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 43,484 can be divided by 12 positive divisors (out of which 8 are even, and 4 are odd). The sum of these divisors (counting 43,484) is 87,024, the average is 7,252.\n\n## Other Arithmetic Functions (n = 43484)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 18624 Total number of positive integers not greater than n that are coprime to n λ(n) 4656 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 4527 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 18,624 positive integers (less than 43,484) that are coprime with 43,484. And there are approximately 4,527 prime numbers less than or equal to 43,484.\n\n## Divisibility of 43484\n\n m n mod m 2 3 4 5 6 7 8 9 0 2 0 4 2 0 4 5\n\nThe number 43,484 is divisible by 2, 4 and 7.\n\n• Arithmetic\n• Abundant\n\n• Polite\n\n## Base conversion (43484)\n\nBase System Value\n2 Binary 1010100111011100\n3 Ternary 2012122112\n4 Quaternary 22213130\n5 Quinary 2342414\n6 Senary 533152\n8 Octal 124734\n10 Decimal 43484\n12 Duodecimal 211b8\n20 Vigesimal 58e4\n36 Base36 xjw\n\n## Basic calculations (n = 43484)\n\n### Multiplication\n\nn×i\n n×2 86968 130452 173936 217420\n\n### Division\n\nni\n n⁄2 21742 14494.7 10871 8696.8\n\n### Exponentiation\n\nni\n n2 1890858256 82222080403904 3575344944283361536 155470299557217693031424\n\n### Nth Root\n\ni√n\n 2√n 208.528 35.1649 14.4405 8.46576\n\n## 43484 as geometric shapes\n\n### Circle\n\n Diameter 86968 273218 5.94031e+09\n\n### Sphere\n\n Volume 3.44411e+14 2.37612e+10 273218\n\n### Square\n\nLength = n\n Perimeter 173936 1.89086e+09 61495.7\n\n### Cube\n\nLength = n\n Surface area 1.13451e+10 8.22221e+13 75316.5\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 130452 8.18766e+08 37658.2\n\n### Triangular Pyramid\n\nLength = n\n Surface area 3.27506e+09 9.68997e+12 35504.5\n\n## Cryptographic Hash Functions\n\nmd5 dfc7ecce6a8dcc1a1575ccf3446b1985 2b3fa369c006051b9caad1b366c9b4499f3acc23 9a46096391718a4d4440eb862810a3018f2d367f4bd55dfd3146340098e50b12 dafa41037e2fd22fbecf936f34fe1b856e69635cdf4bc4bdc4fd1475fac3a880489189e2641c4bdae5bc8ba7ab5f0ba9b930f87479e9c9fea5bdfd4492937e3b c8059c4dd7cfec402a35bd78a61711fb2a7e8ae4"
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{"ft_lang_label":"__label__en","ft_lang_prob":0.633302,"math_prob":0.9765877,"size":4488,"snap":"2020-24-2020-29","text_gpt3_token_len":1595,"char_repetition_ratio":0.11953613,"word_repetition_ratio":0.0254491,"special_character_ratio":0.45209447,"punctuation_ratio":0.07662338,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9954887,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-13T18:00:31Z\",\"WARC-Record-ID\":\"<urn:uuid:3ebce685-a8ae-4950-9380-b6b831e60874>\",\"Content-Length\":\"47647\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1229bb2c-15be-4358-818a-b18654c385d4>\",\"WARC-Concurrent-To\":\"<urn:uuid:a72b9c98-af15-46a7-9da3-1c5fa4c62ffb>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/43484\",\"WARC-Payload-Digest\":\"sha1:QMDECP7Z77N4ALWEAKNWSE7Q2LGVHY3G\",\"WARC-Block-Digest\":\"sha1:ZZJXEVSUEMWWT7QYSYPXCKFH62PNBACN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657146247.90_warc_CC-MAIN-20200713162746-20200713192746-00290.warc.gz\"}"}
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http://www.178linux.com/945
|
[
"# Python函数式编程指南（二）：函数\n\n#### 2. 从函数开始\n\n##### 2.1. 定义一个函数\n\n```def add(x, y):\nreturn x + y\n```\n\n```lambda args: expression\n```\n\n```lambda_add = lambda x, y: x + y\n```\n\n##### 2.2. 使用函数赋值\n\n```add_a_number_to_another_one_by_using_plus_operator = add\n```\n\n##### 2.3. 闭包\n\n```def f():\nn = 1\ndef inner():\nprint n\ninner()\nn = 'x'\ninner()\n```\n\n```#Python 3.x supports `nonlocal'\ndef f():\nn = 1\ndef inner():\nnonlocal n\nn = 'x'\nprint(n)\ninner()\nprint(n)\n```\n\n##### 2.4. 作为参数\n\n```print add('三角形的树', '北极')\n```\n\n```lst = range(5) #[0, 1, 2, 3, 4]\n```\n\n```amount = 0\nfor num in lst:\n```\n\n```def sum_(lst):\namount = 0\nfor num in lst:\nreturn amount\nprint sum_(lst)\n```\n\n1. 使用初始值与列表的第一个元素相加；\n2. 使用上一次相加的结果与列表的下一个元素相加；\n3. 重复第二步，直到列表中没有更多元素；\n4. 将最后一次相加的结果返回。\n\n```def multiply(lst):\nproduct = 1\nfor num in lst:\nproduct = product * num\nreturn product\n```\n\n```def reduce_(function, lst, initial):\nresult = initial\nfor num in lst:\nresult = function(result, num)\nreturn result\n\n```print reduce_(lambda x, y: x * y, lst, 1)\n```\n\nPython有一个内建函数reduce，完整实现并扩展了reduce_的功能。本文稍后的部分包含了有用的内建函数的介绍。请注意我们的目的是没有循环，使用函数替代循环是函数式风格区别于指令式风格的最显而易见的特征。\n\n*像Python这样构建于类C语言之上的函数式语言，由于语言本身提供了编写循环代码的能力，内置函数虽然提供函数式编程的接口，但一般在内部还是使用循环实现的。同样的，如果发现内建函数无法满足你的循环需求，不妨也封装它，并提供一个接口。\n\n##### 2.5. 作为返回值\n\n```def map_(function, lst):\nresult = []\nfor item in lst:\nresult.append(function(item))\nreturn result\n```\n\n```lst = map_(lambda x: add(1, x), lst)\nprint reduce_(lambda x, y: x * y, lst, 1)\n```\n\n```lst = map_(lambda x: add(10, x), lst)\nprint reduce_(lambda x, y: x * y, lst, 1)\n```\n\n```lst = map_(add_to(10), lst) #add_to(10)\n```\n\n```def add_to(n):\n```\n\n```functools.partial(func[, *args][, **keywords])\n```\n\n*题外话，单就例子中的这个功能而言，在一些其他的函数式语言中（例如Scala）可以使用名为柯里化(Currying)的技术实现得更优雅。柯里化是把接受多个参数的函数变换成接受一个单一参数（最初函数的第一个参数）的函数，并且返回接受余下的参数而且返回结果的新函数的技术。如下的伪代码所示：\n\n```#不是真实的代码\nreturn x + y\n```\n\n##### 2.6. 部分内建函数介绍\n• reduce(function, iterable[, initializer])\n这个函数的主要功能与我们定义的reduce_相同。需要补充两点：\n它的第二个参数可以是任何可迭代的对象（实现了__iter__()方法的对象）；\n如果不指定第三个参数，则第一次调用function将使用iterable的前两个元素作为参数。\n由reduce和一些常见的function组合成了下面列出来的内置函数：\n\n```all(iterable) == reduce(lambda x, y: bool(x and y), iterable)\nany(iterable) == reduce(lambda x, y: bool(x or y), iterable)\nmax(iterable[, args...][, key]) == reduce(lambda x, y: x if key(x) > key(y) else y, iterable_and_args)\nmin(iterable[, args...][, key]) == reduce(lambda x, y: x if key(x) < key(y) else y, iterable_and_args)\nsum(iterable[, start]) == reduce(lambda x, y: x + y, iterable, start)\n```\n\nmap(function, iterable, …)\n这个函数的主要功能与我们定义的map_相同。需要补充一点：\nmap还可以接受多个iterable作为参数，在第n次调用function时，将使用iterable1[n], iterable2[n], …作为参数。\n\n• filter(function, iterable)\n这个函数的功能是过滤出iterable中所有以元素自身作为参数调用function时返回True或bool(返回值)为True的元素并以列表返回，与系列第一篇中的my_filter函数相同。\n• zip(iterable1, iterable2, …)\n这个函数返回一个列表，每个元素都是一个元组，包含(iterable1[n], iterable2[n], …)。\n例如：zip([1, 2], [3, 4]) –> [(1, 3), (2, 4)]\n如果参数的长度不一致，将在最短的序列结束时结束；如果不提供参数，将返回空列表。"
] |
[
null
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|
https://tutorialspoint.dev/language/python/mathematical-functions-in-python-set-4-special-functions-and-constants
|
[
"# Mathematical Functions in Python | Set 4 (Special Functions and Constants)\n\nSome of the mathematical functions are discussed in below set 1, set 2 and set 3\nMathematical Functions in Python | Set 1 (Numeric Functions)\nMathematical Functions in Python | Set 2 (Logarithmic and Power Functions)\nMathematical Functions in Python | Set 3 (Trigonometric and Angular Functions)\n\n1. gamma() :- This function is used to return the gamma function of the argument.\n\n `# Python code to demonstrate the working of ` `# gamma() ` ` ` `# importing \"math\" for mathematical operations ` `import` `math ` ` ` `a ``=` `4` ` ` `# returning the gamma() of 4 ` `print` `(``\"The gamma() of 4 is : \"``, end``=``\"\") ` `print` `(math.gamma(a)) `\n\nOutput:\n\n```The gamma() of 4 is : 6.0\n```\n\n2. pi :- This is an inbuilt constant that outputs the value of pi(3.141592).\n\nbr>\n\n3. e :- This is an inbuilt constant that outputs the value of e(2.718281).\n\n `# Python code to demonstrate the working of ` `# const. pi and e ` ` ` `# importing \"math\" for mathematical operations ` `import` `math ` ` ` `# returning the value of const. pi ` `print` `(``\"The value of const. pi is : \"``, end``=``\"\") ` `print` `(math.pi) ` ` ` `# returning the value of const. e ` `print` `(``\"The value of const. e is : \"``, end``=``\"\") ` `print` `(math.e) `\n\nOutput:\n\n```The value of const. pi is : 3.141592653589793\nThe value of const. e is : 2.718281828459045\n```\n\n4. inf :- This is a positive floating point infinity constant. -inf is used to denote the negative floating point infinity. This constant is defined in python 3.5 and above.\n\n5. isinf() :- This function is used to check whether the value is an infinity or not.\n\n6. nan :- This constant denotes “Not a number” in python. This constant is defined in python 3.5 and above.\n\n7. isnan() :- This function returns true if the number is “nan” else returns false.\n\n `# Python code to demonstrate the working of ` `# inf, nan, isinf(), isnan() ` ` ` `# importing \"math\" for mathematical operations ` `import` `math ` ` ` `# checking if number is nan ` `if` `(math.isnan(math.nan)): ` ` ``print` `(``\"The number is nan\"``) ` `else` `: ``print` `(``\"The number is not nan\"``) ` ` ` `# checking if number is positive infinity ` `if` `(math.isinf(math.inf)): ` ` ``print` `(``\"The number is positive infinity\"``) ` `else` `: ``print` `(``\"The number is not positive infinity\"``) `\n\nOutput:\n\n```The number is nan\nThe number is positive infinity\n```\n\nPython"
] |
[
null
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|
https://www.progressivegardening.com/agricultural-engineering-2/field-efficiency.html
|
[
"## Field Efficiency\n\nField efficiency is usually used to evaluate the performance of tillage or harvesting machines. It is a comparison of the actual amount of \"work\" (volume of activity, not Force x Distance) done by a machine compared to what it would do with no lost time or capacity. The maximum rate that a machine can perform is determined by the width of the machine and the speed of travel. When a machine operates with a constant width and travels at a constant speed, it will perform at 100% field efficiency. A machine is capable of operating at 100% field efficiency for short periods of time, but as soon as the speed changes (slow down for turns, etc.), or the width changes (overlap width of the machine to prevent skips), the efficiency drops below 100%. The primary cause of loss efficiency is lost time (unproductive time) and a working width of the machine less than the maximum. Typical field efficiencies for common machines can be found in Appendix IV. This concept is illustrated in more detail in the next section, on capacity.\n\n### 9.4. Capacity\n\nThe term capacity is used to evaluate the productivity of a machine. In agriculture, two types of capacity are commonly used, field capacity and throughput capacity. Field capacity is used to evaluate the productivity of machines used to work the soil, such as plows, cultivators, and drills, sprayers, and harvesting machines. Throughput capacity is used to describe machines that handle or process a product, such as grain augers, balers, forage harvesters, and combines.\n\nAn additional concept relating to both types of capacity is the difference between theoretical and actual productivity. If a tillage machine operates at 100% efficiency, it is operating at 100% capacity. This is called the theoretical field capacity. Theoretical field capacity is determined using the width of the machine and the speed of travel. It can be calculated using units cancellation, but an equation is commonly used.\n\nTheoretical field capacity(CT) =\n\n8.25\n\nwhere Ct = Theoretical field capacity (f); S = Speed of travel (S); W = Width of the machine (ft); 8.25 = Units conversion constant (43,560 f2) ^ (5,280 2^).\n\nThis equation can be used as long as the unit used for speed is miles per hour and the unit used for the width of the machine is feet.\n\nProblem: Determine the theoretical capacity for a machine that travels at 5.0 mph and has an operating width of 20.0 ft.\n\nSolution:\n\nWhen this machine travels at a constant speed and uses a constant width, it has a theoretical capacity of 12 ac/hr.\n\nEffective field capacity is the amount of productivity that actually occurred not what is theoretical possible. Lost capacity is an important concern for the machine operator and/or manager because it represents lost revenues or resources. Usually lost capacity is caused by lost time, time not operating, and operating the machine with less than the maximum working width. Common causes of lost time include:\n\n1. Mechanical breakdowns.\n\n2. Taking time to adjust the machine.\n\n3. Stopping to fill seed hoppers, spray tanks, etc.\n\n4. Slowing down to turn at the end of the row or crossing waterways, etc.\n\n### 5. Operator rest stops.\n\nThe equation for effective capacity is the same as theoretical capacity with a field efficiency added. A range and typical field efficiency values for common machines can be found in Appendix IV. The common equation for effective field capacity is:\n\n8.25\n\nwhere CE = Effective field capacity (ac/hr); S = Average speed of travel (mph); W = Effective width of the machine (ft); Ef = Field efficiency (decimal form).\n\nProblem: Assume that the operator in the previous problem averages 0.75 hr of lost time per 10.0-hr day. What is the effective field capacity?\n\nSolution: The first step is to determine the time efficiency:\n\nf input 10.0 hr\n\nThe second step is to determine the effective capacity:\n\nNow the effects of lost productivity are apparent. The theoretical capacity is 12 ac/hr, but because of lost time, the effective capacity is 11 ac/hr.\n\nThe concept of effective capacity also can be used to determine the amount of time it would take a machine to cover a field.\n\nProblem: How many hours will it take to cultivate 200.0 acres with a field cultivator that is 24.0 ft wide?