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http://pseudomonad.blogspot.com/2011/09/rumour-of-century.html?showComment=1316474735326 | ## Tuesday, September 20, 2011
### Rumour of the Century
We don't usually report on unsubstantiated rumours here at AP, but this one is just too spectacular to ignore. Jester thinks its crazy, Phil sounds excited, and Graham says that Tommaso had a post up with a $6.1 \sigma$ result from OPERA, but the post has now disappeared. Given the number of false rumours that get circulated, we should be doubtful at this point. Here is OPERA's last arxiv paper. The CERN seminar is this coming Friday.
So the rumour is that neutrinos arriving at OPERA have travelled at a speed greater than $c$. Forget fairy fields. If this is true, it demolishes establishment thinking in one falcon swoop. Could the minus sign in Brannen's Koide relation for neutrinos be responsible for such tachyonic behaviour? Why not? Or, perhaps all neutrinos are tachyons. Now the minus sign goes with the lightest neutrino mass state. The literature has an annoying tendency to confuse EW and mass states, but we should note that all mass states can occur in $\nu_{\mu}$-$\nu_{\tau}$ oscillations.
1. As we know, photons always travel at $c$ locally. Particles with mass, such as electrons and muons, travel at speeds less than $c$ precisely because they have mass. But until OPERA, as far as I know, nobody could actually measure neutrino speeds. And we already know that the Koide formula looks different for neutrinos. The tachyonic behaviour would not even violate Lorentzian geometry, because we would simply insist that tachyons always travel at speeds greater than $c$.
2. Even kneemo likes tachyons, because M theory has tachyons.
3. And it would strengthen the argument that the neutrino sector is crucial for understanding gravity.
4. So now we can rethink the strange MiniBooNE/LSND results, and in fact all the appearance disappearance anomalies. With tachyonic neutrinos, hopefully the ad hoc introduction of sterile states can finally be dismissed. As we said some time ago, the local neutrino gas should not behave in a standard fashion.
5. I predict that the rumored result will not stand.
6. Of course you do, Mitchell. You are still a string theorist. But there is no reason to doubt that tachyons exist in our form of M theory. Mind you, I bet OPERA will have a hard time convincing everyone that they know what they are doing.
7. Now according to the rumour, which contains only the sketchiest facts, the OPERA detector was looking for the onset of tau neutrinos from a well timed $700+$ km beam. This strongly suggests that ALL the arriving neutrinos are travelling at a speed $> c$. Duh.
8. So all mass states are tachyonic.
9. Some people are already talking about the implication of classical time travel, but there is no reason to jump to that conclusion here. There is nothing concretely acausal about sending the neutrinos from point A to point B and then measuring the apparent speed. The speed is whatever it is. Relativity is prefectly well respected by tachyons, even in interaction with ordinary matter, provided we consider a complexification of our geometry, which we do with twistor theory anyway.
10. No, wait! The onset time only gives an indication of the fastest speed. It is not true that all neutrinos need travel that fast. So perhaps OPERA actually sees something really amazing, like a triplet of arrival times, one $>c$.
11. And since the fastest speed corresponds to the lowest energy for a tachyon, the low energy excess of MiniBooNE comes from the most tachyonic neutrinos.
12. My understanding of Carl's philosophy of time is that time is absolute and Lorentz symmetry is emergent. I don't know how yours works. I don't know how to "interpret" just two timelike dimensions, let alone three. When you have a two-time signature for twistors, that's not something which shows up in any observable physical state; it's something that you analytically continue back to the physical signature. Similarly, when you have multiple times in F-theory, S-theory... they have to be hidden away with the spacelike compact dimensions. At some point, the formal mathematical concepts of time that are employed in physics have to reconnect with phenomenological time, and I do not at all see how that is possible if you have more than one "time".
13. It smells a bit bad, and rather inconsistent with previous data...
There had been a delay of ~3h between the neutrinos and the gammas in SN1987A (it had been explained by astrophysical reasons, though). If one however interprets it as physical, takes the distance of the SN (168000 ly) and rescales it to the distance (700 km) between CERN and the Gran Sasso (GS), one would expect
Dt ~ 10000 s * (700e3/(168000*3e7*3e8)) ~ 5 ps
which is 1 millimeter of delay... It is true that the SN neutrinos were in the MeV, but it looks strange that something dramatic happens between the MeV and the GeV...
There was also a ~1-day-before claim in 1987, but then it was withdrawn - and in any case it is 2-3 orders of magnitude below the needed sensitivity.
Alessandro De Angelis
14. If it is true, it would mean that neutrino can see more than any other particle. Wow. In a fundamental theory of quantum gravity c is no longer an invariant, the planck lenght or certain fundamental lenght \alpha L_P is the main quantity. Anyway, I hope this could be true. LHC is being something boring yet...The surprinsing discoveries are yet to come! Careful has to be paid to the tachyonic conclusion. OPERA is not a vaccum detector, so a bad definition of group speed in the dispersion relation could appear as a fake v>c. Is the rumour on OPERA a claim on neutrino speed at vaccum? Curiously, it is an experiment I am following less than others. And about a theory with v>c...I only know three theories ( at least published) that could obtain that claim (forget M theory at principle): Gonzalez-Mestres theory of superbradyons, varying speed-of light theories and extended relativities in C-spaces. Of course, they are non main stream theories, but they postulate from first principles the possible existence of particles with v>c without tachyons. I would like to emphasize this: if it is true, if neutrino has v>c at vacuum, it does not necessarily means they are tachyons. Questions: has someone else realized what would happen if there some other EM-like in the Universe very weakly coupled to the SM and whose "speed of light" is NOT the common speed-of-light?
15. Yes, the supernovae data are interesting, but it could be the case that the tachyonic species are only observable more locally.
Juan, many people have thought about these kind of things, since the 1950s. However, very few people think about emergent geometry using modern mathematical methods, with which far more is possible. I have no more information on the rumour, since I did not even get to read Tommaso's post. I don't think the rock medium is an issue, since it is pretty transparent to neutrinos. My guess is that a satellite measurement of the distance, using an accurate angle for the two photon paths, could be used to determine a length for the other side of the triangle, as a reasonable estimate of the distance.
16. Graham knows more about supernovae. And someone at vixra mentioned fibre optics 'down the shaft' from the GPS point.
17. Now we just have to wait. As Graham says, the mistrust of $6.1 \sigma$ results is rather disturbing to those theorists that approve of the result.
18. Like EPR, till they show what really they have got, we only get romours...A pity!What time is the Friday talk, local time? I am getting interested since there are several prominent blogs commenting the rumour. Will it be real after all?
Yeah, I know neutrino is almost transparent to medium ( I am doing my Master thesis on neutrinos) but group velocity and phase velocities can be greater than c. I have to read more about what they are measuring, if it proves to be a real 6.1 sigma claim.
19. By the way: note that something weird is also happening in the existent data on reactor neutrinos. Will the neutrino surprise us ...again? :D
20. Has anyone thought of the possibility of a tunneling-like event in the 'insides' of earth? It is a well known fact that light CAN travel faster than c in case of a tunneling event. (Steinber, PRL 1993 - http://prl.aps.org/abstract/PRL/v71/i5/p708_1 - Or just google 'tunneling time of single photon') In thet perspective, this data would not mean tachyonic behaviour of neutrinos, but simply the occurence of quantum barrier for the neutrinos. Just saying it... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8147882223129272, "perplexity": 1133.8356458233025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627997801.20/warc/CC-MAIN-20190616062650-20190616084650-00125.warc.gz"} |
https://www.researchgate.net/profile/Sabrina-Roscani-2 | # Sabrina RoscaniNational Scientific and Technical Research Council - Austral University (Argentina) · Mathematics
Dr.
29
Publications
2,670
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
195
Citations
Introduction
Sabrina Roscani currently works at the Departamento de Matemática, Universidad Austral de Rosario and at the Rosario National university. Sabrina does research in Applied Mathematics, Analysis and Fractional Calculus. Their current project is 'Inecuaciones variacionales, control óptimo y problemas de frontera libre: teoría, análisis numérico y aplicaciones.'.
August 2008 - present
Position
• Assistant Proffesor
## Publications
Publications (29)
Article
We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary. For each problem we prove existence and uniqueness of solution by a Fourier approach. This will enable us to al...
Article
Full-text available
In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space Stefan problem in terms of the three parametric Mittag-Leffler function Eα,m,l(z). We consider Dirichlet and Neumann conditions at the fixed face, involving Caputo fractional space derivatives of order 0<α<1. We recover the solution for the classical...
Preprint
Full-text available
Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys:2020}, we consider a phase-change problem for a one dimensional material with a non-local flux, expressed in terms of the Caputo derivative, which derives in a space-fractional Stefan problem. We prove existence of a unique solution to a phase-change problem with the fractional N...
Article
The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, w...
Preprint
Full-text available
We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary. For each problem we prove existence and uniqueness of solution by a Fourier approach. This will enable us to al...
Article
Full-text available
In this paper we consider a family of three-dimensional problems in thermoelasticity for elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero. We fully characterize with strong convergence results the limit as the unique solution of a two-dimensional problem, where the reference domain is the...
Preprint
Full-text available
In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong convergence results the limit as the unique solution of a two-dimensional problem, where the reference domain i...
Preprint
Full-text available
In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space one-phase Stefan problem in terms of the three parametric Mittag-Leffer function $E_{\alpha,m;l}(z)$. We consider Dirichlet and Newmann conditions at the fixed face, involving Caputo fractional space derivatives of order $0 < \alpha < 1$. We recover t...
Article
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order α ∈ (0, 1) verifying that they coincide with the same classical Stefan problem at the limit case when α=1. For both problems, explicit solutions in terms of the Wright functions are presented. Even though the similarity of the two...
Preprint
Full-text available
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when $\alpha=1$. For both problems, explicit solutions in terms of the Wright functions are presented. Even though the simil...
Preprint
In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order...
Preprint
Full-text available
This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the fractional Integral of Caputo--Fabrizio is also analyzed. The main result consists in the proof of existence...
Preprint
Full-text available
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered. The model obtained involves fractional derivatives with respect on time in the sense of Caputo and in the sense...
Preprint
Full-text available
A generalized Neumann solution for the two-phase fractional Lam\'e--Clapeyron--Stefan problem for a semi--infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a restriction on data is satisfied. The fractional derivative in the Caputo sense of order $\al \in (0,1)$ respect on t...
Article
Full-text available
A generalized Neumann solution for the two-phase fractional Lamé–Clapeyron–Stefan problem for a semi-infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a restriction on data is satisfied. The fractional derivative in the Caputo sense of order $$\alpha \in (0,1)$$ respect on t...
Article
Full-text available
Two fractional Stefan problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0,1)$ such that in the limit case ($\alpha =1$) both problems coincide with the same classical Stefan problem. For the one and the other problem, explicit solutions in terms of the Wright functions are presented. We prove that these...
Article
Full-text available
We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation. The time-fractional derivative of order $\alpha\in (0,1)$ is taken in the sense of Caputo. We study the asymptotic behaivor, as t tends to infinity, of a general solution by using a fractional weak maximum principle. Also, we give some particular exact...
Article
Full-text available
A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan ( Fract. Calc. Appl. Anal. , 16 , No 4 (2013), 802–815) and Tarzia and Ceretani ( Fract. Calc. Appl. An...
Article
Full-text available
We consider the time-fractional derivative in the Caputo sense of order α ∈ ( 0 , 1 ) . Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in R + , two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Mor...
Article
This paper deals with a theoretical mathematical analysis of a one-dimensional-moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order $\al$ $\in (0,1)$ is taken in the Caputo's sense. A generalization of the Hopf's lemma is proved, and then this result is used to prove a monotonicity proper...
Article
We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order α ∈ (0, 1) is taken in the Caputo sense. A generalization of the Hopf lemma is proved and then used to prove a monotonicity property for the free-boundary when a fractional free-boundary Stefan problem is i...
Article
Full-text available
We obtain a generalized Neumann solution for the two-phase fractional Lam\'{e}-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order $0<\al\leq... Article Full-text available A fractional Stefan's problem with a boundary convective condition is solved, where the fractional derivative of order α (0, 1) is taken in the Caputo sense. Then an equivalence with other two fractional Stefan's problems (the first one with a constant condition on x = 0 and the second with a flux condition) is proved and the convergence to the cla... Article Full-text available This paper deals with a theoretical mathematical analysis of an initial-boundary-value problem for the time-fractional diffusion equation in the quarter plane, where the time-fractional derivative is taken in the Caputo's sense of order$\al\in (0,1)$. For three different cases, changing the condition on the fixed face x=0 (temperature boundary... Article Full-text available Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order$ \al \in (0,1) $is taken in the Caputo's sense. The first one has a constant condition on$ x = 0 $and the second presents a flux condition$ T_x (0, t) = \frac {q} {t ^ {\al/2}} \$. An equivalence between these problems is proved and...
Cited By | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9658227562904358, "perplexity": 617.469721692401}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570921.9/warc/CC-MAIN-20220809094531-20220809124531-00012.warc.gz"} |
https://www.stemcell.com/products/rosettesep-human-t-cell-enrichment-cocktail.html | # RosetteSep™ Human T Cell Enrichment Cocktail
Immunodensity negative selection cocktail
From: 174 USD
## Options
Catalog # (Select a product)
Immunodensity negative selection cocktail
From: 174 USD
# Overview
The RosetteSep™ Human T Cell Enrichment Cocktail is designed to isolate T cells from whole blood by negative selection. Unwanted cells are targeted for removal with Tetrameric Antibody Complexes recognizing non-T cells and glycophorin A on red blood cells (RBCs). When centrifuged over a buoyant density medium such as RosetteSep™ DM-L (Catalog #15705) or Lymphoprep™ (Catalog #07801), the unwanted cells pellet along with the RBCs. The purified T cells are present as a highly enriched population at the interface between the plasma and the buoyant density medium.
• Fast and easy-to-use
• Requires no special equipment or training
• Isolated cells are untouched
• Can be combined with SepMate™ for consistent, high-throughput sample processing
Components:
• RosetteSep™ Human T Cell Enrichment Cocktail (Catalog #15021)
• RosetteSep™ Human T Cell Enrichment Cocktail, 2 mL
• RosetteSep™ Human T Cell Enrichment Cocktail (Catalog #15061)
• RosetteSep™ Human T Cell Enrichment Cocktail, 5 x 2 mL
Subtype:
Cell Isolation Kits
Cell Type:
T Cells
Species:
Human
Sample Source:
Buffy Coat; Whole Blood
Selection Method:
Negative
Application:
Cell Isolation
Brand:
RosetteSep
Area of Interest:
Immunology
Document Type
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Language
(9)
# What is RosetteSep™?
RosetteSep™ is a rapid cell separation procedure for the isolation of purified cells directly from whole blood, without columns or magnets.
# How does RosetteSep™ work?
The antibody cocktail crosslinks unwanted cells to red blood cells (RBCs), forming rosettes. The unwanted cells then pellet with the free RBCs when centrifuged over a density centrifugation medium (e.g. Ficoll-Paque™ PLUS, Lymphoprep™).
# What factors affect cell recovery?
The temperature of the reagents can affect cell recovery. All reagents should be at room temperature (sample, density centrifugation medium, PBS, centrifuge) before performing the isolations. Layering can also affect recovery so be sure to carefully layer the sample to avoid mixing with the density centrifugation medium as much as possible. Be sure to collect the entire enriched culture without disturbing the RBC pellet. A small amount of density centrifugation medium can be collected without worry.
# Which cell samples can RosetteSep™ be used with?
RosetteSep™ can be used with leukapheresis samples, bone marrow or buffy coat, as long as: the concentration of cells does not exceed 5 x 107 per mL (can dilute if necessary); and there are at least 100 RBCs for every nucleated cell (RBCs can be added if necessary).
# Can RosetteSep™ be used with previously frozen or cultured cells?
Yes. Cells should be re-suspended at 2 - 5 x 107 cells / mL in PBS + 2% FBS. Fresh whole blood should be added at 250 µL per mL of sample, as a source of red cells.
# Can RosetteSep™ be used to enrich progenitors from cord blood?
Yes. Sometimes cord blood contains immature nucleated red cells that have a lower density than mature RBCs. These immature red cells do not pellet over Ficoll™, which can lead to a higher RBC contamination than peripheral blood separations.
# Does RosetteSep™ work with mouse cells?
No, but we have developed EasySep™, a magnetic-based cell isolation system which works with mouse and other non-human species.
# Which anticoagulant should be used with RosetteSep™?
Peripheral blood should be collected in heparinized Vacutainers. Cord blood should be collected in ACD.
# Should the anticoagulant be washed off before using RosetteSep™?
No, the antibody cocktail can be added directly to the sample.
# Product Applications
This product is designed for use in the following research area(s) as part of the highlighted workflow stage(s). Explore these workflows to learn more about the other products we offer to support each research area.
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# Data and Publications
## Publications
(46)
Scientific reports 2019 may
D. Park et al.
Abstract
### Abstract
Mucosal-associated invariant T (MAIT) cells exhibit different characteristics from those of TCRalpha7.2- conventional T cells. They play important roles in various inflammatory diseases, including rheumatoid arthritis and inflammatory bowel disease. MAIT cells express a single T cell receptor alpha chain, TCRalpha7.2 segment associated with Jalpha33 and CDR3 with fixed length, which recognizes bacteria-derived vitamin B metabolites. However, the characteristics of MAIT cells and TCRalpha7.2+ CD161- T cells have never been compared. Here, we performed RNA sequencing to compare the properties of MAIT cells, TCRalpha7.2- conventional T cells and TCRalpha7.2+ CD161- T cells. Genome-wide transcriptomes of MAIT cells, TCRalpha7.2- conventional T cells, and TCRalpha7.2+ CD161- T cells were compared and analyzed using causal network analysis. This is the first report comparing the transcriptomes of MAIT cells, TCRalpha7.2- conventional T cells and TCRalpha7.2+ CD161- T cells. We also identified the predominant signaling pathways of MAIT cells, which differed from those of TCRalpha7.2- conventional T cells and TCRalpha7.2+ CD161- T cells, through a gene set enrichment test and upstream regulator analysis and identified the genes responsible for the characteristic MAIT cell phenotypes. Our study advances the complete understanding of MAIT biology.
Nature biotechnology 2019 feb
### Engineered CRISPR-Cas12a variants with increased activities and improved targeting ranges for gene, epigenetic and base editing.
B. P. Kleinstiver et al.
Abstract
### Abstract
Broad use of CRISPR-Cas12a (formerly Cpf1) nucleases1 has been hindered by the requirement for an extended TTTV protospacer adjacent motif (PAM)2. To address this limitation, we engineered an enhanced Acidaminococcus sp. Cas12a variant (enAsCas12a) that has a substantially expanded targeting range, enabling targeting of many previously inaccessible PAMs. On average, enAsCas12a exhibits a twofold higher genome editing activity on sites with canonical TTTV PAMs compared to wild-type AsCas12a, and we successfully grafted a subset of mutations from enAsCas12a onto other previously described AsCas12a variants3 to enhance their activities. enAsCas12a improves the efficiency of multiplex gene editing, endogenous gene activation and C-to-T base editing, and we engineered a high-fidelity version of enAsCas12a (enAsCas12a-HF1) to reduce off-target effects. Both enAsCas12a and enAsCas12a-HF1 function in HEK293T and primary human T cells when delivered as ribonucleoprotein (RNP) complexes. Collectively, enAsCas12a provides an optimized version of Cas12a that should enable wider application of Cas12a enzymes for gene and epigenetic editing.
Nature medicine 2018 OCT
M. Cerezo et al.
Abstract
### Abstract
Preventing the immune escape of tumor cells by blocking inhibitory checkpoints, such as the interaction between programmed death ligand-1 (PD-L1) and programmed death-1 (PD-1) receptor, is a powerful anticancer approach. However, many patients do not respond to checkpoint blockade. Tumor PD-L1 expression is a potential efficacy biomarker, but the complex mechanisms underlying its regulation are not completely understood. Here, we show that the eukaryotic translation initiation complex, eIF4F, which binds the 5' cap of mRNAs, regulates the surface expression of interferon-$\gamma$-induced PD-L1 on cancer cells by regulating translation of the mRNA encoding the signal transducer and activator of transcription 1 (STAT1) transcription factor. eIF4F complex formation correlates with response to immunotherapy in human melanoma. Pharmacological inhibition of eIF4A, the RNA helicase component of eIF4F, elicits powerful antitumor immune-mediated effects via PD-L1 downregulation. Thus, eIF4A inhibitors, in development as anticancer drugs, may also act as cancer immunotherapies.
Journal of immunological methods 2017 MAR
### T cell activation and proliferation following acute exercise in human subjects is altered by storage conditions and mitogen selection.
Siedlik JA et al.
Abstract
### Abstract
Recent work investigating exercise induced changes in immunocompetence suggests that some of the ambiguity in the literature is resultant from different cell isolation protocols and mitogen selection. To understand this effect, we compared post-exercise measures of T cell activation and proliferation using two different stimulation methods (costimulation through CD28 or stimulation with phytohaemagglutinin [PHA]). Further, we investigated whether exercise induced changes are maintained when T cell isolation from whole blood is delayed overnight in either a room temperature or chilled (4°C) environment. As expected, an increased proliferation response was observed post-exercise in T cells isolated from whole blood of previously trained individuals immediately after blood collection. Also, cells stimulated with PHA after resting overnight in whole blood were not adversely impacted by the storage conditions. In contrast, allowing cells to rest overnight in whole blood prior to stimulation through CD28, lessened the proliferation observed by cells following exercise rendering both the room temperature and chilled samples closer to the results seen in the control condition. Changes in early markers of activation (CD25), followed a similar pattern, with activation in PHA stimulated cells remaining fairly robust after overnight storage; whereas cell activation following stimulation through CD3+CD28 was disproportionately decreased by the influence of overnight storage. These findings indicate that decisions regarding cell stimulation methods need to be paired with the timeline for T cell isolation from whole blood. These considerations will be especially important for field based studies of immunocompetence where there is a delay in getting whole blood samples to a lab for processing as well as clinical applications where a failure to isolate T cells in a timely manner may result in loss of the response of interest.
PloS one 2017
Ayuso T et al.
Abstract
### Abstract
OBJECTIVE Vitamin D deficiency has been linked to increased risk of multiple sclerosis (MS) and poor outcome. However, the specific role that vitamin D plays in MS still remains unknown. In order to identify potential mechanisms underlying vitamin D effects in MS, we profiled epigenetic changes in vitamin D receptor (VDR) gene to identify genomic regulatory elements relevant to MS pathogenesis. METHODS Human T cells derived from whole blood by negative selection were isolated in a set of 23 relapsing-remitting MS (RRMS) patients and 12 controls matched by age and gender. DNA methylation levels were assessed by bisulfite cloning sequencing in two regulatory elements of VDR. mRNA levels were measured by RT-qPCR to assess changes in VDR expression between patients and controls. RESULTS An alternative VDR promoter placed at exon 1c showed increased DNA methylation levels in RRMS patients (median 30.08%, interquartile range 19.2%) compared to controls (18.75%, 9.5%), p-valuetextless0.05. Moreover, a 6.5-fold increase in VDR mRNA levels was found in RRMS patients compared to controls (p-valuetextless0.001). CONCLUSIONS An alternative promoter of the VDR gene shows altered DNA methylation levels in patients with multiple sclerosis, and it is associated with VDR mRNA upregulation. This locus may represent a candidate regulatory element in the genome relevant to MS pathogenesis.
STEMCELL TECHNOLOGIES INC.’S QUALITY MANAGEMENT SYSTEM IS CERTIFIED TO ISO 13485. PRODUCTS ARE FOR RESEARCH USE ONLY AND NOT INTENDED FOR HUMAN OR ANIMAL DIAGNOSTIC OR THERAPEUTIC USES UNLESS OTHERWISE STATED. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4980553090572357, "perplexity": 14677.436606368803}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540569146.17/warc/CC-MAIN-20191213202639-20191213230639-00057.warc.gz"} |
http://cfpm.org/~majordom/memetics/old/3506.html | # RE: Memes and Leibniz's view of intellect
Chris Lofting ([email protected])
Wed, 29 Sep 1999 05:02:37 +1000
```From: "Chris Lofting" <[email protected]>
To: <[email protected]>
Subject: RE: Memes and Leibniz's view of intellect
Date: Wed, 29 Sep 1999 05:02:37 +1000
```
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]On Behalf
> Of Mark M. Mills
> Sent: Wednesday, 29 September 1999 3:09
> To: [email protected]
> Subject: Memes and Leibniz's view of intellect
>
>
> This seems an attractive idea to me. It solves the 'chicken and
> egg' problem
> for memes. L-memes emerge from properties of
> bio-electro-chemistry. G-memes
> (cultural expressions) emerge from populations of L-memes.
> puts the G-meme/L-meme conversation in terms of Leibniz, Locke
> and Hobbes.
implicit in this is that L-memes are archetypal and G-memes typal where
archetypal are 'pure'forms that are invarient and typal are 'mixed' forms.
Zoom-in on both and you should be able to easily differentiate the same
distinctions within each concept, thus within L-memes there is a structural
emphasis that is archetypal and an interactive emphasis that is thus typal
in that typal states favour dynamics, change and so transformations. From
the typal emerges a 'new' level, the archetypal G-memes that in turn are
seen to develop typal elements and so on. The further the development the
more 'ethereal' we get.
===============================================================
This was distributed via the memetics list associated with the
Journal of Memetics - Evolutionary Models of Information Transmission
For information about the journal and the list (e.g. unsubscribing)
see: http://www.cpm.mmu.ac.uk/jom-emit | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8370144963264465, "perplexity": 24451.457067708052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745522.86/warc/CC-MAIN-20181119084944-20181119110944-00335.warc.gz"} |
https://brilliant.org/practice/de-moivres-theorem-level-2-3-challenges/ | Algebra
# De Moivre's Theorem: Level 3 Challenges
$\large { z }^{ 3 }=1$
What is the set of all $z$ that satisfy the equation above?
Note: $\omega = \frac{ -1 + \sqrt 3 i}{2}$ where $i =\sqrt{-1}$.
Find the value of $(2-\omega)(2-\omega^2)(2-\omega^{10})(2-\omega^{11}).$
Details and Assumptions:
$\omega$ is a non-real cube root of unity.
The five roots of the equation $z^{5}=4-4i$ each take the form
$\Large \sqrt{2} e ^ { \frac{ k \pi i } { 20} },$
where $k$ is a positive integer less than 40.
Find the sum of all values of $k$.
$\large x + \frac 1 x = \sqrt 3\ , \ \ \ \ \ \ \ x^{200} + \frac {1}{x^{200}} = \ ?$
If the $6$ solutions of $x^{6}=-64$ are written in the form $a+ib$, where $a$ and $b$ are real, then what is the product of those solutions with $a>0$?
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 21, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9598407745361328, "perplexity": 131.16851782331014}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250595787.7/warc/CC-MAIN-20200119234426-20200120022426-00378.warc.gz"} |
https://gateoverflow.in/tag/load-back-cache | In the memory access time formula for the hierarchical cache - which is given as :$Emat = H1\times T1 + (1-H1)(H2\times (T1+T2) + (1-H2)\times (T1+T2+T3))$ (where Hi = Hit Ratio for the i-th level cache and Ti = Access time for i-th level ... been transferred into the cache. Is my intuition correct? If yes, then what should be the Emat formula for Load Back cache ? Should we add extra Ti values? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8447291254997253, "perplexity": 943.9129737123516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738735.44/warc/CC-MAIN-20200811055449-20200811085449-00245.warc.gz"} |
https://toph.co/p/batman-needs-your-help | # Practice on Toph
Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.
By al.noman · Limits 1s, 512 MB
Hello Batman or Joker fans!! You all know that in the history of movie, one of the smartest villain is Joker. The reason behind of it is Joker always gives brainstorming challenges to the Gotham police as well as Batman.
This time Joker locked up Batman. He gave a string related challenge to Gordon(chief of Gotham police) and asked to find a new string from two original strings. This new string is the password to rescue Batman. Gordon came to you to solve this challenge.
Joker gave two non-empty strings $A$ of length $N$ and $B$ of length $M$. You are supposed to take a prefix $P_A$ of any length (maybe 0) from $A$ and a suffix $S_B$ of any length (maybe 0) from $B$. After concatenating $P_A$ and $S_B$, the new resulting string need to be palindrome. And the length of the determined string should be maximum. If multiple string of same length can be determined then choose lexicographically minimum.
Dare you to take this challenge and rescue Batman?
## Input
The first line contains string $A$ and the second line contains string $B$ $(2 \leq N + M \leq 2\cdot10^{6})$.
$A$ and $B$ consist of lowercase Latin alphabet.
## Output
Print the determined string in a single line.
## Samples
InputOutput
abcded
cbaa
aaa
InputOutput
abcded
cba
abcdedcba
### Statistics
72% Solution Ratio
serotoninEarliest, 2w ago
MatrixFastest, 0.0s
imdumbLightest, 6.2 MB
serotoninShortest, 1222B | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29086077213287354, "perplexity": 2586.17189199779}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738015.38/warc/CC-MAIN-20200808165417-20200808195417-00154.warc.gz"} |
https://discourse.mc-stan.org/t/calculate-cumulative-sum-in-stan/9639 | # Calculate cumulative sum in stan
model {
alpha ~ normal(0,10);
sigma ~ cauchy(0,10);
b_0 ~ cauchy(0,10);
b_titer ~ cauchy(0,10);
for (n in 1:N){
vector[N] theta;
theta[n] = inv_logit(b_0 + b_titer*low[n]);
for (i in 1:100){
vector[100] theta_sep;
theta_sep[i] = inv_logit(b_0 + b_titer*(low[n]+i*(diff[n]/100)));
}
theta[n] = theta[n] + sum(theta_sep);
target += bernoulli_lpmf(infection[n] | theta[n]);
}
always error, than there is no thets_sep…
Hi! It seems your `theta_sep` variable gets reassigned every iteration during the for loop over `i` while you only define `theta_sep[i]` in every iteration. This would mean that `theta_sep[-i]` is not defined and therefore you cannot sum this. Can you try the following?
``````model {
alpha ~ normal(0,10);
sigma ~ cauchy(0,10);
b_0 ~ cauchy(0,10);
b_titer ~ cauchy(0,10);
for (n in 1:N){
vector[N] theta;
vector[100] theta_sep;
theta[n] = inv_logit(b_0 + b_titer*low[n]);
for (i in 1:100){
theta_sep[i] = inv_logit(b_0 + b_titer*(low[n]+i*(diff[n]/100)));
}
theta[n] = theta[n] + sum(theta_sep);
target += bernoulli_lpmf(infection[n] | theta[n]);
}
``````
Also, if this doesn’t work, can you copy and paste the exact error message?
You probably also want to move theta out of the n loop. For the same reason.
``````model {
vector[N] theta;
alpha ~ normal(0,10);
sigma ~ cauchy(0,10);
b_0 ~ cauchy(0,10);
b_titer ~ cauchy(0,10);
for (n in 1:N){
vector[100] theta_sep;
theta[n] = inv_logit(b_0 + b_titer*low[n]);
for (i in 1:100){
theta_sep[i] = inv_logit(b_0 + b_titer*(low[n]+i*(diff[n]/100)));
}
theta[n] = theta[n] + sum(theta_sep);
target += bernoulli_lpmf(infection[n] | theta[n]);
}
}
``````
1 Like
Yes, good catch!
yeah, I changed, works now, thanks all :p
1 Like | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.897972047328949, "perplexity": 24639.402537074086}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00461.warc.gz"} |
https://pure.fujita-hu.ac.jp/en/publications/appropriate-nonwoven-filters-effectively-capture-human-peripheral | # Appropriate nonwoven filters effectively capture human peripheral blood cells and mesenchymal stem cells, which show enhanced production of growth factors
Hideo Hori, Ushio Iwamoto, Gen Niimi, Masanori Shinzato, Yoshiyuki Hiki, Yasuo Tokushima, Kazunori Kawaguchi, Atsushi Ohashi, Shigeru Nakai, Mikitomo Yasutake, Nobuya Kitaguchi
Research output: Contribution to journalArticlepeer-review
5 Citations (Scopus)
## Abstract
Scaffolds, growth factors, and cells are three essential components in regenerative medicine. Nonwoven filters, which capture cells, provide a scaffold that localizes and concentrates cells near injured tissues. Further, the cells captured on the filters are expected to serve as a local supply of growth factors. In this study, we investigated the growth factors produced by cells captured on nonwoven filters. Nonwoven filters made of polyethylene terephthalate (PET), biodegradable polylactic acid (PLA), or chitin (1.2–22 μm fiber diameter) were cut out as 13 mm disks and placed into cell-capturing devices. Human mesenchymal stem cells derived from adipose tissues (h-ASCs) and peripheral blood cells (h-PBCs) were captured on the filter and cultured to evaluate growth factor production. The cell-capture rates strongly depended on the fiber diameter and the number of filter disks. Nonwoven filter disks were composed of PET or PLA fibers with fiber diameters of 1.2–1.8 μm captured over 70 % of leukocytes or 90 % of h-ASCs added. The production of vascular endothelial growth factor (VEGF), transforming growth factor β1, and platelet-derived growth factor AB were significantly enhanced by the h-PBCs captured on PET or PLA filters. h-ASCs on PLA filters showed significantly enhanced production of VEGF. These enhancements varied with the combination of the nonwoven filter and cells. Because of the enhanced growth factor production, the proliferation of human fibroblasts increased in conditioned medium from h-PBCs on PET filters. This device consisting of nonwoven filters and cells should be investigated further for possible use in the regeneration of impaired tissues.
Original language English 55-63 9 Journal of Artificial Organs 18 1 https://doi.org/10.1007/s10047-014-0794-9 Published - 03-2015
## All Science Journal Classification (ASJC) codes
• Medicine (miscellaneous)
• Biomaterials
• Biomedical Engineering
• Cardiology and Cardiovascular Medicine
## Fingerprint
Dive into the research topics of 'Appropriate nonwoven filters effectively capture human peripheral blood cells and mesenchymal stem cells, which show enhanced production of growth factors'. Together they form a unique fingerprint. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8051670789718628, "perplexity": 18366.178956267286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662558015.52/warc/CC-MAIN-20220523101705-20220523131705-00681.warc.gz"} |
https://www.homebuiltairplanes.com/forums/threads/how-to-buy-and-fly-cheap-in-2022.37617/page-5#post-641908 | # How to 'buy and fly' cheap in 2022?
### Help Support Homebuilt Aircraft & Kit Plane Forum:
#### JayKoit
##### Well-Known Member
Joined
Jan 17, 2013
Messages
113
Location
Los Angeles, CA
She's kinda like the wife ... "It's cheaper to keep her."
Appreciate the thought though ...
Lol, I totally understand
#### JayKoit
##### Well-Known Member
Joined
Jan 17, 2013
Messages
113
Location
Los Angeles, CA
Where in AZ?
Prescott, and I’ll be 8 minutes from the airport. Are you in AZ?
#### jedi
##### Well-Known Member
Joined
Aug 8, 2009
Messages
3,233
Location
Sahuarita Arizona, Renton Washington, USA
Prescott, and I’ll be 8 minutes from the airport. Are you in AZ?
Yes, Sahuarita is south of Tucson. There is (or at least was?) a small glider club with a winch in Prescott. I spent two semesters there with ERU. Also a local hang glider school and an exciting, to me, launch overlooking Cottonwood.
#### JayKoit
##### Well-Known Member
Joined
Jan 17, 2013
Messages
113
Location
Los Angeles, CA
Our EAA chapter is now digging up the road to prevent him from moving.
Lol! So that's why there's always construction on the interstate whenever I head out there
Joined
Mar 28, 2017
Messages
1,251
Location
Just an Ohioan
#### BBerson
##### Light Plane Philosopher
Supporting Member
Joined
Dec 16, 2007
Messages
15,912
Location
Port Townsend WA
That's nothing. I bought it in Corpus Christi Texas and hauled it to Alaska.
#### Bigshu
##### Well-Known Member
Supporting Member
Joined
Jun 7, 2020
Messages
1,293
Location
KCMO, midwestern USA
Prescott, and I’ll be 8 minutes from the airport. Are you in AZ?
A guy I used to work with always said how nice Prescott is, and that was his planned retirement destination. Didn't retire when he should have....
#### pfarber
##### Well-Known Member
Joined
Feb 21, 2019
Messages
1,002
Location
Dollywood
The thought of no insurance is pretty much a non-starter. if I'm putting years of my hard earned savings into the plane, I'll insure it.
For a $20k airplane your hull insurance will be stupid expensive.$3k a year, in 6 years you just bought another airplane.
#### Daleandee
##### Well-Known Member
Joined
Sep 11, 2015
Messages
1,847
Location
SC
For a $20k airplane your hull insurance will be stupid expensive.$3k a year, in 6 years you just bought another airplane.
Not in every case ... or at least not in mine.
#### Brünner
##### Well-Known Member
Joined
Apr 12, 2020
Messages
323
Location
Beer country
What about a Piper Tripacer? Always wanted one without the nose weight...
#### cluttonfred
##### Well-Known Member
Supporting Member
Joined
Feb 13, 2010
Messages
9,523
Location
World traveler
What about a Piper Tripacer? Always wanted one without the nose weight...
Then it’s a Pacer. ;-)
Tri-Pacers and Colts used to be very cheap because they were looked down on by the collectors. I think those days are over but they still cost less than the earlier taildraggers.
I certainly wouldn’t turn my nose up at a nice one.
Last edited:
#### JayKoit
##### Well-Known Member
Joined
Jan 17, 2013
Messages
113
Location
Los Angeles, CA
A guy I used to work with always said how nice Prescott is, and that was his planned retirement destination. Didn't retire when he should have....
it really is a nice place. In all my conversations with both locals and people who’ve visited, not one person had said they don't like it.
What about a Piper Tripacer? Always wanted one without the nose weight...
Then it’s a Pacer. ;-)
Tri-Pacers and Colts used to be very cheap because they were looked down on by the collectors. I think those days are over but they still cost less than the earlier taildraggers.
I certainly wouldn’t turn my nose up at a nice one.
View attachment 120962
View attachment 120963
I really like the Colts and Tri Pacers. They’re on my list as well, but I’d slightly prefer all metal or composite. But if the right one comes along...
#### jedi
##### Well-Known Member
Joined
Aug 8, 2009
Messages
3,233
Location
Sahuarita Arizona, Renton Washington, USA
it really is a nice place. In all my conversations with both locals and people who’ve visited, not one person had said they don't like it.
When I spent December to February in Prescott I said this is just like Michigan and left. Very nice though the rest of the year.
FWIW- In Michigan February occationally starts in November and doesn't end for sure till March and even later on occasion.
#### fretman_2
##### Active Member
Joined
May 19, 2021
Messages
31
While not the most glamorous, renting is going to be the least expensive way to log an hour in the air. Money only flows when the hourmeter is running.
When you own the clock is running 24/7.
That's not the whole picture. It depends on the number of hours you fly. If you like to fly a lot, you'd better do your cost comparisons because it may be cheaper per hour to own an airplane. If you only fly 30 hours a year or less...might be best to keep renting if you can't afford to buy. Club rental can be ok, but not ok if you want to do something outside what's allowed. The last time I looked at the rules, the local club makes it prohibitive to keep the airplane overnight on xcountries. They want that airplane available for rent. No good for me. A couple of those former club guys are in my EAA chapter...they all own airplanes now.
#### fretman_2
##### Active Member
Joined
May 19, 2021
Messages
31
For a $20k airplane your hull insurance will be stupid expensive.$3k a year, in 6 years you just bought another airplane.
My airplane is insured for $40K and my insurance is less than$800. I'm 65 years old and I flew 65 hours last year. The number of hours I flew got the price down! I'm a member of EAA and my insurance is through them.
#### Bill-Higdon
##### Well-Known Member
Joined
Feb 6, 2011
Messages
2,282
Location
Salem, Oregon, USA
When I spent December to February in Prescott I said this is just like Michigan and left. Very nice though the rest of the year.
FWIW- In Michigan February occationally starts in November and doesn't end for sure till March and even later on occasion.
Nahh they don't use 3 feet of salt for 3 inches of snow in Prescott
#### Turd Ferguson
##### Well-Known Member
Supporting Member
Joined
Mar 13, 2008
Messages
6,112
Location
Upper midwest in a house
That's not the whole picture. It depends on the number of hours you fly. If you like to fly a lot, you'd better do your cost comparisons because it may be cheaper per hour to own an airplane.
Well, it also depends on what kind of plane you want to own.
A basic 2 seat or simple homebuilt has a low operating cost so one can break even with fewer hrs. If one wants to log time in a high perf/retract airplane, the picture changes drastically.
One plane I own now has a break even of about 30 hrs. But the kicker is I only own 1/10 of the airplane. If I owned the plane outright, it would be much cheaper to rent an equivalent airplane 30 hrs a yr by a factor of about 10. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24436944723129272, "perplexity": 6333.452395135055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571147.84/warc/CC-MAIN-20220810040253-20220810070253-00360.warc.gz"} |
http://blog.computationalcomplexity.org/2008/08/discounted-time.html | ## Friday, August 08, 2008
### Discounted Time
A write-up of some ideas I presented at the Complexity Conference Rump Session.
In computational complexity when we talk about time it usually represents a hard limit in the running time, solving the problem in time t(n). So we are happy, say, if we can solve the problem in one hour and miserable if it takes 61 minutes. But our real gradation of happiness over the running time is not so discontinuous.
Let's take an idea from how economists deal with time. They discount the utility by a factor of δ in each time step for some δ<1. What if we did the same for complexity?
Let δ = 1-ε for ε>0 and very small. Think ε about 10-12. We then discount the value of the solution by a factor δt for t steps of computation.
Discounted time gives us a continuous loss due to time. It has the nice property that the future looks like the past: The discount for t steps now is the same as the the discount for the t steps already taken.
When t is small, δt is about 1-εt, a linear decrease. For t large, δt is about e-εt, an exponential decrease.
We can also recover traditional complexity classes. DTIME(O(m(n)) is the set of languages such that for some constant c>0, δt>c for δ=(1-1/m(n)).
I'm not sure what to do with discounted time which is why this is a blog post instead of a FOCS paper.
Some ideas:
• What does average case and expected time mean in the discounted time model?
• What if you take the value of the solution of some approximation problem and discount it with the time taken? Can you determine the optimal point to stop?
1. Instead of talking about the expected time to solve a problem, this transitions nicely to the expected value of that solution. For approximation problems, you can combine that with a function expressing the value of an approximation relative to the value of the optimal solution.
Combining them you get the expected value of approximately solving the problem in time t, given the accuracy you expect to develop in time t, relative to having the optimal solution immediately.
For time constrained problems, this favors algorithms that can produce more than an 1/δ improvement in the value of the approximate result in a given unit of time, over a period of time within the time constraint.
This also suggests an optimal length of time to run such algorithms: until the expected improvement per unit time drops below 1/δ.
2. This reminds me of a poly-time algorithm for factoring integers that I heard from Ed Fredkin. You don't even need quantum computers for it; you only need Moore's law. If processing speed continues increasing exponentially, then you need only wait a number of years that is linear in the number of bits of your input.
If you don't believe Moore's law will last for much longer, then you could instead rely on economic growth. If the economy grows in real terms by at least a constant rate, then you can invest money in a foundation where it will grow exponentially until there is enough to buy enough computers to solve the problem.
(Hopefully it's clear that he was joking.)
3. Actually, the factoring algorithm is sub-linear. If it takes time exp(O(n^{1/3})) to factor an n-bit number, then the same can also be achieved with O(n^{1/3}) doublings of processor power.
4. One of the first papers I read in complexity was a paper by Levin (about complexity-theoretic cryptography, I think), where the first sentence of a proof was: (paraphrase) without loss of generality, we may assume that all algorithms run in O(1) time (/paraphrase)
needless to say, i was stunned - until I realized that the quantity he was analyzing was the product of the running time and success probability of the algorithm, and was alluding to "normalizing" algorithms in the following way: if it was a worst-case t(n) time computation, toss a coin with Pr[heads] = 1/t(n), and perform the computation iff you see heads. This changes the (expected) running time to O(1) while leaving the product of the two quantities still analyzable.
I suspect that one can similarly hack around with your notion of utility (which is certainly an interesting way to think about computations).
5. This concept has been explored in Databases, Real time systems and AI where it is known as a "soft deadline". Typically there is a desired time by which the result should be computed, but thereafter the utility drops according to some function, rather than a sharp threshold.
They were introduced, as far as I know, by Garcia-Molina and Abbott in a
SIGMOD Record paper
in 1988.
6. Just a note to add that the fact that this idea has been proposed before should not stop anyone from doing research on it. In fact, if other people have proposed it this is an indication that there is interest in the study of such a measure. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8834285736083984, "perplexity": 553.18024931015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510270399.7/warc/CC-MAIN-20140728011750-00255-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://www.doubtnut.com/question-answer-physics/there-is-a-constant-homogeneous-electric-field-of-100-vm-1-within-the-region-x0-and-x0167-m-pointing-644108151 | # There is a constant homogeneous electric field of 100 Vm^-1 within the region x=0 and x=0.167 m pointing in x-direction. There is a constant homogeneous mangetic field B within the region x=0.167 m and x=0.334 m pointing in the z-direction. A proton at rest at the origin is released in positive x-direction. Find the minimum strength of the magnetic field B, so that the proton is detected back at x=0, y=0.167 m. (mass of proton = 1.67 xx 10^(-27) kg)
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Updated On: 24-5-2021
Apne doubts clear karein ab Whatsapp par bhi. Try it now.
First of all the proton is accelerated in the electric field. <br> Then it enters in magnetic field and describes a circular path. After that it leaves the magnetic field and describes a circular path. <br> After that it leaves the magnetic field in negative direction. Its <br> motion is retarded in electric field. Finally, it strikes y-axis at <br> the same distance 0.167m. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/BMS_V05_C01_S01_054_S01.png" width="80%"> <br> Let us first calculate the velocity of the proton when it entres in <br> magnetic field after traversing in electric field. <br> Force acting on proton in electric field =eE <br> :. Acceleration of proton a=((eE)/m) <br> Using the formula v^2+u^2=2as, we have <br> v^2=2((eE)/m)s=2((eE)/m) (0.167)....(i) <br> Now consider the motion in magnetic field. The proton describes <br> a circular path of radius (AC//2). <br> Hence, (mv^2)/r=evB or B=(mv)/(er)....(ii) <br> :. B=m/(e(0.1667//2))xxsqrt([(2eE)/m(0.167)]) <br> =2sqrt(((2m)/(e)xxE/(0.167)))=2sqrt([(2(2.67xx10^-27)(100))/(1.6xx10^(-19)(0.167))]) <br> =(10^-2)/sqrt2=7.07xx10^-3T | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4928604066371918, "perplexity": 4439.794785416472}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964361064.58/warc/CC-MAIN-20211201234046-20211202024046-00132.warc.gz"} |
https://www.ias.ac.in/listing/articles/pram/076/04 | • Volume 76, Issue 4
April 2011, pages 533-690
• Travelling wave solutions to nonlinear physical models by means of the first integral method
This paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established first integrals, exact solutions are successfully constructed for the equations considered.
• Bianchi type-I massive string magnetized barotropic perfect fluid cosmological model in bimetric theory
Bianchi type-I massive string cosmological model for perfect fluid distribution in the presence of magnetic field is investigated in Rosen’s [Gen. Relativ. Gravit. 4, 435 (1973)] bimetric theory of gravitation. To obtain the deterministic model in terms of cosmic time, we have used the condition $A = (B C)^n$, where n is a constant, between the metric potentials. The magnetic field is due to the electric current produced along the 𝑥-axis with infinite electrical conductivity. Some physical and geometrical properties of the exhibited model are discussed and studied.
• Entropy of the Kerr–Sen black hole
We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.
• A transformed rational function method for (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation
A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial differential equations.
• Investigation of $\Delta(3,3)$ resonance effects on the properties of neutron-rich double magic spherical finite nucleus, 132Sn, in the ground state and under compression
Within the framework of the radially constrained spherical Hartree–Fock (CSHF) approximation, the resonance effects of delta on the properties of neutron-rich double magic spherical nucleus 132Sn were studied. It was found that most of the increase in the nuclear energy generated under compression was used to create massive 𝛥 particles. For 132Sn nucleus under compression at 3.19 times density of the normal nuclear density, the excited nucleons to 𝛥s were increased sharply up to 16% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels were calculated and their behaviours under compression were examined. A meaningful agreement was obtained between the results with effective Hamiltonian and that with the phenomenological shell model for the low-lying single-particle spectra. The results suggest considerable reduction in compressibility for the nucleus, and softening of the equation of state with the inclusion of 𝛥s in the nuclear dynamics.
• Vibrational analysis of Fourier transform spectrum of the $B^3 \Sigma^-_u (0^+_u) - X^3 \Sigma^-_g (0^+_g)$ transition of 80Se2 molecule
The emission spectra of $B^3 \Sigma^-_u (0^+_u) - X^3 \Sigma^-_g (0^+_g)$ transition of the isotopic species 80Se2, excited in an electrodeless discharge lamp by the microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and 𝑟-centroid values.
• Goos–Hänchen shift for higher-order Hermite–Gaussian beams
We study the reflection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no significant distortion upon reflection. We report Goos–Hänchen shift for all the spots of a higherorder Hermite–Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.
• Acoustic wave propagation in $Ni_3 R$ (𝑅 = Mo, Nb, Ta) compounds
The ultrasonic properties of the hexagonal closed packed structured $Ni_3$Mo, $Ni_3$Nb and $Ni_3$Ta compounds were studied at room temperature for their characterization. For the investigations of ultrasonic properties, the second-order elastic constants using Lennard–Jones potential were computed. The velocities $V_1$ and $V_2$ have minima and maxima respectively at 45° with the unique axis of the crystal, while $V_3$ increases with respect to angle with the unique axis of the crystal. The inconsistent behaviour of angle-dependent velocities is associated with the action of second-order elastic constants. Debye average sound velocities of these compounds increase with the angle and has maximum at $55^{\circ}$ with the unique axis at room temperature. Hence, when a sound wave travels at $55^{\circ}$ with the unique axis of these materials, the average sound velocity is found to be maximum. The results achieved are discussed and compared with the available experimental and theoretical results.
• Dielectric relaxation studies in 5CB nematic liquid crystal at 9 GH$_z$ under the influence of external magnetic field using microwave cavity spectrometer
Resonance width, shift in resonance frequency, relaxation time and activation energy of 5CB nematic liquid crystal are measured using microwave cavity technique under the influence of an external magnetic field at 9 GHz and at different temperatures. The dielectric response in liquid crystal at different temperatures and the effects of applied magnetic field on transition temperatures are studied in the present work. The technique needs a small quantity (< 0.001 cm3) of the sample and provides fruitful information about the macroscopic structure of the liquid crystal.
• Meyer–Neldel DC conduction in chalcogenide glasses
Meyer–Neldel (MN) formula for DC conductivity ($\sigma_{\text{DC}}$) of chalcogenide glasses is obtained using extended pair model and random free energy barriers. The integral equations for DC hopping conductivity and external conductance are solved by iterative procedure. It is found that MN energy ($\Delta E_{\text{MN}}$) originates from temperature-induced configurational and electronic disorders. Single polaron-correlated barrier hopping model is used to calculate $\sigma_{\text{DC}}$ and the experimental data of Se, As2S3, As2Se3 and As2Te3 are explained. The variation of attempt frequency $\upsilon_0$ and $\Delta E_{\text{MN}}$ with parameter $(r/a)$, where 𝑟 is the intersite separation and 𝑎 is the radius of localized states, is also studied. It is found that $\upsilon_0$ and $\Delta E_{\text{MN}}$ decrease with increase of $(r/a)$, and $\Delta E_{\text{MN}}$ may not be present for low density of defects.
• Magnetic behaviour of AuFe and NiMo alloys
We study the electronic structure and a mean-field phase analysis based on the pair–pair energies derived from first-principles electronic structure calculations of AuFe and NiMo alloys. We have used the tight-binding linear muffin-tin orbitals-based augmented space recursion (TB-LMTO-ASR) method to do so. We investigate different behaviours of the two alloy systems by mapping the problems onto equivalent Ising models and then discuss the magnetic phase diagrams using the calculated pair energies. All three phases: paramagnetic, random ferromagnetic and spin glass, have been studied.
• Mismatch of dielectric constants at the interface of nanometer metal-oxide-semiconductor devices with high-𝐾 gate dielectric impacts on the inversion charge density
The comparison of the inversion electron density between a nanometer metal-oxidesemiconductor (MOS) device with high-𝐾 gate dielectric and a SiO2 MOS device with the same equivalent oxide thickness has been discussed. A fully self-consistent solution of the coupled Schrödinger–Poisson equations demonstrates that a larger dielectric-constant mismatch between the gate dielectric and silicon substrate can reduce electron density in the channel of a MOS device under inversion bias. Such a reduction in inversion electron density of the channel will increase with increase in gate voltage. A reduction in the charge density implies a reduction in the inversion electron density in the channel of a MOS device. It also implies that a larger dielectric constant of the gate dielectric might result in a reduction in the source–drain current and the gate leakage current.
• A simplified approach for the generation of projection data for cone beam geometry
To test a developed reconstruction algorithm for cone beam geometry, whether it is transmission or emission tomography, one needs projection data. Generally, mathematical phantoms are generated in three dimensions and the projection for all rotation angles is calculated. For non-symmetric objects, the process is cumbersome and computation intensive. This paper describes a simple methodology for the generation of projection data for cone beam geometry for both transmission and emission tomographies by knowing the object’s attenuation and/or source spatial distribution details as input. The object details such as internal geometrical distribution are nowhere involved in the projection data calculation. This simple approach uses the pixilated object matrix values in terms of the matrix indices and spatial geometrical coordinates. The projection data of some typical phantoms (generated using this approach) are reconstructed using standard FDK algorithm and Novikov’s inversion formula. Correlation between the original and reconstructed images has been calculated to compare the image quality.
• Bianchi type-V string cosmological models in general relativity
Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.
• # Pramana – Journal of Physics
Current Issue
Volume 93 | Issue 5
November 2019
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8841332197189331, "perplexity": 1537.5971650975016}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319470.94/warc/CC-MAIN-20190824020840-20190824042840-00150.warc.gz"} |
https://www.physicsforums.com/threads/preperation-of-bromine-gas.170099/ | # Preperation of bromine gas
1. May 13, 2007
### jamesyboy1990
1. The problem statement, all variables and given/known data
Ok hi. I have this reaction for a lab due in about 2 weeks. It is on the preperation of bromine gas. The exact reaction was assigned (which is why i didn't choose a less-complex method, such as 2KBr + Cl2 --> 2KCl + Br2). My problem is that i need information (ie. internet websites, textbooks) becasue i need to have information such as:
- nature of reaction (atomic/molecular)
- bonding (intermolecular/intramolecular)
- energy (endo/exothermic)
- entropy (chaos)
- number of particles before and after, state of particle, complexity of part
- rate of reaction (actually, thats what my lab will be about)
- acidic/basic/redox
2. Relevant equations
2KBr + MnO2 + 2H2SO4 --> K2SO4 + MnSO4 + 2H2O + Br2 (gas)
3. The attempt at a solution
I have looked through numerous textbooks at the public library and websites and havent found any information on this reaction. If anyone has informaiton on this reaction, that would be very helpful.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. May 13, 2007
### jamesyboy1990
oh yeah, and since this is my first time ever participating in this forum, please tell me if i'm missing anything
3. May 14, 2007
### chemisttree
You have a good start already. In what oxidation state are bromide and manganese oxide. How about manganese sulfate and bromine gas? Is anything being oxidized or reduced? Can you calculate the enthalpy of the reaction? Will the pH change during the reaction?
You probably know these answers already from your coursework. How will you measure the rate of reaction in the lab? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8221551179885864, "perplexity": 3162.8212567191176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560282937.55/warc/CC-MAIN-20170116095122-00479-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://arxiv.org/abs/1609.02898 | cs.RO
(what is this?)
# Title: A Linear-Time Variational Integrator for Multibody Systems
Abstract: We present an efficient variational integrator for multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equations, transforming forward integration into a root-finding problem for the DEL equations. Variational integrators have been shown to be more robust and accurate in preserving fundamental properties of systems, such as momentum and energy, than many frequently used numerical integrators. However, state-of-the-art algorithms suffer from $O(n^3)$ complexity, which is prohibitive for articulated multibody systems with a large number of degrees of freedom, $n$, in generalized coordinates. Our key contribution is to derive a recursive algorithm that evaluates DEL equations in $O(n)$, which scales up well for complex multibody systems such as humanoid robots. Inspired by recursive Newton-Euler algorithm, our key insight is to formulate DEL equation individually for each body rather than for the entire system. Furthermore, we introduce a new quasi-Newton method that exploits the impulse-based dynamics algorithm, which is also $O(n)$, to avoid the expensive Jacobian inversion in solving DEL equations. We demonstrate scalability and efficiency, as well as extensibility to holonomic constraints through several case studies.
Comments: Submitted to the International Workshop on the Algorithmic Foundations of Robotics (2016) Subjects: Robotics (cs.RO) Cite as: arXiv:1609.02898 [cs.RO] (or arXiv:1609.02898v1 [cs.RO] for this version)
## Submission history
From: Jeongseok Lee [view email]
[v1] Fri, 9 Sep 2016 19:23:54 GMT (517kb) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8015760183334351, "perplexity": 1525.9048492573468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190181.34/warc/CC-MAIN-20170322212950-00023-ip-10-233-31-227.ec2.internal.warc.gz"} |
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0 general-topology × 8 0 linear-algebra × 5 0 real-analysis × 8 0 integration × 4 0 calculus × 7 0 metric-spaces × 4 0 cardinals × 5 0 compactness × 3 0 elementary-set-theory × 5 0 matrices × 3
# 2 Accounts
Mathematics 704 rep 39 MathOverflow 101 rep 2 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7159170508384705, "perplexity": 3227.388624591968}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500808153.1/warc/CC-MAIN-20140820021328-00114-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.ques10.com/p/20130/applied-mathematics-4-question-paper-dec-2016-in-1/ | Question Paper: Applied Mathematics 4 : Question Paper Dec 2016 - Information Technology (Semester 4) | Mumbai University (MU)
0
## Applied Mathematics 4 - Dec 2016
### Information Technology (Semester 4)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1(a) Find the Eigenvalues and eigenvectors of the matrix.
A=$\begin{bmatrix} 2 & 2& 0\\\\ 0 & 2& 1\\\\ 0& 0& 2 \end{bmatrix}$/
(5 marks)
1(b) Evaluate the line integral $$\int_{0}^{l+i}\left ( x^2+iy \right )$$ dz along the path y=x(5 marks) 1(c) Find k and then E (x) for the p.d.f.
$f(x)=\left\{\begin{matrix} k(x-x^2),0\leq x\leq 1,k> 0& \\\\ 0, & otherwise \end{matrix}\right.$/
(5 marks)
1(d) Calculate Karl person's coefficient of correlation from the following data.
x 100 200 300 400 500 y 30 40 50 60 70
(5 marks) 2(a) Show that the matrix $A=\begin{bmatrix} 2 & -2& 3\\\\ 1& 1& 1\\\\ 1& 3& -1 \end{bmatrix}$/ is non-derogatory.(6 marks) 2(b) Evaluate $$\int \frac{e^2^z}{\left ( z+1 \right )^4}$$ dz where C is the circle |z-1|=3(6 marks) 2(c) If x is a normal variate with mean 10 and standard deviation 4 find
i) P(|x-14|<1)
ii) P(5≤x≤18)
iii) P(x≤12)
(8 marks)
3(a) Find the relative maximum of minimum (if any) of the $$Z=X_{1}^{2}+X_{2}^{2}+X_{3}^{2}-4X_1-8X_2-12X_3+100$$(6 marks) 3(b) If x is Binomial distributed with E(x)=2 and V(x)=4/3,find the probability distribution of x.(6 marks) 3(c) If $A=\begin{bmatrix} 2& 1\\\\ 1 & 2 \end{bmatrix}$/,
find A50.
(8 marks)
4(a) Solve the following L.P.P by simplex method Minimize
z=3x1+2x2 Subject to 3x1+2x2≤18
0≤x1≤4
0≤x2≤6
x1,x2≥0.
(6 marks)
4(b) The average of marks scored by 32 boys is 72 with statndard deviation 8 while that of 36 girls is 70 with standard deviation 6. Test 1% level significance whether the boys perform better than the girls.(6 marks) 4(c) Find Laurent's series which represents the function
$$f(z)=\frac{2}{\left ( Z-1 \right )\left ( z-2 \right )}$$ When
i) |z| <1,
ii) 1<|z|<2
iii) |z|>2
(8 marks)
5(a) Evaluate $$\int \frac{Z^2}c_{\left ( z-1 \right )^2\left (z+1 \right )}$$ dz where C is|z| =2 using residue theorem(6 marks) 5(b) The regression lines of a sample are x+6y=6 and 3x+2y=10 Find
i) Sample means
$$\bar{x} \ \text{and}\ \bar{y}$$
ii) Correlation coefficient between x ad y. Also estimate y When x=12
(6 marks)
5(c) A die was thrown 132 times and the following frequencies were observed
No.obtained 1 2 3 4 5 6 Total Frequency 15 20 25 15 29 28 132
Using χ2-test examine the hypothesis that the die is unbiased.
(8 marks)
6(a) Evaluate $$\int ^\infty _\\-\infty\frac{x^2+x+2}{x^4+10x^2+9}$$ dx using contour integration.(6 marks) 6(b) If a random variable x follows Poisson distribution such that P(x-1)=2(x=2) Find the mean the variance of the distribution Also find P(x=3).(6 marks) 6(c) Use Penalty method to solve the following L.P.P. Minimize
z=2x,sub>1+3x2
x1+x2≥5
x1+2x2≥6 x1, x2≥0.
(8 marks) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9678152799606323, "perplexity": 5175.007684648988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315695.36/warc/CC-MAIN-20190821001802-20190821023802-00045.warc.gz"} |
https://encyclopediaofmath.org/index.php?title=Matrix_ring&diff=39111&oldid=36229 | # Difference between revisions of "Matrix ring"
2010 Mathematics Subject Classification: Primary: 16S50 [MSN][ZBL]
full matrix ring
The ring of all square matrices of a fixed order over a ring $R$, with the operations of matrix addition and matrix multiplication. The ring of $(n \times n)$-dimensional matrices over $R$ is denoted by $R_n$ or $M_n(R)$. Throughout this article $R$ is an associative ring with identity.
The ring $R_n$ is isomorphic to the ring $\mathop{End}(M)$ of all endomorphisms of the free right $R$-module $M = R^n$, possessing a basis with $n$ elements. The identity matrix $E_n = \text{diag}(1,\ldots,1)$ is the identity in $R_n$. An associative ring $A$ with identity 1 is isomorphic to $R_n$ if and only if there is in $A$ a set of $n^2$ elements $e_{ij}$, $i,j=1,\ldots,n$, subject to the following conditions:
1) $e_{ij}e_{kl} = \delta_{jk} e_{il}$, $\sum_{i=1}^n e_{ii}e_{ii} = 1$;
2) the centralizer of the set of elements $e_{ij}$ in $A$ is isomorphic to $R$.
The centre of $R_n$ coincides with $\mathcal{Z}(R) E_n$, where $\mathcal{Z}(R)$ denotes the centre of $R$; for $n>1$ the ring $R_n$ is non-commutative.
The multiplicative group of the ring $R_n$ (the group of all invertible elements), called the general linear group, is denoted by $\mathop{GL}_n(R)$. A matrix from $R_n$ is invertible in $R_n$ if and only if its columns form a basis of the free right module of all $(n \times 1)$-dimensional matrices over $R$. If $R$ is commutative, then the determinant is defined as a multiplicative map from $R_n$ to $R$ and invertibility of a matrix $X$ in $R_n$ is equivalent to the invertibility of its determinant, $\det X$, in $R$. The isomorphism $R_{mn} \sim (R_m)_n$ holds.