\n\nSolution: This is an example of a problem with a hidden intermediate step. Before the hours can be determined, the effective capacity of the machine must be calculated. Note: The effective capacity equation requires three values. Two of these, speed and field efficiency, are not given in the problem. If the actual speed and the field efficiency are unknown, the typical values found in Appendix IV can be used. In Appendix IV, the typical field efficiency for a field cultivator is 85%, and the typical speed is 5.5 mph. With these values, the effective capacity can be calculated:\n\nOnce the effective capacity is known, the time required to work the field can be calculated. Using units cancellation:\n\n14 ac\n\nIf the average field speed is 5.5 mph and the operator can maintain an 85% field efficiency, it will take 14 hr to cultivate the 200 acre field.\n\n+3 -3\n\n### Responses\n\n• janina\nHow to calculate theoretic field capacity given time lost?\n3 years ago\n• gianfranco\nWhat is theoretical field capacity and effective field capacity in tractor operation?\n3 years ago\n• jyrki\nWhat field efficiency,?\n3 years ago\n• Raffaella\nHow to calculate field efficiency of tractor?\n3 years ago\n• ambrogio\nHow to calculate theoretical field capacity?\n3 years ago\n• giordano\nHow to determine effective field capacity of farm workers?\n3 years ago\n• david\nWhy effective field capacity lower than the theoritical field capacity?\n2 years ago\n• Kerstin\nHow to calculate field efficiency farm machinery?\n2 years ago\n• pentti\nWhat is theoretical capacuty. feikd capacity and effective capacity?\n2 years ago\n• kimberly\nWhy it is difficult to determine the actual field capacity of a machine?\n2 years ago\n• Riikka\nHow to find field efficiency?\n2 years ago\n• salomone\nHow can we find effective field capacity of farm machinery?\n2 years ago\n• fatimah\nHow to calculate time loss in thereotical field capacity?\n2 years ago\n• daria\nWhy it is difficult to obtain actual field capacity?\n2 years ago\n• joe\nWhy it is difficult to obtain actual field capacity of a machine?\n2 years ago\n• Elfstan\nWhat is effictive field capacity?\n2 years ago\n• JULIA WATSON\nWhat is field capacity tractor operation and types?\n2 years ago\n• mehret\nWhat is the difference between field efficiency and machine efficiency?\n2 years ago\nHow is theoritic field capacity is calculated in agriculture engineering is calculated?\n2 years ago\n• claudia\nWhat is the formula of theoretical field capacity?\n2 years ago\n• elias\nWhat is the field efficiencies of a field machinery unit?\n2 years ago\n• Futsum\nWhat is the field efficiencies of a field machine?\n2 years ago\n• emilia\nHow to calculate the efficiency of agricultural machinart?\n2 years ago\n• Amy\nHow to calculate theoretical field capacity with unknown width of an implement?\n1 year ago\n• ralph\nWhat is field capacity of farm tractor?\n9 months ago\n• Ilse Waltari\nHow to calculate effective field capacity of sprayers in agricultural machinery?\n9 months ago\n• balbo\nWhich purpose we are using field efficiency?\n8 months ago\n• alessandra\nWhat is the formula for field efficiency?\n8 months ago\n• Kobe\nHow to calculate field capacity of tractor?\n8 months ago\n• fre-qalsi\nWhat is field efficiency of typical powered field machine unit?\n7 months ago\n• GUNDAHAR\nWhat is field efficience?\n6 months ago\n• NATALIA\nWhat is the formula for calculating effective field capacity?\n5 months ago\n• PETRA WECKMAN\nWhat are the formular for effective field capacity?\n5 months ago\n• Tia Young\nHow to calculate theoretical anf effective field capacity?\n5 months ago\n• Laura\nHow to find the area of a farmland given the theoritical and actual feild capacities?\n5 months ago\n• lee\nHow does machine width or size can be used to imorove field efficiency?\n3 months ago\n• yusef\nWhat is the difference between field efficiency and effective field capacity?\n2 months ago\n• natalia\nWhat is the contstant value in theoretical field capacity?\n1 month ago\n• herbert west\nHow to calculate fied efficiency?\n1 month ago"
] |
[
null
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{"ft_lang_label":"__label__en","ft_lang_prob":0.9217456,"math_prob":0.95412874,"size":5065,"snap":"2019-51-2020-05","text_gpt3_token_len":1077,"char_repetition_ratio":0.17901601,"word_repetition_ratio":0.0385514,"special_character_ratio":0.2201382,"punctuation_ratio":0.12197581,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98572487,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-12T16:02:32Z\",\"WARC-Record-ID\":\"<urn:uuid:e71a8d25-512e-466f-8916-d704bfde6fb7>\",\"Content-Length\":\"38418\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:26255824-2ab9-47aa-afc2-343da644af1b>\",\"WARC-Concurrent-To\":\"<urn:uuid:af12d1e4-4754-43ad-8fc2-8451c6cfde9c>\",\"WARC-IP-Address\":\"104.28.22.127\",\"WARC-Target-URI\":\"https://www.progressivegardening.com/agricultural-engineering-2/field-efficiency.html\",\"WARC-Payload-Digest\":\"sha1:KCFOKQTL4FT5NEEHBV75R5TKYBCIXCSR\",\"WARC-Block-Digest\":\"sha1:MPOIDKUVO5RVSSVALQZ6SDHSP4TSVT4K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540544696.93_warc_CC-MAIN-20191212153724-20191212181724-00411.warc.gz\"}"}
|
https://www.studystack.com/flashcard-2299162
|
[
"",
null,
"or",
null,
"or",
null,
"taken",
null,
"why\n\nMake sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.\n\nDon't know\nKnow\nremaining cards\nSave\n0:01\nEmbed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.\n\nNormal Size Small Size show me how\n\n# Atomic Number/Mass\n\nThe characteristics of each element depend on the nature of its [...]. The characteristics of each element depend on the nature of its atoms.\nan atom has a nucleus that contains [...] and neutrons, and that is surrounded by electrons. an atom has a nucleus that contains protons and neutrons, and that is surrounded by electrons.\nthe part of the atom that most distinguishes one element from another is the number of [...] in the atoms the part of the atom that most distinguishes one element from another is the number of protons in the atoms\nThe number of [...] in an atom is that atom's atomic number. The number of protons in an atom is that atom's atomic number.\nThe number of [...] plus the number of protons in an atom is that atom's mass number. The number of neutrons plus the number of protons in an atom is that atom's mass number.\nThe atomic number and mass number of an atom tell about the organization of its [...]. The atomic number and mass number of an atom tell about the organization of its nucleus.\nThe [...] number minus the atomic number gives you the number of neutrons. The mass number minus the atomic number gives you the number of neutrons.\nThe periodic table gives you the atomic number of each element and its *[...]* atomic mass; the average mass number of its different isotopes. The periodic table gives you the atomic number of each element and its *average* atomic mass; the average mass number of its different isotopes.\nIsotopes are versions of an element that have the same [...] number but different [...] numbers. Isotopes are versions of an element that have the same atomic number but different mass numbers.\nIsotopes of an element have the same number of [...], but a different numbers of neutrons. Isotopes of an element have the same number of protons, but a different numbers of neutrons.\nYou can always find out an atom's atomic number by using the [...]. You can always find out an atom's atomic number by using the periodic table.\nIn the periodic table, the atomic number is never a [...] number, but the average atomic mass usually is. In the periodic table, the atomic number is never a decimal number, but the average atomic mass usually is.\nProtons have a [...] charge ([...]), neutrons are neutral in charge (0), and electrons have a negative charge (-1). Protons have a positive charge (+1), neutrons are neutral in charge (0), and electrons have a negative charge (-1).\nThe electrical balance of an atom is determined only by the numbers of protons and [...]. The electrical balance of an atom is determined only by the numbers of protons and electrons.\nAn electrically neutral atom has an equal number of [...] and electrons, so the positive and negative charges cancel out. An electrically neutral atom has an equal number of protons and electrons, so the positive and negative charges cancel out.\nThe net charge of a [...] atom is 0. The net charge of a neutral atom is 0.\nIf given the number of proton it's also possible to determine the number of [...] in any electrically neutral atom. If given the number of proton it's also possible to determine the number of electrons in any electrically neutral atom.\nan atom has a nucleus that contains protons and [...], and that is surrounded by electrons. an atom has a nucleus that contains protons and neutrons, and that is surrounded by electrons.\nan atom has a nucleus that contains protons and neutrons, and that is surrounded by [...]. an atom has a nucleus that contains protons and neutrons, and that is surrounded by electrons.\nThe number of protons in an atom is that atom's atomic [...] The number of protons in an atom is that atom's atomic number.\nThe number of neutrons plus the number of [...] in an atom is that atom's mass number. The number of neutrons plus the number of protons in an atom is that atom's mass number.\nThe number of neutrons plus the number of protons in an atom is that atom's [...]. The number of neutrons plus the number of protons in an atom is that atom's mass number.\nThe mass number minus the [...] number gives you the number of neutrons. The mass number minus the atomic number gives you the number of neutrons.\nThe mass number minus the atomic number gives you the number of [...]. The mass number minus the atomic number gives you the number of neutrons.\nIsotopes of an element have the same number of protons, but a different numbers of [...]. Isotopes of an element have the same number of protons, but a different numbers of neutrons.\nProtons have a positive charge (+1), [...] are neutral in charge ([...]), and electrons have a negative charge (-1). Protons have a positive charge (+1), neutrons are neutral in charge (0), and electrons have a negative charge (-1).\nProtons have a positive charge (+1), neutrons are neutral in charge (0), and [...] have a negative charge ([...]). Protons have a positive charge (+1), neutrons are neutral in charge (0), and electrons have a negative charge (-1).\nThe electrical balance of an atom is determined only by the numbers of [...] and electrons. The electrical balance of an atom is determined only by the numbers of protons and electrons.\nAn electrically neutral atom has an equal number of protons and [...], so the positive and negative charges cancel out. An electrically neutral atom has an equal number of protons and electrons, so the positive and negative charges cancel out.\nAn electrically neutral atom has an equal number of protons and electrons, so the positive and negative charges [...]. An electrically neutral atom has an equal number of protons and electrons, so the positive and negative charges cancel out.\nThe net charge of a neutral atom is [...]. The net charge of a neutral atom is 0.\nIf given the number of proton it's also possible to determine the number of electrons in any electrically [...] atom. If given the number of proton it's also possible to determine the number of electrons in any electrically neutral atom.\nCreated by: mr.shapard"
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null
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|
https://www.semanticscholar.org/author/S.-Bravyi/1726247
|
[
"• Publications\n• Influence\nFermionic Quantum Computation\n• Physics\n• 29 March 2000\nWe define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs\nLieb-Robinson bounds and the generation of correlations and topological quantum order.\n• Physics\nPhysical review letters\n• 14 March 2006\nThe Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.\nA no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes\n• Computer Science\n• 11 October 2008\nIt is shown that for D=1,2 the height of the energy barrier separating different logical states is upper bounded by a constant independent of the lattice size L, and it is demonstrated that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D= 1,2.\nError Mitigation for Short-Depth Quantum Circuits.\n• Physics\nPhysical review letters\n• 6 December 2016\nTwo schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits by resampling randomized circuits according to a quasiprobability distribution.\nQuantum codes on a lattice with boundary\n• Physics\n• 20 November 1998\nA new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices.\n• Computer Science\n• 11 September 2012\nA new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation on all logical qubits are proposed and lead to a two-fold overhead reduction for distilling magic states with output accuracy compared with the best previously known protocol.\nImproved Classical Simulation of Quantum Circuits Dominated by Clifford Gates.\n• Physics, Computer Science\nPhysical review letters\n• 27 January 2016\nThe algorithm may serve as a verification tool for near-term quantum computers which cannot in practice be simulated by other means and can be used in practice to simulate medium-sized quantum circuits dominated by Clifford gates.\nSimulation of quantum circuits by low-rank stabilizer decompositions\n• Computer Science\nQuantum\n• 1 August 2018\nA comprehensive mathematical theory of the stabilizerRank and the related approximate stabilizer rank is developed and a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art are presented.\nTapering off qubits to simulate fermionic Hamiltonians\n• Physics, Computer Science\n• 27 January 2017\nIt is shown that encodings with a given filling fraction $\\nu=N/M$ and a qubit-per-mode ratio $\\eta=Q/M<1$ can be constructed from efficiently decodable classical LDPC codes with the relative distance $2\\nu$ and the encoding rate $1-\\eta$."