The two-sided ideals in $R_n$ are of the form $J_n$, where $J$ is a two-sided ideal in $R$ and so the ring $R_n$ is simple if and only if $R$ is simple. An Artinian ring is simple if and only if it is isomorphic to a matrix ring over a skew-field (the Wedderburn–Artin theorem). If $\mathcal{J}(R)$ denotes the Jacobson radical of the ring $R$, then $\mathcal{J}(R_n) = \mathcal{J}(R)_n$. Consequently, every matrix ring over a semi-simple ring $R$ is semi-simple. If $R$ is a regular ring (in the sense of von Neumann) (i.e. if for every $a \in R$ there is a $b \in R$ such that $aba = a$), then so is $R_n$. If $R$ is a ring with an invariant basis number, i.e. the number of elements in a basis of each free $R$-module does not depend on the choice of the basis, then $R_n$ also has this property. The rings $R$ and $R_n$ are equivalent in the sense of Morita (see Morita equivalence): The category of $R$-modules is equivalent to the category of $R_n$-modules. However, the condition that projective $R$-modules are free does not necessarily entail that projective $R_n$-modules are free too. For instance, if $R$ is a field and $n>1$, then there exist finitely-generated projective $R_n$-modules which are not free.
#### References
[1] C. Faith, "Algebra: rings, modules, and categories" , 1 , Springer (1973) [2] J. Lambek, "Lectures on rings and modules" , Blaisdell (1966) [3] L.A. Bokut', "Associative rings" , 1 , Novosibirsk (1977) (In Russian) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9647879600524902, "perplexity": 79.91553328037124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103573995.30/warc/CC-MAIN-20220628173131-20220628203131-00690.warc.gz"} |
https://mathematica.stackexchange.com/questions/102618/how-to-find-the-outline-of-a-country-given-the-imperfect-outlines-of-its-adminis?noredirect=1 | # How to find the outline of a country given the imperfect outlines of its administrative subdivisions?
I have a larger outline divided into several regions. While my data represents something else, let us think of this as the provinces/counties of a country, for the sake of simplicity. This is, for example, a 90 degrees rotated Uzbekistan I made for illustration purposes:
What I have is the polygon for each subdivision, as above. What I want to get is the outline of the whole country, as below:
How can I get the big outline starting with the outlines of the individual subdivisions?
The problem is that in my data the subdivision outlines do not fit perfectly because they have been simplified slightly to reduce the number of data points. Thus if I try BoundaryDiscretizeGraphics[Graphics[polygons]], I get the error
BoundaryMeshRegion::binsect: The boundary curves self-intersect or cross each other in ...
It is important that the result should be in the same coordinate system as the input data. The result should be in vector format (polygon or region). A small loss of precision is acceptable.
Below you'll find the code to artificially generate sample data that has this difficulty.
poly = #["Polygon"] & /@ CountryData["Uzbekistan"]["AdministrativeDivisions"] /. GeoPosition -> Identity;
spoly = poly /. Polygon[{line_}] :> Polygon@SimplifyLine[line, 0.01];
Graphics[spoly]
Update: An alternative problem dataset, without the need to run simplification: spoly = #["Polygon"] & /@ CountryData["Chad"]["AdministrativeDivisions"] /. GeoPosition -> Identity;
SimplifyLine is a simple implementation of the Ramer-Douglas-Peucker algorithm that I use here to artificially create the difficulty I have in my actual data (which unfortunately I cannot post). Code is below:
rot[{x_, y_}] := {y, -x}
Options[SimplifyLine] = {Method -> "RamerDouglasPeucker"}
SimplifyLine::method = "Unknown method: .";
SimplifyLine[points_, threshold_, opt : OptionsPattern[]] :=
With[{method = OptionValue[Method]},
Switch[method,
"RamerDouglasPeucker", rdp[DeleteDuplicates[points, #1 == #2 &], threshold],
_, Message[SimplifyLine::method, method]; \$Failed
]
]
rdp[{p1_, p2_}, _] := {p1, p2}
rdp[points_, th_] :=
Module[{p1 = First[points], p2 = Last[points], b, dist, maxPos},
b = Normalize@rot[p2 - p1];
dist = Abs[b.(# - p1) & /@ points];
maxPos = First@Ordering[dist, -1];
If[
dist[[maxPos]] < th
,
{p1, p2},
rdp[points[[;; maxPos]], th] ~Join~ Rest@rdp[points[[maxPos ;;]], th]
]
]
• Sorry to comment outside the context of the question, can you let me know what is the meaning of SimplifyLine::method = "Unknown method: ."; and its usage in Message[SimplifyLine::method, method]; or direct me to any source that can help me understand this. thank you – Algohi Dec 23 '15 at 2:43
• @Algohi It just issues a message. The last part of this tutorial deals with how to set up your own messages. – Szabolcs Dec 23 '15 at 8:11
• I'm guessing you've already seen Mark's implementation of Douglas-Peucker here? – J. M. is away Sep 10 '17 at 17:40
The issue with BoundaryDiscretizeGraphics[Graphics[polygons]] can sometimes be resolved by discretizing each polygon individually and taking the RegionUnion.
RegionUnion[BoundaryDiscretizeGraphics /@ spoly]
However for the Chad polygons there is a problem - BoundaryDiscretizeGraphics doesn't like some of them and returns unevaluated. I don't understand the reason for this, but it appears that rounding the coordinates helps. You can then use this to find the outer boundary.
spoly = #["Polygon"] & /@
GeoPosition -> Identity;
spoly = spoly /. x_Real :> Round[x, 0.0001];
br = RegionUnion[BoundaryDiscretizeGraphics /@ spoly];
merged = MeshRegion[MeshCoordinates[br],
br["IndexedBoundaryPolygons"][[br["BoundaryGroups"][[All, 1]]]]];
GraphicsRow[{Graphics[{Yellow, EdgeForm[Red], spoly}, Frame -> True],
RegionPlot[merged, AspectRatio -> Automatic]}]
The hack with Round is rather unsatisfactory, of course. Hopefully someone can explain what causes BoundaryDiscretizeGraphics to fail on some polygons and provide a better fix.
• The failure of BoundaryDiscretizeGraphics to cooperate with the 3rd and 15th polygon is rather mysterious indeed. For #3 I thought it might be the south-most region where the border is drawn very strangely (and probably incorrectly), but removing this part makes no difference. Removing numbers 3 and 15 from the list (RegionUnion[BoundaryDiscretizeGraphics /@ spoly[[Complement[Range@Length@spoly, {3, 15}]]]], where spoly is the one above without Round) makes the kernel crash. [cont'd] – Sjoerd C. de Vries Dec 22 '15 at 17:05
• ... I noticed that each of the polygons has a list of lists of coordinates as argument (i.e., {{{x1,y1},{x2,y2},...{xn,yn}}}) which is an acceptable syntax that can be used to pass various (possibly disjunct) polygons to a single Polygon function. Removing the outer pair of curly brackets yields polygons that can still be drawn and on which BoundaryDiscretizeGraphics does work. However, RegionUnion doesn't seem to like working on those: RegionUnion[BoundaryDiscretizeGraphics[Polygon[#[[1, 1]]]] & /@ spoly] yields this. Looks buggy to me. – Sjoerd C. de Vries Dec 22 '15 at 17:05
• Interesting this: you really should study the output of InputForm[ BoundaryDiscretizeGraphics@Polygon[{{{0, 0}, {1, 1}, {2, 0}, {#, 0}}}]] & /@ {10^-5, 10^-11, 10^-12}. – Sjoerd C. de Vries Dec 22 '15 at 21:18
• Also very interesting and revealing: BoundaryDiscretizeGraphics@ Polygon[{{{0, 0}, {1, 1}, {1, 1} + {#, 0}, {2, 0}}}] & /@ {10^-5, 10^-11, 10^-13} – Sjoerd C. de Vries Dec 22 '15 at 21:19
As I already pointed out in chat and similar to @Kuba's solution, a reasonably simple approach is to render the set of outlines as polygons. Due to the image grid, small differences at the borders are closed. And even if not, there exist many image filters to close gaps.
Once you have rendered the outlines, you are stuck with image pixel coordinates and you lost your original coordinate system, but with storing the original plot-range, this coordinate transformation can be reversed.
One of the important steps when you have your outlines as binary image is to get an ordered list of boundary pixel coordinates. To my knowledge, no built-in Mathematica routine exist that does exactly (and only) this. There are imperfect solutions like FindCurvePath or things like FindShortestTour, but these lack of an important thing: They don't know about image pixels, their neighborhood and that we have a solid object. What they do is trying to find a path based on a set of points, which is a harder problem.
Therefore, let me give an implementation of an algorithm that can be found in [Gonzalez & Woods] in chapter 11.1 which works directly on the image pixels and traces the boundary around the object.
This algorithm works by starting at the uppermost, leftmost object-pixel b0. This object-pixel's left neighbor is obviously a background pixel c0. From this neighbor, we go clockwise through all other neighbors n1, n2, ... of b0 until we find another object-pixel b1. The neighbor before b1 was of course a background-pixel that we set to c1.
This is basically, the iteration step. We start with a pair (b,c) and calculate the next pair by the above description. In Mathematica I can describe the iteration through all 8 neighbors by a repeated rotation:
NestList[
Round[{{1/Sqrt[2], 1/Sqrt[2]}, {-(1/Sqrt[2]), 1/Sqrt[2]}}.#] &,
{-1, 0}, 8]
(* {{-1, 0}, {-1, 1}, {0, 1}, {1, 1},
{1, 0}, {1, -1}, {0, -1}, {-1, -1}, {-1, 0}} *)
Therefore, a function that takes {{bx,by}, {cx,cy}} where b is the object pixel and c its background-neighbor, and a set of all object-positions pts could look like this
With[{rot = {{1/Sqrt[2], 1/Sqrt[2]}, {-(1/Sqrt[2]), 1/Sqrt[2]}}},
nextPairC = Compile[{{p, _Integer, 2}, {pts, _Integer, 2}},
Module[{n0 = Plus @@ ({1, -1}*Reverse[p]), n1 = {0, 0},
b = First[p]},
Do[
n1 = Round[rot.n0];
If[MemberQ[pts, b + n1],
Break[];
];
n0 = n1, {8}
];
{n1 + b, n0 + b}
]
]
]
Since this is the core of the algorithm, the rest is a short wrapper around this. In the following, we use NestWhileList to repeatedly apply nextPairC until we reach the starting point. Exactly, the stop-condition reads: do until we reach an object point that is equal to b0 and its next object neighbor is equal to b1:
MooreBoundaryTracking[img_Image] := Module[{
pixel = PixelValuePositions[img, 1],
p0, p1
},
p0 = {#, # - {1, 0}} &[First[SortBy[pixel, {Last, First}]]];
p1 = nextPairC[p0, pixel];
NestWhileList[
nextPairC[#, pixel] &,
p1,
#1[[1]] != First[p0] && #2[[1]] != First[p1] &,
2,
10^5][[All, 1]]
]
The method runs about 2 seconds for image-sizes of about 1000 pixel. With spoly as defined in Szabolcs question:
img = Rasterize[Graphics[spoly]] // ColorNegate // Binarize;
Graphics[Line@MooreBoundaryTracking[img]]
• Guys, please give me a million upvotes if you like, but don't forget to upvote Simon and Kuba, because my answer only answers a small sub-problem, while theirs give a solution for the whole question! – halirutan Dec 22 '15 at 16:19
Not sure what an outline really is so maybe:
Composition[
Graphics[GraphicsComplex[#, Line@Last@FindShortestTour@#], Frame -> True] &
, Function[image,
Rescale[#, {#2, #3}, {##4}] &,
{Transpose[#], {0., 0.}, ImageDimensions@image,
Sequence @@ Transpose@{{5, 25}, {13, 25}}}
] & @ PixelValuePositions[image, 1]
]
, Binarize
, Thinning
, EdgeDetect
, Binarize
, ColorNegate
, Rasterize[#, ImageSize -> 500] &
] @ Graphics[
spoly,
PlotRange -> {{5, 25}, {13, 25}},
ImageMargins -> 0]
• Thanks! This is halfway there. What's missing is the ordering of the boundary points. In other words, I would like a Polygon as the output. Based on another post (see chat), FindShortestTour will often work for getting the right ordering. (FindCurvePath will not). Handling shapes with holes in them (i.e. not singly connected) is more trouble, but I didn't mention that intentionally: I might be able to work around that. – Szabolcs Dec 22 '15 at 11:51
• Can you add the FindShortestTour and make it into a Polygon? – Szabolcs Dec 22 '15 at 11:52
• @Szabolcs Yep, I skipped it thinking maybe there is a faster method for such "obvious" and dense set. – Kuba Dec 22 '15 at 11:57
• For this data, FindShortestTour returns the result instantaneously and the result is good. Going to test for more complex cases soon. I think that for such cases fast heuristics will usually return the best solution (shortest tour). – Szabolcs Dec 22 '15 at 12:00
• @Szabolcs Ok, done. Good luck. – Kuba Dec 22 '15 at 12:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2695065140724182, "perplexity": 2591.790543008317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232260358.69/warc/CC-MAIN-20190527005538-20190527031538-00481.warc.gz"} |
http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=1440306 | 0
Multiphase Flows
# On the Volume Fraction Effects of Inertial Colliding Particles in Homogeneous Isotropic Turbulence
[+] Author and Article Information
Martin Ernst1
Mechanische Verfahrenstechnik, Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), [email protected]
Martin Sommerfeld
Mechanische Verfahrenstechnik, Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), [email protected]
1
Corresponding author.
J. Fluids Eng 134(3), 031302 (Mar 23, 2012) (16 pages) doi:10.1115/1.4005681 History: Received April 19, 2011; Revised December 20, 2011; Published March 20, 2012; Online March 23, 2012
## Abstract
The main objective of the present study is the investigation of volume fraction effects on the collision statistics of nonsettling inertial particles in a granular medium as well as suspended in an unsteady homogeneous isotropic turbulent flow. For this purpose, different studies with mono-disperse Lagrangian point-particles having different Stokes numbers are considered in which the volume fraction of the dispersed phase is varied between 0.001 and 0.01. The fluid behavior is computed using a three-dimensional Lattice-Boltzmann method. The carrier-fluid turbulence is maintained at Taylor microscale Reynolds number 65.26 by applying a spectral forcing scheme. The Lagrangian particle tracking is based on considering the drag force only and a deterministic model is applied for collision detection. The influence of the particle phase on the fluid flow is neglected at this stage. The particle size is maintained at a constant value for all Stokes numbers so that the ratio of particle diameter to Kolmogorov length scale is fixed at 0.58. The variation of the particle Stokes number was realized by modifying the solids density. The observed particle Reynolds and Stokes numbers are in between [1.07, 2.61] and [0.34, 9.79], respectively. In the present simulations, the fluid flow and the particle motion including particle-particle collisions are based on different temporal discretization. Hence, an adaptive time stepping scheme is introduced. The particle motion as well as the occurrence of inter-particle collisions is characterized among others by Lagrangian correlation functions, the velocity angles between colliding particles and the collision frequencies. Initially, a fluid-free particle system is simulated and compared with the principles of the kinetic theory to validate the implemented deterministic collision model. Moreover, a selection of results obtained for homogeneous isotropic turbulence is compared with in literature available DNS and LES results as well. According to the performed simulations, the collision rate of particles with large Stokes numbers strongly depends on the adopted volume fraction, whereas for particles with small Stokes numbers the influence of particle volume fraction is less pronounced.
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## Figures
Figure 1
Velocity direction vectors of the D3Q19 model
Figure 2
Program flow chart for the deterministic collision model (in analogy to Ref. [36]).
Figure 3
Pictorial representation of two colliding particles [38]
Figure 4
Fluctuation of collision rates N observed in a fluid-free particle system as a function of the nondimensional tracking time (closed symbols). The solid line indicates the theoretical reference value based on the kinetic theory, cf. Eq. 2.
Figure 5
Comparison of the probability density functions of the velocity modulus between colliding particles with theoretical results from the kinetic theory. The kinetic theory corresponds to the velocity distribution of the injected particles.
Figure 6
Fluid velocity field (vector plot) and particle field distribution (spheres, St = 2.57, αP = 0.01) for a single plane in the computational domain.
Figure 7
Three-dimensional energy spectrum of the turbulent flow field (solid line with symbols: ReT = 65.26) and Kolmogorov spectrum (dashed line: universal Kolmogorov constant C = 1.5) as a function of the nondimensional wave number.
Figure 8
Viscous dissipation spectrum computed from the present DNS (ReT = 65.26) and plotted against the nondimensional wave number.
Figure 9
Probability density functions of the fluid velocity fluctuations for the three velocity components averaged over a single eddy turnover time.
Figure 10
Probability density function of the free path between particle collisions depending on the particle Stokes number StP = 0.01). The indicated particle mean free path λFP¯ is also normalized by the Kolmogorov length scale λK .
Figure 11
Effect of the particle response behavior (i.e., St) on the mean time between two particle-particle collisions τC : Here, the particle response time τP is normalized by the constant Kolmogorov timescale τK and plotted against the Stokes number St with the solid volume fraction αP as a parameter.
Figure 12
Averaged collision frequencies fC , which are normalized by their corresponding particle response times τP , as a function of the Stokes number St and solid volume fraction αP .
Figure 13
Computed collision frequencies fC as a function of the Stokes number StP = 0.01): Comparison of results obtained by direct numerical simulations (present study) with the analytical Saffman and Turner limit [2] as well as the kinetic theory limit [3].
Figure 14
Ratio of the computed collision frequency to the collision frequency obtained from kinetic theory plotted against the Stokes number StInt which is based on the fluid Lagrangian integral timescale: Comparison of results obtained by direct numerical simulations (open and partly filled symbols: present study), large eddy simulations for different volume fractions (closed symbols: Laviéville [21]) and analytical approximations (solid line: Kruis and Kusters [5]). Note: Symbols of one shape represent a comparable Stokes number, e.g., circle, square or triangle. Moreover, symbols of one filling level (present DNS) indicate the results for different volume fractions, i.e.,
P = 0.001,
P = 0.005,
P = 0.01.
Figure 15
Averaged Lagrangian correlation functions of the particle velocities RP,u (τ) and their corresponding Lagrangian integral timescales τL,P as a function of the particle Stokes number StP = 0.01).
Figure 16
Influence of the volume fraction αP on the Lagrangian correlation functions of the particles RP,u (τ) in presence as well as in absence of inter-particle collisions (St = 9.78). In case of particle-particle collision, the ratio of the particle Lagrangian integral timescale to the mean time between two successive inter-particle collisions τL,PC is given as well.
Figure 17
Particle Lagrangian integral timescales τL,P as function of the Stokes number St with the solid volume fraction αP as a parameter: The calculated timescales are normalized by the Kolmogorov timescale τK as well as the mean time between successive inter-particle collisions τC Â .
Figure 18
Comparison of the ratio of kinetic energy of the particle fluctuation motion kP to the turbulent kinetic energy of the flow field kF obtained by the present DNS (triangle: ReT = 65.26) with results from other DNS, published by Sundaram and Collins [12] (circle: ReT = 54.20) and Fede and Simonin [15] (square: ReT = 34.10), depending on the Stokes number St (Note: (1) symbols of one kind indicate the results for the different volume fractions, and (2) the results of all three DNS are based on a one-way momentum coupling of the dispersed phase with the fluid flow).
Figure 19
Probability density function of the relative velocity modulus of colliding particles |uPij | which is normalized by Kolmogorov velocity uK with the Stokes number St as a parameter (αP = 0.01). In addition, the mean values of relative velocity modulus are printed for easy comparison.
Figure 20
Influence of the volume fraction αP on (a) the mean relative velocity modulus |uPij|¯ and (b) the mean particle velocity angles ϕ¯ between colliding particles as a function of the Stokes number St.
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https://www.gnu.org/software/gnuastro/manual/html_node/Distance-on-a-2D-curved-space.html | GNU Astronomy Utilities
Next: , Previous: , Up: CosmicCalculator [Contents][Index]
9.1.1 Distance on a 2D curved space
The observations to date (for example the Plank 2013 results), have not measured the presence of a significant curvature in the universe. However to be generic (and allow its measurement if it does in fact exist), it is very important to create a framework that allows curvature. As 3D beings, it is impossible for us to mentally create (visualize) a picture of the curvature of a 3D volume in a 4D space. Hence, here we will assume a 2D surface and discuss distances on that 2D surface when it is flat, or when the 2D surface is curved (in a 3D space). Once the concepts have been created/visualized here, in Extending distance concepts to 3D, we will extend them to the real 3D universe we live in and hope to study.
To be more understandable (actively discuss from an observer’s point of view) let’s assume we have an imaginary 2D friend living on the 2D space (which might be curved in 3D). So here we will be working with it in its efforts to analyze distances on its 2D universe. The start of the analysis might seem too mundane, but since it is impossible to imagine a 3D curved space, it is important to review all the very basic concepts thoroughly for an easy transition to a universe we cannot visualize any more (a curved 3D space in 4D).
To start, let’s assume a static (not expanding or shrinking), flat 2D surface similar to Figure 9.1 and that our 2D friend is observing its universe from point $$A$$. One of the most basic ways to parametrize this space is through the Cartesian coordinates ($$x$$, $$y$$). In Figure 9.1, the basic axes of these two coordinates are plotted. An infinitesimal change in the direction of each axis is written as $$dx$$ and $$dy$$. For each point, the infinitesimal changes are parallel with the respective axes and are not shown for clarity. Another very useful way of parameterizing this space is through polar coordinates. For each point, we define a radius ($$r$$) and angle ($$\phi$$) from a fixed (but arbitrary) reference axis. In Figure 9.1 the infinitesimal changes for each polar coordinate are plotted for a random point and a dashed circle is shown for all points with the same radius.
Figure 9.1: Two dimensional Cartesian and polar coordinates on a flat plane.
Assuming a certain position, which can be parameterized as $$(x,y)$$, or $$(r,\phi)$$, a general infinitesimal change change in its position will place it in the coordinates $$(x+dx,y+dy)$$ and $$(r+dr,\phi+d\phi)$$. The distance (on the flat 2D surface) that is covered by this infinitesimal change in the static universe ($$ds_s$$, the subscript signifies the static nature of this universe) can be written as:
$$ds_s=dx^2+dy^2=dr^2+r^2d\phi^2$$
The main question is this: how can our 2D friend incorporate the (possible) curvature in its universe when it is calculating distances? The universe it lives in might equally be a locally flat but globally curved surface like Figure 9.2. The answer to this question but for a 3D being (us) is the whole purpose to this discussion. So here we want to give our 2D friend (and later, ourselves) the tools to measure distances if the space (that hosts the objects) is curved.
Figure 9.2 assumes a spherical shell with radius $$R$$ as the curved 2D plane for simplicity. The spherical shell is tangent to the 2D plane and only touches it at $$A$$. The result will be generalized afterwards. The first step in measuring the distance in a curved space is to imagine a third dimension along the $$z$$ axis as shown in Figure 9.2. For simplicity, the $$z$$ axis is assumed to pass through the center of the spherical shell. Our imaginary 2D friend cannot visualize the third dimension or a curved 2D surface within it, so the remainder of this discussion is purely abstract for it (similar to us being unable to visualize a 3D curved space in 4D). But since we are 3D creatures, we have the advantage of visualizing the following steps. Fortunately our 2D friend knows our mathematics, so it can follow along with us.
With the third axis added, a generic infinitesimal change over the full 3D space corresponds to the distance: $$ds_s^2=dx^2+dy^2+dz^2=dr^2+r^2d\phi^2+dz^2.$$It is very important to recognize that this change of distance is for any point in the 3D space, not just those changes that occur on the 2D spherical shell of Figure 9.2. Recall that our 2D friend can only do measurements in the 2D spherical shell, not the full 3D space. So we have to constrain this general change to any change on the 2D spherical shell. To do that, let’s look at the arbitrary point $$P$$ on the 2D spherical shell. Its image ($$P'$$) on the flat plain is also displayed. From the dark triangle, we see that
Figure 9.2: 2D spherical plane (centered on $$O$$) and flat plane (gray) tangent to it at point $$A$$.
$$\sin\theta={r\over R},\quad\cos\theta={R-z\over R}.$$These relations allow our 2D friend to find the value of $$z$$ (an abstract dimension for it) as a function of r (distance on a flat 2D plane, which it can visualize) and thus eliminate $$z$$. From $$\sin^2\theta+\cos^2\theta=1$$, we get $$z^2-2Rz+r^2=0$$ and solving for $$z$$, we find: $$z=R\left(1\pm\sqrt{1-{r^2\over R^2}}\right).$$The $$\pm$$ can be understood from Figure 9.2: For each $$r$$, there are two points on the sphere, one in the upper hemisphere and one in the lower hemisphere. An infinitesimal change in $$r$$, will create the following infinitesimal change in $$z$$:
$$dz={\mp r\over R}\left(1\over \sqrt{1-{r^2/R^2}}\right)dr.$$Using the positive signed equation instead of $$dz$$ in the $$ds_s^2$$ equation above, we get:
$$ds_s^2={dr^2\over 1-r^2/R^2}+r^2d\phi^2.$$
The derivation above was done for a spherical shell of radius $$R$$ as a curved 2D surface. To generalize it to any surface, we can define $$K=1/R^2$$ as the curvature parameter. Then the general infinitesimal change in a static universe can be written as: $$ds_s^2={dr^2\over 1-Kr^2}+r^2d\phi^2.$$Therefore, we see that a positive $$K$$ represents a real $$R$$ which signifies a closed 2D spherical shell like Figure 9.2. When $$K=0$$, we have a flat plane (Figure 9.1) and a negative $$K$$ will correspond to an imaginary $$R$$. The latter two cases are open universes (where $$r$$ can extend to infinity). However, when $$K>0$$, we have a closed universe, where $$r$$ cannot become larger than $$R$$ as in Figure 9.2.
A very important issue that can be discussed now (while we are still in 2D and can actually visualize things) is that $$\overrightarrow{r}$$ is tangent to the curved space at the observer’s position. In other words, it is on the gray flat surface of Figure 9.2, even when the universe if curved: $$\overrightarrow{r}=P'-A$$. Therefore for the point $$P$$ on a curved space, the raw coordinate $$r$$ is the distance to $$P'$$, not $$P$$. The distance to the point $$P$$ (at a specific coordinate $$r$$ on the flat plane) on the curved surface (thick line in Figure 9.2) is called the proper distance and is displayed with $$l$$. For the specific example of Figure 9.2, the proper distance can be calculated with: $$l=R\theta$$ ($$\theta$$ is in radians). using the $$\sin\theta$$ relation found above, we can find $$l$$ as a function of $$r$$:
$$\theta=\sin^{-1}\left({r\over R}\right)\quad\rightarrow\quad l(r)=R\sin^{-1}\left({r\over R}\right)$$$$R$$ is just an arbitrary constant and can be directly found from $$K$$, so for cleaner equations, it is common practice to set $$R=1$$, which gives: $$l(r)=\sin^{-1}r$$. Also note that if $$R=1$$, then $$l=\theta$$. Generally, depending on the the curvature, in a static universe the proper distance can be written as a function of the coordinate $$r$$ as (from now on we are assuming $$R=1$$):
$$l(r)=\sin^{-1}(r)\quad(K>0),\quad\quad l(r)=r\quad(K=0),\quad\quad l(r)=\sinh^{-1}(r)\quad(K<0).$$With $$l$$, the infinitesimal change of distance can be written in a more simpler and abstract form of
$$ds_s^2=dl^2+r^2d\phi^2.$$
Until now, we had assumed a static universe (not changing with time). But our observations so far appear to indicate that the universe is expanding (isn’t static). Since there is no reason to expect the observed expansion is unique to our particular position of the universe, we expect the universe to be expanding at all points with the same rate at the same time. Therefore, to add a time dependence to our distance measurements, we can simply add a multiplicative scaling factor, which is a function of time: $$a(t)$$. The functional form of $$a(t)$$ comes from the cosmology and the physics we assume for it: general relativity.
With this scaling factor, the proper distance will also depend on time. As the universe expands (moves), the distance will also move to larger values. We thus define a distance measure, or coordinate, that is independent of time and thus doesn’t ‘move’ which we call the comoving distance and display with $$\chi$$ such that: $$l(r,t)=\chi(r)a(t)$$. We thus shift the $$r$$ dependence of the proper distance we derived above for a static universe to the comoving distance:
$$\chi(r)=\sin^{-1}(r)\quad(K>0),\quad\quad \chi(r)=r\quad(K=0),\quad\quad \chi(r)=\sinh^{-1}(r)\quad(K<0).$$
Therefore $$\chi(r)$$ is the proper distance of an object at a specific reference time: $$t=t_r$$ (the $$r$$ subscript signifies “reference”) when $$a(t_r)=1$$. At any arbitrary moment ($$t\neq{t_r}$$) before or after $$t_r$$, the proper distance to the object can simply be scaled with $$a(t)$$. Measuring the change of distance in a time-dependent (expanding) universe will also involve the speed of the object changing positions. Hence, let’s assume that we are only thinking about the change in distance caused by something (light) moving at the speed of light. This speed is postulated as the only constant and frame-of-reference-independent speed in the universe, making our calculations easier, light is also the major source of information we receive from the universe, so this is a reasonable assumption for most extra-galactic studies. We can thus parametrize the change in distance as
$$ds^2=c^2dt^2-a^2(t)ds_s^2 = c^2dt^2-a^2(t)(d\chi^2+r^2d\phi^2).$$
Next: , Previous: , Up: CosmicCalculator [Contents][Index] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8928858041763306, "perplexity": 276.7153343628416}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824357.3/warc/CC-MAIN-20171020211313-20171020231313-00276.warc.gz"} |
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13:45
The 8Be excess and search for the X → e+e− decay of a new light boson with NA64 detector / Gninenko, Sergei The X → e+e− decay of a new short-lived neutral boson X with a mass mX = 16.7 MeV and coupling to electrons in the range 10−4 < εe < 10−3 could explain the excess of e+e− pairs recently observed in the excited 8Be nucleus decays. [...] CERN-SPSC-2017-016 ; SPSC-SR-211. - 2017. Fulltext
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Status report for the Neutrino Platform NP05 - Baby MIND - experiment / Noah, E (University of Geneva) The Baby-MIND collaboration is actively working towards the completion of a muon spectrometer to be operated at J-PARC from autumn 2017. [...] CERN-SPSC-2017-015 ; SPSC-SR-210. - 2017. Fulltext
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ProtoDUNE-SinglePhase short written report / Cavanna, F (FNAL) short written report CERN-SPSC-2017-014 ; SPSC-SR-209. - 2017. Fulltext
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Status and plans of WA104/ICARUS / Rubbia, C (INFN GSSI, L’Aquila, Italy and CERN, Switzerland on behalf of the ICARUS Coll.) ; Montanari, C S (INFN Sez. di Pavia, Pavia, Italy and CERN on behalf of the ICARUS Coll.) Presently at CERN, the ICARUS-T600 detector will be soon transported to FNAL and exposed to the 0.8 GeV FNAL Booster neutrino beam at 600 m from the target, in the framework of the SBN program where measured neutrino spectra will be compared with the standard predictions simultaneously on three different locations in association with the MICROBOONE and SBND detectors. [...] CERN-SPSC-2017-012 ; SPSC-SR-207. - 2017. Fulltext
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Yearly progress report on WA105/ProtoDUNE dual-phase (2017) / Aimard, B WA105/ProtoDUNE dual-phase aims at fully demonstrating the concept of a very large dual-phase LAr TPC and calibrating it with a charged particles test beam, in view of the application of this detector design for the construction of DUNE 10 kton far detector modules. [...] CERN-SPSC-2017-011 ; SPSC-SR-206. - 2017. Fulltext - Original Document (SPSC-TDR-004)
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RD52 Progress Report 2017: Dual-Readout Calorimetry for High-Quality Energy Measurements / Wigmans, R This document constitutes the sixth RD52 progress report. [...] CERN-SPSC-2017-010 ; SPSC-SR-205. - 2017. Fulltext
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Minutes of the 124th Meeting of the SPSC, Tuesday and Wednesday, 17-18 January, 2017 CERN-SPSC-2017-008 ; SPSC-124. - 2017. Fulltext
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OSQAR Addendum for the 2017 run / Pugnat, P (CNRS/LNCMI-Grenoble) Requested clarifications concerning the OSQAR-CHASE experimental run planned for 2017 are provided.. CERN-SPSC-2017-007 ; SPSC-P-331-ADD-1-ADD-1. - 2017. Fulltext - Original Document (SPSC-P-331-ADD-1)
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ATRAP Progress Report 2016 / Gabrielse, G 2016 Progress Report by the Antihydrogen TRAP Collaboration (ATRAP) for the SPSC annual review 2017 CERN-SPSC-2017-006 ; SPSC-SR-204. - 2017. Fulltext | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8863716721534729, "perplexity": 17033.86777667842}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607649.26/warc/CC-MAIN-20170523183134-20170523203134-00417.warc.gz"} |
http://tex.stackexchange.com/questions/57289/problem-with-shorthand-for-scope-environments | # problem with Shorthand for Scope Environments
I try in this in this question to use some shorthands with the library scopes.
I discover some difficulties and I can't explain why I get problems. (I use pgf 2.1 cvs)
The main code comes from the pgfmanual
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{scopes}
\begin{tikzpicture}
{ [ultra thick]
{ [red]
\draw (0mm,10mm) -- (10mm,10mm);
\draw (0mm,8mm) -- (10mm,8mm);
}
\draw (0mm,6mm) -- (10mm,6mm);
}
{ [green]
\draw (0mm,4mm) -- (10mm,4mm);
\draw (0mm,2mm) -- (10mm,2mm);
\draw[blue] (0mm,0mm) -- (10mm,0mm);
}
\end{tikzpicture}
\end{document}
This is perfect. Now I want to draw three times these lines
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{scopes}
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,5,10}{%
\begin{scope}[xshift=\i cm]
{ [ultra thick]
{ [red]
\draw (0mm,10mm) -- (10mm,10mm);
\draw (0mm,8mm) -- (10mm,8mm);
}
\draw (0mm,6mm) -- (10mm,6mm);
}
{ [green]
\draw (0mm,4mm) -- (10mm,4mm);
\draw (0mm,2mm) -- (10mm,2mm);
\draw[blue] (0mm,0mm) -- (10mm,0mm);
}
\end{scope}}
\end{tikzpicture}
\end{document}
This is always perfect but now if I replace \begin{scope} ...\end{scope} by {..}, the code compiles but the scopes disappear.
\begin{tikzpicture}
\foreach \i in {0,5,10}{%
{[xshift=\i cm]
{ [ultra thick]
{ [red]
\draw (0mm,10mm) -- (10mm,10mm);
\draw (0mm,8mm) -- (10mm,8mm);
}
\draw (0mm,6mm) -- (10mm,6mm);
}
{ [green]
\draw (0mm,4mm) -- (10mm,4mm);
\draw (0mm,2mm) -- (10mm,2mm);
\draw[blue] (0mm,0mm) -- (10mm,0mm);
}
}}
\end{tikzpicture}
I know that { is the beginning of a TikZ's scope only if [ comes after { otherwise{..} is a simple TeX's group.
Is-it possible to explain this problem?
-
To answer this, you need to know when TikZ looks for the {[...] ... } scoping shortcut. The TikZ parser has many different states and it has to be in the right state to recognise certain syntax, otherwise it either passes over it or complains vociferously.
The check for the scoping shortcut is handled by a macro \tikz@lib@scope@check. Without the scopes library, this is empty. With the scopes library then it becomes equivalent to:
• Look at the next (non-space) token on the stream.
1. Is it \tikz@intersect@finish? If so, do that and check again.
2. Is it \par? If so, do that and check again.
3. Is it \bgroup? If so, look for [ and if found, go into a scope.
An important thing to note is that this is a test on the next token, and there is only limited support for delaying the test.
Now let us see when this is invoked:
1. When a tikzpicture starts. So the first thing in a TikZ picture can be {[red] and that will get detected correctly.
2. When a scope starts. This can be an implicit or explicit one (so nesting of {[..] ..} syntax is fine, as is intermingling with ordinary \begin{scope} .. \end{scope} pairs).
3. When a scope ends. Actually, this is less useful than it at first seems. The problem is that an explicit scope ends within a group so the next token is not the next thing that the user thinks it is but probably an \endgroup (or something else buried in the \end{environment} code). To make use of this, the previous scope has to be either an implicit scope or of the form \scope ... \endscope. In the following, the first line is not red. Note that this can have knock-on effects: if the first implicit scope is not recognised and another follows it, that will also not be recognised.
\begin{scope}
\end{scope}
{[red]
\draw[ultra thick] (0,0) -- (0,1);
}
\scope
\endscope
{[red]
\draw[ultra thick] (2,0) -- (2,1);
}
{[red]
\draw[ultra thick] (1,0) -- (1,1);
}
4. After a path. So an implicit scope can follow a path command.
Unfortunately, none of those match your syntax because by the time the \foreach is processed, the check that is made at the start of the picture has been made and failed (since it found \foreach). So to get the initial implicit scope recognised (and, incidentally, the fact that the first doesn't get recognised has the knock-on effect that none of the others do either: the [ultra thick] one doesn't follow the opening of a scope, so then neither does the [red] one, and the [green] one doesn't follow the ending of a scope so it isn't recognised) we need to invoke the recognition code. Two ways to do this are by ensuring that one of the conditions is met. Either an explicit but groupless scope has to start the \foreach (so \scope\endscope) or an empty path (so \path;).
These might be considered a little "hackish". There is an alternative. This is to ensure that the actual check is carried out at the start of the \foreach command. As the pgffor routines are meant to stand to one side of TikZ, this is not - and should not - be explicitly in the pgffor.code.tex file. But what is there are some hooks that can be invoked: \pgffor@beginhook and \pgffor@endhook (and \pgffor@afterhook). Indeed, these are used by TikZ for when \foreach is encountered inside a path. But they aren't used for external encounters. Since the internal one overwrites these hooks, we can just set them for the picture. As we want to make sure that the scope check is the very last thing that is added to these hooks, I've chosen a slightly circumspect way of doing it:
\tikzset{every picture/.append style={
execute at begin picture={
\expandafter\def\expandafter\pgffor@beginhook\expandafter{\pgffor@beginhook\tikz@lib@scope@check}
}
}
}
This means that when the picture starts, the code for adding the code is added to the code that is executed at the start of the picture. So it will be added after anything that is added either globally or in the options at the start of the picture. I'm sure it could be done better!
With that, then your code works:
\documentclass{article}
%\url{http://tex.stackexchange.com/q/57289/86}
\usepackage{tikz}
%\usepackage{trace-pgfkeys}
\usetikzlibrary{scopes}
\makeatletter
\tikzset{every picture/.append style={
execute at begin picture={
\expandafter\def\expandafter\pgffor@beginhook\expandafter{\pgffor@beginhook\tikz@lib@scope@check}
}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,5,10}{%
{[xshift=\i cm]
{ [ultra thick]
{ [red]
\draw (0mm,10mm) -- (10mm,10mm);
\draw (0mm,8mm) -- (10mm,8mm);
}
\draw (0mm,6mm) -- (10mm,6mm);
}
{ [green]
\draw (0mm,4mm) -- (10mm,4mm);
\draw (0mm,2mm) -- (10mm,2mm);
\draw[blue] (0mm,0mm) -- (10mm,0mm);
}
}
}
\end{tikzpicture}
\end{document}
Finally, the trace-pgfkeys was very useful here as it showed straight away that the scopes weren't getting seen at all.
-
Very great answer as usual. I need to work with trace-pgfkeys` if If I want to progress. Thanks Sherlock ! – Alain Matthes May 25 '12 at 11:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8648639917373657, "perplexity": 2588.4860153590175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119647865.10/warc/CC-MAIN-20141024030047-00252-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://tug.org/pipermail/tex-live/2009-October/023412.html | Ralph Martin Ralph.Martin at cs.cardiff.ac.uk
Mon Oct 26 17:41:51 CET 2009
Herb, all
On 26 Oct 2009, at 4:08:08PM, Herbert Schulz wrote:
> I don't find repstopdf as part of MacTeX(TeX Live)-2008 so I'm wondering what it is.
I presume its the restricted epstopdf which cannot stomp all over the filesystem...
On 26 Oct 2009, at 4:35:48PM, Herbert Schulz wrote:
> Since restricted shell escape is effectively turned off (i.e., nothing is on the list of applications allowed to execute) right now I wouldn't be surprised if repstopdf isn't part of the TeX Live 2009 package at this time.
Fine.
But then \usepackage{epstopdf} shouldn't try to use it if it has been removed - if, indeed, \usepackage{epstopdf} is what has triggered the message.
I certainly didn't explicitly use repstopdf, and something in texlive is trying to use it, even though it is not there.
Best wishes
Ralph
--
Prof Ralph Martin Phone: +44(0)29 2087 5536
School of Computer Science Fax: +44(0)29 2087 4598
Cardiff University Email: mailto:ralph at cs.cf.ac.uk
5 The Parade, Roath WWW: http://ralph.cs.cf.ac.uk/
Cardiff, CF24 3AA, UK VOIP: sip:17476235487 at proxy01.sipphone.com | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9196783900260925, "perplexity": 14111.858759650058}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315558.25/warc/CC-MAIN-20190820180442-20190820202442-00486.warc.gz"} |
https://en.xen.wiki/w/9801/9800 | # 9801/9800
Ratio 9801/9800 Factorization 2-3 × 34 × 5-2 × 7-2 × 112 Monzo [-3 4 -2 -2 2⟩ Size in cents 0.17664752¢ Names kalisma,Gauss' comma Color name 1oorrgg-2, Bilorugu comma FJS name $\text{M}{-2}^{11,11}_{5,5,7,7}$ Special properties square superparticular,reduced Tenney height (log2 n⋅d) 26.5173 Weil height (max(n, d)) 9801 Benedetti height (n⋅d) 96049800 Harmonic entropy(Shannon, $\sqrt{n\cdot d}$) ~2.39763 bits Comma size unnoticeable S-expressions S99,S33 / S35 open this interval in xen-calc
9801/9800, the kalisma or Gauss' comma, is an 11-limit unnoticeable comma measuring about 0.18 ¢. It is the smallest 11-limit superparticular interval.
## Theory
It can be described as the difference between 99/98 and 100/99, and between 99/70 and its octave complement, 140/99. It is also the difference between 245/243 and 121/120, and a stack of two 11/7s and 81/80 against a 5/4. Tempering it out also means that 10/9 and 11/7 are 600 cents apart, as well as are 11/10 and 14/9.
It factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200.
## Temperaments
Tempering it out leads to the kalismic temperament, which splits the octave into two equal parts, each representing 99/70~140/99. Odd edos cannot temper it out. See Rank-4 temperament #Kalismic (9801/9800) for some technical details. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31712785363197327, "perplexity": 20300.33349515318}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711376.47/warc/CC-MAIN-20221209011720-20221209041720-00377.warc.gz"} |
http://math.stackexchange.com/questions/106473/prove-that-x-12x-22x-32-1-yields-sum-i-13-fracx-i1x-i2-le | # Prove that $x_1^2+x_2^2+x_3^2=1$ yields $\sum_{i=1}^{3}\frac{x_i}{1+x_i^2} \le \frac{3\sqrt{3}}{4}$
Prove this inequality, if $x_1^2+x_2^2+x_3^2=1$: $$\sum_{i=1}^{3}\frac{x_i}{1+x_i^2} \le \frac{3\sqrt{3}}{4}$$
So far I got to $x_1^4+x_2^4+x_3^4\ge\frac{1}3$ by using QM-AM for $(2x_1^2+x_2^2, 2x_2^2+x_3^2, 2x_3^2+x_1^2)$, but to be honest I'm not sure if that's helpful at all.
(You might want to "rename" those to $x,y,z$ to make writing easier): $$\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2} \le \frac{3\sqrt3}4$$
-
Do you know Lagrange Multipliers? – Will Jagy Feb 6 '12 at 23:25
Nope, I'm high school student, I only know basic inequalities (HM-GM-AM-QM, Cauchy-Schwarz-Bunyakowski, Jensen's, Minkowski, Schur and such). – Lazar Ljubenović Feb 6 '12 at 23:34
Well, maybe someone will answer by those methods. LM says that the extrema, and other critical points, of the functional occur when $x=y=z,$ which means $\pm(1/\sqrt 3, 1/\sqrt 3, 1/\sqrt 3).$ – Will Jagy Feb 6 '12 at 23:42
Suggestion: make substitution $x=r\cos\theta\sin\phi$, $y=r\sin\theta\sin\phi$, $z=r\cos\phi$. Let r = 1. Still not easy, but now a spherical trig problem. Perhaps trig identities would help. – daniel Feb 7 '12 at 9:47
We assume that $x_i\geq 0$ and let $\theta_i\in \left(0,\frac{\pi}2\right)$ sucht that $x_i=\tan\frac{\theta_i}2$. We have $\sin(\theta_i)=\frac{2x_i}{1+x_i^2}$ and since $\sin$ in concave on $\left(0,\frac{\pi}2\right)$, we have $$\sum_{i=1}^3\frac{x_i}{1+x_i^2}=\frac 32\sum_{i=1}^3\frac 13\sin(\theta_i)\leq \frac 32\sin\frac{\theta_1+\theta_2+\theta_3}3.$$ We have, using the convextiy of $x\mapsto \tan^2 x$: $$\frac 13=\frac 13\sum_{i=1}^3\tan^2\frac{\theta_i}2\geq \tan^2\frac{\theta_1+\theta_2+\theta_3}6,$$ so $\tan\frac{\theta_1+\theta_2+\theta_3}6\leq \frac 1{\sqrt 3}$ and $\frac{\theta_1+\theta_2+\theta_3}6\leq \frac{\pi}6$. Finally $$\sum_{i=1}^3\frac{x_i}{1+x_i^2}\leq \frac 32\sin \frac{\pi}3=\frac{3\sqrt 3}4,$$ with equality if and only if $(x_1,x_2,x_3)=\left(\frac 1{\sqrt 3},\frac 1{\sqrt 3},\frac 1{\sqrt 3}\right)$.
The second derivative of the auxiliary function $$f(u)\ :=\ {\sqrt{u}\over 1+u}\qquad (u\geq0)$$ computes to $$f''(u)={3(u-1)^2 -4\over 4u^{3/2}(1+u)^3} \ <\ 0\qquad(0\leq u\leq 1)\ ;$$ whence $f$ is concave for $0\leq u\leq 1$. Putting $u_i:=x_i^2$ we therefore have $${1\over3}\sum_{i=1}^3{x_i\over 1+x_i^2}\leq\sum_{i=1}^3{1\over3}f(u_i)\ \leq\ f\Bigl({\sum_{i=1}^3 u_i\over3}\Bigr)=f\Bigl({1\over3}\Bigr)={\sqrt{3}\over4}\ ,$$ as claimed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9840844869613647, "perplexity": 429.94854908576883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00428-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://mathhelpforum.com/statistics/3004-combinatorics.html | 1. ## combinatorics
A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committe can have at most two girls?
Thanks,
2. Originally Posted by gogo08
A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committe can have at most two girls?
Thanks,
Possibilities
0 Girls
1 Girl
2 Girls
In each case respectively we have,
$\displaystyle _{10}C_4 \cdot _{12}C_0=210$
$\displaystyle _{10}C_3 \cdot _{12}C_1=1440$
$\displaystyle _{10}C_2 \cdot _{12}C_2=2970$
In total,
4260 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8673934936523438, "perplexity": 447.1528671614919}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864848.47/warc/CC-MAIN-20180623000334-20180623020334-00081.warc.gz"} |
http://mkweb.bcgsc.ca/printing.genomes/ | Trance opera—Spente le Stellebe dramaticmore quotes
# art is science is art
In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017
# What if we were to print what we sequence?
Expressing the amount of sequence in the human genome in terms of the number of printed pages has been done before. At the Broad Institute, all of the human reference genome is printed in bound volumes.
At our sequencing facility, we sequence about 1 terabases per day. This is equivalent to 167 diploid human genomes (167 × 6 gigabases). The sequencing is done using a pool of 13 Illumina HiSeq 2500 sequencers, of which about 50% are sequencing at any given time.
A single letter-size page (8.5" × 11") of 6pt Courier using 0.25 inch margins accomodates 18,126 bases on 114 lines. Shown here is a portion of sequence from human chromosome 1. (PDF)
This sequencing is extremely fast.
To understand just how fast this is, consider printing this amount of sequence using a modern office laser printer. Let's pick the HP P3015n which costs about $400—a cheap and fast network printer. It can print at about 40 pages per minute. If we print the sequence at 6pt Courier using 0.25" margins, each 8.5" × 11" page will accomodate 18,126 bases. I chose this font size because it's reasonably legible. To print 1 terabases we need $10^12 / 18126 = 55.2$ million pages. If we print continuously at 40 pages per minute, we need $10^12 / (18126*40*1440) = 957.8$ days. If we had 958 printers working around the clock, we could print everything we sequence and not fall behind. This does not account for time required to replenish toner or paper. ## what's cheaper, sequencing or printing? It costs us about$12,000 to sequence a terabase in reagents. If we do it on a cost-recovery basis, it is about twice that, to include labor and storage. Let's say $25,000 per terabase. Coincidentally, this is about$150 per 1× coverage of a diploid human genome. The cost of sequencing a single genome would be significantly higher because of overhead. To overcome gaps in coverage and to be sensitive to alleles in heterogenous samples, sequencing should be done to 30× or more. For example, we sequence cancer genomes at over 100×. For theory and review see Aspects of coverage in medical DNA sequencing by Wendl et al. and Sequencing depth and coverage: key considerations in genomic analyses by Sims et al.. (Thanks to Nicolas Robine for pointing out that redundant coverage should be mentioned here).
Printing is 44× more expensive than sequencing, per base: 25 n$vs 1.1 μ$.
I should mention that the cost of analyzing the sequenced genome should be considered—this step is always the much more expensive one. In The $1,000 genome, the$100,000 analysis? Mardis asks "If our efforts to improve the human reference sequence quality, variation, and annotation are successful, how do we avoid the pitfall of having cheap human genome resequencing but complex and expensive manual analysis to make clinical sense out of the data?"
The cost of a single printed page (toner, power, etc) is about $0.02–0.05, depending on the printer. Let's be generous and say it's$0.02. To print 55.2 million pages would cost us $1.1M. This is about 44 times as expensive as sequencing. To print what we sequence we would require 958 office laser printers (shown here as HP3015n) at a cost of$1,100,000 per day. (PDF)
Think about this. It's 44× more expensive to merely print a letter on a page than it is to determine it from the DNA of a cell. In other words, to go from the physical molecule to a bit state on a disk is much cheaper than from a bit state on a disk to a representation of the letter on a page.
Per base, our sequencing costs $$25000/10^12 =$25*10^-9$, or 25 nanodollars. At $0.02 and 18,126 bp per page, printing costs $0.02/18126 =$1.1*10^-6$ or 1.1 microdollars.
If at this point you're thinking that printing isn't practical, the fact that the pages would weigh 248,000 kg and stack to 5.5 km should cinch the argument.
The capital cost of sequencing is, of course, much higher. The printers themselves would cost about $400,000 to purchase. The 6 sequencers, on the other hand, cost about$3,600,000.
We sequence at a rate close to the average internet bandwidth available to the public.
At 3.86 Mb/s, we could download a terabase of compressed sequence in a day, assuming the sequence can be compressed by a factor of 3. This level of compression is reasonable—the current human assembly is 938 Mb zipped).
In other words, you would have to be downloading essentially continuously to keep up with our sequencing.
VIEW ALL
# Happy 2018 $\pi$ Day—Boonies, burbs and boutiques of $\pi$
Wed 14-03-2018
Celebrate $\pi$ Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.
Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!
A great 10 km run loop between Istanbul, Copenhagen, San Francisco and Dublin. Stop off for halva, smørrebrød, espresso and a Guinness on the way. (details)
Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.
In the Boonies, Burbs and Boutiques of $\pi$ we draw progressively denser patches using the digit sequence 159 to inform density. (details)
No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.
Roads from cities rearranged according to the digits of $\pi$. (details)
The art is featured in the Pi City on the Scientific American SA Visual blog.
Check out art from previous years: 2013 $\pi$ Day and 2014 $\pi$ Day, 2015 $\pi$ Day, 2016 $\pi$ Day and 2017 $\pi$ Day.
# Machine learning: supervised methods (SVM & kNN)
Thu 18-01-2018
Supervised learning algorithms extract general principles from observed examples guided by a specific prediction objective.
We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).
SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.
Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)
We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.
Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.
# Human Versus Machine
Tue 16-01-2018
Balancing subjective design with objective optimization.
In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.
Nature 10, 18 December 2017
# Machine learning: a primer
Thu 18-01-2018
Machine learning extracts patterns from data without explicit instructions.
In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.
The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.
Nature Methods Points of Significance column: Machine learning: a primer. (read)
We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.
# Snowflake simulation
Tue 16-01-2018
Symmetric, beautiful and unique.
Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.
A few of the beautiful snowflakes generated by the Gravner-Griffeath model. (explore)
The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.
Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38634321093559265, "perplexity": 3331.4331543551725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647519.62/warc/CC-MAIN-20180320170119-20180320190119-00540.warc.gz"} |
https://brilliant.org/discussions/thread/chemistry-doubt-3/ | # Chemistry doubt
$$0.5\text{ g}$$ sample of a sulphite salt was dissolved in $$200\text{ ml}$$ and $$20\text{ ml}$$ of this solution required $$10\text{ ml}$$ of $$0.02\text{ M}$$ acidified permanganate solution.Find the percentage by mass of sulphite in sulphite ore?
Note by Shivam Mishra
2 years, 7 months ago
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My solution :
Let the number of moles of sulphite ions be $$M$$. Clearly on oxidation the sulphite ion changes to sulphate so the oxidation number changes from $$4+$$ to $$6+$$, hence the valence factor is $$2$$. The product of moles and valence factor gives the equivalents. The valence factor permagnate solution in acidified solution is $$5$$. Equate the equivalents as :
$M ×2×\frac{20}{200} = \frac{10}{1000} × 0.02 × 5$
$M=\frac{5}{1000}$
As molecular weight of sulphite ion is $$80$$, percentage by mass is :
$\frac{0.005 × 80}{0.5} × 100$ $=80 %$
- 2 years, 6 months ago
Is the information complete?
- 2 years, 7 months ago
Yes
- 2 years, 7 months ago
- 2 years, 7 months ago
Tell me is this question based on molarity
- 2 years, 7 months ago
Yes,but it can also be solved using milliequivalents.
- 2 years, 7 months ago
Thanks @Utkarsh Dwivedi
- 2 years, 6 months ago
80%
- 2 years, 4 months ago | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9993759989738464, "perplexity": 13734.85228715665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583897417.81/warc/CC-MAIN-20190123044447-20190123070447-00485.warc.gz"} |
http://mathoverflow.net/users/943?tab=recent | # Dmitri
16,543 Reputation 7743 views
## Registered User
Name Dmitri Member for 3 years Seen 14 hours ago Website Location London Age 36
May14 awarded ● Enlightened May13 awarded ● Nice Answer Apr7 awarded ● Popular Question Mar30 comment How many polynomial Morse functions on the sphere?If you consider the case $n=2$, I believe the precise answer to your question should be known for all $d$. V.I. Arnol'd was interested in such type of questions, originally in the case when you replace $S^1$ by $\mathbb R^1$ and homogeneous polynomials by inhomogeneous. Probably one should chase the references to Arnold's article : mathnet.ru/php/… You might also want to have a look on the article of Barannikov "On the space of real polynomials without multiple critical values" Mar29 awarded ● Nice Answer Mar23 comment finite dimensional real division algebrasThere is a readable proof in the book of Shafarevich "basic algebraic geometry" of the fact that these algebras have dimension $2^n$. The proof indeed uses Bezout's theorem. Mar23 comment cohomology of a normal crossing divisorThis is not true, consider for example a divisor $D$ on a surface that is a wheel of $\mathbb P^1$'s, i.e, each $\mathbb P^1$ intersects two neighbouring $\mathbb P^1$'s. Then $\pi_1(D)=\mathbb Z$, so $H^1(D)=\mathbb Z$. Mar21 awarded ● Nice Question Mar19 awarded ● Enlightened Mar19 accepted Solid angles of a tetrahedron Mar19 awarded ● Nice Answer Mar18 revised Solid angles of a tetrahedronadded 29 characters in body Mar18 answered Solid angles of a tetrahedron Mar16 awarded ● Popular Question Mar10 revised Bolza curve admits no anticonformal fixedpointfree involutionadded 117 characters in body Mar10 answered Bolza curve admits no anticonformal fixedpointfree involution Mar1 comment Darboux SurfaceNoam, sure I want lines to vary too, so this becomes YQ's question in dimension one less. Mar1 comment Darboux SurfaceThis a very nice question! I wonder if a similar statement holds in $\mathbb P^2$ - if you take five lines, $10$ intersection points of them and consider quartics that contain these $10$ points, is it true that double conic is not in the Zariski closure of the space of such quartics? Feb28 comment What can one say about (differentiable) topological structure of CY3s?Dear Kim, by Bogomolov-Beuaville theorem every CY manifold has a finite cover that is a product of Tori, hyperkahler manifolds and manifolds $M^n$ such that $H^k(M^n,O)=0$ for $k\ne 0,n$. So for some people "proper" CY manifolds are only those that satisfy the last condition: $H^k(M^n,O)=0$ for $k\ne 0,n$. Such manifolds also have the property that the holonomy group of CY metrics on them coincide with $SU(n)$ (and not smaller than this). Such manifolds do have finite fundamental groups. Maybe for Oguis-Sakurai a Kahler manifold is $CY$ iff it has a holomorphic volume form... Feb28 revised What can one say about (differentiable) topological structure of CY3s?the answer is corrected and expanded Feb28 answered What can one say about (differentiable) topological structure of CY3s? Feb23 accepted Betti numbers of Proper nonprojective varieties Feb23 comment Betti numbers of Proper nonprojective varietiesDonu, thanks for the reference, I'll have a look (and will try to see if indeed I have an alternative proof :) ). LMN, you are welcome :) Feb23 revised Betti numbers of Proper nonprojective varietiesadded 32 characters in body Feb23 answered Betti numbers of Proper nonprojective varieties Feb14 comment Properties of quotient varietyConsider the following example: $(x,y)\to (x^2,y)$. Then the preimage of the curve $x=y^2$ under this map is $x=\pm y$. It is singular at $(0,0)$. It seems to me that you need to make the question a bit more specific... Feb6 revised Birational Automorphisms and infinite divisibilityadded 4 characters in body Feb6 revised Birational Automorphisms and infinite divisibilityadded 102 characters in body Feb6 comment Birational Automorphisms and infinite divisibilityYves, thanks I was a bit sloppy :) . But for \mathbb Q this is ture :) Feb5 revised Birational Automorphisms and infinite divisibilityadded 165 characters in body; added 10 characters in body Feb5 comment Birational Automorphisms and infinite divisibilityDaniel, the claim is that any homomorphism from $\mathbb Z[1/2]$ to $GL(n,\mathbb Z)$ sends $\mathbb Z[1/2]$ to $1$, since $1$ in $GL(n,\mathbb Z)$ is the only infinitely divisible element. Feb5 revised Birational Automorphisms and infinite divisibilitydeleted 2 characters in body Feb5 revised Birational Automorphisms and infinite divisibilityadded 202 characters in body; added 36 characters in body Feb5 answered Birational Automorphisms and infinite divisibility Feb4 accepted singular divisors in a complete linear system Feb4 comment Are rational varieties simply connected?Thank you Vesselin. The property of been rationally connected is a birational invariant, I guess? Feb4 comment Are rational varieties simply connected?Sandor, thank you :), I completely agree with you, I added missing words. In fact I was meaning "rational complex projective varieties". I don't know what is the definition of rationally connected projective varieties in the case they are singular. For example, if you consider a cone over a genus $g>0$ curve, every to points can be connected by a two $\mathbb P^1$'s (through the center of the cone), but I don't think this variety should be called rationally connected... Feb4 revised Are rational varieties simply connected?deleted 24 characters in body Feb4 revised Are rational varieties simply connected?added 42 characters in body Feb4 comment Are rational varieties simply connected?Dear Laurent I decided to check the reference and it looks to me that the proof of the fact is not really there. It is proven in two ways that projective spaces over algebraically closed fields are simply connected SGA 1. XI. Prop. 1.1, ( arxiv.org/pdf/math/0206203v2.pdf) and then comes corollary 1.2 without an actual proof. It is just said there that the proof is the same as for projective space :). Could you indicate how to make this an actual proof? I am asking this because I want to see how to make a proof over C without Hironaka's resolution of singularities. Feb3 answered another diameter-perimeter-area inequality Feb3 comment Why are the holomorphic line bundle sections finite dimensional?I really like this reasoning with Montel theorem :) Feb3 answered Why are the holomorphic line bundle sections finite dimensional? Feb2 accepted a diameter-perimeter-area inequality for convex figures Feb2 revised singular divisors in a complete linear systemadded 132 characters in body Feb2 comment singular divisors in a complete linear systemJames, thank you! Of course this is what I meant :) Feb2 revised singular divisors in a complete linear systemadded 3 characters in body Feb2 answered singular divisors in a complete linear system Feb2 comment a diameter-perimeter-area inequality for convex figuresConnor, that is of course correct. In fact, I was thinking of exactly this example but for some reason (I guess to make the answer as short :) ) as possible put the vertices of the rombus in $\pm 1, \pm varepsilon$) instead of what I had in mind. Feb2 comment a diameter-perimeter-area inequality for convex figuresI also called rectangle what should be called a rombus :) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8834314942359924, "perplexity": 1181.4388108208689}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699755211/warc/CC-MAIN-20130516102235-00070-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.ck12.org/measurement/Conversion-Using-Unit-Analysis/lesson/Solve-Problems-Involving-Rates-and-Unit-Analysis/ | <meta http-equiv="refresh" content="1; url=/nojavascript/">
# Conversion Using Unit Analysis
## Solve problems by converting units using unit analysis.
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Practice Conversion Using Unit Analysis
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Solve Problems Involving Rates and Unit Analysis
“I would LOVE to climb Mount Everest!” Josh exclaimed at breakfast one morning.
“Really?” his Dad said smiling. “Well son, you had better start saving now.”
Josh looked up from his oatmeal with a puzzled look on his face.
“What makes you say that?” Josh asked.
“What makes me say that is that the going rate for one climb on Everest is about $60,000. That’s what makes me say that,” his Dad explained taking a sip of his coffee. “Really? Wow! I had no idea,” Josh said. “Well, I guess I’ll just have to make a lot of money!” Josh said leaving the table. He kept thinking about what his Dad had said all the way to school. Sixty thousand dollars was a lot of money to climb a mountain, but what really amazed Josh was thinking about the numbers of people who had climbed the mountain more than once. When he got to class, he looked up in his book that Apa Sherpa a man from Nepal had successfully climbed Everest 19 times. Now he was often a guide who was paid, but still, Josh couldn’t help thinking about how much money Apa Sherpa would have spent if he had paid to climb Everest nineteen times at the rate his father spoke about. How much would it have cost? We can use units, ratios and proportions to solve this problem. By thinking of one trip as a unit, we can look at the proportion and solve for the correct amount of money. ### Guidance A rate refers to speed or a rate can refer to the amount of money someone makes per hour. When we talk about a unit rate, we look at comparing a rate to 1, or how much it would take for 1 of something. It could be one apple, one mile, one gallon. We are comparing a quantity to one. A key word when working with unit rate is the word “per”. We can use ratios and proportions to solve problems involving rates and unit rates. Jeff makes$150.00 an hour as a consultant. What is his rate per minute?
To figure this out, we have to think about the unit rate that Jeff is paid as a consultant. You will see that we have “an hour” written into the problem. This is the unit rate. Also notice that the would "per" is used in the problem.
Let’s write the unit rate as a ratio compared to 1.
Next, we need to think about what the problem is asking for. It is asking for his rate per minute. The given information is in hours, so we need to write a ratio that compares hours to minutes.
\begin{align*}\frac{1 \ hour}{60 \ minutes}\end{align*}
Now we can write an expression combining the two ratios.
\begin{align*}\frac{\ 150}{1 \ hour} \cdot \frac{1 \ hour}{60 \ minutes}\end{align*}
That’s a great question. We don’t compare hours to hours because we aren’t comparing hours. We are comparing money to hours and we need to figure out the rate of money per minute. You always have to think about what is being compared when working with proportions.
Next, we can solve. Notice that because 1 hour is diagonal from 1 hour, we can cross cancel the hours. That leaves us with a ratio that compares money to minutes.
\begin{align*}\frac{\ 150}{60 \ minutes}\end{align*}
This also helped us to convert hours to minutes making it easier to figure out the answer to the problem. Now we can divide to figure out our answer.