] |
[
null
] |
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|
https://questions.llc/questions/1078164/in-a-certain-class-there-are-12-boys-and-18-girls-if-the-class-average-for-an-algebra
|
[
"# In a certain class there are 12 boys and 18 girls. If the class average for an algebra exam is 90 and the boys' average score is 87, what is the girls' average score?\n\n1. 👍\n2. 👎\n3. 👁\n4. ℹ️\n5. 🚩\n1. (12*87+18x)/(12+18) = 90\nNow just solve for x\n\n1. 👍\n2. 👎\n3. ℹ️\n4. 🚩\n2. X is 92\n\n1. 👍\n2. 👎\n3. ℹ️\n4. 🚩\n3. The ratio of boys to girls is 12 to 18 if they are 87 girls how many boys are there\n\n1. 👍\n2. 👎\n3. ℹ️\n4. 🚩"
] |
[
null
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{"ft_lang_label":"__label__en","ft_lang_prob":0.80776155,"math_prob":0.98591,"size":369,"snap":"2022-27-2022-33","text_gpt3_token_len":148,"char_repetition_ratio":0.17534247,"word_repetition_ratio":0.2840909,"special_character_ratio":0.34688348,"punctuation_ratio":0.07936508,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97249955,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-16T16:04:22Z\",\"WARC-Record-ID\":\"<urn:uuid:5bfe23ef-b572-4f38-b81e-66c5203a78f4>\",\"Content-Length\":\"17423\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b98d7927-9e2e-43b2-bb94-15148b0a0a19>\",\"WARC-Concurrent-To\":\"<urn:uuid:59164745-eb58-4ffc-82c9-1353ba193cfb>\",\"WARC-IP-Address\":\"45.79.29.166\",\"WARC-Target-URI\":\"https://questions.llc/questions/1078164/in-a-certain-class-there-are-12-boys-and-18-girls-if-the-class-average-for-an-algebra\",\"WARC-Payload-Digest\":\"sha1:5PEDGFDCBGQTDCBPC3MGARBIQSNBH77J\",\"WARC-Block-Digest\":\"sha1:G7IY6CCT4HGDXS5PRN3FQRCYGKL3H6XA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572408.31_warc_CC-MAIN-20220816151008-20220816181008-00424.warc.gz\"}"}
|
https://crypto.stackexchange.com/questions/tagged/paillier?sort=active
|
[
"# Questions tagged [paillier]\n\nA public-key cryptosystem invented by Pascal Paillier in 1999.\n\n121 questions\nFilter by\nSorted by\nTagged with\n61 views\n\n### Paillier Decryption?\n\nLet $c_1$ and $c_2$ two encryptions of $m_1$ and $m_2$ using the Paillier Cryptosystem. $c_1= E(m_1,r_1) = g^{m_1} r_1^n \\bmod n^2$ and $c_2= E(m_2,r_2) = g^{m_2} r_2^n \\bmod n^2$ Paillier ...\n115 views\n\n### Proof of lemma 1 Paillier encryption\n\nIn the original paper of Paillier, lemma 1 shows why $n$ must divide the order of $g$. What I don't understand in the proof of this lemma is why $g^{x_2-x_1}(y_2/y_1)^n$ implies $g^{\\lambda(x_2-x_1)}$....\n40 views\n\n### Paillier scheme and noise growth\n\nDoes the problem of noise growth exist in the Paillier homomorphic scheme ?\n125 views\n\n### Do any probabilistic hashing algorithms have additive homomorphism?\n\nWhat I am looking for is a function that meets the following criteria: For each possible input (assume integers from [0, 255]), there must be trillions of possible outputs so as to prevent preimage ...\n312 views\n\n### Zero knowledge proof for Paillier addition under multiple keys\n\nSuppose $m_0, m_1, m_2 \\in \\mathbb{N}$ such that $m_0 = m_1 + m_2$, $m_i > 0$ (none of them can be 0 or lower) Under a Paillier cryptosystem, set $e_0 = E(m_0, r_0)$ for a public key $(g_0, n_0)$ ...\n55 views\n\n### Homomorphic encrypted streams (Paillier)\n\nSituation: Alice (violin) and Bob (drums) play music together and want to (real-time) stream the concert to Carol. In order for Carol to save bandwidth, the stream is sent through a server which ...\n72 views\n\n### random mask reversible after homomorphic encryption\n\nI would like to know if this process is feasible under homomorphic encryption, ideally under paillier or any other additive scheme Apply a mask X to obfuscate a message A ie. Am = A (op) X where (op)...\n44 views\n\n108 views\n\n### Order of g in Paillier Scheme\n\nI'm trying to understand the Paillier Scheme but there's something I can't understand in the keyGen algorithm: Ensure $n$ divides the order of $g$ by checking the existence of the following ...\n65 views\n\n### Is it possible to calculate the random factor $r$ from a encrypted message and the private key in a Paillier cryptosystem?\n\nI have already done my research and found various sources that state that it is possible but there are also a lot of them that says it is not possible to recover $r$. This Q/A on this site for example ...\n48 views\n\n### Deterministic procedure for mapping an arbitrary value into a 𝑝,𝑞 pair for public key cryptography\n\nI want public key cryptosystem to used for re-encryption as describe in Can Paillier ,RSA or any other schemes be used for universal re-encryption like elGamal? Now i have little solution for ...\n59 views\n\n### Paillier Complex Residuosity problem?\n\nPaillier Cryptosystem depends on both the factorization where $n = p.q$ and the complex residuosity problem which is defined in the original paper as: The problem of deciding n-th residuosity, i.e. ...\n285 views\n\n### Comparison of values in Paillier homomorphic encryption\n\nFor a project, I am using homomorphic encryption with the Paillier cryptosystem, and I have to compare two values... Can this be done using homomorphic encryption? And I know subtraction can be done ...\n9k views\n\n### What are some disadvantages of homomorphic encryption schemes?\n\nI'm doing some self-teaching / research for my own benefit in homomorphic cryptography. I've studied both additive and multiplicative schemes (Paillier and RSA respectively), but all I can seem to ...\n221 views\n\n### Weakening of Paillier cryptosystem due to ciphertext equivalence and order in CryptDB\n\nThe Paillier cryptosystem is probabilistic in nature and IND-CPA secure. By design given two ciphertexts one cannot distinguish whether decrypting those two ciphertexts will result in same or ...\n52 views\n\n### Why is the Paillier cryptosystem not considered fully homomorphic encryption? [duplicate]\n\nPaillier is an additive homomorphic encryption system that can achieve the encrypted version of its sums. However, we can calculate the encrypted version of their multiplications by raising an ...\n61 views\n\n### Compute ln function of a Paillier encrypted value [closed]\n\nIf I have an encrypted value $Enc(x)$ with Paillier cryptosystem, is it feasible to compute an encryption form of $\\ln(x)$ or its approximation using homomorphic properties? The input $x$ is always ...\n32 views\n\n### Can Paillier Encryption has independent decryption key?\n\nAs Pailliear cryptosystem secret key $\\lambda$, depends on primes $p$ and $q$. As $\\lambda = \\operatorname{lcm}(p-1,q-1)$. I want decryption key to independent from $p$ and $q$. It can be possible ...\n104 views\n\n### How Paillier cryptosystem can be used practically to encrypt and decrypt big messages “m”?\n\nI want to use the Paillier cryptosystem for encryption and decryption purposes in my research work. But i haven't found a way to encrypt big input messages; As i want to encrypt the message i,e m : <...\n70 views\n\n### Is there any relationship between Paillier Cryptosystem's random r and other factors\n\nI want to try run an example of Paillier cryptosystem(Algorithm), So i just started with some basic examples, but cannot obtain correct result/decryption. I just change random factor ...\n1k views\n\n### In which public key encryption algorithms are the private and public key not reversible?\n\nThe RSA public key encryption system has the characteristic that the public key and the private key can be reversed. That is, information encrypted with the public key can be decrypted with the ...\n95 views\n\n### Homomorphic/Paillier crypto system for use case?: overflow for multiple counter exponent possible? Different cipher factor needed all the time?\n\nRecently I read about homomorphic cryptosystem. They might solve a problem. To do this there need to be some modifications from standard version. Using Paillier here but a solution for other also ...\n155 views\n\n### Zero-knowledge proof for Paillier parameters\n\nFor RSA one can give a non-interactive zero-knowledge proof that RSA with parameters $(e,N)$ form a permutation and a proof of knowledge of the associated RSA secret key. For example, such a proof can ...\n117 views\n\n### homomorphic division with scaling/Paillier\n\nLet's say that I have to use fractions instead of integers and I am using Paillier cryptosystem. So, I use scaling to obtain integers. Assume that I have a secure division protocol. What happens if ...\n39 views\n\n98 views\n\n### Verification in Threshold RSA or Threshold Paillier\n\nIn the key generation of the threshold version of RSA or the threshold version of the Paillier cryptosystem (e.g. \"Shoup - 2000 - Practical threshold signatures\" or \"Fouque et al. - 2000 - Sharing ...\n80 views\n\n### The way to calculate $r$ from $c=r^t\\mod{n}$ where $(c,t,n)$ is known\n\nI want to know if there is a easy way to calculate $r$ from $c=r^t\\mod{n}$ where $(c,t,n)$ is known and $t=pq$ is an RSA? If $n=t^2$, is it more easier?"
] |
[
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|
https://justaaa.com/statistics-and-probability/201681-find-the-margin-of-error-for-the-given-values-of
|
[
"Question\n\n# Find the margin of error for the given values of c, σ, and n. c=0.90, σ=3.3,...\n\nFind the margin of error for the given values of c, σ, and n.\n\nc=0.90, σ=3.3, n=81.\n\nEequals= _ (Round to three decimal places as needed.)\n\nWe know that :-\n\nMargin of error = Critical value",
null,
"Standard error of the sample\n\nStandard error of the sample =",
null,
"=",
null,
"= 0.3667\n\nCritical value = Z",
null,
"/2\n\nAccording to the problem : 1-",
null,
"= 0.90",
null,
"",
null,
"=0.1",
null,
"",
null,
"/2 = 0.05",
null,
"Critical value = Z",
null,
"/2 = Z0.05 = 1.645\n\nThus;\n\nMargin of error = 1.645",
null,
"0.3667 = 0.6031667\n\n#### Earn Coins\n\nCoins can be redeemed for fabulous gifts."
] |
[
null,
"https://imgs.justaaa.com/questions/62366130-9160-11ed-bee9-53b149b1adaf.png",
null,
"https://imgs.justaaa.com/questions/62539360-9160-11ed-87cc-4f4d03b6d24d.png",
null,
"https://imgs.justaaa.com/questions/625e4ba0-9160-11ed-b42b-078367fda14c.png",
null,
"https://imgs.justaaa.com/questions/6283de20-9160-11ed-ae51-55b96ca4fb96.png",
null,
"https://imgs.justaaa.com/questions/6283de20-9160-11ed-ae51-55b96ca4fb96.png",
null,
"https://imgs.justaaa.com/questions/629b1290-9160-11ed-b2cd-773886515ac4.png",
null,
"https://imgs.justaaa.com/questions/6283de20-9160-11ed-ae51-55b96ca4fb96.png",
null,
"https://imgs.justaaa.com/questions/629b1290-9160-11ed-b2cd-773886515ac4.png",
null,
"https://imgs.justaaa.com/questions/6283de20-9160-11ed-ae51-55b96ca4fb96.png",
null,
"https://imgs.justaaa.com/questions/62c70490-9160-11ed-a86d-f54be47cb143.png",
null,
"https://imgs.justaaa.com/questions/6283de20-9160-11ed-ae51-55b96ca4fb96.png",
null,
"https://imgs.justaaa.com/questions/62366130-9160-11ed-bee9-53b149b1adaf.png",
null
] |
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|
https://topic.alibabacloud.com/a/what-is-the-way-to-change-the-first-subscript-of-an-array-and-use-dump--to-print-out-a-new-subscript-code-the-following_4_86_31038067.html
|
[
"# What is the way to change the first subscript of an array, and use Dump () to print out a new subscript. Code the following workaround\n\nSource: Internet\nAuthor: User\nWhat is the way to change the first subscript of an array, and use Dump () to print out a new subscript. The code is as follows\nPHP Code\n```\nArray ( 1 = = Array ( 0 = = Array ( ' created ' = = integer 1332383287 ' updated ' = = integer 1332385146 ' id ' = ' + String ' (length=2) ' level ' = = ' tag_id ' = ' 1 ' status ' = = integer 0 ' creator_uid ' = = integer 6 ' assign_uid ' = = integer 6 ' assign_history ' = = String ' |6| | 6|6| ' (length=8) ' Title ' = = String ' [iBay365] ' (length=10) ' context ' = = String ')) //requirement is \"1 = = Array (0=> , Array (...)) \" This 1 becomes php or Ajax text, and then once again with the dump ()//becomes the \"PHP = = Array (0=>array (...))\" Ask what method can do, I think for a long while really can't think out, manual also check//seemingly no such function, to you can help, thank you```\n\n------Solution--------------------\nBy deleting and merging, you probably don't have a function that directly implements this function.\n\nPHP Code\n```\\$key = ...; \\$arr = Array_merge (Array (\\$key = Array_shift (\\$arr)), \\$arr);------Solution--------------------For a bit.------Solution--------------------Re-construct an array.------Solution--------------------\n\nPHP Code\n\n\\$ar 1 = Array (1 = = Array (' 111 '), 6 = = Array (' 666 '), 2 = = Array (' 222 ')), \\$ar 2 = Array (' PHP ', ' AJAX ', ' MySQL '); \\$ar 2 = Array_combine (\\$ar 2, Array_values (\\$ar 1)), Echo '';p Rint_r (\\$ar 2);------Solution--------------------\n\nPHP Code\n\n[[email protected] csdn]\\$ php exchange.php Array ([PHP]/= Array ( = index 1) [ AJAX] = = Array ( = = Index 6) [MySQL] = Array ( = = Inde x 2)) [[email protected] csdn]\\$ cat exchange.php\nArray (\"Index 1\"), 6 = a Rray (\"index 6\"), 2 = AR Ray (\"Index 2\")), \\$arr 2 = Array ( ' PHP ' = = Array (), ' AJAX ' = = Array (), ' MySQL ' => ; Array ()); \\$arr 2 = Array_combine (Array_keys (\\$arr 2), Array_values (\\$arr 1));p Rint_r (\\$arr 2);? > \n\n```\nRelated Keywords:\nRelated Article\n\nThe content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.\n\nIf you find any instances of plagiarism from the community, please send an email to: [email protected] and provide relevant evidence. A staff member will contact you within 5 working days.\n\n## A Free Trial That Lets You Build Big!\n\nStart building with 50+ products and up to 12 months usage for Elastic Compute Service\n\n• #### Sales Support\n\n1 on 1 presale consultation\n\n• #### After-Sales Support\n\n24/7 Technical Support 6 Free Tickets per Quarter Faster Response\n\n• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs."
] |
[
null
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{"ft_lang_label":"__label__en","ft_lang_prob":0.587345,"math_prob":0.8631759,"size":1897,"snap":"2023-40-2023-50","text_gpt3_token_len":570,"char_repetition_ratio":0.21236134,"word_repetition_ratio":0.032520324,"special_character_ratio":0.4717976,"punctuation_ratio":0.13202247,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95494944,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-01T18:58:44Z\",\"WARC-Record-ID\":\"<urn:uuid:f0514cdb-96c5-47f9-92ef-2e39c33690da>\",\"Content-Length\":\"79917\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5f2476d3-520c-473a-b4d2-2697cfb10bfc>\",\"WARC-Concurrent-To\":\"<urn:uuid:4df3f5ce-2bed-4883-92c0-d537cb988d6b>\",\"WARC-IP-Address\":\"47.88.128.4\",\"WARC-Target-URI\":\"https://topic.alibabacloud.com/a/what-is-the-way-to-change-the-first-subscript-of-an-array-and-use-dump--to-print-out-a-new-subscript-code-the-following_4_86_31038067.html\",\"WARC-Payload-Digest\":\"sha1:UAZMAL5AQV5KQWEOFLT47EAELVBM4ZWO\",\"WARC-Block-Digest\":\"sha1:BBLP2FHBGTLSJ2FUDALG5LHW2DJ2LFJM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100304.52_warc_CC-MAIN-20231201183432-20231201213432-00065.warc.gz\"}"}
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https://www.geeksforgeeks.org/gate-gate-cs-2015-set-1-question-12/
|
[
"# GATE | GATE-CS-2015 (Set 1) | Question 12\n\nWhich one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n(≥ 2) numbers? In the recurrence equations given in the options below, c is a constant.\n\n(A) T(n) = 2T (n/2) + cn\n(B) T(n) = T(n – 1) + T(0) + cn\n(C) T(n) = 2T (n – 2) + cn\n(D) T(n) = T(n/2) + cn\n\nExplanation: In worst case, the chosen pivot is always placed at a corner position and recursive call is made for following.\n\na) for subarray on left of pivot which is of size n-1 in worst case.\nb) for subarray on right of pivot which is of size 0 in worst case.\n\nQuiz of this Question\n\nMy Personal Notes arrow_drop_up\nArticle Tags :\n\nBe the First to upvote.\n\nPlease write to us at [email protected] to report any issue with the above content."