Jeff makes $2.50 per minute. What is unit analysis? Unit analysis is when we look at how to measure individual units in different measurement amounts and it is used to convert units of measurement. When we use unit analysis, we convert different measurement units by comparing the units using ratios and proportions. Unit analysis is very helpful when checking results. Take a look at this dilemma. Juanita worked for 18 hours. She made$116.00 at the end of her shift. Juanita was sure that her manager had made a mistake and that she should have made more money. Juanita makes 9.00 per hour. Did Juanita make the correct amount of money or was there a mistake? To work on this problem, we can use unit analysis. Let’s start by writing a ratio to compare how much Juanita made for the hours worked. \begin{align*}\frac{18 \ hours}{\ 116.00}\end{align*} Next, we can use her hourly rate to work with. She makes9.00 per hour.
\begin{align*}\frac{\ 9}{1 \ hour}\end{align*}
Solution: .39
#### Example B
Fifteen gallons of gasoline costs $45.00. How much is it per gallon? Solution:$3.00
#### Example C
Two tickets to a ballgame costs $111.50. What is the cost for one ticket? Solution:$55.75
Now let's go back to the dilemma from the beginning of the Concept.
Now let’s look at solving this problem.
We know that it costs 60,000 for 1 trip up Mount Everest. \begin{align*}\frac{\ 60,000}{1} &= \frac{x}{19}\\ x &= \ 1,140,000\end{align*} We can also use unit analysis to solve this problem.60,000 dollars \begin{align*}\left( \frac{19}{x \ dollars}\right)\end{align*}
\begin{align*}60,000 \times 19 = \ 1,140,000\end{align*} is the cost of the nineteen trips.
This is our solution.
### Guided Practice
Here is one for you to try on your own.
Solve and then check using unit analysis.
Jesse has a car that holds 14 gallons of gasoline. During the first week of the month, gasoline cost $2.75 per gallon. During the second week of the month, gasoline cost$2.50 per gallon. How much was the total cost for the 28 gallons of gasoline?
Solution
Let’s start by writing a variable expression to work on this problem. We know that the number of gallons of gasoline does not change. That can be our variable.
\begin{align*}x = \end{align*} number of gallons of gasoline
The other parts of the expression include the different prices for the gasoline.
\begin{align*}2.75x+2.50x\end{align*}
This expression will help us to determine how much money Jesse spent on 28 gallons of gasoline. Each full tank is 14 gallons. We can substitute 14 for our variable \begin{align*}x\end{align*} .
\begin{align*}2.75(14)&+ 2.50(14)\\ \ 38.50 &+ \ 35.00\end{align*}
The total amount of money spent was 73.50. We can check our work by using unit analysis. \begin{align*}\frac{2.75}{1 \ gallon} &= \frac{x}{14 \ gallons} = \ 38.50\\ \frac{2.50}{1 \ gallon} & = \frac{x}{14 \ gallons} = \ 35.00\end{align*} The sum of the money spent was73.50.
### Explore More
Directions: Use what you have learned to solve each problem.
1. Peter runs at a rate of 10 kilometers per hour. How many kilometers will he cover in 8 hours?
2. A cheetah can run at a speed of 60 miles per hour. What is his distance after 6 hours?
3. What is the distance formula?
4. If a car travels at a rate of 65 miles per hour for 30 minutes, how far will it travel?
5. A train travels at a rate of 50 miles per hour. If it needs to travel 320 miles, how many minutes will it take?
6. A car travels 65 mph for 12 hours. How many miles will it travel?
7. A bus traveled 300 miles at an average speed of 50 miles per hour. How long did this trip take the bus?
8. A car traveled at an average speed of 40 miles per hour through a construction zone. If the car traveled 20 miles at this rate, how many hours did it take to travel the 20 miles?
9. What is velocity?
10. What is the formula for velocity?
11. What is the velocity of an object that travels 500 miles in 2.5 hours?
12. If an object has a velocity of 125 miles per hour, how long will it take to travel 4,375 miles?
13. If an object has a velocity of 7 kilometers per minute, how far will it travel in 2 hours?
14. If an object has a velocity of 4 meters per second, how many kilometers will it travel in 2 days?
15. The formula for density is \begin{align*}D = \frac{m}{v}\end{align*} where \begin{align*}D\end{align*} represents the density of an object, \begin{align*}m\end{align*} represents the mass of the object, and \begin{align*}v\end{align*} represents the volume of the object. What is the density of a brick that weighs 9 pounds and has a volume of 36 cu. in.?
### Vocabulary Language: English
Rate
Rate
A rate is a special kind of ratio that compares two quantities.
Unit Analysis
Unit Analysis
Unit analysis is a method of converting units of measurement by using ratios and proportions.
Unit Rate
Unit Rate
A unit rate is a ratio that compares a quantity to one. The word “per” is a key word with unit rates. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8437894582748413, "perplexity": 1026.4338910137592}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042981525.10/warc/CC-MAIN-20150728002301-00327-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/miniboone-results-at-6-1-sigma-potential-evidence-for-sterile-neutrinos.948730/ | FeaturedI MiniBooNE results at 6.1 sigma: Potential evidence for sterile neutrinos
Tags:
1. Jun 2, 2018
2. Jun 2, 2018
Orodruin
Staff Emeritus
I assume that by "IceCube" you mean "MiniBooNE".
You have to take these results with a (big) grain of salt. The best-fit they present is already ruled out by other experiments. Even more so if you consider experiments that measure different channels. In addition, the oscillation fit is still a pretty bad one. Although they have a $\chi^2/$dof of 35.2/28, many of the bins are not in the region where they have a signal and I imagine that if you would focus on that region the $\chi^2/$dof would be rather nasty. They also cover their bases on this in the last sentence of the abstract: "Although the data are fit with a standard oscillation model, other models may provide better fits to the data."
Edit: Let me also point out that Sabine has misinterpreted some of the paper in her blog post. In particular with respect to what other experiments are shown in the "money plot". Those shown are other experiments trying to measure the exact same oscillation channel. There is no way to reconcile the best-fit with OPERA even assuming sterile neutrino oscillations. Something is going on, but it is probably not sterile neutrinos.
3. Jun 2, 2018
Staff Emeritus
Also, MiniBooNE was against sterile neutrinos before they were for them.
4. Jun 2, 2018
Staff: Mentor
Based on figure 4, they rule out $\Delta m^2 < 0.01 eV^2$ with more than 3 sigma. This means at least one neutrino mass eigenstate has to be at least 100 meV, right? 140 meV if we go by the 95% CL. And this is for the optimal case of $\theta = 45^\circ$. This could come in conflict with cosmological measurements in the not so distant future - in addition to the existing conflict with the other measurements of the same parameter.
Edit: Oops, wrong sign
Last edited: Jun 3, 2018
5. Jun 3, 2018
kimmm
Is this interpretation correct?
LSND experimet observed and excess number of electron neutrinos,so by considering a sterIle neutrino we can explain that the muon neutrinos oscillate 5o sterile neutrinos and then theses sterile neutrinos oscillate to electron neutrinos in the short baseline experiment?
6. Jun 3, 2018
Orodruin
Staff Emeritus
The best fit is ruled out by so many things (including the OPERA results that they show in the figure!) that I think cosmology would be one of the weaker ... It is completely incompatible with essentially everything else we know about neutrinos. Also, a state with maximal mixing is not very sterile ...
I also believe the best fit would actually already be ruled out by Planck. A "sterile" neutrino with that kind of interactions would easily thermalise and send $\Delta N_{\rm eff}$ to at least 1. And then we have not even started to talk about atmospheric and reactor neutrino experiments ...
Many would put it like this as a kind of a mental picture. However, it is a quantum process and you are never measuring the neutrino state in between production and detection so you can not say it was a sterile neutrino at some point. A more accurate way of putting it is that it would change the interference pattern among the neutrino mass eigenstates.
7. Jun 3, 2018
kimmm
It is a very naive and basic question,but I just get confused, that all the neutrinos are like that, that they do not exist at some points, or just for sterile neutrinos?
if for others also then how we can say we have a muon neutrino beams or electron neutrinos observed by their interactions?
8. Jun 3, 2018
Orodruin
Staff Emeritus
I did not say they did not exist. I said you do not measure their flavour state.
9. Jun 3, 2018
kimmm
I understand,and the reason that long baseline experiments could not see any result about sterile neutrinos, is because in their baseline and their energy ranges the feature of the sterile neutrinos could not affect the probabilities of neutrino oscillation?
10. Jun 3, 2018
Orodruin
Staff Emeritus
At longer baselines the oscillations of eV range sterile neutrinos would be completely averaged out. That does not necessarily mean you would have no information, but it would be more difficult to extract it.
11. Jun 3, 2018
Ygggdrasil
12. Jun 3, 2018
Staff: Mentor
@Ygggdrasil - that is primarily why I posted this in the first place. I was confused - the original title of the post reflected a popular science name 'Ice Cube', @mfb corrected me. Thanks for that.
What also confused me is why I saw nothing on PF about it except Bee H's blog, and the kinds of articles you cited.
13. Jun 4, 2018
Orodruin
Staff Emeritus
A clear example of why one should not always trust the popular press. The NBC article does not mention that the interpretation as sterile neutrinos is in direct conflict with other experiments until pretty far down and you certainly do not get that impression from the first part of the article. The Quantamagazine article is a bit more forthcoming with this information.
You are welcome.
Also I am not sure IceCube is more "popular science" than MiniBooNE. Both are actual names of particle physics experiments. One just happens to be more known than the other.
14. Jun 4, 2018
Ygggdrasil
Exactly why after seeing and skimming through the NBC article (mainly to see if the claims had any basis in a published article), I came here to see if you all had anything to say about the paper.
15. Jun 4, 2018
Chronos
John Baez offers some interesting comments here: https://johncarlosbaez.wordpress.com/2018/06/02/miniboone/. The fact is MiniBooNE detected an excess of electron neutrinos over their 15 years of data collection. It isn't a huge number, but, given the confidence we have in the expected number of detections is very high, it is enough to establish a very high confidence [4.8 sigma] that something very curious is going on that is not explained by the standard model. That does not mean it is proof of sterile neutrinos, but, that is probably as good a guess as anyone has offered thus far. It should be interesting to see if MiniBooNE can nudge up the signal they currently have to up over the magic 5 sigma level with more data.
16. Jun 4, 2018
Staff: Mentor
17. Jun 4, 2018
Orodruin
Staff Emeritus
First of all, it is a 4.8 sigma difference with the no oscillation scenario for the best fit. This best fit happens to already be strongly excluded by other experiments, which puts the interpretation as sterile neutrinos in serious doubt. I would certainly agree that it is curious and worthy of scrutiny, but I would be very surprised if the signal is due to sterile neutrinos (see the comments I made on Backreaction).
Edit: Also, it is as good a guess as someone has offered thus far and has therefore also been much more scrutinised. It has been scrutinised to the point that it seems unlikely to be able to explain the MiniBooNE low-energy excess as oscillations just don't give a good fit of the data.
Last edited: Jun 4, 2018
18. Jun 4, 2018
Chronos
My interest in sterile neutrinos dates back to this paper: https://arxiv.org/abs/1402.2301, Detection of An Unidentified Emission Line in the Stacked X-ray spectrum of Galaxy Clusters, which sparked an enduring controversy over the plausibility of sterile neutrinos as a component of the dark matter budget. Particle physics is not really my thing, although I have tried to keep a finger on the sterile neutrino pulse since then.
19. Jun 5, 2018
Staff: Mentor
20. Jun 5, 2018
Orodruin
Staff Emeritus | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8268582224845886, "perplexity": 908.7114367268634}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201672.12/warc/CC-MAIN-20190318191656-20190318213656-00158.warc.gz"} |
https://www.omnicalculator.com/health/fetal-weight-percentile | # Fetal Weight Percentile Calculator
Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Steven Wooding
Based on research by
Kiserud T, Piaggio G, Carroli G, Widmer M, Carvalho J, Neerup Jensen L, et al. The World Health Organization Fetal Growth Charts: A Multinational Longitudinal Study of Ultrasound Biometric Measurements and Estimated Fetal Weight. PLoS Medicine (January 2017)See 2 more sources
Blue NR, Savabi M, Beddow ME, Katukuri VR, Fritts CM, Izquierdo LA, Chao CR. The Hadlock Method Is Superior to Newer Methods for the Prediction of the Birth Weight Percentile. Journal of Ultrasound in Medicine (March 2019)Hadlock FP, Harrist RB, Martinez-Poyer J. In utero analysis of fetal growth: a sonographic weight standard. Radiology (October 1991)
Last updated: May 09, 2022
Our fetal weight percentile calculator computes your child's growth and compares it to the general population. Our BPD, HC, AC, and FL calculator uses all the necessary ultrasound fetal measurements to compute your child's weight at a given week of the pregnancy.
We use the Hadlock equation and . 👶👶🏾👶🏽👶🏻
Want to know more? Follow the article below to discover fetal weight percentile chart by week, and details of our baby weight predictor calculator. We'll also cover the baby percentiles during pregnancy as well as the SGA and LGA definitions.
## What percentile is my baby, and what does it mean?
We use percentiles to measure values that are extremely variable in the population - especially in children. For example, we can't give a precise value of height that a healthy 2-year old boy should achieve - it all depends on his individual and genetic characteristics. 🔬
However, doctors love all the hard data and numbers that help them make critical clinical decisions. They needed a tool that allows quick and precise evaluation of their patients.
So how did we tackle this problem? 🤔
Percentiles are a great solution! Instead of giving us a precise number, they inform us about the range in which your baby's height or weight should fall. Thanks to percentiles, we can tell how your child's health looks when compared to the general population and detect any significant abnormalities.
When we talk about fetal weight abnormalities, two most important definitions come to mind:
1. Small for the gestational age (age of the pregnancy, counted from the conception)
2. Large for the gestational age
💡 SGA - Small for Gestational Age babies are all babies that fall below the 10th percentile of the population, when it comes to their EFW percentile. It means that over 90% of the population grew larger than they did.
💡 LGA - Large for Gestational Age babies exceed the 90th percentile of their Estimated Fetal Weight. It means that only 10% of population is larger than them.
These two explanations are based on an Estimated Fetal Weight (EFW) calculations that use the ultrasound technique to evaluate a baby's weight inside its mother's uterus.
To estimate the fetal weight, we use the following measurements:
• Abdominal circumference - circumference of the baby's belly, measured at the liver's height. (Advanced: an umbilical portion of the left portal vein should be in the center of the abdomen.)
• Head circumference - measured at the point where specific brain structures are visible. (Advanced: plane that traverses the thalami and cavum septum pellucidum.)
• Biparietal diameter - length of a distance between two parietal bones of a baby's skull.
• Femur length - a length of the baby's thigh bone.
Our fetal growth calculator uses all four of the enumerated measurements; additionally, we can also measure the humerus length.
💡 We could also measure the estimated fetal weight by assessing the fundal height - this method, however, is not as accurate.
You've learned everything about fetal weight percentiles - go on and check our other percentile-themed tools:
## How to use the fetal weight percentile calculator?
Our estimated fetal weight percentile calculator needs just a few easy steps:
1. Enter the gender of your baby
Be specific; if you already know the baby's gender, reveal it. 🎉
2. Enter the gestational age
This calculator is for fetuses older than 14 weeks. (We use a different type of measurement in younger pregnancies: the Crown-rump length (CRL)).
3. Find all the enumerated ultrasound measurements
Remember to choose the correct unit - imperial or metric.
🔅 Our tool also works as a large and small for gestational age calculator: along with the results, you will receive feedback concerning your child's weight's location on the chart and its meaning. Read more about LGA/SGA in the .
## Fetal growth chart
Here you can find the fetal weight week by week for the fetuses of an unknown gender ♀️/♂️:
Gestational Age (weeks) Estimated Fetal Weight (g) by percentile 2.5 5 10 25 50 75 90 95 97.5 14 70 73 78 83 90 98 104 109 113 15 89 93 99 106 114 124 132 138 144 16 113 117 124 133 144 155 166 174 181 17 141 146 155 166 179 193 207 217 225 18 174 181 192 206 222 239 255 268 278 19 214 223 235 252 272 292 313 328 340 20 260 271 286 307 330 355 380 399 413 21 314 327 345 370 398 428 458 481 497 22 375 392 412 443 476 512 548 575 595 23 445 465 489 525 565 608 650 682 705 24 523 548 576 618 665 715 765 803 830 25 611 641 673 723 778 836 894 938 970 26 707 743 780 838 902 971 1,038 1,087 1,125 27 813 855 898 964 1,039 1,118 1,196 1,251 1,295 28 929 977 1,026 1,102 1,189 1,279 1,368 1,429 1,481 29 1,053 1,108 1,165 1,251 1,350 1,453 1,554 1,622 1,682 30 1,185 1,247 1,313 1,410 1,523 1,640 1,753 1,828 1,897 31 1,326 1,394 1,470 1,579 1,707 1,838 1,964 2,046 2,126 32 1,473 1,548 1,635 1,757 1,901 2,047 2,187 2,276 2,367 33 1,626 1,708 1,807 1,942 2,103 2,266 2,419 2,516 2,619 34 1,785 1,872 1,985 2,134 2,312 2,492 2,659 2,764 2,880 35 1,948 2,038 2,167 2,330 2,527 2,723 2,904 3,018 3,148 36 2,113 2,205 2,352 2,531 2,745 2,959 3,153 3,277 3,422 37 2,280 2,372 2,537 2,733 2,966 3,195 3,403 3,538 3,697 38 2,446 2,536 2,723 2,935 3,186 3,432 3,652 3,799 3,973 39 2,612 2,696 2,905 3,135 3,403 3,664 3,897 4,058 4,247 40 2,775 2,849 3,084 3,333 3,617 3,892 4,135 4,312 4,515
Along with monitoring the baby's growth and weight, we can also check if the mother's pregnancy weight gain is also within a healthy range. 🤰
## How to calculate the fetal weight percentile?
It's easier than you think!
1. Calculate the weight of the fetus 📉
Our fetal percentile calculator faciliates the process of computing the fetus weight, based on the ultrasound measurements; however, if you'd like to calculate it yourself, you're more than welcome to try the equation we used:
\footnotesize \begin{align*} &\log{}_{10}\left(\text{Fetal weight}\right) = \\ &1.3596 - (0.00386 \cdot \text{AC} \cdot \text{FL}) +\\ &(0.0064 \cdot \text{HC}) + (0.00061 \cdot \text{BPD} \cdot \text{AC}) \\ &+ (0.0424 \cdot \text{AC}) + (0.174 \cdot \text{FL}) \end{align*}
where:
• Fetal weight is given in grams (g);
• AC means the Abdominal Circumference and is given in centimeters (cm);
• FL means the Femur Length and is given in centimeters (cm);
• HC means the Head Circumference and is given in centimeters (cm);
• BPD means the Biparietal Diameter and is given in centimeters (cm); and
• log10(Fetal weight) means the fetal weight logarithm of the base of 10.
2. Find the percentile 📈
When you already know the fetus's weight, all you need to do is check the fetal growth charts or tables for a given gestational age.
• Find your baby's gestational age on the bottom of the page: draw a vertical line starting from that point.
• Find its weight on the left or right edge of the chart, and draw a horizontal line beginning from that point.
• Mark the crossing of these two lines with a dot.
• Check which fetal weight percentile line on the chart is located the closest to the dot you've just drawn.
❗ Our birth weight calculator for the US is a tool prepared for measuring children of different ethinicites - despite that fact, you shouldn't use it as a single source of clinical knowledge. Always consult your doctor, and double check any measurements that may have any impact on clinical practice.
## FAQ
### What is a percentile?
A percentile is a score used in statistics and medicine to indicate where a certain measurement places among the same measurement in its peers.
When we say that a measurement belongs to the k-th percentile, we mean that k % of the measurements in a population are below the one we are considering. Percentiles are largely used when assessing widely variable quantities, like the heights and weights of individuals.
### What is the estimated fetal weight?
The estimated fetal weight is the baby's weight at a specific time of the pregnancy. Because the measurement cannot be taken directly, it is estimated using an ultrasound scan, which finds:
• Abdominal and head circumference (AC and HC);
• Biparietal diameter (the distance between parietal bones in the skull) (BPD); and
• Femur length (occasionally also humerus length) (HL).
Plug those measurements in the following formula to find the estimated fetal weight:
log₁₀(Fetal weight) = 1.3596 - (0.00386 × AC × FL) + (0.0064 × HC) + (0.00061 × BPD × AC) + (0.0424 × AC) + (0.174 × FL).
### How do I find the fetal weight percentile?
To find the fetal weight percentile, follow these steps:
1. Calculate the estimated fetal weight.
2. On a fetal weight percentile chart, find the intersection between the value of the estimated fetal weight and the gestational age.
3. The intersection will fall close to a line on the graph: each line is associated with a specific percentile, which in this case, corresponds to your baby's percentile.
### Which percentile is a fetus with estimated fetal weight 250 g at 18 weeks?
75ᵗʰ percentile. To calculate the percentile, find a fetal weight percentile chart and find the intersection between the lines corresponding to the values:
• Estimated fetal weight 250 g; and
• Gestational age 18 weeks.
The closest line to the point is the 75ᵗʰ percentile, which means that the baby is heavier than 75% of all other babies the same age.
Łucja Zaborowska, MD, PhD candidate
Sex
Unknown
Gestational age
wks
Abdominal Circumference
mm
mm
Biparietal Diameter
mm
Femur Length
mm
Result
Estimated fetal weight
g
Your baby is in the 50th percentile! 👶
✅ Your baby's weight is within normal range.
• Y axis: fetal weight in grams (g).
• X axis: gestational age in weeks.
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https://desfontain.es/privacy/differential-privacy-awesomeness.html?utm_source=hs_email&utm_medium=email&_hsenc=p2ANqtz-9akndY1VGiOZkt1s9fpVbR2RydzgB6-1wBeA7RgTtx7kVzpHp0twDkOZgOReiuj5rRqNTf | # Ted is writing things
On privacy, research, and privacy research.
# Why differential privacy is awesome
— updated
This is the first blog post in a series about differential privacy. Check out the table of contents to see the next articles!
How to publish data about people while protecting their privacy? This question is far from new. Statistical agencies have grappled with it for decades. Computer scientists have proposed a whole bunch of creative notions to capture this idea. None of them was very satisfactory, though: all these notions were shown to be broken in some circumstances. They were also hard to apply without destroying the utility of the data.
This all changed in 2006, when four researchers introduced differential privacy. This new notion took a novel approach to defining privacy leakage, one that would prove much more rigorous and fruitful. So, what makes differential privacy special? How did it get so successful in adademic circles? Why did governments and tech companies start adopting it for their data publications?
This first article introducing differential privacy will attempt to answer that question. First, we'll describe the high-level intuition behind this successful notion. Then, we'll explain why it's so successful: why is it so much more awesome than all the definitions that came before?
# The core idea behind differential privacy
Suppose you have a process that takes some database as input, and returns some output.
This process can be anything. For example, it can be:
• a process calculating some statistics ("tell me how many users have red hair")
• a de-identification strategy ("remove names and last three digits of ZIP codes")
• a machine learning training process ("build a model to predict which users like cats")
• … you get the idea.
To make a process differentially private, you usually have to modify it a little bit. Typically, you add some randomness, or noise, in some places. What exactly you do, and how much noise you add, depends on which process you're modifying. I'll abstract that part away and simply say that your process is now doing some unspecified ✨ magic ✨.
Now, remove somebody from your database, and run your new process on it. If the new process is differentially private, then the two outputs are basically the same. This must be true no matter who you remove, and what database you had in the first place.
By "basically the same", I don't mean "it looks a bit similar". Instead, remember that the magic you added to the process was randomized. You don't always get the same output if you run the new process several times. So what does "basically the same" means in this context? It means that you can get the exact same output from both databases with similar likelihood.
What does this have to do with privacy? Well, suppose you're a creepy person trying to figure out whether your target is in the original data. By looking at the output, you can't be 100% certain of anything. Sure, it could have come from a database with your target in it. But it could also have come from the exact same database, without your target. Both options have a similar probability, so there's not much you can say.
You might have noticed that this definition doesn't say anything about what the output data looks like. Differential privacy is not a property of the output data. It's very different from, say, $$k$$-anonymity, one of the first data privacy definitions. You can't look at the output data and determine whether it satisfies differential privacy. Instead, differential privacy is a property of the process: you have to know how the data was generated to determine whether it's differentially private.
That's about it for the high-level intuition. It's a little abstract, but not very complicated. So, why all the hype? What makes it so awesome compared to older, more straightforward definitions?
# What makes differential privacy special
Privacy experts, especially in academia, are enthusiastic about differential privacy. It was first proposed by Cynthia Dwork, Frank McSherry, Kobbi Nissim and Adam Smith in 20061. Very soon, almost all researchers working on anonymization started building differentially private algorithms. Tech companies and governments are adopting it fast. So, why all the hype? I can count three main reasons.
## You no longer need attack modeling
All definitions that came before needed some assumptions about the attacker. To choose the right notion, you needed to figure out the attacker's capabilities and goals. How much prior knowledge do they have? What auxiliary data are they allowed to use? What kind of information do they want to learn?
Doing in practice was difficult and very error-prone. Answering these questions is very tricky: in particular, you might not know exactly what the attacker wants or is capable of. Worse, there might be unknown unknowns: attack vectors that you didn't anticipate at all. For that reason, you couldn't make very broad statements with these old-school definitions. You had to make some assumptions, which you couldn't be 100% sure of.
By contrast, when you use differential privacy, you get two awesome guarantees.
1. You protect any kind of information about an individual. It doesn't matter what the attacker wants to do. Reidentify their target, know if they're in the dataset, deduce some sensitive attribute… All those things are protected. Thus, you don't have to think about the goals of your attacker.
2. It works no matter what the attacker knows about your data. They might already know some people in the database. They might even add some fake users to your system. With differential privacy, it doesn't matter. The users that the attacker doesn't know are still protected.
## You can quantify the privacy loss
Differential privacy, like older notions, comes with a numeric parameter that you can tweak. There is a big difference, though, in how meaningful that parameter is. Take $$k$$-anonymity, for example. It tells you that each record in the output dataset "looks like" at least $$k-1$$ other records. But does the value of $$k$$ tell us about the level of protection?
The answer is… not much. There is no clear link between the value of $$k$$ and how private the dataset is. So choosing $$k$$ is very handwavy, and can't be justified in a formal way. The problem is even worse with other old-school definitions.
Differential privacy is much better. When you use it, you can quantify the greatest possible information gain by the attacker. The corresponding parameter, named $$\varepsilon$$, allows you to make formal statements. Suppose $$\varepsilon=1.1$$. Then, you can say: "an attacker who thinks their target is in the dataset with probability 50% can increase their level of certainty to at most 75%." Choosing the exact value of $$\varepsilon$$ isn't easy, but at least, it can be interpreted in a formal way.
And do you remember the previous point about attack modeling? It means you can change this statement in many ways. You can replace "their target is is the dataset" by anything about one individual. And you can add "no matter what the attacker knows" if you want to be extra-precise. Altogether, that makes differential privacy much stronger than all definitions that came before.
## You can compose multiple mechanisms
Suppose you have some data. You want to share it with Alex and with Brinn, in some anonymized fashion. You trust Alex and Brinn equally, so you use the same definition of privacy for both of them. They are not interested in the same aspects of the data, so you give them two different versions of your data. Both versions are "anonymous", for the definition you've chosen.
What happens if Alex and Brinn decide to conspire, and compare the data you gave them? Will the union of the two anonymized versions still be anonymous? It turns out that for most definitions of privacy, this is not the case. If you put two $$k$$-anonymous versions of the same data together, the result won't be $$k$$-anonymous. So if Alex and Brinn collaborate, they might be able to reidentify users on their own… or even reconstruct all the original data! That's not good news.
With differential privacy, you can avoid this failure mode. Suppose that you gave differentially private data to Alex and Brinn. Each time, you used a parameter of $$\varepsilon$$. Then if they conspire, the resulting data is still protected by differential privacy. The level of privacy is now weaker: the parameter becomes $$2\varepsilon$$. So they still gain some information, but you can now quantify how much. This property is called composition.
This scenario sounds a bit far-fetched, but composition is super useful in practice. Organizations often want to do many things with data. Publish statistics, release an anonymized version, train machine learning algorithms… Composition is a way to stay in control of the level of risk as new use cases appear and processes evolve.
# Conclusion
I hope the basic intuition behind differential privacy is now clear. If you remember a single thing, let this be this one-line summary: uncertainty in the process means uncertainty for the attacker, which means better privacy.
I also hope that you're now wondering how it actually works! What hides behind this magic that makes everything safe and private? Why does differential privacy have all the awesome properties I've mentioned? This is the exact topic of the next article in this series, which explains this in more detail while still staying clear of heavy math.
1. The idea was first proposed in a scientific paper (pdf) presented at TCC 2006, and can also be found in a patent (pdf) filed by Dwork and McSherry in 2005. The name differential privacy seems to have appeared first in an invited paper (pdf) presented at ICALP 2006 by Dwork.
All opinions here are my own, not my employer's. | Feedback on these posts are very welcome! Please reach out via e-mail (se.niatnofsed@neimad) or Twitter (@TedOnPrivacy) for comments and suggestions. | Interested in deploying formal anonymization methods? My colleagues and I at Tumult Labs can help. Contact me at oi.tlmt@neimad, and let's chat! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18712376058101654, "perplexity": 823.2055483350773}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585911.17/warc/CC-MAIN-20211024050128-20211024080128-00271.warc.gz"} |
https://docs.gpytorch.ai/en/stable/examples/08_Advanced_Usage/TorchScript_Exact_Models.html | # Converting Exact GP Models to TorchScript¶
In this notebook, we’ll demonstrate converting an Exact GP model to TorchScript. In general, this is the same as for standard PyTorch models where we’ll use torch.jit.trace, but there are two pecularities to keep in mind for GPyTorch:
1. The first time you make predictions with a GPyTorch model (exact or approximate), we cache certain computations. These computations can’t be traced, but the results of them can be. Therefore, we’ll need to pass data through the untraced model once, and then trace the model.
2. For exact GPs, we can’t trace models unless gpytorch.settings.fast_pred_var is used. This is a technical issue that may not be possible to overcome due to limitations on what can be traced in PyTorch; however, if you really need to trace a GP but can’t use the above setting, open an issue so we have visibility on there being demand for this.
3. You can’t trace models that return Distribution objects. Therefore, we’ll write a simple wrapper than unpacks the MultivariateNormal that our GPs return in to just a mean and variance tensor.
## Define and train an exact GP¶
In the next cell, we define some data, define a GP model and train it. Nothing new here – pretty much just move on to the next cell after this one.
[1]:
import math
import torch
import gpytorch
from matplotlib import pyplot as plt
%matplotlib inline
# Training data is 100 points in [0,1] inclusive regularly spaced
train_x = torch.linspace(0, 1, 100)
# True function is sin(2*pi*x) with Gaussian noise
train_y = torch.sin(train_x * (2 * math.pi)) + torch.randn(train_x.size()) * 0.2
# We will use the simplest form of GP model, exact inference
class ExactGPModel(gpytorch.models.ExactGP):
def __init__(self, train_x, train_y, likelihood):
super(ExactGPModel, self).__init__(train_x, train_y, likelihood)
self.mean_module = gpytorch.means.ConstantMean()
self.covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernel())
def forward(self, x):
mean_x = self.mean_module(x)
covar_x = self.covar_module(x)
return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)
# initialize likelihood and model
likelihood = gpytorch.likelihoods.GaussianLikelihood()
model = ExactGPModel(train_x, train_y, likelihood)
# this is for running the notebook in our testing framework
import os
smoke_test = ('CI' in os.environ)
training_iter = 2 if smoke_test else 50
# Find optimal model hyperparameters
model.train()
likelihood.train()
optimizer = torch.optim.Adam(model.parameters(), lr=0.1) # Includes GaussianLikelihood parameters
# "Loss" for GPs - the marginal log likelihood
mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)
for i in range(training_iter):
# Zero gradients from previous iteration
# Output from model
output = model(train_x)
# Calc loss and backprop gradients
loss = -mll(output, train_y)
loss.backward()
optimizer.step()
## Trace the Model¶
In the next cell, we trace our GP model. To overcome the fact that we can’t trace Modules that return Distributions, we write a wrapper Module that unpacks the GP output in to a mean and variance.
Additionally, we’ll need to run with the gpytorch.settings.trace_mode setting enabled, because PyTorch can’t trace custom autograd Functions. Note that this results in some inefficiencies.
Then, before calling torch.jit.trace we first call the model on test_x. This step is required, as it does some precomputation using torch functionality that cannot be traced.
[8]:
class MeanVarModelWrapper(torch.nn.Module):
def __init__(self, gp):
super().__init__()
self.gp = gp
def forward(self, x):
output_dist = self.gp(x)
return output_dist.mean, output_dist.variance
model.eval()
test_x = torch.linspace(0, 1, 51)
pred = model(test_x) # Do precomputation
traced_model = torch.jit.trace(MeanVarModelWrapper(model), test_x)
## Compare Predictions from TorchScript model and Torch model¶
[6]:
with torch.no_grad():
traced_mean, traced_var = traced_model(test_x)
print(torch.norm(traced_mean - pred.mean))
print(torch.norm(traced_var - pred.variance))
tensor(0.)
tensor(0.)
[7]:
traced_model.save('traced_exact_gp.pt')
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https://people.maths.bris.ac.uk/~matyd/GroupNames/320/Dic5.Q16.html | Copied to
clipboard
## G = Dic5.Q16order 320 = 26·5
### 2nd non-split extension by Dic5 of Q16 acting via Q16/C4=C22
Series: Derived Chief Lower central Upper central
Derived series C1 — C2×C20 — Dic5.Q16
Chief series C1 — C5 — C10 — C2×C10 — C2×Dic5 — C4×Dic5 — Dic5⋊C8 — Dic5.Q16
Lower central C5 — C2×C10 — C2×C20 — Dic5.Q16
Upper central C1 — C22 — C2×C4 — C2×Q8
Generators and relations for Dic5.Q16
G = < a,b,c,d | a10=c8=1, b2=a5, d2=a5c4, bab-1=a-1, cac-1=a3, ad=da, cbc-1=dbd-1=a5b, dcd-1=a5bc-1 >
Subgroups: 266 in 64 conjugacy classes, 26 normal (14 characteristic)
C1, C2, C2, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C10, C42, C4⋊C4, C2×C8, C2×Q8, C2×Q8, Dic5, Dic5, C20, C2×C10, C4⋊C8, C4⋊Q8, C5⋊C8, Dic10, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C5×Q8, C4.6Q16, C4×Dic5, C10.D4, C2×C5⋊C8, C2×Dic10, Q8×C10, Dic5⋊C8, Dic5⋊Q8, Dic5.Q16
Quotients: C1, C2, C4, C22, C2×C4, D4, C22⋊C4, SD16, Q16, F5, C4.D4, Q8⋊C4, C2×F5, C4.6Q16, C22⋊F5, Q8⋊F5, C23.F5, Dic5.Q16
Character table of Dic5.Q16
class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 5 8A 8B 8C 8D 8E 8F 8G 8H 10A 10B 10C 20A 20B 20C 20D 20E 20F size 1 1 1 1 4 8 10 10 10 10 40 4 20 20 20 20 20 20 20 20 4 4 4 8 8 8 8 8 8 ρ1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 trivial ρ2 1 1 1 1 1 -1 1 1 1 1 -1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 1 1 -1 -1 -1 linear of order 2 ρ3 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1 1 1 1 -1 -1 -1 1 1 1 -1 1 1 -1 -1 -1 linear of order 2 ρ4 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 linear of order 2 ρ5 1 1 1 1 1 -1 -1 -1 -1 -1 1 1 -i -i -i i i i i -i 1 1 1 -1 1 1 -1 -1 -1 linear of order 4 ρ6 1 1 1 1 1 1 -1 -1 -1 -1 -1 1 -i i i -i -i i i -i 1 1 1 1 1 1 1 1 1 linear of order 4 ρ7 1 1 1 1 1 1 -1 -1 -1 -1 -1 1 i -i -i i i -i -i i 1 1 1 1 1 1 1 1 1 linear of order 4 ρ8 1 1 1 1 1 -1 -1 -1 -1 -1 1 1 i i i -i -i -i -i i 1 1 1 -1 1 1 -1 -1 -1 linear of order 4 ρ9 2 2 2 2 -2 0 2 2 -2 -2 0 2 0 0 0 0 0 0 0 0 2 2 2 0 -2 -2 0 0 0 orthogonal lifted from D4 ρ10 2 2 2 2 -2 0 -2 -2 2 2 0 2 0 0 0 0 0 0 0 0 2 2 2 0 -2 -2 0 0 0 orthogonal lifted from D4 ρ11 2 2 -2 -2 0 0 2 -2 0 0 0 2 0 √2 -√2 -√2 √2 0 0 0 -2 -2 2 0 0 0 0 0 0 symplectic lifted from Q16, Schur index 2 ρ12 2 -2 2 -2 0 0 0 0 -2 2 0 2 -√2 0 0 0 0 -√2 √2 √2 2 -2 -2 0 0 0 0 0 0 symplectic lifted from Q16, Schur index 2 ρ13 2 -2 2 -2 0 0 0 0 -2 2 0 2 √2 0 0 0 0 √2 -√2 -√2 2 -2 -2 0 0 0 0 0 0 symplectic lifted from Q16, Schur index 2 ρ14 2 2 -2 -2 0 0 2 -2 0 0 0 2 0 -√2 √2 √2 -√2 0 0 0 -2 -2 2 0 0 0 0 0 0 symplectic lifted from Q16, Schur index 2 ρ15 2 2 -2 -2 0 0 -2 2 0 0 0 2 0 -√-2 √-2 -√-2 √-2 0 0 0 -2 -2 2 0 0 0 0 0 0 complex lifted from SD16 ρ16 2 -2 2 -2 0 0 0 0 2 -2 0 2 -√-2 0 0 0 0 √-2 -√-2 √-2 2 -2 -2 0 0 0 0 0 0 complex lifted from SD16 ρ17 2 2 -2 -2 0 0 -2 2 0 0 0 2 0 √-2 -√-2 √-2 -√-2 0 0 0 -2 -2 2 0 0 0 0 0 0 complex lifted from SD16 ρ18 2 -2 2 -2 0 0 0 0 2 -2 0 2 √-2 0 0 0 0 -√-2 √-2 -√-2 2 -2 -2 0 0 0 0 0 0 complex lifted from SD16 ρ19 4 4 4 4 4 4 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 orthogonal lifted from F5 ρ20 4 4 4 4 4 -4 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 -1 -1 1 -1 -1 1 1 1 orthogonal lifted from C2×F5 ρ21 4 -4 -4 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 -4 4 -4 0 0 0 0 0 0 orthogonal lifted from C4.D4 ρ22 4 4 4 4 -4 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 -1 -1 √5 1 1 √5 -√5 -√5 orthogonal lifted from C22⋊F5 ρ23 4 4 4 4 -4 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 -1 -1 -√5 1 1 -√5 √5 √5 orthogonal lifted from C22⋊F5 ρ24 4 -4 -4 4 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 1 2ζ52+2ζ5+1 -√5 √5 2ζ54+2ζ53+1 2ζ53+2ζ5+1 2ζ54+2ζ52+1 complex lifted from C23.F5 ρ25 4 -4 -4 4 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 1 2ζ53+2ζ5+1 √5 -√5 2ζ54+2ζ52+1 2ζ54+2ζ53+1 2ζ52+2ζ5+1 complex lifted from C23.F5 ρ26 4 -4 -4 4 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 1 2ζ54+2ζ52+1 √5 -√5 2ζ53+2ζ5+1 2ζ52+2ζ5+1 2ζ54+2ζ53+1 complex lifted from C23.F5 ρ27 4 -4 -4 4 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 1 2ζ54+2ζ53+1 -√5 √5 2ζ52+2ζ5+1 2ζ54+2ζ52+1 2ζ53+2ζ5+1 complex lifted from C23.F5 ρ28 8 8 -8 -8 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 symplectic lifted from Q8⋊F5, Schur index 2 ρ29 8 -8 8 -8 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 -2 2 2 0 0 0 0 0 0 symplectic lifted from Q8⋊F5, Schur index 2
Smallest permutation representation of Dic5.Q16
Regular action on 320 points
Generators in S320
(1 2 3 4 5 6 7 8 9 10)(11 12 13 14 15 16 17 18 19 20)(21 22 23 24 25 26 27 28 29 30)(31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50)(51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70)(71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90)(91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110)(111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130)(131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150)(151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170)(171 172 173 174 175 176 177 178 179 180)(181 182 183 184 185 186 187 188 189 190)(191 192 193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208 209 210)(211 212 213 214 215 216 217 218 219 220)(221 222 223 224 225 226 227 228 229 230)(231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250)(251 252 253 254 255 256 257 258 259 260)(261 262 263 264 265 266 267 268 269 270)(271 272 273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288 289 290)(291 292 293 294 295 296 297 298 299 300)(301 302 303 304 305 306 307 308 309 310)(311 312 313 314 315 316 317 318 319 320)
(1 71 6 76)(2 80 7 75)(3 79 8 74)(4 78 9 73)(5 77 10 72)(11 254 16 259)(12 253 17 258)(13 252 18 257)(14 251 19 256)(15 260 20 255)(21 82 26 87)(22 81 27 86)(23 90 28 85)(24 89 29 84)(25 88 30 83)(31 54 36 59)(32 53 37 58)(33 52 38 57)(34 51 39 56)(35 60 40 55)(41 66 46 61)(42 65 47 70)(43 64 48 69)(44 63 49 68)(45 62 50 67)(91 167 96 162)(92 166 97 161)(93 165 98 170)(94 164 99 169)(95 163 100 168)(101 158 106 153)(102 157 107 152)(103 156 108 151)(104 155 109 160)(105 154 110 159)(111 139 116 134)(112 138 117 133)(113 137 118 132)(114 136 119 131)(115 135 120 140)(121 141 126 146)(122 150 127 145)(123 149 128 144)(124 148 129 143)(125 147 130 142)(171 247 176 242)(172 246 177 241)(173 245 178 250)(174 244 179 249)(175 243 180 248)(181 237 186 232)(182 236 187 231)(183 235 188 240)(184 234 189 239)(185 233 190 238)(191 219 196 214)(192 218 197 213)(193 217 198 212)(194 216 199 211)(195 215 200 220)(201 223 206 228)(202 222 207 227)(203 221 208 226)(204 230 209 225)(205 229 210 224)(261 312 266 317)(262 311 267 316)(263 320 268 315)(264 319 269 314)(265 318 270 313)(271 294 276 299)(272 293 277 298)(273 292 278 297)(274 291 279 296)(275 300 280 295)(281 308 286 303)(282 307 287 302)(283 306 288 301)(284 305 289 310)(285 304 290 309)
(1 213 51 177 28 225 62 190)(2 220 60 180 29 222 61 183)(3 217 59 173 30 229 70 186)(4 214 58 176 21 226 69 189)(5 211 57 179 22 223 68 182)(6 218 56 172 23 230 67 185)(7 215 55 175 24 227 66 188)(8 212 54 178 25 224 65 181)(9 219 53 171 26 221 64 184)(10 216 52 174 27 228 63 187)(11 170 279 113 311 157 281 124)(12 167 278 116 312 154 290 127)(13 164 277 119 313 151 289 130)(14 161 276 112 314 158 288 123)(15 168 275 115 315 155 287 126)(16 165 274 118 316 152 286 129)(17 162 273 111 317 159 285 122)(18 169 272 114 318 156 284 125)(19 166 271 117 319 153 283 128)(20 163 280 120 320 160 282 121)(31 250 83 205 42 237 79 193)(32 247 82 208 43 234 78 196)(33 244 81 201 44 231 77 199)(34 241 90 204 45 238 76 192)(35 248 89 207 46 235 75 195)(36 245 88 210 47 232 74 198)(37 242 87 203 48 239 73 191)(38 249 86 206 49 236 72 194)(39 246 85 209 50 233 71 197)(40 243 84 202 41 240 80 200)(91 297 139 266 105 309 150 253)(92 294 138 269 106 306 149 256)(93 291 137 262 107 303 148 259)(94 298 136 265 108 310 147 252)(95 295 135 268 109 307 146 255)(96 292 134 261 110 304 145 258)(97 299 133 264 101 301 144 251)(98 296 132 267 102 308 143 254)(99 293 131 270 103 305 142 257)(100 300 140 263 104 302 141 260)
(1 94 23 103)(2 95 24 104)(3 96 25 105)(4 97 26 106)(5 98 27 107)(6 99 28 108)(7 100 29 109)(8 91 30 110)(9 92 21 101)(10 93 22 102)(11 223 316 216)(12 224 317 217)(13 225 318 218)(14 226 319 219)(15 227 320 220)(16 228 311 211)(17 229 312 212)(18 230 313 213)(19 221 314 214)(20 222 315 215)(31 127 47 111)(32 128 48 112)(33 129 49 113)(34 130 50 114)(35 121 41 115)(36 122 42 116)(37 123 43 117)(38 124 44 118)(39 125 45 119)(40 126 46 120)(51 147 67 131)(52 148 68 132)(53 149 69 133)(54 150 70 134)(55 141 61 135)(56 142 62 136)(57 143 63 137)(58 144 64 138)(59 145 65 139)(60 146 66 140)(71 169 90 151)(72 170 81 152)(73 161 82 153)(74 162 83 154)(75 163 84 155)(76 164 85 156)(77 165 86 157)(78 166 87 158)(79 167 88 159)(80 168 89 160)(171 288 189 271)(172 289 190 272)(173 290 181 273)(174 281 182 274)(175 282 183 275)(176 283 184 276)(177 284 185 277)(178 285 186 278)(179 286 187 279)(180 287 188 280)(191 251 208 269)(192 252 209 270)(193 253 210 261)(194 254 201 262)(195 255 202 263)(196 256 203 264)(197 257 204 265)(198 258 205 266)(199 259 206 267)(200 260 207 268)(231 291 249 308)(232 292 250 309)(233 293 241 310)(234 294 242 301)(235 295 243 302)(236 296 244 303)(237 297 245 304)(238 298 246 305)(239 299 247 306)(240 300 248 307)
G:=sub<Sym(320)| (1,2,3,4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30)(31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70)(71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90)(91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110)(111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130)(131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150)(151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170)(171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190)(191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220)(221,222,223,224,225,226,227,228,229,230)(231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250)(251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270)(271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290)(291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310)(311,312,313,314,315,316,317,318,319,320), (1,71,6,76)(2,80,7,75)(3,79,8,74)(4,78,9,73)(5,77,10,72)(11,254,16,259)(12,253,17,258)(13,252,18,257)(14,251,19,256)(15,260,20,255)(21,82,26,87)(22,81,27,86)(23,90,28,85)(24,89,29,84)(25,88,30,83)(31,54,36,59)(32,53,37,58)(33,52,38,57)(34,51,39,56)(35,60,40,55)(41,66,46,61)(42,65,47,70)(43,64,48,69)(44,63,49,68)(45,62,50,67)(91,167,96,162)(92,166,97,161)(93,165,98,170)(94,164,99,169)(95,163,100,168)(101,158,106,153)(102,157,107,152)(103,156,108,151)(104,155,109,160)(105,154,110,159)(111,139,116,134)(112,138,117,133)(113,137,118,132)(114,136,119,131)(115,135,120,140)(121,141,126,146)(122,150,127,145)(123,149,128,144)(124,148,129,143)(125,147,130,142)(171,247,176,242)(172,246,177,241)(173,245,178,250)(174,244,179,249)(175,243,180,248)(181,237,186,232)(182,236,187,231)(183,235,188,240)(184,234,189,239)(185,233,190,238)(191,219,196,214)(192,218,197,213)(193,217,198,212)(194,216,199,211)(195,215,200,220)(201,223,206,228)(202,222,207,227)(203,221,208,226)(204,230,209,225)(205,229,210,224)(261,312,266,317)(262,311,267,316)(263,320,268,315)(264,319,269,314)(265,318,270,313)(271,294,276,299)(272,293,277,298)(273,292,278,297)(274,291,279,296)(275,300,280,295)(281,308,286,303)(282,307,287,302)(283,306,288,301)(284,305,289,310)(285,304,290,309), (1,213,51,177,28,225,62,190)(2,220,60,180,29,222,61,183)(3,217,59,173,30,229,70,186)(4,214,58,176,21,226,69,189)(5,211,57,179,22,223,68,182)(6,218,56,172,23,230,67,185)(7,215,55,175,24,227,66,188)(8,212,54,178,25,224,65,181)(9,219,53,171,26,221,64,184)(10,216,52,174,27,228,63,187)(11,170,279,113,311,157,281,124)(12,167,278,116,312,154,290,127)(13,164,277,119,313,151,289,130)(14,161,276,112,314,158,288,123)(15,168,275,115,315,155,287,126)(16,165,274,118,316,152,286,129)(17,162,273,111,317,159,285,122)(18,169,272,114,318,156,284,125)(19,166,271,117,319,153,283,128)(20,163,280,120,320,160,282,121)(31,250,83,205,42,237,79,193)(32,247,82,208,43,234,78,196)(33,244,81,201,44,231,77,199)(34,241,90,204,45,238,76,192)(35,248,89,207,46,235,75,195)(36,245,88,210,47,232,74,198)(37,242,87,203,48,239,73,191)(38,249,86,206,49,236,72,194)(39,246,85,209,50,233,71,197)(40,243,84,202,41,240,80,200)(91,297,139,266,105,309,150,253)(92,294,138,269,106,306,149,256)(93,291,137,262,107,303,148,259)(94,298,136,265,108,310,147,252)(95,295,135,268,109,307,146,255)(96,292,134,261,110,304,145,258)(97,299,133,264,101,301,144,251)(98,296,132,267,102,308,143,254)(99,293,131,270,103,305,142,257)(100,300,140,263,104,302,141,260), (1,94,23,103)(2,95,24,104)(3,96,25,105)(4,97,26,106)(5,98,27,107)(6,99,28,108)(7,100,29,109)(8,91,30,110)(9,92,21,101)(10,93,22,102)(11,223,316,216)(12,224,317,217)(13,225,318,218)(14,226,319,219)(15,227,320,220)(16,228,311,211)(17,229,312,212)(18,230,313,213)(19,221,314,214)(20,222,315,215)(31,127,47,111)(32,128,48,112)(33,129,49,113)(34,130,50,114)(35,121,41,115)(36,122,42,116)(37,123,43,117)(38,124,44,118)(39,125,45,119)(40,126,46,120)(51,147,67,131)(52,148,68,132)(53,149,69,133)(54,150,70,134)(55,141,61,135)(56,142,62,136)(57,143,63,137)(58,144,64,138)(59,145,65,139)(60,146,66,140)(71,169,90,151)(72,170,81,152)(73,161,82,153)(74,162,83,154)(75,163,84,155)(76,164,85,156)(77,165,86,157)(78,166,87,158)(79,167,88,159)(80,168,89,160)(171,288,189,271)(172,289,190,272)(173,290,181,273)(174,281,182,274)(175,282,183,275)(176,283,184,276)(177,284,185,277)(178,285,186,278)(179,286,187,279)(180,287,188,280)(191,251,208,269)(192,252,209,270)(193,253,210,261)(194,254,201,262)(195,255,202,263)(196,256,203,264)(197,257,204,265)(198,258,205,266)(199,259,206,267)(200,260,207,268)(231,291,249,308)(232,292,250,309)(233,293,241,310)(234,294,242,301)(235,295,243,302)(236,296,244,303)(237,297,245,304)(238,298,246,305)(239,299,247,306)(240,300,248,307)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30)(31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70)(71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90)(91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110)(111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130)(131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150)(151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170)(171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190)(191,192,193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220)(221,222,223,224,225,226,227,228,229,230)(231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250)(251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270)(271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290)(291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310)(311,312,313,314,315,316,317,318,319,320), (1,71,6,76)(2,80,7,75)(3,79,8,74)(4,78,9,73)(5,77,10,72)(11,254,16,259)(12,253,17,258)(13,252,18,257)(14,251,19,256)(15,260,20,255)(21,82,26,87)(22,81,27,86)(23,90,28,85)(24,89,29,84)(25,88,30,83)(31,54,36,59)(32,53,37,58)(33,52,38,57)(34,51,39,56)(35,60,40,55)(41,66,46,61)(42,65,47,70)(43,64,48,69)(44,63,49,68)(45,62,50,67)(91,167,96,162)(92,166,97,161)(93,165,98,170)(94,164,99,169)(95,163,100,168)(101,158,106,153)(102,157,107,152)(103,156,108,151)(104,155,109,160)(105,154,110,159)(111,139,116,134)(112,138,117,133)(113,137,118,132)(114,136,119,131)(115,135,120,140)(121,141,126,146)(122,150,127,145)(123,149,128,144)(124,148,129,143)(125,147,130,142)(171,247,176,242)(172,246,177,241)(173,245,178,250)(174,244,179,249)(175,243,180,248)(181,237,186,232)(182,236,187,231)(183,235,188,240)(184,234,189,239)(185,233,190,238)(191,219,196,214)(192,218,197,213)(193,217,198,212)(194,216,199,211)(195,215,200,220)(201,223,206,228)(202,222,207,227)(203,221,208,226)(204,230,209,225)(205,229,210,224)(261,312,266,317)(262,311,267,316)(263,320,268,315)(264,319,269,314)(265,318,270,313)(271,294,276,299)(272,293,277,298)(273,292,278,297)(274,291,279,296)(275,300,280,295)(281,308,286,303)(282,307,287,302)(283,306,288,301)(284,305,289,310)(285,304,290,309), (1,213,51,177,28,225,62,190)(2,220,60,180,29,222,61,183)(3,217,59,173,30,229,70,186)(4,214,58,176,21,226,69,189)(5,211,57,179,22,223,68,182)(6,218,56,172,23,230,67,185)(7,215,55,175,24,227,66,188)(8,212,54,178,25,224,65,181)(9,219,53,171,26,221,64,184)(10,216,52,174,27,228,63,187)(11,170,279,113,311,157,281,124)(12,167,278,116,312,154,290,127)(13,164,277,119,313,151,289,130)(14,161,276,112,314,158,288,123)(15,168,275,115,315,155,287,126)(16,165,274,118,316,152,286,129)(17,162,273,111,317,159,285,122)(18,169,272,114,318,156,284,125)(19,166,271,117,319,153,283,128)(20,163,280,120,320,160,282,121)(31,250,83,205,42,237,79,193)(32,247,82,208,43,234,78,196)(33,244,81,201,44,231,77,199)(34,241,90,204,45,238,76,192)(35,248,89,207,46,235,75,195)(36,245,88,210,47,232,74,198)(37,242,87,203,48,239,73,191)(38,249,86,206,49,236,72,194)(39,246,85,209,50,233,71,197)(40,243,84,202,41,240,80,200)(91,297,139,266,105,309,150,253)(92,294,138,269,106,306,149,256)(93,291,137,262,107,303,148,259)(94,298,136,265,108,310,147,252)(95,295,135,268,109,307,146,255)(96,292,134,261,110,304,145,258)(97,299,133,264,101,301,144,251)(98,296,132,267,102,308,143,254)(99,293,131,270,103,305,142,257)(100,300,140,263,104,302,141,260), (1,94,23,103)(2,95,24,104)(3,96,25,105)(4,97,26,106)(5,98,27,107)(6,99,28,108)(7,100,29,109)(8,91,30,110)(9,92,21,101)(10,93,22,102)(11,223,316,216)(12,224,317,217)(13,225,318,218)(14,226,319,219)(15,227,320,220)(16,228,311,211)(17,229,312,212)(18,230,313,213)(19,221,314,214)(20,222,315,215)(31,127,47,111)(32,128,48,112)(33,129,49,113)(34,130,50,114)(35,121,41,115)(36,122,42,116)(37,123,43,117)(38,124,44,118)(39,125,45,119)(40,126,46,120)(51,147,67,131)(52,148,68,132)(53,149,69,133)(54,150,70,134)(55,141,61,135)(56,142,62,136)(57,143,63,137)(58,144,64,138)(59,145,65,139)(60,146,66,140)(71,169,90,151)(72,170,81,152)(73,161,82,153)(74,162,83,154)(75,163,84,155)(76,164,85,156)(77,165,86,157)(78,166,87,158)(79,167,88,159)(80,168,89,160)(171,288,189,271)(172,289,190,272)(173,290,181,273)(174,281,182,274)(175,282,183,275)(176,283,184,276)(177,284,185,277)(178,285,186,278)(179,286,187,279)(180,287,188,280)(191,251,208,269)(192,252,209,270)(193,253,210,261)(194,254,201,262)(195,255,202,263)(196,256,203,264)(197,257,204,265)(198,258,205,266)(199,259,206,267)(200,260,207,268)(231,291,249,308)(232,292,250,309)(233,293,241,310)(234,294,242,301)(235,295,243,302)(236,296,244,303)(237,297,245,304)(238,298,246,305)(239,299,247,306)(240,300,248,307) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10),(11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30),(31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50),(51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70),(71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90),(91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110),(111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130),(131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150),(151,152,153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168,169,170),(171,172,173,174,175,176,177,178,179,180),(181,182,183,184,185,186,187,188,189,190),(191,192,193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208,209,210),(211,212,213,214,215,216,217,218,219,220),(221,222,223,224,225,226,227,228,229,230),(231,232,233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248,249,250),(251,252,253,254,255,256,257,258,259,260),(261,262,263,264,265,266,267,268,269,270),(271,272,273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288,289,290),(291,292,293,294,295,296,297,298,299,300),(301,302,303,304,305,306,307,308,309,310),(311,312,313,314,315,316,317,318,319,320)], [(1,71,6,76),(2,80,7,75),(3,79,8,74),(4,78,9,73),(5,77,10,72),(11,254,16,259),(12,253,17,258),(13,252,18,257),(14,251,19,256),(15,260,20,255),(21,82,26,87),(22,81,27,86),(23,90,28,85),(24,89,29,84),(25,88,30,83),(31,54,36,59),(32,53,37,58),(33,52,38,57),(34,51,39,56),(35,60,40,55),(41,66,46,61),(42,65,47,70),(43,64,48,69),(44,63,49,68),(45,62,50,67),(91,167,96,162),(92,166,97,161),(93,165,98,170),(94,164,99,169),(95,163,100,168),(101,158,106,153),(102,157,107,152),(103,156,108,151),(104,155,109,160),(105,154,110,159),(111,139,116,134),(112,138,117,133),(113,137,118,132),(114,136,119,131),(115,135,120,140),(121,141,126,146),(122,150,127,145),(123,149,128,144),(124,148,129,143),(125,147,130,142),(171,247,176,242),(172,246,177,241),(173,245,178,250),(174,244,179,249),(175,243,180,248),(181,237,186,232),(182,236,187,231),(183,235,188,240),(184,234,189,239),(185,233,190,238),(191,219,196,214),(192,218,197,213),(193,217,198,212),(194,216,199,211),(195,215,200,220),(201,223,206,228),(202,222,207,227),(203,221,208,226),(204,230,209,225),(205,229,210,224),(261,312,266,317),(262,311,267,316),(263,320,268,315),(264,319,269,314),(265,318,270,313),(271,294,276,299),(272,293,277,298),(273,292,278,297),(274,291,279,296),(275,300,280,295),(281,308,286,303),(282,307,287,302),(283,306,288,301),(284,305,289,310),(285,304,290,309)], [(1,213,51,177,28,225,62,190),(2,220,60,180,29,222,61,183),(3,217,59,173,30,229,70,186),(4,214,58,176,21,226,69,189),(5,211,57,179,22,223,68,182),(6,218,56,172,23,230,67,185),(7,215,55,175,24,227,66,188),(8,212,54,178,25,224,65,181),(9,219,53,171,26,221,64,184),(10,216,52,174,27,228,63,187),(11,170,279,113,311,157,281,124),(12,167,278,116,312,154,290,127),(13,164,277,119,313,151,289,130),(14,161,276,112,314,158,288,123),(15,168,275,115,315,155,287,126),(16,165,274,118,316,152,286,129),(17,162,273,111,317,159,285,122),(18,169,272,114,318,156,284,125),(19,166,271,117,319,153,283,128),(20,163,280,120,320,160,282,121),(31,250,83,205,42,237,79,193),(32,247,82,208,43,234,78,196),(33,244,81,201,44,231,77,199),(34,241,90,204,45,238,76,192),(35,248,89,207,46,235,75,195),(36,245,88,210,47,232,74,198),(37,242,87,203,48,239,73,191),(38,249,86,206,49,236,72,194),(39,246,85,209,50,233,71,197),(40,243,84,202,41,240,80,200),(91,297,139,266,105,309,150,253),(92,294,138,269,106,306,149,256),(93,291,137,262,107,303,148,259),(94,298,136,265,108,310,147,252),(95,295,135,268,109,307,146,255),(96,292,134,261,110,304,145,258),(97,299,133,264,101,301,144,251),(98,296,132,267,102,308,143,254),(99,293,131,270,103,305,142,257),(100,300,140,263,104,302,141,260)], [(1,94,23,103),(2,95,24,104),(3,96,25,105),(4,97,26,106),(5,98,27,107),(6,99,28,108),(7,100,29,109),(8,91,30,110),(9,92,21,101),(10,93,22,102),(11,223,316,216),(12,224,317,217),(13,225,318,218),(14,226,319,219),(15,227,320,220),(16,228,311,211),(17,229,312,212),(18,230,313,213),(19,221,314,214),(20,222,315,215),(31,127,47,111),(32,128,48,112),(33,129,49,113),(34,130,50,114),(35,121,41,115),(36,122,42,116),(37,123,43,117),(38,124,44,118),(39,125,45,119),(40,126,46,120),(51,147,67,131),(52,148,68,132),(53,149,69,133),(54,150,70,134),(55,141,61,135),(56,142,62,136),(57,143,63,137),(58,144,64,138),(59,145,65,139),(60,146,66,140),(71,169,90,151),(72,170,81,152),(73,161,82,153),(74,162,83,154),(75,163,84,155),(76,164,85,156),(77,165,86,157),(78,166,87,158),(79,167,88,159),(80,168,89,160),(171,288,189,271),(172,289,190,272),(173,290,181,273),(174,281,182,274),(175,282,183,275),(176,283,184,276),(177,284,185,277),(178,285,186,278),(179,286,187,279),(180,287,188,280),(191,251,208,269),(192,252,209,270),(193,253,210,261),(194,254,201,262),(195,255,202,263),(196,256,203,264),(197,257,204,265),(198,258,205,266),(199,259,206,267),(200,260,207,268),(231,291,249,308),(232,292,250,309),(233,293,241,310),(234,294,242,301),(235,295,243,302),(236,296,244,303),(237,297,245,304),(238,298,246,305),(239,299,247,306),(240,300,248,307)]])
Matrix representation of Dic5.Q16 in GL6(𝔽41)
40 0 0 0 0 0 0 40 0 0 0 0 0 0 1 40 0 0 0 0 1 0 40 0 0 0 17 18 10 0 0 0 8 13 22 31
,
40 36 0 0 0 0 25 1 0 0 0 0 0 0 1 14 40 2 0 0 2 6 20 35 0 0 18 3 21 26 0 0 35 14 35 13
,
1 0 0 0 0 0 16 40 0 0 0 0 0 0 26 11 18 2 0 0 30 9 15 34 0 0 40 13 7 13 0 0 27 10 40 40
,
30 34 0 0 0 0 35 11 0 0 0 0 0 0 19 5 28 0 0 0 11 12 40 0 0 0 13 34 9 0 0 0 2 7 32 1
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,1,17,8,0,0,40,0,18,13,0,0,0,40,10,22,0,0,0,0,0,31],[40,25,0,0,0,0,36,1,0,0,0,0,0,0,1,2,18,35,0,0,14,6,3,14,0,0,40,20,21,35,0,0,2,35,26,13],[1,16,0,0,0,0,0,40,0,0,0,0,0,0,26,30,40,27,0,0,11,9,13,10,0,0,18,15,7,40,0,0,2,34,13,40],[30,35,0,0,0,0,34,11,0,0,0,0,0,0,19,11,13,2,0,0,5,12,34,7,0,0,28,40,9,32,0,0,0,0,0,1] >;
Dic5.Q16 in GAP, Magma, Sage, TeX
{\rm Dic}_5.Q_{16}
% in TeX
G:=Group("Dic5.Q16");
// GroupNames label
G:=SmallGroup(320,269);
// by ID
G=gap.SmallGroup(320,269);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,141,232,219,100,1571,570,136,6278,3156]);
// Polycyclic
G:=Group<a,b,c,d|a^10=c^8=1,b^2=a^5,d^2=a^5*c^4,b*a*b^-1=a^-1,c*a*c^-1=a^3,a*d=d*a,c*b*c^-1=d*b*d^-1=a^5*b,d*c*d^-1=a^5*b*c^-1>;
// generators/relations
Export
×
𝔽 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8985499739646912, "perplexity": 498.0187421039998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989012.26/warc/CC-MAIN-20210509183309-20210509213309-00169.warc.gz"} |
https://www.physicsforums.com/threads/homomorphism-final.212741/ | # Homomorphism final
1. Feb 2, 2008
### mathusers
heres my final one. thnx.