] |
[
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https://www.stata.com/statalist/archive/2011-05/msg00374.html
|
[
"",
null,
"Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.\n\n# Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design\n\n From \"Joseph Coveney\" To Subject Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design Date Sun, 8 May 2011 17:20:14 +0900\n\n```David Airey wrote:\n\nMath is helpful! I think I remember reading the mixed model routine in JMP 9\nallows negative estimates of variance components. I don't quite understand the\nchoice between SAS and StataCorp statisticians on this point.\n\n--------------------------------------------------------------------------------\n\nI get the impression that the NOBOUND option of PROC MIXED is used more often\nthan not for diagnostic purposes for a nonpositive-definite G matrix, so it\nmight not be so much a difference between statisticians.\n\nJoseph Coveney\n\nMath would be even more helpful if I could do it:\n\n> MS_e = 0.00273899 = sigma2_e\n> MS_s#a = 0.012825848 = sigma2_e + 2 * sigma2_s#a\n> MS_s#b = 0.014614037 = sigma2_e + 3 * sigma2_s#b\n> MS_s = 0.02026831 = sigma2_e + 6 * sigma2_s + 2 * sigma2_s#a + 3 * sigma2_s#b\n>\n> sigma2_s#a = (0.012825848 - 0.00273899) / 2 = 0.00504343\n> sigma2_s#b = (0.014614037 - 0.00273899) / 3 = 0.00395835\n> sigma2_s = (0.02026831 - 0.01008686 - 0.01187505) / 6 = -0.00028227\n\nsigma2_s = (0.02026831 - 0.00273899 - 0.01008686 - 0.01187505) / 6 = -0.00073876\n\n*\n* For searches and help try:\n* http://www.stata.com/help.cgi?search\n* http://www.stata.com/support/statalist/faq\n* http://www.ats.ucla.edu/stat/stata/\n```"
] |
[
null,
"https://s7.addthis.com/static/btn/lg-share-en.gif",
null
] |
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http://21.resistance-mining.org/logic-diagram-of-2-to-4-line-decoder.html
|
[
"Logic Diagram Of 2 To 4 Line Decoder\n\n60-265 Winter 2009 Question 2. Multiplexers and Demultiplexers [ 3 marks ]\n\nLogic Diagram Of 2 To 4 Line Decoder - 1 to 2 Demux Reality Desk. The circuit reveals the 1 to 2 demultiplexer schematic. 1 to 2 Demux 3 Line to 8 Line Decoder . This decoder circuit offers 8 logic outputs for 3 inputs and has a enable pin.. Fig.4 Functional diagram. Fig.5 Logic diagram (one decoder/demultiplexer). September 1993 5 Philips Semiconductors Product specification Dual 2-to-4 line decoder/demultiplexer 74HC/HCT139 AC WAVEFORMS PACKAGE OUTLINES See “74HC/HCT/HCU/HCMOS Logic Package Outlines”.. n to 2 n Decoder. The logic diagram of a 2-to-4 decoder is shown. The two data inputs are decoded into 4 outputs , each output representing one of the combinations of the two binary input variables .Where required the inputs are inverted and each of the AND gates generates one.\n\nDual 2-to-4 Decoder/ Demultiplexer Figure 3. Expanded Logic Diagram (1/2 of Device) INPUT Figure 4. Input Equivalent Circuit 4 Figure 5. IEC Logic Diagram Y0a Y1a Y2a Y3a Y0b Y1b Y2b Y3b 5 6 7 12 11 10 MC74VHCT139A - Dual 2-to-4 Decoder/Demultiplexer. In a similar fashion a 3-to-8 line decoder can be made from a 1-to-2 line decoder and a 2-to-4 line decoder, and a 4-to-16 line decoder can be made from two 2-to-4 line decoders. You might also consider making a 2-to-4 decoder ladder from 1-to-2 decoder ladders.. DM74LS154 4-Line to 16-Line Decoder/Demultiplexer DM74LS154 4-Line to 16-Line Decoder/Demultiplexer General Description Connection Diagram Logic Diagram Order Number Package Number Package Description DM74LS154WM M24B 24-Lead Small Outline Integrated Circuit (SOIC), JEDEC MS-013, 0.300 Wide.\n\nAug 04, 2015 · Understand the operating principles of decoder circuits. 6.2 Background Draw the logic diagram and truth table of a 2 by 4 decoder circuit. • Use the data sheet of the Design a 4-line to 16-line decoder using two ICs 138. (show schematic. decoder with just four '138' ICs and one inverter. Ideal for memory chip select decoding 4. Functional diagram.. LOGIC DIAGRAM This logic diagram has not be used to estimate propagation delays PIN No SYMBOL NAME AND FUNCTION 1, 2, 3 A, B, C Address Inputs 4, 5 G2A, G2B Enable Inputs 6 G1 Enable Input 3 TO 8 LINE DECODER (INVERTING). Jul 08, 2015 · to-seven segment-display decoder is ~hown in Figure\" 9-3. 9.2.2 BCD-A logic diagram for this type of encoder is shown in Figure 9-4. 9. 8 j 4..\n\nThe following is a list of 7400-series digital logic integrated circuits. 2 dual 2-line to 4-line decoder/demultiplexer, inverting outputs three-state 16 74LS255: 74x256 2 dual 4-bit addressable latch 16 MC74F256: 74x257 4 quad 2-line to 1-line data selector/multiplexer, non-inverting outputs. 2 FUNCTIONAL BUILDING BLOCKS I 1. Functional building blocks,an overview 2. Encoders, decoders, code converters 3. Code conversion (combinational) networks . 2012.11.27. 2 2-to-4 line decoder, gate level logic diagram 16 3-TO-8 DECODER s a. Tutorial 5: Decoders in VHDL. Created on: 31 December 2012 Two to Four Decoder. The block diagram of the two to four decoder is shown here. 2 to 4 Decoder. The source code for the 2 to 4 decoder can be downloaded here. The UCF and JED files are.\n\nThis page of VHDL source code section covers 2 to 4 Decoder VHDL Code. The block diagram and truth table of 2 to 4 Decoder VHDL Code is also mentioned. The block diagram and truth table of 2 to 4 Decoder VHDL Code is also mentioned.. Binary Encoder. Binary encoder has 2n input lines and n-bit output lines. It can be 4-to-2, 8-to-3 and 16-to-4 line configurations. VHDL Code for 4 to 2 encoder can be designed both in structural and behavioral modelling..\n\n74 series digital circuit of 74LS139 and 74S139 2-4 line decoder ... 74 series digital circuit of 74LS139 and 74S139 2-4 line decoder/multi-\nLogic Circuitry Part 1 (PIC Microcontroller) The 74LS138 and '139 MSI natural decoders.\nDecoder/Encoder Implementation | Anode | Electrical Engineering\nIAY0340-Digital Systems Modeling and Synthesis Shift Register Figure 1. A 2 to 4 decoder ...\nUnderstanding decoders and comparators - Electrical Engineering ... ... decoders 2/4 and required logic gates: enter image description here"
] |
[
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https://www.nelson.com/mathfocus/grade3/quizzes/ch03/ch03_9.htm
|
[
"Name: Lesson 9 - Estimating Sums and Differences\n\n1.\n\nWhat ten is close to 57?\n a. 60 b. 50 c. 55\n\n2.\n\nWhat ten is close to 32?\n a. 50 b. 40 c. 30\n\n3.\n\nWhat ten is close to 86?\n a. 90 b. 100 c. 80\n\n4.\n\nWhat ten is close to 65?\n a. 60 b. 70 c. 50\n\n5.\n\nUse tens to find a number that is close to the sum 36 + 41.\n a. 30 + 40 = 70 b. 40 + 40 = 80 c. 40 + 50 = 90\n\n6.\n\nUse tens to find a number that is close to the sum 53 + 24.\n a. 50 + 20 = 70 b. 50 + 30 = 80 c. 60 + 30 = 90\n\n7.\n\nUse tens to find a number that is close to the sum 78 + 38.\n a. 70 + 40 = 110 b. 80 + 30 = 110 c. 80 + 40 = 120\n\n8.\n\nUse tens to find a number that is close to the difference 52 - 17.\n a. 50 - 10 = 40 b. 50 - 20 = 30 c. 60 - 20 = 40\n\n9.\n\nUse tens to find a number that is close to the difference 71 - 44.\n a. 70 - 40 = 30 b. 70 - 50 = 20 c. 80 - 40 = 40\n\n10.\n\nUse tens to find a number that is close to the difference 97 - 56.\n a. 90 - 60 = 30 b. 100 - 60 = 40 c. 100 - 50 = 50"
] |
[
null
] |
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|
https://byjus.com/intensity-formula/
|
[
"",
null,
"# Intensity Formula\n\n## What is Intensity\n\nIntensity is the quantity of energy the wave conveys per unit time across a surface of unit area, and it is also equivalent to the energy density multiplied by the wave speed. It is generally measured with units of watts per square meter. Intensity will depend on the strength and amplitude of a wave. Intensity is represented as I. The formula for intensity is articulated by,\n\nWhere I is the intensity, P is the power, and A is the area of cross-section.\n\n### Solved Examples\n\nLet us discuss the questions related to intensity.\n\nProblem 1: Calculate the intensity of a wave whose power is 25 KW and the area of cross-section is 35×106m2?\n\nKnown measures are,\nP = 25 KW = 25×10W, A =35×106m2\nIntensity formula is,\n\nI=25×10/35×106\n\n=7.14×10-2W/m2\n\nProblem 2: Calculate the power of a wave whose intensity and area of the cross-section are 30×10-5W/m2 and 50m2 respectively?\n\nKnown quantities are,\nI = 30×10-5W/m2 and A = 50m2\nIntensity formula is,\n\nP= I x A\n\nP = 30 x 10-5 x 50\n\nP= 0.015W\n\nStay tuned with BYJU’S for more such interesting articles."