Show that $A_4$, the group of even permutations on 4 letters, is a semidirect product:
$A_4 \cong (C_2 \times C_2) \rtimes_{\varphi} C_3$
and describe explicitly the associated homomorphism:
$\varphi : C_3 \rightarrow Aut(C_2 \times C_2)$
thnx for help on the previous posts.
any help here and ill attempt the rest myself
kind regards
x
2. Feb 3, 2008
### morphism
Have you tried thinking about what A_4 looks like? It's not a very complicated group.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook
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http://crypto.stackexchange.com/tags/aes/new | # Tag Info
1
TLDR: Don't invent your own protocol, use an existing one. Reusing an initialization vector with the same key is always a problem, even if the attacker is read-only. For CBC, you can see whether a beginning part of one message is the same as the beginning part of a different message (and you get to know the length of the common prefix, on block-level). ...
1
Wrapping my (now deleted) comments into an answer… OMAC, as described in the OMAC spec and its addendum, is what Rogaway et al provide security proofs for in their EAX paper. If you take a quick look at RFC 4493, you’ll notice that it states: The National Institute of Standards and Technology (NIST) has recently specified the Cipher-based Message ...
4
Assuming you really had broken AES or another frequently used algorithm that is thought to be secure, the first step would be to prove it. Write the code for the attack. Verify that it works on randomly generated data of the kind it requires. If it can break some challenge (e.g. these), do it. Post the results to the challenger or show the results ...
2
Assuming for the moment that your claim is correct, I would suggest caution in revealing the details of your findings. After having your results validated by one or two people with the skills to do so (and whom you trust to keep things confidential), then some sort of general announcement (without specifics) would be best, to give people time (say three ...
10
In complete honesty: if you have to ask this question, it's overwhelmingly unlikely that you have actually succeeded in breaking the security of AES. At best, you may have discovered a well-known attack against misuse of particular block cipher modes; for instance, plaintext recovery with a chosen-ciphertext attack against ECB, or blind manipulation of the ...
-1
Make sure you put your name prominently in the source, and publish the source anywhere. If you're right, everyone else will make you famous. If wrong, someone will point out your error. Send it to Bruce Schneier if you want to start at the top.
2
It seems that you are trying to implement your own KBKDF (Key Based Key Derivation Function) using HMAC. Maybe it is better to use a pre-defined one. It would be more sensible maybe to use an HSM that is FIPS certified for NIST SP 800-108. These use one of the KBKDFs defined in NIST SP 800-108. You can still use the idea of the random by putting it in the ...
8
It looks like, given your adversary model, things should be secure. HMAC as a randomness extractor has been shown to be good, especially when we can assume the hash function is collision resistant. That paper also has some results which tell how you could guard against the collision resistance being broken (basically use a hash function with larger output ...
1
If you use the hash as a known key, then you do not need any additional authentication to ensure plaintext integrity. An attacker cannot find another plaintext with that hash value unless the hash is broken. However, there are two problems with that: Like MAC-then-encrypt the hash only ensures authenticity of the plaintext, not of the ciphertext. This ...
1
As additional detail, while the two keys need to be distinct and secret, you can derive the CBC-MAC key and the CBC encryption key from the same master key. Generate a random master key, then use any key derivation algorithm with two different salts to derive the authentication and encryption keys. For example, $K(m, \text{'auth'})$ and $K(m, \text{'enc'})$ ...
4
From the sound of your questions, it almost appears that you have some confusion between the CBC-MAC key and the CBC-MAC tag. The CBC-MAC algorithm takes the message (in this case, most likely the ciphertext) and a secret key; it outputs a tag (which can be public). The security property of CBC-MAC is that someone who does not know the key cannot generate ...
2
There is book Algebraic Aspects of the Advanced Encryption Standard thats gives a good algebraic description of the AES algorithm. Reading it you'll see that there was some freedom in choosing some parametres to fix a standard. Changing this choices, but keeping the algebric properties should give you an equivalent algorithm. This mainly means you can ...
4
You basically want a full disk encryption mode for a block cipher; XTS mode seems to be the current standard. In your case each "disk block" is actually a file offset. Note that using a stream cipher or counter mode is NOT secure if the data is ever modified in the file, as it would violate the cardinal sin of using the same key and initialization vector to ...
6
There is no uniform permutation; there is a permutation uniformly chosen from the set of all possible permutations over $Z_2^{128}$. It is evident that AES is not a uniformly chosen permutation, since its permutation is fixed for any key. One can consider a family $\{AES_K\}$ of AES permutations under all possible keys $K$. Even if the key is chosen ...
3
If you can read the intermediate states of the encryption algorithm you could recover, one by one all the round keys. Given a AES round, all the operation between the two AddRoundKey (at the beginning and the ond of the round) are invertible. Take for example round 1: you get the internal state before AddRoundKey (of round 2), you get back at the beginning ...
3
The catch how ever is that if a small part of the file is given along with the location of that bytes from the beginning of the file we should be able to decrypt just that piece. Normal CTR mode encryption allows one to decrypt any block of the file independent of the rest, so no need to invent your own mode. With AES the block size is always 128 bits, ...
1
There are good reasons to think an algorithm being in Suite B is evidence NSA thinks it's secure (they are used to protect classified materials). There are also reasons to think algorithms they recommend for others may not be (it's happened before). So I don't think you can objectively say much about an algorithm either way just on the basis of whether it's ...
4
It mainly depends on how the algorithm was selected. If it was selected by a public competition like for AES, then it is likely to be secure. If it was forced in by the NSA such as Dual-EC random number generator, then you may have some doubts. Other questions you may want to ask yourself are: Is this an "original" algorithm or was the problem that it ...
0
Parallelization is not a necessity but it can help to speed things up if you have a multicore processor. This is because of the parallel nature of CTR mode where the blocks are encrypted independently of each other. Another main advantage, besides being parallelizable, is that unlike CBC, CTR mode can perform certain calculations offline to prepare the key ...
3
Other advantages of CTR are: easier to decrypt from a certain offset within the ciphertext no randomness requirements for the nonce nonce can be calculated, e.g. be a simple counter nonce can be a message identifier $E = D$: encryption is the same as decryption, which means only encryption or decryption required from the block cipher less logic ...
3
There seems to be an attack on SSH when using CBC: Plaintext Recovery Attacks Against SSH. I have just scanned the paper and they state, that this will not be possible when CTR mode is used. I don't think that en-/decryption parallelization is need or even utilized in SSH. Update: Link to CERT concerning the topic: Vulnerability Note VU#958563 SSH CBC ...
3
You should never keep keystreams. You should keep a key, and store an IV or Nonce with the ciphertext. You first need to think about where to store the key, if you store it in the same location or with the same security as your ciphertext, your scheme is meaningless. Check this answer I just created on Stackoverflow, and learn about key management. This ...
1
If the question is "can we define a function that, given $s(a)$ and $s(b)$, gives us the value $s(a \oplus b)$, the answer is, yes, of course we can; the obvious implementation of such a function is: $F(x, y) = s( s^{-1}(x) \oplus s^{-1}(y))$ With this function, if $x=s(a)$ and $y=s(b)$, the $F(x,y) = s(a \oplus b)$ However, the real question you need to ...
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https://www.physicsforums.com/threads/help-lesson-3-physics.64662/ | # Help! lesson 3 physics!
1. Feb 23, 2005
### mark9159
greetings...i need some help please and someone to check if i did the problems correctly.
1.) How much kinetic energy will a 5kg ball have after rolling down a 1m high incline?
If Potential Energy=mgh, then P=(5kg)(9.81m/s^2)(1m) so P=49.05 J. If this is true, then Kinetic energy = 49.05 J = 1/2mv^2. 49.05=1/2(5)v^2. Then i divided 49.05 by 2.5 (49.05/2.5) which gave me v^2=19.62. I then took the square root of 19.62 which is approximately 4.43 J.
2.) Why are no collisions perfectly inelastic?
My Answer: Almost all collisions involve some rebounding.
3.) A lever is used to raise a 300N rock a distance of 0.6 meters. You must use a force of 75N to accomplish this task. What work is done?
If work can equal mass times gravity times height, then work equals 300N times 0.6 meters, which equals 180. I then did 180 divided by 75N (the amount of force needed), coming up with the solution: 2.45 J
thank you very much for checking my work!
mark
2. Feb 23, 2005
### scholar
1) After 1m, all potential energy will have been converted to kinetic energy. So your calculation should read:
Ep=Ek
mgh=Ek
Ek=5x9.81x1
Ek=49.05 J
You went the whole way and calculated the velocity, which is measured in m.s^-1. It looks as though you got confused between kinetic energy and velocity.
3) This is quite clearly incorrect. You certainly used more than 2.45 J of energy to lift a 30kg rock from the ground! Read up on levers and you should be able to get this one.
3. Feb 23, 2005
### Edgardo
EDIT! Not correct, read scholar's post. Your solution would be correct if
the question was: Calculate the velocity.
That doesn't seem correct. First of all I can see that's not correct because
of the units:
You divided 180Nm=180J by 75N which gives you 2.4m and NOT 2.45J
ALWAYS check the units, it gives you a first hint if your calculation is correct.
Last edited: Feb 23, 2005
4. Feb 23, 2005
### mark9159
so if Work= Force Times Distance, then Work= (75N)(0.6m) which equals 45 Joules...where exactly does the 300N rock come ino the equation?
the problem im facing is that 45 J is not one of the choices i have to choose from
oh and i really thank you guys for the tip/help..im going to look up more information about levers now.
5. Feb 23, 2005
### Edgardo
Mark,
I just send you a private message. I think it's just 300N times 0.6m.
The 75N is the force you need if you use a lever.
Sorry, my fault.
6. Feb 23, 2005
### mark9159
oh, ok. thank you edgardo.
One more question.
What power is required to accelerate a 500kg car from zero to 18 m/s in one minute?
First i found the kinetic energy
Ek=1/2mv^2
Ek=1/2(500kg)(18m/s)^2
Ek=250(324)=81000 J
Power= Joules per second
Power= 81000 J / 60
Power= 1350 W
It takes 1350 W to accelerate a 500kg car from zero to 18 m/s in one minute.
7. Feb 23, 2005
### Edgardo
Hello Mark, that seems to be correct.
Regards
Edgardo
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https://brilliant.org/problems/calculations-with-trig/ | # Calculations with Trig
Geometry Level 3
What is the value of $2(\sin^6\theta + \cos^6\theta) -3(\sin^4\theta+\cos^4\theta)=?$
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7708902955055237, "perplexity": 14006.771032754497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400192783.34/warc/CC-MAIN-20200919173334-20200919203334-00742.warc.gz"} |
https://cab.inta-csic.es/publicaciones/confirming-interstellar-c-60-using-the-hubble-space-telescope/ | # Confirming Interstellar C-60(+) Using the Hubble Space Telescope
Cordiner, M. A., Linnartz, H., Cox, N. L. J., Cami, J., Najarro, F., Proffitt, C. R., Lallement, R., Ehrenfreund, P., Foing, B. H., Gull, T. R. 2019. Confirming Interstellar C-60(+) Using the Hubble Space Telescope. Astrophysical Journal Letters 875, 2 DOI: 10.3847/2041-8213/ab14e5
Recent advances in laboratory spectroscopy lead to the claim of ionized Buckminsterfullerene (C-60(+)) as the carrier of two diffuse interstellar bands (DIBs) in the near-infrared. However, irrefutable identification of interstellar C-60(+) requires a match between the wavelengths and the expected strengths of all absorption features detectable in the laboratory and in space. Here we present Hubble Space Telescope (HST) spectra of the region covering the C-60(+) 9348, 9365, 9428, and 9577 angstrom absorption bands toward seven heavily reddened stars. We focus in particular on searching for the weaker laboratory C-60(+) bands, the very presence of which has been a matter for recent debate. Using the novel STIS-scanning technique to obtain ultra-high signal-to-noise spectra without contamination from telluric absorption that afflicted previous ground-based observations, we obtained reliable detections of the (weak) 9365, 9428 angstrom and (strong) 9577 angstrom C-60(+) bands. The band wavelengths and strength ratios are sufficiently similar to those determined in the latest laboratory experiments that we consider this the first robust identification of the 9428 angstrom band, and a conclusive confirmation of interstellar C-60(+).
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Sahai, R., Sanz-Forcada, J., Guerrero, M., Ortiz, R., Sánchez Contreras, | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8980491757392883, "perplexity": 14154.48634093701}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710789.95/warc/CC-MAIN-20221201021257-20221201051257-00032.warc.gz"} |
https://eips.ethereum.org/EIPS/eip-225 | # EIP 225: Clique proof-of-authority consensus protocol Source
Author Péter Szilágyi https://github.com/ethereum/EIPs/issues/225 Final Standards Track Core 2017-03-06
## Abstract
Clique is a proof-of-authority consensus protocol. It shadows the design of Ethereum mainnet, so it can be added to any client with minimal effort.
## Motivation
Ethereum’s first official testnet was Morden. It ran from July 2015 to about November 2016, when due to the accumulated junk and some testnet consensus issues between Geth and Parity, it was finally laid to rest in favor of a testnet reboot.
Ropsten was thus born, clearing out all the junk and starting with a clean slate. This ran well until the end of February 2017, when malicious actors decided to abuse the low PoW and gradually inflate the block gas limits to 9 billion (from the normal 4.7 million), at which point sending in gigantic transactions crippling the entire network. Even before that, attackers attempted multiple extremely long reorgs, causing network splits between different clients, and even different versions.
The root cause of these attacks is that a PoW network is only as secure as the computing capacity placed behind it. Restarting a new testnet from zero wouldn’t solve anything, since the attacker can mount the same attack over and over again. The Parity team decided to go with an emergency solution of rolling back a significant number of blocks, and enacting a soft-fork rule that disallows gas limits above a certain threshold.
While this solution may work in the short term:
• It’s not elegant: Ethereum supposed to have dynamic block limits
• It’s not portable: other clients need to implement new fork logic themselves
• It’s not compatible with sync modes: fast and light clients are both out of luck
• It’s just prolonging the attacks: junk can still be steadily pushed in ad infinitum
Parity’s solution although not perfect, is nonetheless workable. I’d like to propose a longer term alternative solution, which is more involved, yet should be simple enough to allow rolling out in a reasonable amount of time.
### Standardized proof-of-authority
As reasoned above, proof-of-work cannot work securely in a network with no value. Ethereum has its long term goal of proof-of-stake based on Casper, but that is heavy research so we cannot rely on that any time soon to fix today’s problems. One solution however is easy enough to implement, yet effective enough to fix the testnet properly, namely a proof-of-authority scheme.
The main design goals of the PoA protocol described here is that it should be very simple to implement and embed into any existing Ethereum client, while at the same time allow using existing sync technologies (fast, light, warp) without needing client developers to add custom logic to critical software.
## Design constraints
There are two approaches to syncing a blockchain in general:
• The classical approach is to take the genesis block and crunch through all the transactions one by one. This is tried and proven, but in Ethereum complexity networks quickly turns out to be very costly computationally.
• The other is to only download the chain of block headers and verify their validity, after which point an arbitrary recent state may be downloaded from the network and checked against recent headers.
A PoA scheme is based on the idea that blocks may only be minted by trusted signers. As such, every block (or header) that a client sees can be matched against the list of trusted signers. The challenge here is how to maintain a list of authorized signers that can change in time? The obvious answer (store it in an Ethereum contract) is also the wrong answer: fast, light and warp sync don’t have access to the state during syncing.
The protocol of maintaining the list of authorized signers must be fully contained in the block headers.
The next obvious idea would be to change the structure of the block headers so it drops the notions of PoW, and introduces new fields to cater for voting mechanisms. This is also the wrong answer: changing such a core data structure in multiple implementations would be a nightmare development, maintenance and security wise.
The protocol of maintaining the list of authorized signers must fit fully into the current data models.
So, according to the above, we can’t use the EVM for voting, rather have to resort to headers. And we can’t change header fields, rather have to resort to the currently available ones. Not much wiggle room.
### Repurposing header fields for signing and voting
The most obvious field that currently is used solely as fun metadata is the 32 byte extra-data section in block headers. Miners usually place their client and version in there, but some fill it with alternative “messages”. The protocol would extend this field to with 65 bytes with the purpose of a secp256k1 miner signature. This would allow anyone obtaining a block to verify it against a list of authorized signers. It also makes the miner section in block headers obsolete (since the address can be derived from the signature).
Note, changing the length of a header field is a non invasive operation as all code (such as RLP encoding, hashing) is agnostic to that, so clients wouldn’t need custom logic.
The above is enough to validate a chain, but how can we update a dynamic list of signers. The answer is that we can repurpose the newly obsoleted miner field and the PoA obsoleted nonce field to create a voting protocol:
• During regular blocks, both of these fields would be set to zero.
• If a signer wishes to enact a change to the list of authorized signers, it will:
• Set the miner to the signer it wishes to vote about
• Set the nonce to 0 or 0xff...f to vote in favor of adding or kicking out
Any clients syncing the chain can “tally” up the votes during block processing, and maintain a dynamically changing list of authorized signers by popular vote.
To avoid having an infinite window to tally up votes in, and also to allow periodically flushing stale proposals, we can reuse the concept of an epoch from ethash, where every epoch transition flushes all pending votes. Furthermore, these epoch transitions can also act as stateless checkpoints containing the list of current authorized signers within the header extra-data. This permits clients to sync up based only on a checkpoint hash without having to replay all the voting that was done on the chain up to that point. It also allows the genesis header to fully define the chain, containing the list of initial signers.
### Attack vector: Malicious signer
It may happen that a malicious user gets added to the list of signers, or that a signer key/machine is compromised. In such a scenario the protocol needs to be able to defend itself against reorganizations and spamming. The proposed solution is that given a list of N authorized signers, any signer may only mint 1 block out of every K. This ensures that damage is limited, and the remainder of the miners can vote out the malicious user.
### Attack vector: Censoring signer
Another interesting attack vector is if a signer (or group of signers) attempts to censor out blocks that vote on removing them from the authorization list. To work around this, we restrict the allowed minting frequency of signers to 1 out of N/2. This ensures that malicious signers need to control at least 51% of signing accounts, at which case it’s game over anyway.
### Attack vector: Spamming signer
A final small attack vector is that of malicious signers injecting new vote proposals inside every block they mint. Since nodes need to tally up all votes to create the actual list of authorized signers, they need to track all votes through time. Without placing a limit on the vote window, this could grow slowly, yet unbounded. The solution is to place a moving window of W blocks after which votes are considered stale. A sane window might be 1-2 epochs. We’ll call this an epoch.
### Attack vector: Concurrent blocks
If the number of authorized signers are N, and we allow each signer to mint 1 block out of K, then at any point in time N-K+1 miners are allowed to mint. To avoid these racing for blocks, every signer would add a small random “offset” to the time it releases a new block. This ensures that small forks are rare, but occasionally still happen (as on the main net). If a signer is caught abusing it’s authority and causing chaos, it can be voted out.
## Specification
We define the following constants:
• EPOCH_LENGTH: Number of blocks after which to checkpoint and reset the pending votes.
• Suggested 30000 for the testnet to remain analogous to the mainnet ethash epoch.
• BLOCK_PERIOD: Minimum difference between two consecutive block’s timestamps.
• Suggested 15s for the testnet to remain analogous to the mainnet ethash target.
• EXTRA_VANITY: Fixed number of extra-data prefix bytes reserved for signer vanity.
• Suggested 32 bytes to retain the current extra-data allowance and/or use.
• EXTRA_SEAL: Fixed number of extra-data suffix bytes reserved for signer seal.
• 65 bytes fixed as signatures are based on the standard secp256k1 curve.
• NONCE_AUTH: Magic nonce number 0xffffffffffffffff to vote on adding a new signer.
• NONCE_DROP: Magic nonce number 0x0000000000000000 to vote on removing a signer.
• UNCLE_HASH: Always Keccak256(RLP([])) as uncles are meaningless outside of PoW.
• DIFF_NOTURN: Block score (difficulty) for blocks containing out-of-turn signatures.
• Suggested 1 since it just needs to be an arbitrary baseline constant.
• DIFF_INTURN: Block score (difficulty) for blocks containing in-turn signatures.
• Suggested 2 to show a slight preference over out-of-turn signatures.
We also define the following per-block constants:
• BLOCK_NUMBER: Block height in the chain, where the height of the genesis is block 0.
• SIGNER_COUNT: Number of authorized signers valid at a particular instance in the chain.
• SIGNER_INDEX: Index of the block signer in the sorted list of current authorized signers.
• SIGNER_LIMIT: Number of consecutive blocks out of which a signer may only sign one.
• Must be floor(SIGNER_COUNT / 2) + 1 to enforce majority consensus on a chain.
We repurpose the ethash header fields as follows:
• beneficiary: Address to propose modifying the list of authorized signers with.
• Should be filled with zeroes normally, modified only while voting.
• Arbitrary values are permitted nonetheless (even meaningless ones such as voting out non signers) to avoid extra complexity in implementations around voting mechanics.
• Must be filled with zeroes on checkpoint (i.e. epoch transition) blocks.
• Transaction execution must use the actual block signer (see extraData) for the COINBASE opcode.
• nonce: Signer proposal regarding the account defined by the beneficiary field.
• Should be NONCE_DROP to propose deauthorizing beneficiary as a existing signer.
• Should be NONCE_AUTH to propose authorizing beneficiary as a new signer.
• Must be filled with zeroes on checkpoint (i.e. epoch transition) blocks.
• Must not take up any other value apart from the two above (for now).
• extraData: Combined field for signer vanity, checkpointing and signer signatures.
• First EXTRA_VANITY bytes (fixed) may contain arbitrary signer vanity data.
• Last EXTRA_SEAL bytes (fixed) is the signer’s signature sealing the header.
• Checkpoint blocks must contain a list of signers (N*20 bytes) in between, omitted otherwise.
• The list of signers in checkpoint block extra-data sections must be sorted in ascending order.
• mixHash: Reserved for fork protection logic, similar to the extra-data during the DAO.
• Must be filled with zeroes during normal operation.
• ommersHash: Must be UNCLE_HASH as uncles are meaningless outside of PoW.
• timestamp: Must be at least the parent timestamp + BLOCK_PERIOD.
• difficulty: Contains the standalone score of the block to derive the quality of a chain.
• Must be DIFF_NOTURN if BLOCK_NUMBER % SIGNER_COUNT != SIGNER_INDEX
• Must be DIFF_INTURN if BLOCK_NUMBER % SIGNER_COUNT == SIGNER_INDEX
### Authorizing a block
To authorize a block for the network, the signer needs to sign the block’s hash containing everything except the signature itself. The means that the hash contains every field of the header (nonce and mixDigest included), and also the extraData with the exception of the 65 byte signature suffix. The fields are hashed in the order of their definition in the yellow paper.
This hash is signed using the standard secp256k1 curve, and the resulting 65 byte signature (R, S, V, where V is 0 or 1) is embedded into the extraData as the trailing 65 byte suffix.
To ensure malicious signers (loss of signing key) cannot wreck havoc in the network, each singer is allowed to sign maximum one out of SIGNER_LIMIT consecutive blocks. The order is not fixed, but in-turn signing weighs more (DIFF_INTURN) than out of turn one (DIFF_NOTURN).
#### Authorization strategies
As long as signers conform to the above specs, they can authorize and distribute blocks as they see fit. The following suggested strategy will however reduce network traffic and small forks, so it’s a suggested feature:
• If a signer is allowed to sign a block (is on the authorized list and didn’t sign recently).
• Calculate the optimal signing time of the next block (parent + BLOCK_PERIOD).
• If the signer is in-turn, wait for the exact time to arrive, sign and broadcast immediately.
• If the signer is out-of-turn, delay signing by rand(SIGNER_COUNT * 500ms).
This small strategy will ensure that the in-turn signer (who’s block weighs more) has a slight advantage to sign and propagate versus the out-of-turn signers. Also the scheme allows a bit of scale with the increase of the number of signers.
### Voting on signers
Every epoch transition (genesis block included) acts as a stateless checkpoint, from which capable clients should be able to sync without requiring any previous state. This means epoch headers must not contain votes, all non settled votes are discarded, and tallying starts from scratch.
For all non-epoch transition blocks:
• Signers may cast one vote per own block to propose a change to the authorization list.
• Only the latest proposal per target beneficiary is kept from a single signer.
• Votes are tallied live as the chain progresses (concurrent proposals allowed).
• Proposals reaching majority consensus SIGNER_LIMIT come into effect immediately.
• Invalid proposals are not to be penalized for client implementation simplicity.
A proposal coming into effect entails discarding all pending votes for that proposal (both for and against) and starting with a clean slate.
A complex corner case may arise during signer deauthorization. When a previously authorized signer is dropped, the number of signers required to approve a proposal might decrease by one. This might cause one or more pending proposals to reach majority consensus, the execution of which might further cascade into new proposals passing.
Handling this scenario is non obvious when multiple conflicting proposals pass simultaneously (e.g. add a new signer vs. drop an existing one), where the evaluation order might drastically change the outcome of the final authorization list. Since signers may invert their own votes in every block they mint, it’s not so obvious which proposal would be “first”.
To avoid the pitfalls cascading executions would entail, the Clique proposal explicitly forbids cascading effects. In other words: Only the beneficiary of the current header/vote may be added to/dropped from the authorization list. If that causes other proposals to reach consensus, those will be executed when their respective beneficiaries are “touched” again (given that majority consensus still holds at that point).
#### Voting strategies
Since the blockchain can have small reorgs, a naive voting mechanism of “cast-and-forget” may not be optimal, since a block containing a singleton vote may not end up on the final chain.
A simplistic but working strategy is to allow users to configure “proposals” on the signers (e.g. “add 0x…”, “drop 0x…”). The signing code can then pick a random proposal for every block it signs and inject it. This ensures that multiple concurrent proposals as well as reorgs get eventually noted on the chain.
This list may be expired after a certain number of blocks / epochs, but it’s important to realize that “seeing” a proposal pass doesn’t mean it won’t get reorged, so it should not be immediately dropped when the proposal passes.
## Test Cases
// block represents a single block signed by a parcitular account, where
// the account may or may not have cast a Clique vote.
type block struct {
signer string // Account that signed this particular block
voted string // Optional value if the signer voted on adding/removing someone
auth bool // Whether the vote was to authorize (or deauthorize)
checkpoint []string // List of authorized signers if this is an epoch block
}
// Define the various voting scenarios to test
tests := []struct {
epoch uint64 // Number of blocks in an epoch (unset = 30000)
signers []string // Initial list of authorized signers in the genesis
blocks []block // Chain of signed blocks, potentially influencing auths
results []string // Final list of authorized signers after all blocks
failure error // Failure if some block is invalid according to the rules
}{
{
// Single signer, no votes cast
signers: []string{"A"},
blocks: []block{
{signer: "A"}
},
results: []string{"A"},
}, {
// Single signer, voting to add two others (only accept first, second needs 2 votes)
signers: []string{"A"},
blocks: []block{
{signer: "A", voted: "B", auth: true},
{signer: "B"},
{signer: "A", voted: "C", auth: true},
},
results: []string{"A", "B"},
}, {
// Two signers, voting to add three others (only accept first two, third needs 3 votes already)
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "C", auth: true},
{signer: "B", voted: "C", auth: true},
{signer: "A", voted: "D", auth: true},
{signer: "B", voted: "D", auth: true},
{signer: "C"},
{signer: "A", voted: "E", auth: true},
{signer: "B", voted: "E", auth: true},
},
results: []string{"A", "B", "C", "D"},
}, {
// Single signer, dropping itself (weird, but one less cornercase by explicitly allowing this)
signers: []string{"A"},
blocks: []block{
{signer: "A", voted: "A", auth: false},
},
results: []string{},
}, {
// Two signers, actually needing mutual consent to drop either of them (not fulfilled)
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "B", auth: false},
},
results: []string{"A", "B"},
}, {
// Two signers, actually needing mutual consent to drop either of them (fulfilled)
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "B", auth: false},
{signer: "B", voted: "B", auth: false},
},
results: []string{"A"},
}, {
// Three signers, two of them deciding to drop the third
signers: []string{"A", "B", "C"},
blocks: []block{
{signer: "A", voted: "C", auth: false},
{signer: "B", voted: "C", auth: false},
},
results: []string{"A", "B"},
}, {
// Four signers, consensus of two not being enough to drop anyone
signers: []string{"A", "B", "C", "D"},
blocks: []block{
{signer: "A", voted: "C", auth: false},
{signer: "B", voted: "C", auth: false},
},
results: []string{"A", "B", "C", "D"},
}, {
// Four signers, consensus of three already being enough to drop someone
signers: []string{"A", "B", "C", "D"},
blocks: []block{
{signer: "A", voted: "D", auth: false},
{signer: "B", voted: "D", auth: false},
{signer: "C", voted: "D", auth: false},
},
results: []string{"A", "B", "C"},
}, {
// Authorizations are counted once per signer per target
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "C", auth: true},
{signer: "B"},
{signer: "A", voted: "C", auth: true},
{signer: "B"},
{signer: "A", voted: "C", auth: true},
},
results: []string{"A", "B"},
}, {
// Authorizing multiple accounts concurrently is permitted
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "C", auth: true},
{signer: "B"},
{signer: "A", voted: "D", auth: true},
{signer: "B"},
{signer: "A"},
{signer: "B", voted: "D", auth: true},
{signer: "A"},
{signer: "B", voted: "C", auth: true},
},
results: []string{"A", "B", "C", "D"},
}, {
// Deauthorizations are counted once per signer per target
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "B", auth: false},
{signer: "B"},
{signer: "A", voted: "B", auth: false},
{signer: "B"},
{signer: "A", voted: "B", auth: false},
},
results: []string{"A", "B"},
}, {
// Deauthorizing multiple accounts concurrently is permitted
signers: []string{"A", "B", "C", "D"},
blocks: []block{
{signer: "A", voted: "C", auth: false},
{signer: "B"},
{signer: "C"},
{signer: "A", voted: "D", auth: false},
{signer: "B"},
{signer: "C"},
{signer: "A"},
{signer: "B", voted: "D", auth: false},
{signer: "C", voted: "D", auth: false},
{signer: "A"},
{signer: "B", voted: "C", auth: false},
},
results: []string{"A", "B"},
}, {
signers: []string{"A", "B", "C"},
blocks: []block{
{signer: "C", voted: "B", auth: false},
{signer: "A", voted: "C", auth: false},
{signer: "B", voted: "C", auth: false},
{signer: "A", voted: "B", auth: false},
},
results: []string{"A", "B"},
}, {
signers: []string{"A", "B", "C"},
blocks: []block{
{signer: "C", voted: "D", auth: true},
{signer: "A", voted: "C", auth: false},
{signer: "B", voted: "C", auth: false},
{signer: "A", voted: "D", auth: true},
},
results: []string{"A", "B"},
}, {
// Cascading changes are not allowed, only the account being voted on may change
signers: []string{"A", "B", "C", "D"},
blocks: []block{
{signer: "A", voted: "C", auth: false},
{signer: "B"},
{signer: "C"},
{signer: "A", voted: "D", auth: false},
{signer: "B", voted: "C", auth: false},
{signer: "C"},
{signer: "A"},
{signer: "B", voted: "D", auth: false},
{signer: "C", voted: "D", auth: false},
},
results: []string{"A", "B", "C"},
}, {
// Changes reaching consensus out of bounds (via a deauth) execute on touch
signers: []string{"A", "B", "C", "D"},
blocks: []block{
{signer: "A", voted: "C", auth: false},
{signer: "B"},
{signer: "C"},
{signer: "A", voted: "D", auth: false},
{signer: "B", voted: "C", auth: false},
{signer: "C"},
{signer: "A"},
{signer: "B", voted: "D", auth: false},
{signer: "C", voted: "D", auth: false},
{signer: "A"},
{signer: "C", voted: "C", auth: true},
},
results: []string{"A", "B"},
}, {
// Changes reaching consensus out of bounds (via a deauth) may go out of consensus on first touch
signers: []string{"A", "B", "C", "D"},
blocks: []block{
{signer: "A", voted: "C", auth: false},
{signer: "B"},
{signer: "C"},
{signer: "A", voted: "D", auth: false},
{signer: "B", voted: "C", auth: false},
{signer: "C"},
{signer: "A"},
{signer: "B", voted: "D", auth: false},
{signer: "C", voted: "D", auth: false},
{signer: "A"},
{signer: "B", voted: "C", auth: true},
},
results: []string{"A", "B", "C"},
}, {
// Ensure that pending votes don't survive authorization status changes. This
// corner case can only appear if a signer is quickly added, removed and then
// readded (or the inverse), while one of the original voters dropped. If a
// past vote is left cached in the system somewhere, this will interfere with
// the final signer outcome.
signers: []string{"A", "B", "C", "D", "E"},
blocks: []block{
{signer: "A", voted: "F", auth: true}, // Authorize F, 3 votes needed
{signer: "B", voted: "F", auth: true},
{signer: "C", voted: "F", auth: true},
{signer: "D", voted: "F", auth: false}, // Deauthorize F, 4 votes needed (leave A's previous vote "unchanged")
{signer: "E", voted: "F", auth: false},
{signer: "B", voted: "F", auth: false},
{signer: "C", voted: "F", auth: false},
{signer: "D", voted: "F", auth: true}, // Almost authorize F, 2/3 votes needed
{signer: "E", voted: "F", auth: true},
{signer: "B", voted: "A", auth: false}, // Deauthorize A, 3 votes needed
{signer: "C", voted: "A", auth: false},
{signer: "D", voted: "A", auth: false},
{signer: "B", voted: "F", auth: true}, // Finish authorizing F, 3/3 votes needed
},
results: []string{"B", "C", "D", "E", "F"},
}, {
// Epoch transitions reset all votes to allow chain checkpointing
epoch: 3,
signers: []string{"A", "B"},
blocks: []block{
{signer: "A", voted: "C", auth: true},
{signer: "B"},
{signer: "A", checkpoint: []string{"A", "B"}},
{signer: "B", voted: "C", auth: true},
},
results: []string{"A", "B"},
}, {
// An unauthorized signer should not be able to sign blocks
signers: []string{"A"},
blocks: []block{
{signer: "B"},
},
failure: errUnauthorizedSigner,
}, {
// An authorized signer that signed recenty should not be able to sign again
signers: []string{"A", "B"},
blocks []block{
{signer: "A"},
{signer: "A"},
},
failure: errRecentlySigned,
}, {
// Recent signatures should not reset on checkpoint blocks imported in a batch
epoch: 3,
signers: []string{"A", "B", "C"},
blocks: []block{
{signer: "A"},
{signer: "B"},
{signer: "A", checkpoint: []string{"A", "B", "C"}},
{signer: "A"},
},
failure: errRecentlySigned,
},,
}
## Implementation
A reference implementation is part of go-ethereum and has been functioning as the consensus engine behind the Rinkeby testnet since April, 2017.