] |
[
null,
"https://www.facebook.com/tr",
null
] |
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|
https://codereview.stackexchange.com/questions/144814/vba-lookup-to-complete-matrix/144846
|
[
"VBA lookup to complete matrix\n\nI have written the following the code to complete a matrix based on data provided in a second worksheet, but the code is really slow (note that s1=12,000, s2=40 and s3 = 200,000). Any suggestions on how to make this code faster?\n\nSub UpdateMatrix()\n\nDim wsOverview As Worksheet, wsData As Worksheet\nDim rngTable As Range\nDim varAccount As Variant, varData As Variant\nDim i As Long, t As Long\n\nSet wsOverview = ThisWorkbook.Worksheets(1)\nSet wsData = ThisWorkbook.Worksheets(2)\n\nSet rngTable = wsOverview.Range(\"A:A\")\ni = Application.WorksheetFunction.CountA(rngTable) + 1\n\nSet rngTable = wsData.Range(\"A:A\")\nt = Application.WorksheetFunction.CountA(rngTable)\n\nFor s1 = 2 To i\nvarAccount = wsOverview.Range(\"A\" & s1).Value\n\nFor s2 = 1 To 37\nvarData = wsOverview.Range(\"A1\").Offset(0, s2).Value\n\nFor s3 = 2 To t\n\nIf varAccount = wsData.Range(\"B\" & s3).Value And varData = wsData.Range(\"A\" & s3).Value Then\n\nwsOverview.Range(\"A\" & s1).Offset(0, s2).Value = wsData.Range(\"F\" & s3).Value\n\nExit For\n\nEnd If\n\nNext s3\n\nNext s2\n\nNext s1\n\nEnd Sub\n• What do you mean s1=12000, s2=40, s3=200000 - are those the actual loop iterations rather than 3, 37, t? – Raystafarian Oct 20 '16 at 20:02\n• You have nearly half a million lookups(40 x 12,000). Each looking down a dataset of 200k rows. I suggest you use binary lookups on the wsData. If the ranges cannot be sorted in the worksheet(because maybe they need to remain in default order, then you can make a copy of the original unsorted dataRange and write back afterwards. You can also use arrays and a binary array_lookup function, or the standard vlookup worksheetfunction with parameter set to true. – MacroMarc Oct 20 '16 at 21:50\n• You already have 2 good reviews with great advice, but I want to personally attest that internalizing the matrix as an array and binary search will both make huge differences for your performance. I had a very reasonably performant disassembler in open office that started with a trace log of comparible size and added go-to and branch-not-taken disassembly, and it would hang forever if I tried to go row by row and in some cases use the sheet object at every data access. You are at the scale where both will make a huge improvement. – sqykly Oct 21 '16 at 2:34\n• @sqykly is correct, simply pulling the information into an array rather than working on the sheet will make an incredible difference, even without any other changes. – Raystafarian Oct 22 '16 at 12:09\n• Thanks for all of your help guys. I will look into feeding the data into arrays. – VBA Pete Oct 25 '16 at 15:22\n\nI'm seeing several good practices in your code, you have a solid foundation to build upon. There are a few things to point out, but to answer your basic performance question -- process all your data in memory arrays. You'll see a tremendous performance improvement.\n\nSeveral comments then, illustrated in the example code below:\n\n1. Good declarations for your separate Worksheet variables; they are nicely descriptive.\n2. Single-letter variables are not very descriptive (though a common practice is to restrict use of single-letter variables as loop indexes). So my suggestion is to rename these to ovRows and dataRows. These hold the number of rows detected on each sheet, so the variable name should echo that usage.\n3. Use constants declared for fixed values. From what I can tell in your code, you have a limit to the number of columns on both sheets. Assuming this is a hard-coded value, declaring these as Const makes it easier to understand (and to change later if necessary).\n4. Pull the overview and data ranges into local (memory-based) arrays for processing. This is the setup for the real speed.\n5. Modify the loop to use the memory arrays. The example below is all-array, all the time. (If I've correctly understood your rows/columns logic.)\n6. When the processing is completed, \"write\" the updated data back to the worksheet.\n\nThanks to @MacroMarc, I've updated the errors in my code (which was all done off the top of my head).\n\nOption Explicit\n\nSub UpdateMatrix()\nDim wsOverview As Worksheet, wsData As Worksheet\nDim rngTable As Range\n\nSet wsOverview = ThisWorkbook.Worksheets(\"Sheet1\")\nSet wsData = ThisWorkbook.Worksheets(\"Sheet2\")\n\nDim ovRows As Long\nSet rngTable = wsOverview.Range(\"A:A\")\novRows = Application.WorksheetFunction.CountA(rngTable) + 1\n\nDim dataRows As Long\nSet rngTable = wsData.Range(\"A:A\")\ndataRows = Application.WorksheetFunction.CountA(rngTable)\n\n'--- set up memory based arrays\nDim overviewRange as Range\nDim overview As Variant\nConst OV_COL_LIMIT = 37\nset overviewRange = wsOverview.Range(\"A1\").Resize(ovRows, COL_LIMIT)\noverview = overviewRange\n\nDim dataRange As Range\nDim data As Variant\nConst DATA_COL_LIMIT = 6\nset dataRange = wsData.Range(\"A1\").Resize(dataRows, DATA_COL_LIMIT)\ndata = dataRange\n\nDim varAccount As Variant, varData As Variant\nDim dataAcct As Variant, dataData As Variant\nFor s1 = 2 To 3\nvarAccount = overview(s1, 1)\nFor s2 = 1 To COL_LIMIT\nvarData = overview(1, s2)\nFor s3 = 2 To dataRows\ndataAcct = data(s3, 2)\ndataData = data(s3, 1)\nIf (varAccount = datraacct) And (varData = dataData) Then\noverview(s1, 1) = data(s3, 6)\nExit For\nEnd If\nNext s3\nNext s2\nNext s1\n\n'--- put the data array back on the sheet\noverviewRange = overview\nEnd Sub\n• Thanks for your help PeterT. Your comments and code are much appriciated! I will review your code to get a grasp to get my array loops down. – VBA Pete Oct 25 '16 at 15:27\n\nYou have nearly half a million lookups(40 x 12,000). Each looking down a dataset of 200k rows. I suggest you use binary lookups on the wsData.\n\nIf the ranges cannot be sorted in the worksheet(because maybe they need to remain in default order, then you can make a copy of the original unsorted dataRange and write back afterwards.\n\n.....\nt = Application.WorksheetFunction.CountA(rngTable)\nDim dataRange As Range\nSet dataRange = wsData.Range(\"A1:F\" & t) 'whatever the entire dataset is\n'Dim originalData as variant\n'originalData = dataRange.value\ndataRange.Sort Key1:=wsData.Range(\"B2\"), Order1:=xlAscending, Key2:=wsData.Range(\"A2\"), Order2:=xlAscending, _\nHeader:=xlYes 'sort the data so that binary Lookup can take place\nDim dataArr As Variant\ndataArr = dataRange.Value\n\nDim overviewRange As Range\nSet overviewRange = wsOverview.Range(\"A2:AN\" & i) 'whatever the width and length of that range\nDim overviewArr As Variant\noverviewArr = overviewRange.Value\n\nDim headers As Variant\nheaders = wsOverview.Range(\"B1:AN1\").Value 'whatever the width of the headers that are gonna be varData assignments\n\nDim accountSpot As Long\nDim varData As Variant\nDim varAccount As Variant\ndim stepper as long\nFor s1 = LBound(overviewArr) To UBound(overviewArr)\nvarAccount = overviewArr(s1, 1)\naccountSpot = wsArrayBinaryLookup(varAccount, dataArr, 2, 1, True, True) 'get the first match of varAccount which we save for this iteration for efficiency\n'handle #NA errors\nvarData = headers(1, s2)\nstepper = accountSpot 'for each varData we can search from the first match of varAccount in the sorted dataArray\nDo While stepper <= UBound(dataArr) And dataArr(stepper, 2) = varAccount\nIf dataArr(stepper, 1) = varData Then\noverviewArr(s1, s2 + 1) = dataArr(stepper, 6)\nExit Do\nEnd If\nstepper = stepper + 1\nLoop\nNext s2\nNext s1\noverviewRange = overviewArr\n'dataRange = originalData\nend sub\n\nThe wsArrayBinaryLookup functions:\n\nPublic Function wsArrayBinaryLookup(ByVal val As Variant, arr() As Variant, ByVal searchCol As Long, ByVal returnCol As Long, Optional match As Boolean = True, Optional exactMatch As Boolean = True) As Variant\n\nDim a As Long, z As Long, curr As Long\n\nwsArrayBinaryLookup = CVErr(xlErrNA)\na = LBound(arr)\nz = UBound(arr)\n\nIf compare(arr(a, searchCol), val) = 1 Then\nExit Function\nEnd If\n\nIf compare(arr(a, searchCol), val) = 0 Then\nwsArrayBinaryLookup = IIf(match, a, arr(a, returnCol))\nExit Function\nEnd If\n\nIf compare(arr(z, searchCol), val) = -1 Then\nExit Function\nEnd If\n\nWhile z - a > 1\ncurr = Round((CLng(a) + CLng(z)) / 2, 0)\nIf compare(arr(curr, searchCol), val) = 0 Then\nz = curr\nwsArrayBinaryLookup = IIf(match, curr, arr(curr, returnCol))\nEnd If\n\nIf compare(arr(curr, searchCol), val) = -1 Then\na = curr\nElse\nz = curr\nEnd If\nWend\n\nIf compare(arr(z, searchCol), val) = 0 Then\nwsArrayBinaryLookup = IIf(match, z, arr(z, returnCol))\nElse\nIf Not exactMatch Then\nwsArrayBinaryLookup = IIf(match, a, arr(a, returnCol))\nEnd If\nEnd If\n\nEnd Function\n\nPublic Function compare(ByVal x As Variant, ByVal y As Variant) As Long\n\nIf IsNumeric(x) And IsNumeric(y) Then\nSelect Case x - y\nCase Is = 0\ncompare = 0\nCase Is > 0\ncompare = 1\nCase Is < 0\ncompare = -1\nEnd Select\nElse\nIf TypeName(x) = \"String\" And TypeName(y) = \"String\" Then\ncompare = StrComp(x, y, vbBinaryCompare) 'may wish to change this to vbTextCompare\nEnd If\nEnd If\n\nEnd Function\n• Thanks for the comment MacroMarc. Your answer works great, but I am struggling to follow what the code is doing. I guess, I am still to much of a VBA rookie :) – VBA Pete Oct 25 '16 at 15:29"
] |
[
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https://similargeeks.com/code/c/print-multiplication-table-from-1-to-n/
|
[
"Home » Print Multiplication Table from 1 to N in C\n\n# Print Multiplication Table from 1 to N in C\n\nLearn about Print Multiplication Table from 1 to N in the below code example. Also refer the comments in the code snippet to get a detailed view about what’s actually happening.\n\nContents\n\n#### Print Multiplication Table from 1 to N\n\nThe below program prints the multiplication table from 1 to given number. The number is taken from the user input and for loop is used to print the multiplication tables.\n\nSource code:\n\n``````#include<stdio.h>\nint main()\n{\nint n, t, i;\n\nprintf(\"Enter number of tables: \");\nscanf(\"%d\",&n);\n\nfor(i=1; i<=10; i++)\n{\nfor(t=1; t<=n; t++)\nprintf(\"%d*%d=%d\\t\",t,i,t*i);\nprintf(\"\\n\");\n}\n\nreturn 0;\n}``````\n\nOutput:\n\n```Enter number of tables: 2\n1*1=1\t2*1=2\n1*2=2\t2*2=4\n1*3=3\t2*3=6\n1*4=4\t2*4=8\n1*5=5\t2*5=10\n1*6=6\t2*6=12\n1*7=7\t2*7=14\n1*8=8\t2*8=16\n1*9=9\t2*9=18\n1*10=10\t2*10=20```\n\nHope above code works for you and Refer the below Related Codes to gain more insights. Happy coding and come back again."
] |
[
null
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|
https://www.zora.uzh.ch/id/eprint/21896/
|
[
"",
null,
"# A posteriori error estimation for the Dirichlet problem with account of the error in the approximation of boundary conditions\n\nRepin, S; Sauter, S; Smolianski, A (2003). A posteriori error estimation for the Dirichlet problem with account of the error in the approximation of boundary conditions. Computing, 70(3):205-233.\n\n## Abstract\n\nThe present work is devoted to the a posteriori error estimation for 2nd order elliptic problems with Dirichlet boundary conditions. Using the duality technique we derive the reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H1, independently of the discretization method chosen. In particular, our error estimator can be applied also to problems and discretizations where the Galerkin orthogonality is not available. We will present different strategies for the evaluation of the error estimator. Only one constant appears in its definition which is the one from Friedrichs' inequality; that constant depends solely on the domain geometry, and the estimator is quite non-sensitive to the error in the constant evaluation. Finally, we show how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.\n\n## Abstract\n\nThe present work is devoted to the a posteriori error estimation for 2nd order elliptic problems with Dirichlet boundary conditions. Using the duality technique we derive the reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H1, independently of the discretization method chosen. In particular, our error estimator can be applied also to problems and discretizations where the Galerkin orthogonality is not available. We will present different strategies for the evaluation of the error estimator. Only one constant appears in its definition which is the one from Friedrichs' inequality; that constant depends solely on the domain geometry, and the estimator is quite non-sensitive to the error in the constant evaluation. Finally, we show how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.\n\n## Statistics\n\n### Citations\n\nDimensions.ai Metrics\n37 citations in Web of Science®\n37 citations in Scopus®\n\n### Altmetrics\n\nDetailed statistics\n\n##",
null,
"",
null,
"",
null,
""
] |
[
null,
"https://www.zora.uzh.ch/images/uzh_logo_en.jpg",
null,
"https://www.zora.uzh.ch/images/oa_lock_green.png",
null,
"https://www.zora.uzh.ch/21896/1.hassmallThumbnailVersion/03-02.pdf",
null,
"https://www.zora.uzh.ch/21896/1.haspreviewThumbnailVersion/03-02.pdf",
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] |
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|
https://discourse.julialang.org/t/frustrated-using-dataframes/67833?page=3
|
[
"# Frustrated using DataFrames\n\nThat is pretty clean to read and reason through. I will have to get used to `df` just floating there in the middle and the interpolated variables, but that’s not unique to `DataFramesMeta.jl`. I’m still afraid of BenchmarkTools.jl too.\n\n2 Likes\n\nDoes `@subset!` from `DataFramesMeta` essentially replace `filter!` from `DataFrames`? Why do the names differ?\n\nThe names differ for a few reasons\n\n1. `subset` acts on full columns, while the operations on `filter` act on rows. We can’t make `filter` act on columns because a DataFrame is conceptualized as a collection of rows, where possible. The contract of `Base.filter` is that the operation `f` in `filter(f, x)` will act on elements of `x`.\n2. Similarly, we want operations on a `GroupedDataFrame` to be split-apply-combine style transformations. Since a `GroupedDataFrame` iterates through sub-dataframes, to keep a contract with `Base.filter`, we would need `filter` to return only some groups.\n\nTherefore we need a different function with it’s own name. This gives us the flexibility to have consistent sub-setting behavior with `transform` and `select`.\n\n@Nathan_Boyer: note that in DataFrames.jl we have both `filter!` and `subset!`. In general it would be great if you put your concerns in an issue in DataFrames.jl and I will think how to handle them (probably via docs updates).\n\n2 Likes\n\nNot really,\n\n``````df = DataFrame(Time = [3., 4., 5.], TopTemp = [70., 73., 100.], BottomTemp = [50., 55., 80.])\ndf[!, :id] = 1:nrow(df)\nsdf = stack(df)\n\nusdf = @sqldf \"\"\"\nselect variable,\n(case when variable like '%Temp' then (value-32)/1.8 else value end) as value,\nid\nfrom sdf\n\"\"\"\n\nunstack(usdf)\n\n3×4 DataFrame\nRow │ id Time TopTemp BottomTemp\n│ Int64 Float64? Float64? Float64?\n─────┼───────────────────────────────────────\n1 │ 1 3.0 21.1111 10.0\n2 │ 2 4.0 22.7778 12.7778\n3 │ 3 5.0 37.7778 26.6667\n\n``````\n\nHowever, in general I would say we should not expect DataFrames.jl or any equivalent package to offer direct solutions to all possible transformations we need.\n\nIn my case I follow these guidelines when it comes to transformations:\n\n1. Simple → DataFrames.jl\n2. Complex but SQL simple → DataFrames.jl with SQLdf.jl\n3. Complex and Beyond SQL simple → Julia Code\n1 Like\n\nI want to push back on this.\n\nThey key feature of DataFrames is that all of it’s columns are just plain old normal Julia vectors. Everything you can do with Julia vectors you can do in DataFrames. The `source => fun => dest` syntax (or alternatively, DataFramesMeta.jl) provides type-stable, performant ways to work with these columns.\n\nBut there is no different in performance between working with DataFrames and plain Julia vectors. Additionally, as long as transformations go in a function, you can define as complicated a function you want `fun` without ever thinking about DataFrames.jl, and then use it with `source => fun => dest` syntax.\n\nThis is not necessarily true when working with `dplyr` or Pandas.\n\nAdditionally, the macro `@with` in DataFrames.jl creates an anonymous function which acts on the DataFrames columns and executes it.\n\nConsider the following\n\n``````@with df begin\nz = :x + :y\nt = mean(z) * 100\nend\n``````\n\nThough `@with` acts on a `DataFrame`, the actual code it produces and executes has nothing to do with any implementation of DataFrames.jl.\n\n3 Likes\n\nI will work on that.\n\nIn general:\n\n1. Docs are hard to read for those whose data does not benefit from split-apply-combine. (My elements are all unique, so there is nothing to split or groupby.)\n2. I have trouble figuring out what is and isn’t needed/allowed inside the function syntax: `ByRow()` , `eachcol()` , `names()` , `Cols()` , `:` , `.=>` , `.()` , `...` etc.\n3. General confusion about whether a function operates on a row, column, elements of a row, or elements of a column.\n4. There is no way to test if an argument is valid or test individual pieces of an argument. I would like to be able to print, check type, save to variable, etc. the input and output from each of x => y => z; maybe even deeper if y becomes complicated with nesting.\n``````julia> filter!(names(df, Not(:node)) .=> ByRow(row -> any(x -> x>0, row)), df)\nERROR: MethodError: no method matching !(::Vector{Pair{String, ByRow{var\"#204#206\"}}})\n\njulia> transform!(df, r\"Temp\" .=> ByRow.(fahrenheit_to_celsius), renamecols = false)\nERROR: LoadError: MethodError: no method matching fahrenheit_to_celsius(::Int64, ::Int64)\n``````\n``````julia> filter(x -> ismissing(eachcol(x)), df)\nERROR: MethodError: no method matching eachcol(::DataFrameRow{DataFrame,DataFrames.Index})\n\njulia> filter(x -> ismissing.(x), df)\nERROR: ArgumentError: broadcasting over `DataFrameRow`s is reserved\n``````\n\nNote:\nI would like to emphasize again that my initial assumption was either:\n\n• DataFrames is built for a different type of data processing and I should be using something else.\n\n1 Like\n\nOh, I myself I think I would use Julia code in this case, I was just showing an example with no loops. However, when it comes to transformations performance is not always relevant but rather accuracy and simplicity.\n\nI do think a lot of the problems could be solved by changing the way you reason about these calls. More emphasis should be placed on creating a valid `source => fun => dest` object.\n\n`source` is a collection of names, i.e. `String`s or `Symbol`s\n\n`fun`, is just a function. `ByRow(fun)` is a wrapper function, i.e. `f` is a function and `ByRow(f)` is a function. Since a function is not iterable, `ByRow.(f)` makes no sense.\n\n`dest` is most commonly a single column name, like a `String` or `Symbol`. But can also be a collection of `String`s or `Symbol`s.\n\n### `.=>`:\n\nSimilarly, `r\"Temp\"` is a regular expression. Because regular expressions are not iterable, `r\"Temp\" .=>` doesn’t make sense.\n\nSince functions are not iterable, we know we have the following behavior\n\n``````julia> foo(x) = x;\n\njulia> [:a, :b] .=> foo\n2-element Vector{Pair{Symbol, typeof(foo)}}:\n:a => foo\n:b => foo\n``````\n\nthe `fun` will get repeated.\n\nThis is all super complicated and requires a lot of pretty detailed knowledge of Julia’s broadcasting rules. In no way is this meant to answer your specific questions or invalidate your frustrations, which definitely make sense.\n\nI mean only to show that a validation function (which Bogumil has already filed an issue for) might go a long way. If I were to give advice about this, I would say you should put more effort into understanding the way common Julia idioms, like broadcasting and regular expressions, are used in the construction of the `source => fun => dest` pairs.\n\n3 Likes\n\nThis is a good point. DataFrames.jl could benefit from looking at dplyr’s functions for this: Apply a function (or functions) across multiple columns — across • dplyr\n\n3 Likes\n\nDoes `Not(:node)` create an iterable vector? That is another element I wish I could have inspected for type, but it only makes sense in the context of the DataFrame call.\n\nNo, `Not(:node)` does not create an iterable vector. And neither do `Between` or `Cols` at the moment. Or, it was just fixed on `master` and I don’t know when the next release will be. For now use `names(df, Not(:node))`.\n\nThis is definitely frustrating. I’m glad the JuliaData maintainers have fixed it though. It will make it so people don’t experience that frustration in the future.\n\nIn general, I would say, make the pair first, especially if it’s complicated, and then inspect the result with `print`. DataFrames is not doing any special evaluation, so if the pair you constructed looks bad, it probably won’t work.\n\nThe following is a complicated pair, but you can see pretty clearly that it’s doing what you want.\n\n``````julia> p1 = [:a, :b] .=> f .=> [:z1, :z2]\n2-element Vector{Pair{Symbol, Pair{typeof(f), Symbol}}}:\n:a => (f => :z1)\n:b => (f => :z2)\n``````\n1 Like\n\nAlthough there are lots of great macros and other tricks, sometimes it’s easy to just handle stuff using regular iteration and higher order functions like map, filter. Also remember you can create a column by assigning to it\n\n``````df.hasmissing = map(x->any(ismissing,x),eachrow(df))\n``````\n\nConvert temperatures:\n\n``````df.tempC = map(ftoc, df.tempF)\n``````\n\nFilter out rows that are all zero:\n\n``````filter(x -> all(==(0),x),foo)\n``````\n4 Likes\n\nI equally find DataFrames frustrating at times, especially coming from R / tidyverse. Take the second example you gave. In R this would be one very readable line of code:\n\n``````mutate(df, across(contains(\"Temp\"), ~ (.x - 32)*(5/9)))\n``````\n\nNo need to worry about calling the `names` function, regular expressions, creating a separate `fahrenheit_to_celsius` function, or giving a rename option.\n\n3 Likes\n\nYes it’s readable because it’s not a lot of code, but my questions would be what does `contains(\"Temp\")` return, is that composable or is it a nonstandard evaluation kind of thing, also what does `~` do in this context and what’s `.x`. Just pointing out that this is a DSL that’s also not understandable with just R knowledge.\n\n5 Likes\n\nWhat @jules says above together with\n\nare key to me: DataFrames has built an infinitely composable mini-language based on standard Julia syntax. Admittedly, because it is so powerful and composable, it requires good knowledge of how Julia works and a good mental model of what is happening in the mini-language, but it does not require learning a new language/DSL.\n\n3 Likes\n\nI agree R syntax is usually problematic, but in this case I think it wins. What does it matter what the `contains` function returns? All I need to know is that it selects columns that contain a string I provide (you could also swap in the `endswith` function in this case). As for the ~ and .x they are useful but kind of ugly shorthand for an anonymous function. I prefer Julia’s `x -> f(x)` syntax but you could just as easily provide a named function instead.",
null,
"I would argue that this DSL is more intuitive as I read the code: “mutate this data frame across columns that contain “Temp” with this provided function”.\n\n2 Likes\n\n``````julia> node = rand(Int8, 10000); x = rand(Int8, 10000); y = rand(Int8,10000);\njulia> sa = StructArray(node = node, x = x, y = y)\njulia> df = DataFrame(node = node, x = x, y = y)\n\njulia> @benchmark \\$sa[(\\$sa.x .== 0) .| (\\$sa.y .== 0),:]\nBenchmarkTools.Trial: 10000 samples with 8 evaluations.\nRange (min … max): 3.542 μs … 494.832 μs ┊ GC (min … max): 0.00% … 94.94%\nTime (median): 3.756 μs ┊ GC (median): 0.00%\nTime (mean ± σ): 4.266 μs ± 10.912 μs ┊ GC (mean ± σ): 7.69% ± 3.04%\n\n▄▇██▇▇▆▄▃▃▄▄▄▃▂▂▂▁▂▂▂▁▁▂▂▂▂▂▁▁▁▁▁ ▂\n▇██████████████████████████████████▇███▇▇▆▇▇▅▆▅▅▅▆▆▆▄▅▅▅▅▅▆ █\n3.54 μs Histogram: log(frequency) by time 5.82 μs <\n\nMemory estimate: 6.02 KiB, allocs estimate: 6.\n\njulia> @benchmark \\$df[(\\$df.x .== 0) .| (\\$df.y .== 0),:]\nBenchmarkTools.Trial: 10000 samples with 1 evaluation.\nRange (min … max): 11.897 μs … 3.326 ms ┊ GC (min … max): 0.00% … 99.04%\nTime (median): 12.627 μs ┊ GC (median): 0.00%\nTime (mean ± σ): 13.714 μs ± 33.332 μs ┊ GC (mean ± σ): 2.40% ± 0.99%\n\n▄▇██▇▆▅▃▂▂▂▁ ▁▃▅▅▅▄▄▃▂▁ ▁▂▂▂▂▂▁▁ ▃\n███████████████████████████████████▇███▇▇▇▆▇▆▆▄▁▄▅▅▆▆▅▄▄▃▃▅ █\n11.9 μs Histogram: log(frequency) by time 20.4 μs <\n\nMemory estimate: 7.92 KiB, allocs estimate: 25.\n\njulia> @benchmark @subset(\\$df, ((:x .== 0) .| (:y .== 0)))\nBenchmarkTools.Trial: 10000 samples with 1 evaluation.\nRange (min … max): 64.454 μs … 5.446 ms ┊ GC (min … max): 0.00% … 93.48%\nTime (median): 66.507 μs ┊ GC (median): 0.00%\nTime (mean ± σ): 69.103 μs ± 75.999 μs ┊ GC (mean ± σ): 1.48% ± 1.33%\n\n▁█▇▁\n▁▃████▅▃▃▃▃▃▂▂▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂\n64.5 μs Histogram: frequency by time 89.7 μs <\n\nMemory estimate: 21.28 KiB, allocs estimate: 170.\n``````\n\nIt looks like StructArrays is a clear winner at least for speed.\n\nIt’s certainly intuitive to read for a lot of people. Some people value a “from first principles” approach higher, where hopefully nothing works “magically” but everything can be derived from the simple building blocks of the language. That’s what base DataFrames does, but of course it trades off syntactic simplicity. I agree that the macro packages DataFramesMeta / DataFrameMacros might take another look at this `across` scenario, maybe there are improvements to be made there.\n\n3 Likes\n\nAs others have said, it’s a bit of a special case that applying a function to multiple columns is currently not covered by the macro packages.\n\nBut I still think DataFrames.jl wins here because you don’t need to learn all this fancy stuff (whether `ByRow` and `=>` and `cpycols` in Julia, or `accross`, `contains`, `~` and `.x` for R) to get the job done. You can just write:\n\n``````df[:, r\"Temp\"] = (df[:, r\"Temp\"] .- 32) .* (5/9)\n``````\n\nSprinkle in some `!` and `.` for performance, but that’s not necessary.\n\n(To be honest there is one non obvious trick to know if the original columns where `Int`: you cannot put `Float64` values in tem so you need to write `df[!, r\"Temp\"] = ...` to replace the columns with the right hand side, rather than overwrite them.)\n\n4 Likes"
] |
[
null,
"https://emoji.discourse-cdn.com/twitter/man_shrugging/2.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8079621,"math_prob":0.8933266,"size":12765,"snap":"2022-27-2022-33","text_gpt3_token_len":3660,"char_repetition_ratio":0.109004,"word_repetition_ratio":0.04353999,"special_character_ratio":0.26839012,"punctuation_ratio":0.17399618,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.951177,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-19T11:15:39Z\",\"WARC-Record-ID\":\"<urn:uuid:8895e2f4-cff4-4fb2-8ac5-c0224d965627>\",\"Content-Length\":\"79466\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:113acf41-b6c0-4d13-bfd9-86fa67332815>\",\"WARC-Concurrent-To\":\"<urn:uuid:917fb0f8-284f-4f67-98a9-73cd88d74c23>\",\"WARC-IP-Address\":\"64.71.144.205\",\"WARC-Target-URI\":\"https://discourse.julialang.org/t/frustrated-using-dataframes/67833?page=3\",\"WARC-Payload-Digest\":\"sha1:ZPH3KG4HJ2KUVNR7KHTFK4ZGZU3B6N6Q\",\"WARC-Block-Digest\":\"sha1:35XDM2GJ3EOJMRZFIRSGMQQ45UJIYLZG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573667.83_warc_CC-MAIN-20220819100644-20220819130644-00050.warc.gz\"}"}
|
https://devsolus.com/2023/05/22/models-relation-not-working-when-trying-to-get-the-children-models-in-laravel/
|
[
"# Models relation not working when trying to get the children models in Laravel\n\nI’m having a model `Question` that belongs to model `Exam`. `Exam` can have many questions (one-to-many relation). I’ve no problem with storing the data, but when I try to get the questions for the exam with `Exam::find(\\$exam->id)->questions;` I get `NULL`. I’ve `dd` the result for `Exam::find(\\$exam->id)` and the relations are empty: `#relations: []`.\n\nThis is how I’ve registered my `Question` model:\n\n``````namespace App\\Models;\n\nuse Illuminate\\Database\\Eloquent\\Model;\nuse Illuminate\\Database\\Eloquent\\Relations\\BelongsTo;\n\nclass Question extends Model\n{\n\npublic \\$timestamps = false;\nprotected \\$fillable = ['question', 'correct_answer', 'category_id', 'type'];\n\npublic function questionCategory():belongsTo {\nreturn \\$this->belongsTo(QuestionCategory::class);\n}\n\npublic function exam(): BelongsTo {\nreturn \\$this->belongsTo(Exam::class);\n}\n}\n``````\n\nAnd this is the `Exam` model:\n\n``````namespace App\\Models;\n\nuse Illuminate\\Database\\Eloquent\\Model;\nuse Illuminate\\Database\\Eloquent\\Relations\\HasMany;\n\nclass Exam extends Model\n{\npublic \\$timestamps = false;\nprotected \\$fillable = ['name'];\n\npublic function question(): HasMany\n{\nreturn \\$this->hasMany(Question::class);\n}\n}\n``````\n\nHere is the DB schema for the question’s table from the migration file:\n\n``````Schema::create('questions', static function (Blueprint \\$table) {\n\\$table->id();\n\\$table->string('question');\n\\$table->integer('question_category_id')->default(1);\n\\$table->integer('exam_id');\n\\$table->string('type')->default('text');\n});\n``````\n\nAlso this is how I’m saving the data for the questions:\n\n``````\\$request->validate([\n'examId' => ['required', 'numeric'],\n'questions' => 'required'\n]);\n\n\\$exam = Exam::find(\\$request->input('examId'));\n\\$questions = \\$request->input('questions');\n\nforeach (\\$questions as &\\$question_entry) {\n// create the question if it doesn't exist\nif ((int)\\$question_entry['id'] === 0) {\n\\$question = new Question();\n} else {\n\\$question = Question::find(\\$question_entry['id']);\n}\n\n\\$question->exam_id = \\$exam->id;\n\\$question->question = \\$question_entry['body'];\n\\$question->type = \\$question_entry['type'];\n\\$question->question_category_id = \\$question_entry['category'];\n\\$question->save();\n}\n``````\n\nThe saving to the DB is successful and I can see the entries in the DB. And if I try to do something like `Question::where('exam_id',1)->get()` I will get the questions from that exam, but I don’t understand why when I try to get the results from the parent model (like `Exam::find(1)->questions) I get `NULL`. It seems like there is no relation between the two models.\n\nI’m using Laravel 10 with Homestead and Breeze.\n\n### >Solution :\n\nIs see you are using the singular `question` in your relation definition in the `Exam` model.\nThat could be the reason why it is null.\n\nDid you also try the plural `questions`, like this:\n\n``````public function questions(): HasMany\n{\nreturn \\$this->hasMany(Question::class);\n}\n``````\n\nThe rest of the code seems fine, but you could also create the foreign id like this:\n\n``````\\$table->foreignId('exam_id');\n``````"
] |
[
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{"ft_lang_label":"__label__en","ft_lang_prob":0.6922468,"math_prob":0.4858834,"size":2993,"snap":"2023-14-2023-23","text_gpt3_token_len":702,"char_repetition_ratio":0.15791234,"word_repetition_ratio":0.059620596,"special_character_ratio":0.2659539,"punctuation_ratio":0.172147,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9898345,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-09T11:46:28Z\",\"WARC-Record-ID\":\"<urn:uuid:9f1a91c6-7b92-4a9a-9694-4b58633bbf9d>\",\"Content-Length\":\"75048\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1c2abde1-2f9f-4bb5-a315-ca05cfeb8057>\",\"WARC-Concurrent-To\":\"<urn:uuid:3488f1d4-a85b-45a8-8cdd-b195215da8bd>\",\"WARC-IP-Address\":\"192.0.78.211\",\"WARC-Target-URI\":\"https://devsolus.com/2023/05/22/models-relation-not-working-when-trying-to-get-the-children-models-in-laravel/\",\"WARC-Payload-Digest\":\"sha1:TDREAEPPPCQXIYHNQZP2YKPDSDALXA6W\",\"WARC-Block-Digest\":\"sha1:DKZYE7EZD6KXQ3W2AC4T3ZN37P3GZOMJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224656675.90_warc_CC-MAIN-20230609100535-20230609130535-00573.warc.gz\"}"}
|
https://mathspace.co/textbooks/syllabuses/Syllabus-411/topics/Topic-7313/subtopics/Subtopic-97544/?activeTab=interactive
|
[
"NZ Level 8 (NZC) Level 3 (NCEA) [In development]",
null,
"Applications of hyperbolas\n\n## Interactive practice questions\n\nThe physicist Ernest Rutherford discovered that when alpha particles are directed towards the nuclei of gold atoms, they are eventually deflected along hyperbolic paths.\n\nIf a particle can get as close as $8$8 units to the nucleus along a hyperbolic path with an asymptote given by $y=\\frac{1}{4}x$y=14x, what is the equation of its path?\n\nEasy\nApprox 5 minutes\n\nAn astronomer is studying the remains of an old star that has ejected its outer atmosphere in bursts of material. A cross section of the nebula has the shape of a hyperbola as plotted below. The units are given in light years. The point $Q$Q$\\left(0.6,0.2\\right)$(0.6,0.2) is on the asymptote of the gas shells. The point $V$V$\\left(1.2,0\\right)$(1.2,0) is the vertex of one of the gas shells.\n\nComets around the sun sometimes have a hyperbolic orbit. One such comet had a path that could be approximately described by the equation $25x^2-y^2=25$25x2y2=25.\n\nUnits are measured in Astronomical units (AU), the distance from the Earth to the Sun.\n\nTwo stationary communication beacons $55317$55317 m apart, send out a transmission to a ship at the same time. The ship receives the transmissions $120$120 microseconds apart. The ship can use this information to determine where it might be located using LORAN (LOng RAnge Navigation). The possible locations lie along a hyperbola.\n\n### Outcomes\n\n#### M8-1\n\nApply the geometry of conic sections\n\n#### M8-7\n\nForm and use trigonometric, polynomial, and other non-linear equations\n\n#### 91573\n\nApply the geometry of conic sections in solving problems\n\n#### 91575\n\nApply trigonometric methods in solving problems"
] |
[
null,
"https://mathspace-production-static.mathspace.co/permalink/badges/v3/rates-of-change.svg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9463459,"math_prob":0.9862933,"size":550,"snap":"2021-31-2021-39","text_gpt3_token_len":124,"char_repetition_ratio":0.093406595,"word_repetition_ratio":0.05,"special_character_ratio":0.19454545,"punctuation_ratio":0.06122449,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9966686,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-23T04:55:01Z\",\"WARC-Record-ID\":\"<urn:uuid:acd3901d-cc0a-4147-b681-f25ad71e9419>\",\"Content-Length\":\"301925\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a123e419-1169-459a-80cb-e5cb1fa52988>\",\"WARC-Concurrent-To\":\"<urn:uuid:ac2b8ae2-9691-4c9e-953d-eb57b45e8acb>\",\"WARC-IP-Address\":\"172.67.36.184\",\"WARC-Target-URI\":\"https://mathspace.co/textbooks/syllabuses/Syllabus-411/topics/Topic-7313/subtopics/Subtopic-97544/?activeTab=interactive\",\"WARC-Payload-Digest\":\"sha1:362BOIB7BUFR2W4SJFSKZKPCXQCMDY4C\",\"WARC-Block-Digest\":\"sha1:ROREBIE22N7D43YVMXX52DYRAE2JEOPW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057417.10_warc_CC-MAIN-20210923044248-20210923074248-00716.warc.gz\"}"}
|
https://programming.vip/docs/2019-technical-posts-written-examination-gardener-small-q.html
|
[
"# 2019 technical posts, written examination, gardener, small Q\n\nThe gardener Xiao Q raised two kinds of flowers, one white flower and one safflower. Now Xiao Q put these flowers on display. When placed, the number of continuous white flowers can only be multiple of K (multiple can be 0), otherwise it will wither. Given A and B now, little Q wants to know how many kinds of pendulum schemes with length [a,b].",
null,
"",
null,
"Analysis:\n1. Let the current length be X and X belong to [a,b].\n2. When X < K, it can only be all safflower, one kind\n3. When X=K, it can only be white or safflower.\n4. When X > K, the situation needs to be divided.\n1. White flowers are 0 * k.\n2. White flowers are 1 * k.\n3. White flowers are 2*k...\nAt this time, the k white flowers are regarded as one, and the current problems are simplified as the following examples:\n\n```Example: Five pots of safflower and three pots of yellow flower are arranged in a row.\nThese flowers are the same except for their color.\nHow many methods are there in the end when yellow flowers are not adjacent to each other?\nInterpolation is considered because yellow flowers are not adjacent to each other.\nFirst put the safflower, the safflower grows the same, so no matter how it is placed, there is only one way.\nBecause yellow flowers grow the same, so insert yellow flowers into six empty safflower, a total of C3 6=20 methods.\n```\n\nBut the white flowers here can be adjacent, so:",
null,
"```Example: Place three pots of safflower and two pots of yellow flowers in a row.\nHow many methods do these flowers have in common except for their color?\nAnalysis: Consider the arrangement of repeatable elements.\nAccording to the formula: there are (5!) / (3! 2! = 10 kinds, complete ok\nrrrhh hhrrr rhrhr rhrrh\nrrhrh hrhrr rrhhr hrrhr\nrhhrr hrrrh\n```\n\nNext, it's easy to write code:\nI wrote the output of the process for easy understanding.",
null,
"```#include <stdio.h>\n#include <stdlib.h>\n\nint calculateN(int num)\n{\nint i=1;\nint calcu=1;\ndo\n{\ncalcu*=i;\ni++;\n}\nwhile(i<=num);\n//printf(\"%d n!=%d\\n\",num,calcu);\nreturn calcu;\n}\n\nint main()\n{\nint t=0;\nint k=0;\nscanf(\"%d %d\",&t,&k);\nint flowerlength;\nint i=0;\nfor(i=0; i<t; i++)\n{\nscanf(\"%d %d\",&flowerlength[i],&flowerlength[i]);\n}\n\nfor(i=0; i<t; i++)\n{\nint x=0;\nint sum=0;\nfor(x=flowerlength[i]; x<=flowerlength[i]; x++)\n{\nprintf(\"For intervals:[%d,%d],current x Value:%d\\n\",flowerlength[i],flowerlength[i],x);\nif(x<k)\n{\nsum+=1;\nprintf(\"%d A flower,%d Flos Carthamus,Combination number:%d\\n\",x,x,sum);\n}\nelse if(x==k)\n{sum+=2;\nprintf(\"%d A flower,%d White flower,%d Flos Carthamus,Combination number:%d\\n\",x,x,x,sum);\n\n}\nelse if(x>k)\n{\nint n=0;//Limit the number of white flowers\nwhile(n*k<=x)\n{\nint cal=calculateN(n+x-n*k)/(calculateN(n)*calculateN(x-n*k));\nsum+=cal;\nprintf(\"Regard as%d The combination of flowers,%d Group of white flowers,%d Flos Carthamus,Combination number:%d\\n\",n+x-n*k,n,x-n*k,cal);\nn+=1;\n}\n}\nelse\n{\nprintf(\"error!\\n\");\n}\n\n}\nprintf(\"sum:%d\\n\",sum);\n\n}\n\nreturn 0;\n}\n\n```\n\nAdded by daydie2008 on Fri, 04 Oct 2019 06:53:33 +0300"
] |
[
null,
"https://programming.vip/images/doc/d7d374cb161cb545576546ad8a80ce8e.jpg",
null,
"https://programming.vip/images/doc/fe71717ba49f74eb64075526139cee62.jpg",
null,
"https://programming.vip/images/doc/b9103aa6b0478213446b1238ea8626a3.jpg",
null,
"https://programming.vip/images/doc/4df3c497bbf50ebd4ae47427c7567da5.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.75337756,"math_prob":0.9940102,"size":2895,"snap":"2021-31-2021-39","text_gpt3_token_len":851,"char_repetition_ratio":0.14873746,"word_repetition_ratio":0.013363029,"special_character_ratio":0.29879102,"punctuation_ratio":0.19622093,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99638885,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-25T18:48:13Z\",\"WARC-Record-ID\":\"<urn:uuid:1936c36a-dfd7-450e-8ef4-56c5f4c1a129>\",\"Content-Length\":\"9476\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f9aafea4-6f52-4f26-96fa-3fc1c6592119>\",\"WARC-Concurrent-To\":\"<urn:uuid:d672435f-9f5d-479e-bcf9-11ad46fee23d>\",\"WARC-IP-Address\":\"213.136.76.254\",\"WARC-Target-URI\":\"https://programming.vip/docs/2019-technical-posts-written-examination-gardener-small-q.html\",\"WARC-Payload-Digest\":\"sha1:OOLXA2HAXIFPWNI77HPSSMZ7UNNESJ5E\",\"WARC-Block-Digest\":\"sha1:6XXXDS4E55ZZB5DEUAIUXP3Y5KWSGNAN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057733.53_warc_CC-MAIN-20210925172649-20210925202649-00467.warc.gz\"}"}
|
http://biomaterials-2011-dfg-nsf-conference.com/adaptive-clinical-trial-designs-incorporating-treatment-selection-at-pre-specified-interim-analyses/
|
[
"# Adaptive clinical trial designs incorporating treatment selection at pre-specified interim analyses\n\nAdaptive clinical trial designs incorporating treatment selection at pre-specified interim analyses have recently attracted considerable attention. the discussion with clinical teams to choose a suitable multiple test procedure tailored to the study objectives. In the meantime, the graphical approach has been extended to more complex applications, including group-sequential trials (Maurer and Bretz, 2013b) and (non group-sequential) two-stage adaptive clinical trials (Sugitani et al., 2013). Extending these previous works, in this paper, we introduce a graphical approach to testing multiple hypotheses in group-sequential clinical trials allowing for mid-term design modifications, such as hypotheses sample or selection size reestimation. We refer to such trials as adaptive group-sequential clinical trials. The adaptive group-sequential clinical trials have been investigated in various practical settings, such as for comparing several treatments to a common control (Stallard and Friede, 2008; Di Glimm and Scala, 2011), combined testing of non-inferiority and superiority (Wang et al., 2001; ?jennison and hrn, 2010; Gao et al., 2013), exploring primary and secondary endpoints (Tamhane et al., 2012), studying population enrichment designs (Brannath et al., 2009; Turnbull and Magnusson, 2013), and adaptively analyzing microarray experiments (Zehetmayer et al., 2008). Speaking Roughly, Ursolic acid in such trials, closed test procedures (Marcus et al., 1976) are used in connection with either combination tests (Bauer and Kieser, 1999; Hommel, 2001; Bretz et al., 2006) or conditional error rates (Mller and Sch?fer, 2001). This Ursolic acid approach, however, is not originally intended Ursolic acid for testing hierarchically structured study objectives and therefore cannot easily be applied to more complex adaptive clinical trials. Thus, we introduce in this paper a have and marginal to be significant. In the marginal or if denotes some index set. In this paper we consider Bonferroni-based closed test procedures, which apply Mouse monoclonal to GST weighted Bonferroni tests to each intersection hypothesis Ursolic acid = ? ? a collection of weights if for at least one denotes the unadjusted with are rejected. This strongly controls the FWER at level as long as each intersection hypothesis is tested at level implies rejection of at least one elementary null hypothesis the unadjusted = 1, 2. Usually, the weights are chosen proportional to the planned sample size per stage. See the remark in Section 5 also, regarding the recommended choice of in case of treatment selection designs. Let denote the index set of hypotheses dropped at the interim analysis (= 1). At the final analysis (= 2), the marginal = ? for at least one under for at least one < < while strongly controlling the FWER at level if all intersection hypotheses with are rejected at level in a (0,1) denote a pre-specified significance level, and the information time or information fraction at certain analysis time point for the data from stages 1 to stages. Let further with for any < 1 and 0 < 1. Moreover, we assume that the nominal significance levels are Ursolic acid nondecreasing in for any number of analyses and information fraction log{1 + (? 1)(OBrien and Fleming, 1979) for < 0.318, where denotes the 100(1?denote the from stage = 1, 2,, and = 1,, uses in order to control the Type I error rate at level = 1,, can be rejected at time point if = 1, equation (5) reduces to satisfying equations (4) and (5), using."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9316854,"math_prob":0.7962478,"size":4227,"snap":"2022-05-2022-21","text_gpt3_token_len":1075,"char_repetition_ratio":0.11934644,"word_repetition_ratio":0.0,"special_character_ratio":0.27773836,"punctuation_ratio":0.12244898,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9707481,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-16T22:05:57Z\",\"WARC-Record-ID\":\"<urn:uuid:17d3e5f6-4f59-40f7-a803-eb69a6663eef>\",\"Content-Length\":\"65653\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9a336d27-43ca-4184-9d95-4c5d780236f7>\",\"WARC-Concurrent-To\":\"<urn:uuid:1cb54719-c90f-4662-a242-16a5a13d6241>\",\"WARC-IP-Address\":\"207.244.103.92\",\"WARC-Target-URI\":\"http://biomaterials-2011-dfg-nsf-conference.com/adaptive-clinical-trial-designs-incorporating-treatment-selection-at-pre-specified-interim-analyses/\",\"WARC-Payload-Digest\":\"sha1:7A3WUNBXHVVVD4Z3TZ2UN6JDY66DWGLN\",\"WARC-Block-Digest\":\"sha1:Q4WILHJLWV6TENIH5ZYHHNZEIIXSH5BW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662512249.16_warc_CC-MAIN-20220516204516-20220516234516-00334.warc.gz\"}"}
|
http://www.xue366.cn/132.html
|
[
"# python如何实现反向迭代\n\n>>> for x in reversed(a):… print(x)\n\n… 4321\n\nf= open(‘somefile’)\n\nfor line in reversed(list(f)):\n\nprint(line, end=”)\n\ndef__init__(self, start):\n\nself.start= start# Forward iterator def__iter__(self):\n\nn= self.start while n> 0:\n\nyield n n-= 1\n\n# Reverse iterator\n\ndef__reversed__(self):\n\nn= 1\n\nwhile n<= self.start:\n\nyield n n+= 1\n\nfor rr in reversed(Countdown(30)):\n\nprint(rr)\n\nfor rr in Countdown(30):\n\nprint(rr)"
] |
[
null
] |
{"ft_lang_label":"__label__zh","ft_lang_prob":0.65528196,"math_prob":0.7487874,"size":721,"snap":"2022-40-2023-06","text_gpt3_token_len":369,"char_repetition_ratio":0.12831241,"word_repetition_ratio":0.0,"special_character_ratio":0.2857143,"punctuation_ratio":0.15384616,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9662713,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-06T02:26:04Z\",\"WARC-Record-ID\":\"<urn:uuid:2f80264e-85c5-4035-aa14-afe492382a07>\",\"Content-Length\":\"34569\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:01a5ca1c-b96b-4b3d-9a23-aa60ab8e1d8f>\",\"WARC-Concurrent-To\":\"<urn:uuid:685d907b-bcfa-4f6c-b01f-8a528eeb4be2>\",\"WARC-IP-Address\":\"47.92.227.48\",\"WARC-Target-URI\":\"http://www.xue366.cn/132.html\",\"WARC-Payload-Digest\":\"sha1:AWCQ3VMCLONVNO4MB4RCPC37KKBCC4PP\",\"WARC-Block-Digest\":\"sha1:7UEMDWNXB3XYBD6A6JFO4ATBH5LYZLEJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500303.56_warc_CC-MAIN-20230206015710-20230206045710-00546.warc.gz\"}"}
|
https://math.stackexchange.com/questions/3354216/hypothetical-computer-marc-32
|
[
"# Hypothetical Computer Marc-32\n\nI'm studying numerical analysis and i am stuck with one of my exercises. In the book \"Numerical Analysis: Mathematics of scientific Computing\" they introduce a hypothetical computer called MARC-32. In the book the computer is a 32-bits computer representing a nonzero real number with the form: x = ±q * 2^m\n\nwith the allocation:\n\n• sign of the real number x: 1 bit\n• biased exponent (integer e): 8 bits\n• mantissa part (real number f): 23 bits\n\nmarc-32\n\nMy problem is that i really do not understand the computer and hence can not solve the following problems:\n\nDetermine whether the following numbers are machine numbers in the Marc-32:\n\n• 10^40\n• 2^-1+2^-29\n• 1/3\n• 1/5\n\nI have read the chapter a couple of times and still i don't get it. I really want to know what they mean by the hypothetical computer and how to solve it.\n\n• What about the description of the representation is it you don't understand? – hmakholm left over Monica Sep 12 '19 at 15:38\n• It is relevant to add how the true exponent is computed from the biased exponent, i.e., what is the shift used by the Marc-32. The answers depend on the exact shift. Moreover, can you determine the exact binary representation of the four numbers? – Carl Christian Sep 12 '19 at 18:05\n• @CarlChristian - while technically you are correct, I have a hard time believing it would be anything other than e = m + 128, thereby allowing exponents of 2 from -128 to +127. – Paul Sinclair Sep 13 '19 at 3:44\n• @PaulSinclair: The shift used in IEEE single precision is 127 and not 128. Assuming OP is referring to a book by Kincaid and Cheney, the Marc-32 has a permissible range of exponents from -126 to 127. This is consistent with IEEE SP where the smallest exponent, i.e. -127 is used for zero or subnormal numbers, while the largest exponent 128 is used for infinities or NaN. – Carl Christian Sep 13 '19 at 10:00\n• @CarlChristian - all of which has no impact on the answers to the questions asked, because none of the questions involve exponents in that range. – Paul Sinclair Sep 13 '19 at 16:01\n\nIf you write $$x$$ in binary, it would looks something like this (as an example): $$x=1010011.011010010001_b$$ Then you convert it to the binary version of scientific notation: $$x = 1.010011011010010001_b \\times 2^{110_b}$$\n• The number is positive, so the sign bit would be $$1$$ (or possibly $$0$$, depending on the system architecture - for these problems, it doesn't matter which is used.)\n• The exponent $$m = 6 = 110_b$$. But we want to store positive and negative exponents in the eight bits, and there is no sign bit. So we bias the result by adding a value. 8 bits can store 256 different values, so if we alot half of them for negative exponents, that is 128. This means the range of allowable exponents is from $$-128$$ to $$+127$$. When the exponent is stored, we add $$128$$ so the value we store is from $$0$$ to $$255$$. For the example, the exponent stored is $$110_b + 10000000_b = 10000110_b$$.\n• The bit in front of the point is always $$1$$. This is what defines the exponent value. It is the exponent that brings the leading $$1$$ to be right in front of the \"decimal\" point. Since this bit is always $$1$$, there is no need to store it. The \"mantissa\" is the part of the number to the right of the point. In the example, the mantissa is $$010011011010010001_b$$. Since we have 23 bits, it is actually stored as: $$01001101101001000100000$$\n• I should note about the final bullet, that when $x = 0$, the bit in front of the decimal point cannot be $1$, even though it is for every other number. It is usual to assign a particular value as representing $0$ (for example, all 32 bits being 0), instead of interpreting per the scheme described above. – Paul Sinclair Sep 13 '19 at 4:12\n• It is not impossible, but the result will be roughly 132 bits, of which about 92 will be significant (i.e., either $1$ or followed by a $1$ somewhere in lower orders). And that is all you need to know. As Carl Christian points out, you need to double-check that the Marc 32 doesn't do something weird to allow exponents greater than 128 (even though it would be rather pointless to do so). But unless it does, the fact that $10^{40}$ has an base-2 exponent of 132 rules out this as being a machine number, so there is no reason to check it any farther. – Paul Sinclair Sep 16 '19 at 3:30\n• As for your steps, I was just trying to clarify the basic storage scheme to improve your understanding, not give step-by-step instructions on solving the problem. As you've noticed, following those steps in that order can be daunting. But you don't have to actually do it - you just have to figure out if it will be possible. That is usually easier. $10^{40}$ fails because it is relatively easy to find the base 2 exponent. It is the only one that actually takes a calculator or paper to figure out. The second is matter of counting, and the other two a matter of divisibility. – Paul Sinclair Sep 16 '19 at 3:43"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.92159,"math_prob":0.9885943,"size":813,"snap":"2020-10-2020-16","text_gpt3_token_len":204,"char_repetition_ratio":0.12978986,"word_repetition_ratio":0.0,"special_character_ratio":0.26199263,"punctuation_ratio":0.07453416,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99853754,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-19T22:49:37Z\",\"WARC-Record-ID\":\"<urn:uuid:c744b181-a625-477e-9bcf-6fccb7b6da48>\",\"Content-Length\":\"155464\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de951655-be6b-4b9d-8e7f-8b32cac053c0>\",\"WARC-Concurrent-To\":\"<urn:uuid:1592ea4f-763d-487d-9053-3356e27898d8>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/3354216/hypothetical-computer-marc-32\",\"WARC-Payload-Digest\":\"sha1:BOQFM6ZVAAGGZRVS23AKK73Z4RV6FMF2\",\"WARC-Block-Digest\":\"sha1:LX4Y37IEXN7WX5D7VKOWHPLQCSOG3FYZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875144429.5_warc_CC-MAIN-20200219214816-20200220004816-00314.warc.gz\"}"}
|
https://restaurantzurglocke.de/steam-boiler/1220-for-boiler-convert-1-bhp-to-kg-hr.html
|
[
"### Boiler Capacity - Engineering ToolBox\n\nh g = enthalpy steam (Btu/lb, kJ/kg) h f = enthalpy condensate (Btu/lb, kJ/kg) m = steam evaporated (lb/h, kg/s) Boiler Horsepower - BHP. The Boiler Horsepower (BHP) is. the amount of energy required to produce 34.5 pounds of steam per hour at a pressure and temperature of 0 Psig and 212 o F, with feedwater at 0 Psig and 212 o F. A BHP is\n\n### Convert bhp to kgf m/h | Boiler horsepower to kilograms\n\n·\n\nDiferent power units conversion from Boiler horsepower to kilograms force meter/hour. Between bhp and kgf m/h measurements conversion chart page. Convert 1 bhp into kilogram metre per hour and Boiler horsepower to kgf m/h. The other way around, how many kilograms force meter/hour - kgf m/h are in one Boiler horsepower - bhp unit? Calculate from power into other power unit measures.\n\n### Convert bhp to Btu/h | Boiler horsepower to BTU's per hour\n\n·\n\nDiferent power units conversion from Boiler horsepower to BTU's per hour. Between bhp and Btu/h measurements conversion chart page. Convert 1 bhp into BTU per hour and Boiler horsepower to Btu/h. The other way around, how many BTU's per hour - Btu/h are in one Boiler horsepower - bhp unit? Calculate from power into other power unit measures.\n\n### boiler steam production conversion ton hr to kw – oil\n\nConversion Factors ; Energy: 1 1 boiler horsepower (BHP) = 33520 BTU/hr 1 boiler horsepower (BHP) = 9803 Watts 1 lb/mmbtu = 1.548 kg/MW-hr 1 lb steam/hr (300 psi . Boiler Capacity Steam boilers output can be expressed in Boiler Horsepower, W = boiler capacity (Btu/h, kW) Lbs of Steam to Boiler Horsepower Conversion.\n\n### CONVERSION OF BOILER IN KG/H AND KW - cni.co.th\n\nCONVERSION OF BOILER IN KG/H AND KW (Approximate) G.B. and U.S.A. Steam from and at 100°C Boiler HP Kg/h 2.26MJ/kg Metric System Steam from 0°C to 100°C Kg/h 2.26MJ/kg Power In kW 1 5 10 15 20 30 40 50 60 70 80 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 15.65 78 156 235 313 470 626 783 940 1096 1252 1566 2350 3130 3915 4700 5480\n\n### Pick a table to convert boiler horsepower [BHP] - unit of\n\n55 · Pick a table with which to convert boiler horsepower to any other unit of measurement of …\n\n### Convert horsepower (boiler) [hp (boiler)] to ton\n\nPower also is measured in dBm, a relative logarithmic measure with 1 milliwatt as reference, calories per hour, Btu per hour (Btu/h). Electric power is defined as the amount of work done by an electric current, or the rate at which electrical energy is transmitted. The SI unit of electric power is the watt. Using the Power Converter Converter\n\n### Boiler Horsepower to Btus Per Hour | Kyle's Converter\n\nInstantly Convert Boiler Horsepower (bhp) to Btus Per Hour (BTU IT /h) and Many More Power Conversions Online. Boiler Horsepower Conversion Charts. Many Other Conversions.\n\n### Unit Conversion--How to Calculate Boiler Horsepower\n\n“Boiler horsepower, a unit of measurement of power of steam boilers” from Wiki. A BHP is equivalent to 33,475 BTU/Hr or 8430 Kcal/Hr and it should be noted that a boiler horsepower is 13.1547 times a normal horsepower. Click on the Icon above will initiate Heat Converter, Pressure Converter, Temperature Converter. Converted HP into LB\n\n### Boiler Horsepower - Engineering ToolBox\n\nBoiler horsepower - a power unit from the 19 th-20 th centuries - was used to rate the capacity of a boiler to deliver steam to steam engines.. A common definition of one boiler horsepower is the amount of energy required to produce 34.5 pounds (15.65 kg) of steam per hour at pressure and temperature 0 psig (0 bar) and 212 o F (100 o C) - with feed water at pressure 0 psig and temperature 212 o F."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.76780313,"math_prob":0.7783485,"size":3707,"snap":"2021-31-2021-39","text_gpt3_token_len":1018,"char_repetition_ratio":0.19335674,"word_repetition_ratio":0.116564415,"special_character_ratio":0.2792015,"punctuation_ratio":0.081190795,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9623689,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-29T03:07:18Z\",\"WARC-Record-ID\":\"<urn:uuid:8b96710d-012f-495d-9f8a-8c586b206fd0>\",\"Content-Length\":\"31115\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:59673afe-59cc-4757-b585-a13d8b66a8ac>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc4bde1c-6427-4267-8ce2-791bfa4ac9c1>\",\"WARC-IP-Address\":\"140.82.49.177\",\"WARC-Target-URI\":\"https://restaurantzurglocke.de/steam-boiler/1220-for-boiler-convert-1-bhp-to-kg-hr.html\",\"WARC-Payload-Digest\":\"sha1:X4YYEFAAXTWRSMJR2CU6NJBLVZWDOC2A\",\"WARC-Block-Digest\":\"sha1:LGXCE5CDU7JGOBTRK4JG626MLRM3ZYW4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046153814.37_warc_CC-MAIN-20210729011903-20210729041903-00481.warc.gz\"}"}
|
https://www.numerade.com/questions/graphical-reasoning-in-exercises-67-and-68-find-a-b-and-c-such-that-the-graph-of-the-function-matche/
|
[
"🎉 The Study-to-Win Winning Ticket number has been announced! Go to your Tickets dashboard to see if you won! 🎉View Winning Ticket",
null,
"### Graphical Reasoning In Exercises 67 and $68,$ fin…\n\nView",
null,
"University of California, Berkeley\nProblem 67\n\n# Graphical Reasoning In Exercises 67 and $68,$ find $a, b,$ and $c$ such that the graph of the function matches the graph in the figure.$$y=a \\cos (b x-c)$$\n\n## Discussion\n\nYou must be signed in to discuss.\n\n## Video Transcript\n\nOkay, so we're asked to write an equation. Why Her phone? Uh, the coefficient terms. Why? This is a co sign of the ex minister. Okay, so we know aids the amplitude, right? So it passes to and it's a little hard lesson for So let's say it's approximately three. So since the attitude is always absolute value of a, um so if we had absolute value of A, that could be either plus minus three. Okay, Now, for part B for another party, I'm looking for BEA, which is our period. What a period of coastline is two pi over feet. And from the looks of this, our period is almost for pie. So it's this secret for pipe. This offer B B would equal 1/2 an important part me our original coast autograph. But it looks like a sign right coast. I'm usually starts, uh, like over here somewhere. So it seems like they shifted it by prior to it. See if you could fire every cube, make a good positive. Great. So our equation is why he could, too. A 123 co sign B, which is 1/2 X minus five bridges"
] |
[
null,
"https://cdn.numerade.com/previews/d134d55e-c53d-4a1a-905a-c4e8c0b73624.gif",
null,
"https://d1ras9cbx5uamo.cloudfront.net/eyJidWNrZXQiOiAiY29tLm51bWVyYWRlIiwgImtleSI6ICJpbnN0cnVjdG9ycy8zZjA0MDAwNjIwZWI0NGNjODNmMTMxMDhkODc5YjhkZS5qcGciLCAiZWRpdHMiOiB7InJlc2l6ZSI6IHsid2lkdGgiOiAyNTYsICJoZWlnaHQiOiAyNTZ9fX0=",
null
] |
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|
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