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http://crypto.stackexchange.com/questions/2220/what-are-the-advantages-of-totp-over-hotp?answertab=active | # What are the advantages of TOTP over HOTP?
HMAC-based One Time Password (HOTP) was published as an informational IETF RFC 4226 in December 2005. In May, 2011, Time-based One-time Password Algorithm (TOTP) officially became RFC 6238. What advantages it introduces?
-
One of the advantages is purely on the human side of security. From RFC 6238's abstract:
The HOTP algorithm specifies an event-based OTP algorithm, where the moving factor is an event counter. The present work bases the moving factor on a time value. A time-based variant of the OTP algorithm provides short-lived OTP values, which are desirable for enhanced security.
(Emphasis mine.)
The TOTP passwords are short-lived, they only apply for a given amount of human time. HOTP passwords are potentially longer lived, they apply for an unknown amount of human time.
The reference to "enhanced security" is referencing (at least) two areas: The value of a compromised key, and ability to attack one.
First, should a current HOTP password be compromised it will potentially be valid for a "long time". Ensuring frequent use of the HOTP in human time is not a part of the HOTP design, so it is unknown how long the current HOTP password will be valid for and we have to assume the worst case, namely, that it will be a "long" time. This allows the attacker to use a compromised password at their leisure. But should the current TOTP be compromised, it will not be useful for very long because in one TOTP time increment it will be invalidated. Of course, in theory the attacker could grab and use the password in negligible time, but it does prevent a practical human aspect. For example, someone who gets a look at your current Paypal key (which rotates every 30 seconds, IIRC) can't go home and try to use it later, they would have to lunge for a computer in the moment. Someone who compromises they key may not realize it until after the key has expired. Etc.
Second, if you are attacking a key, your work is potentially invalidated or set back every time increment of the TOTP because the target has moved. Perhaps an attacker has discovered an attack against an OTP scheme that allows them to predict the next password only if they have some number of the last 10 passwords, but it takes about 2 hours of computing time to do so. If the OTP changes every minute, their attack is pretty much useless. Brute-force attacks are inhibited as well, because the next password is chosen the same distribution each time; it is possible to brute-force exhaust the password space and not find the password. TOTP doesn't eliminate those sorts of attacks, but hopefully it limits which ones have the ability to be effective.
-
Is there any case where HOTP requires an internet connection while TOTP doesn't? Or vice-versa? – Jader Dias Mar 30 '12 at 1:28
I think the real challenge is getting the time to be SYNCHRONIZED on the client end along with the server , in case of TOTP. – Franklin Jun 3 '12 at 7:24
@JaderDias - Neither of the algorithms need an internet connection – user93353 Sep 6 '13 at 1:10
Neither is worthwile. Changing number codes were invented by RSA in 1984 to block keyloggers. More than 90% of todays internet breakins take place as a result of phishing, and we're seeing incidence of entire countries having more malware infected machines than clean ones (the boleto bandits, have pocketed \$1bn cash so far, & are still going strong).
TOTP and HOTP are almost completely ineffective against todays' risks.
You need solutions that include mutual authentication, and transaction verification, not 30-years-old gizmos.
-
This answer makes no sense in relation with the question. TOTP and HOTP are intended as a form of authentication (usually as a what-you-have factor as the values are read off a token). They have nothing to do with other aspects of establishing a secure channel. – Gilles Aug 25 '14 at 14:23
@Chris I must be missing something… how does that answer the question asking about the potential advantages (comparing RFC 4226 and RFC 6238)? Also, you state TOTP and HOTP are almost completely ineffective against todays' risks. – do you have any reliable source to backup that statement? (Note that I’m not asking for a link to some weird blog, but for a pointer to one or more scientific papers that provide analysis and proofs to the “complete ineffectiveness” you claim to exist.) – e-sushi Aug 25 '14 at 18:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39114323258399963, "perplexity": 2124.8184883812387}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246640001.64/warc/CC-MAIN-20150417045720-00128-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://physics.aps.org/synopsis-for/10.1103/PhysRevC.79.021302 | # Synopsis: Finding the missing sign
#### Sign of the overlap of Hartree-Fock-Bogoliubov wave functions
L. M. Robledo
Published February 20, 2009
In a many-body physics problem, the first approximation to account for interactions is to assume that each particle moves in an effective mean field created by all of the other particles. The mutual interactions of neutrons and protons in nuclei, for example, generate a mean field in which the nucleons move in single-particle orbits. Hartree-Fock is a simple mean-field theory in which the single-particle orbits are either fully occupied or not at all. A generalization of this method that can describe quasiparticles in the presence of pairing is Hartree-Fock-Bogoliubov (HFB) theory (called Bogoliubov–de Gennes theory in condensed matter physics).
In going beyond mean-field theory, different HFB solutions are mixed and the overlap of HFB wave functions must be computed. However, standard formulas leave the sign of the overlap of the wave functions undetermined. This is not a problem for systems with discrete symmetries, but it is present when the HFB wave functions are triaxial, which occurs in the low-lying rotational bands of ${}^{24}\text{Mg}$, or break time-reversal symmetry.
In a Rapid Communication appearing in Physical Review C, Luis Robledo of Universidad Autonoma de Madrid uses the technique of fermion coherent states to determine the sign of wave-function overlap. The overlap is given in terms of a quantity similar to a determinant called the Pfaffian of a skew-symmetric matrix. The goal is to simplify the implementation of challenging theory projects, such as those that calculate the projection of triaxial angular momentum. – John Millener and Ben Gibson | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8521015048027039, "perplexity": 665.0566977521494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500824209.82/warc/CC-MAIN-20140820021344-00177-ip-10-180-136-8.ec2.internal.warc.gz"} |
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FQXi FORUM
March 17, 2018
CATEGORY: High Energy Physics [back]
TOPIC: Ed Witten on the Nature of Reality [refresh]
FQXi Administrator Zeeya Merali wrote on Dec. 4, 2017 @ 15:04 GMT
Natalie Wolchover has a fascinating interview with string theorist Ed Witten, in Quanta on dualities and what is real and fundamental. Thank you to Steve Agnew for suggesting that this would be a could discussion topic.
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Pentcho Valev wrote on Dec. 4, 2017 @ 22:14 GMT
Edward Witten: "I tend to assume that space-time and everything in it are in some sense emergent. By the way, you'll certainly find that that's what Wheeler expected in his essay. As you'll read, he thought the continuum was wrong in both physics and math. He did not think one's microscopic description of space-time should use a continuum of any kind - neither a continuum of space nor a continuum of time, nor even a continuum of real numbers. On the space and time, I'm sympathetic to that."
One of my comments in Quanta:
"Emergent space-time" is a category mistake. Specetime has already emerged - it is a deductive consequence of Einstein's constant-speed-of-light postulate:
"Special relativity is based on the observation that the speed of light is always the same, independently of who measures it, or how fast the source of the light is moving with respect to the observer. Einstein demonstrated that as an immediate consequence, space and time can no longer be independent, but should rather be considered a new joint entity called "spacetime."
Anything deduced from different premises would fall in a different category and would have nothing to do with Einstein's spacetime - combining the two concepts would be absurd. For instance, bringing granularity to spacetime is equivalent to painting spacetime in yellow. If the original concept of spacetime is unacceptable and should be replaced, then the underlying premise, Einstein's constant-speed-of-light postulate, is false and should be abandoned. The step is unavoidable if logic is obeyed.
Pentcho Valev
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Pentcho Valev replied on Dec. 5, 2017 @ 12:33 GMT
Nima Arkani-Hamed (06:09): "Almost all of us believe that space-time doesn't really exist, space-time is doomed and has to be replaced by some more primitive building blocks."
Any substitute for spacetime that emerges from "some more primitive building blocks", that is, is deduced from premises different from the principle of relativity and the constancy of the speed of light, has nothing to do with Einstein's spacetime. The two fall in different categories. The new "spacetime" could replace the old one, but then the rejection of Einstein's spacetime would entail that at least one of Einstein's 1905 postulates is false.
Marcelo Gleiser: "The challenge is to somehow bring the notion of granularity to spacetime, bring the discrete to the continuous. This is the problem that has baffled theoretical physicists for at least half a century."
This is insane. Spacetime is not an ab initio model that one can modify, e.g. by introducing granularity. It is a DEDUCTIVE CONSEQUENCE of Einstein's constant-speed-of-light postulate, and if the consequence is unacceptable, the postulate is false (logic forbids the combination "true postulate, unacceptable consequence"). In other words, you cannot "retire" Einstein's spacetime without declaring the postulate false:
What scientific idea is ready for retirement? Steve Giddings: "Spacetime. Physics has always been regarded as playing out on an underlying stage of space and time. Special relativity joined these into spacetime... [...] The apparent need to retire classical spacetime as a fundamental concept is profound..."
Pentcho Valev
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John R. Cox replied on Dec. 5, 2017 @ 15:28 GMT
All due respects for Ed Witten, but quantum communications are looking very realistic today. And it's the Chineese whom are taking the lead, at least publicly, with the first of a planned 20 satellites. It takes no great leap of understanding to recognize that an instantaneous correlation of paired events making communications undetectable in the first place, let alone decipherable, would render...
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Robert H McEachern replied on Dec. 5, 2017 @ 17:34 GMT
John,
Your comment about "making communications undetectable in the first place, let alone decipherable" is not quite correct. The communications are potentially both detectable and decipherable. But they are non-compromisable, since, for example, it is possible to determine that someone has attempted to intercept a distributed key. In effect, an adversary can jam the system by constantly attempting to intercept such a system. Thus, while one might know when the system is in a secure state, that state can be denied by a suitable denial-of-service attack. Denying an adversary their secure form of communications, in order to force them to use an insecure one, whenever it is essential for them to communicate, is a common strategy in communications warfare.
Rob McEachern
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Steve Agnew wrote on Dec. 5, 2017 @ 04:05 GMT
It is all a question of numbers after all...if a continuum is composed of 1e39 bits per angstrom, why is that different from a continuum?
Einstein's spacetime is a continuum approximation of a very large number of discrete quanta. So spacetime works very well and quantum works very well and all we need is a connection that also works very well...
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Georgina Woodward wrote on Dec. 5, 2017 @ 10:27 GMT
The space-time continuum has issues. What is seen in a reference frame has to be a sensory product or product of a device, post receipt and processing of EM signals. Vision requires that causal order of EM signal receipt preceding product seen. The process from detection of signal to product generation gives a resolution to the product so that it is not a continuum. Whether because of the limited number of cells of the visual cortex or pixels display-able on a screen.
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Georgina Woodward replied on Dec. 5, 2017 @ 10:45 GMT
Quote: "I tend to assume that space-time and everything in it are in some sense emergent." Edward Witten. Yes, it has to be because Einstein was referring to what is seen. Being a physicist and not a biologist the process of seeing was not built into the work.
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Georgina Woodward replied on Dec. 6, 2017 @ 06:41 GMT
As discreet sensors of some kind or another have to collect the em signals prior to their processing, discreetness is input to the production of seen space-time products. Even though some aggregation and averaging of the information generated from the signals occurs it isn't amalgamated into a fully continuous whole. The information is carried by discreet neurons or circuits. The information that ends up as the product is confined to the discreet components of the host surface.
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paul ryan ryan wrote on Jan. 16, 2018 @ 11:53 GMT
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Ajay Pokhrel wrote on Jan. 20, 2018 @ 04:35 GMT
Hello everyone,
Needed some help please with a question.
Suppose we have an equation f(t) which is a function showing the displacement of a particle at a different point in time.
$f(t)=x[1-exp[-(t/y)^z]$
How do I try to model this equation into a quantum oscillator, like Schrodinger?
Thanks!
Ajay Pokharel
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Arnold Ejiofor Ejiofor wrote on Jan. 29, 2018 @ 06:31 GMT
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Paul Henry wrote on Mar. 15, 2018 @ 05:43 GMT
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http://physics.stackexchange.com/tags/terminology/new | # Tag Info
1
A constraint condition can reduce the DOF of the system if it can be used to express a coordinate in terms of the others. This can always be done in case of holonomic constraints which are basically just algebraic functions of the coordinates and time. This means that you just have to manipulate the constraint equation in such a way that one of the ...
0
2nd law of thermodynamics has many almost equivalent formulations. The traditional ones always assume closed system, isolation is not needed - heat and work transfer are assumed to be allowed. One formulation: When thermodynamic system goes from equilibrium state 1 to equilibrium state 2, the entropies of these states obey the relation $$S(2) - S(1) \geq ... 0 ANS: It is basically the same. All of them are anomalies for chiral fermion in even dimensional spacetime, like 1+1D, 3+1D, etc. Or, in odd dimensional space. ABJ anomaly is named after the discovers: Adler-Bell-Jackiw. - Chiral anomaly is named after and implies that the chiral current is not conserved. Chiral, means the left and the ... 0 In the context of Relativty, the adjective "coincident" characterizes all that which belongs together ("at once") to only one event without any temporal or spatial or light-like separation; i.e. indications (of any participant at this one event) or occurences (as far as they are understood to be contained within this one event). In contrast, the adjective ... 1 The "adjustable constant" in that statement is the total energy E, and they mean it's "adjustable" in that the behavior of the system is completely independent of E - this is known in physics as a symmetry, in that they system doesn't change if it has a different total amount of energy. In this case, the way to "adjust" the amount of energy would be ... 0 Positron is as "elementary" as the electron, in the current theory. Period. I took the word "elementary" in quote marks because if you hit a charged particle, it gets "broken apart" into the following pieces: the same charge and lots of neutral photons. It looks like the "target" is not that "elementary", but has "internal degrees of freedom", and sometimes ... 1 Positron IS an elementary particle, the anti-particle to the electron as you already know. But we do not get a "free positron" as a "free electron". They are usually generated through pair-production and get annihilated fast, or through radioactive decay (beta-decay) in weak interactions or in particle accelerators, and are present in cosmic rays too. A ... 1 The equation you are quoting gives the power of a lens in terms of its geometry and refractive index. Simply rearranging the terms (dividing by n) gives you an expression for \frac{1}{f} which is known as the power of the lens and is expressed in diopters. For the usual situation of a lens in air, we can put n=1 which leaves you with an even simpler ... 1 Dunno what book you're quoting, but you should realize that the index of refraction of air is n = 1+ \epsilon (where I'm using the mathematics standard of \epsilon being a tiny number). Thus the power in air is 1/F 2 As I recall, covariant refers to how an object transforms when you boost to another inertial frame. An example would be the relativistic 4-momentum P^{\mu}. Invariant refers to quantities which are unchanged under boosts to different frames. For example the product P^{\mu}P_{\mu}=m has the same numerical value in any frame. Sometimes a relativistic ... 1 "Coincident" is defined in the Google online dictionary as (1) "occurring together in space OR time" (emphasis mine), and (2) "in agreement or harmony". "Simultaneous" is defined in the same dictionary as "occurring, operating, or done at the same time". (This begs the question: "Whose time?") Unfortunately, this dictionary lists "coincident" as a synonym ... 1 Regarding your assertions: Events \varepsilon_{AJ} and \varepsilon_{BK} were simultaneous in the inertial frame of participants A, B, M. This is a perfectly reasonable statement and it is the sort of language used in everyday physics. Participant M was the middle between J and K, in the inertial frame of participants A, B, M. ... 1 I would like to bring the ladder paradox here to explain simultaneity of events.A ladder (an inertial frame) is moving horizontally with a relatively high constant speed with respect to a garage (another inertial frame). The garage has an open door where the ladder can not actually enter if the ladder was at rest in the garage's frame but that is not ... 0 It's the net resultant that a force would react with on application of a certain change in momentum in the body, on which the force is applied. 1 A site is just a place or location with given coordinates e.g. (x_0,y_0,z_0) 0 Kinetics are focused on the rate and mechanism of chemical processes, so you are definitely right to say that you gain a lot of insight about mechanism from kinetics. Many kinetic theory make extensive use of statistical thermodynamics methods, and that's why you perceive a resemblance. However, keep in mind that in kinetics the system is not in ... 4 The Weights and Measures Act (the origin of the Imperial Units) does not speak of temperature. It was intended to create a uniform system for trade. You don't sell temperature, in the way you sell a pint of milk or a yard of cloth. And frankly, when it was first conceived (before Magna Carta, which already stated: "There shall be but one Measure ... 2 According to the wiki page on Imperial and US customary units Fahrenheit is part of both the Imperial and US customary system. I can't think of any reason it wouldn't be included in the Imperial system. Note that in the wiki page on Imperial units it is mentioned that the weight's and measures act (which defined the Imperial system) explicitly used the ... 0 The effective potential is the potential of interaction you measure between two (or more) emergent physical objects when you forget (or "trace over" in the jargon) certain degrees of freedom of a more detailed model. If you take two pinned charges in vacuum for instance, they will interact with a "bare" Coulomb interaction in \sim 1/r. If you put these ... 1 As wiki says "The effective potential (also known as effective potential energy) is a mathematical expression combining multiple (perhaps opposing) effects into a single potential." Basically the concept of the effective potential simplifies the equations of motion and simplifies their analysis. 0 More on the perytons being caused by microwave ovens being opened while still operating. The microwave oven's magnetron is still generating the microwaves when the door is open before the timer has stopped the microwave. Article: http://phenomena.nationalgeographic.com/2015/04/10/rogue-microwave-ovens-are-the-culprits-behind-mysterious-radio-signals Study: ... 1 Four component formalism is the "right" formalism, but it has negative energy eigenstates corresponding to the antiparticles. Most chemists and solid state physics are not interested in the antiparticles, and such negative energy solution causes trouble for conventional variational methods, where you might end up falling to negative infinity energy. It is ... 0 Rolling friction result from for example small changes in the surface or in the wheel material (the rubber in a tire). The surface is not perfectly flat and rigid so there will be some small forces trying to stop the rotating motion: On the contrary, the static friction is not trying to stop the rotation of the wheel. Static and rolling friction are ... 0 Cicle is the smallest repatable segment between two points, where: 1. These point lies on one line and the line is parallel to direction of wave propagation. 2. These two points have the always same sign of slope. Thanks to Floris in help of derivation of the definition. 1 The below seems to be a candidate for the first use of the term 'Majorana fermion'. (I'm not sure if it satisfies your other criteria.) Salam, Abdus, and J. Strathdee. Super-symmetry and non-Abelian gauges. International Centre for Theoretical Physics, Trieste (Italy), 1974. 2 Using elementary graph theory identities one can show that the number of loops in a connected diagram is related to the number of external lines and the number of vertices of type i each of which has n_i lines attached to it, is related by$$ \sum \left(\frac{n_i}{2}-1\right) V_i -\tfrac{1}{2}E +1= L $$So you can see that for a fixed process (fixed ... 5 A paper came out this week pointing to them having a banal (if amusing) origin: they are from two 27 year old microwave ovens. When people get impatient and open the door before the timer runs down, a short burst from the ovens' magnetron is released, which appears as a peryton if the telescope is pointed in the right direction. Figure 7. shows the perytons ... 0 Let's check that parity is violated by the weak interaction lagrangian:$$\mathcal{L}(x) = \bar{\psi}(x) \gamma^\mu \frac{(1-\gamma^5)}{2} \psi(x) W_\mu(x)$$Saying that parity is violated means that the transformed lagrangian \mathcal{L}'(x) is not equal to the old lagrangian resulting from new coordinates \mathcal{L}(x') where x'^0 = x^0 and ... 2 The order of a quantity in general refers to the exponent of the quantity in an expression, ie$$x^3y^2$$would be 3rd order in x and 2nd order in y. According to the Feynman rules, each vertex in a Feynman diagrams contributes a factor of the coupling constant, so the order of each coupling constant is simply the number of vertices of that interaction. ... 0 Pressure-sensitive paints? Is that what you need? http://en.wikipedia.org/wiki/Pressure-sensitive_paint 0 I guess you have some typos in your question (or your lecture notes), since the two lines you give just differ by the index names (as already commented) . Starting from$$ R^n_{ikl;m} +R^n_{imk;l} +R^n_{ilm;k} =0 $$you can rewrite that with the symmetry relations R^n_{ikl}=- R^n_{ilk}=-R^i_{nkl} to$$ R^n_{ikl;m} - R^n_{ikm;l} +R^n_{ilm;k}=0. $$Now let ... 2 To contract a tensor is to set two of the indices equal and sum over them, so given a tensor A^i_j the contraction is A=A^i_i=A^1_1+A^2_2+A^3_3+A^4_4 The Bianchi identities you list have five indices. To contract them, you would set some pair equal and sum over them. Your second version is the same as the first, it just has the indices renamed. ... 2 Static comes from the same root as stasis, meaning stop, immovable, To create static electricity, you have to rub two different materials. At the moment you rub them, the electrons already moved Note the word "create", creation is not static, and yes there are transient fields and currents during creation of a static field. The static describes the ... 1 UV stands for Ultraviolet and it is referring to a special kind of divergences in quantum field theory. In NLO loop diagrams, we often encounter divergences (infinite integrals) when we investigate what happens at k \to \infty, where k is the internal momentum of a virtual particle in Feynman diagrams. These are precisely the divergences we call "UV ... 0 UV = Ultra-Violet = High energy = Small length-scale. 0 This is just a wild guess, but could it be the position vector of the element? 1 I think the magnon is a special case of the spin wave. Whereas spinon refers to the general quasiparticle that carries all spin of an electron, magnon refers to the limiting case of spin wave quantized in such a manner that it becomes part of an anti-magnetic cloud of quasiparticles. However, this may not be the complete story! Some usage of the terms: ... 0 In this context, it is a change of variables. The variable in the original Lagrangian is q, and Goldstein is asking you to use another variable s, which is related to the original q via the "transformation":$$s = \exp(\gamma t) \ q$$and later on, make sense of it (with the later questions). Point transformation in this context refers merely to this ... 1 i searched for the exact same problem recently after a debate with one of my colleagues. In my opinion, you already gave the answer to your question yourself. A source dipole is the flow field resulting from a sink and a source brought together. In a sink, all streamlines point radially inward to the singularity at the origin, in a source, all point ... 0 \hat{I}_D(k)={{g^2}\over4}\int_0^1d\alpha\int_0^\infty d\sigma\int\sigma\mathrm{e}^{-[q^2+\alpha(1-\alpha)k^2+m^2]\sigma}\vec{a}q. Just a wild guess. [Oh, you asked for two formulae. Sorry.] Either that, or it is \int_0^\infty\mathrm{e}^{-a\alpha}\sigma d\sigma=a^{-2}. 4 I got a translation of the article from the German Wikipedia. Here's an excerpt: Perytons are in radio astronomy short radio signals having a length of a few milliseconds, which probably terrestrial are origin. The Perytons are named after mythical creatures . In radio astronomy, terrestrial are noise is always a problem. A well-known noise signal ... 1 This paper describes them. http://www.ursi.org/proceedings/procGA11/ursi/GP2-41.pdf They were apparently given a new name because their origin was uncertain. 0 If the observer is not in free-fall, the metric-tensor g_{\mu,\nu}(s) at the observer's position, expressed in local coordinates around the observer, will not be \eta_{\mu,\nu}. Your first assumption about the path (\gamma) is wrong. I guess what you are aiming at is the notion of the space of coordinates around a point, which is indeed a flat space ... 2 When you say If something goes outside, then it will decrease inside! what you assume is exactly a conservation law. It may seem trivial, but it is not necessarily. Consider the population of a city, for example. At one point in time, you measure how many people are within the city borders; let's call this number N_0. Then, you observe all city ... 2 When we say something is conserved or that there is a conservation law for a given thing, we mean that the quantity of it does not change. You neither lose nor gain any of that thing. More specifically, conservation can come in two flavours. Something can be globally conserved. This means that the total amount of that something in the universe does not ... 1 It has a very simple yet important meaning.It simply means that the quantity that you are observing will always stay the same,even if that means that it gets transferred to another form or convert to another medium.You can not simply create more "stuff" of that quantity and you can not destroy it.It can not be created from nothing and it can not just be ... 3 Let M be your spacetime, a smooth manifold equipped with (pseudo) Riemannian metric (for example \mathbb{R}^{(1,3)} for special relativity). The set of reference frames is the frame bundle over M, usually denoted FM. Explicitly a frame at point p in M can be viewed as an ordered orthonormal basis (with respect to the the inner product defined ... 2 The kinetic term of the Lagrangian is proportional to$$g_{ij}v^iv^j$$where the vs are the generalised velocities. Writing them as the time derivative of the generalised coordinates, i.e. v^i\dot q^i, taking the square root, and multiplying by a small time lapse \epsilon you get$$\sqrt{g_{ij}\dot q^i\dot q^j}\epsilon, which is a first order ...
1
The name T-duality stands for Target-space duality, see e.g. this preprint.
1
It comes from S matrix theory, long before quarks were imagined, S,T and U characterize the type of exchange in the Feynman diagrams entering the S matrix calculation, and they are called Mandelstam variables. s channel-------------------------- t channel------------------------u channel duality meant that the sums could be done either in S ...
Top 50 recent answers are included | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9493299722671509, "perplexity": 1543.5508871812192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246654264.98/warc/CC-MAIN-20150417045734-00252-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://brilliant.org/problems/every-problem-has-a-solution-isnt-it/ | # Every Problem Has A Solution, isn't it?
Algebra Level 4
$\sqrt{x^2 - 4x + 3} + \sqrt{x^2 - 9} = \sqrt{4x^2 - 14x + 6 }$
How many solutions are there for the given equation?
Treat the square root as a real valued function.
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9513381719589233, "perplexity": 1369.0994475384032}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655878639.9/warc/CC-MAIN-20200702080623-20200702110623-00027.warc.gz"} |
https://community.cloudera.com/t5/Support-Questions/How-to-put-files-in-flume-spooldir-one-by-one/td-p/44188 | Support Questions
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Alert: Welcome to the Unified Cloudera Community. Former HCC members be sure to read and learn how to activate your account here.
## How to put files in flume spooldir one by one
SOLVED Go to solution
## How to put files in flume spooldir one by one
Explorer
i am using flume spooldir to put files in HDFS , but i am getting so many small files in HDFS. I thought of using batch size and roll interval but i don't want to get dependent on size and interval. So I decided to push files in flume spooldir one at a time. How can i do this ? Please help
1 ACCEPTED SOLUTION
Accepted Solutions
## Re: How to put files in flume spooldir one by one
Champion
You can refer Hdfs sink timestamp escape sequence , there is alot of them you can use accordingly .
example
U can use hdfs bucketing , for every one hour.
```agen1.sinks.hdfsSinks.hdfs.path = /data/flume/%{aa}/%y/%m/%d/%H/%M
agent1.sinks.hdfsSinks.hdfs.round = true
agen1.sinks.hdfsSinks.roundUnit = hour
agen1.sinks.hdfsSinks.roundValue = 1 ```
3 REPLIES 3
## Re: How to put files in flume spooldir one by one
Champion
Try using the timestamp interceptor.
## Re: How to put files in flume spooldir one by one
Explorer
any examples you have ?
## Re: How to put files in flume spooldir one by one
Champion
You can refer Hdfs sink timestamp escape sequence , there is alot of them you can use accordingly .
example
U can use hdfs bucketing , for every one hour.
```agen1.sinks.hdfsSinks.hdfs.path = /data/flume/%{aa}/%y/%m/%d/%H/%M
agent1.sinks.hdfsSinks.hdfs.round = true
agen1.sinks.hdfsSinks.roundUnit = hour
agen1.sinks.hdfsSinks.roundValue = 1 ```
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Coming from Hortonworks? Activate your account here | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9330170154571533, "perplexity": 7000.950953374752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316075.15/warc/CC-MAIN-20190821152344-20190821174344-00441.warc.gz"} |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/384/3/e/d/ | # Properties
Label 384.3.e.d Level $384$ Weight $3$ Character orbit 384.e Analytic conductor $10.463$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 384.e (of order $$2$$, degree $$1$$, minimal)
## Newform invariants
Self dual: no Analytic conductor: $$10.4632421514$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ Defining polynomial: $$x^{8} + 18 x^{6} + 99 x^{4} + 170 x^{2} + 81$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{10}\cdot 3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{7}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + \beta_{1} q^{3} + \beta_{3} q^{5} + ( 1 + \beta_{2} ) q^{7} + ( \beta_{2} + \beta_{7} ) q^{9} +O(q^{10})$$ $$q + \beta_{1} q^{3} + \beta_{3} q^{5} + ( 1 + \beta_{2} ) q^{7} + ( \beta_{2} + \beta_{7} ) q^{9} + ( \beta_{4} + \beta_{5} - \beta_{7} ) q^{11} + ( 1 - \beta_{1} - \beta_{5} + \beta_{6} - \beta_{7} ) q^{13} + ( 2 + \beta_{1} - \beta_{2} + 2 \beta_{3} + \beta_{4} - \beta_{5} + \beta_{6} - \beta_{7} ) q^{15} + ( 1 - 3 \beta_{1} - 2 \beta_{3} - 2 \beta_{4} - \beta_{5} - \beta_{6} + \beta_{7} ) q^{17} + ( -3 + \beta_{1} - 2 \beta_{2} - 2 \beta_{5} + \beta_{6} - 2 \beta_{7} ) q^{19} + ( 1 + \beta_{1} + 2 \beta_{2} + \beta_{3} + 2 \beta_{4} + \beta_{5} - \beta_{6} - \beta_{7} ) q^{21} + ( 4 \beta_{3} + 2 \beta_{5} - 2 \beta_{7} ) q^{23} + ( -2 - 5 \beta_{1} - 2 \beta_{2} + \beta_{5} + \beta_{6} + \beta_{7} ) q^{25} + ( -6 + \beta_{1} + 2 \beta_{2} + 4 \beta_{3} - \beta_{4} + \beta_{5} - \beta_{7} ) q^{27} + ( -2 + 6 \beta_{1} + 3 \beta_{3} + 2 \beta_{5} + 2 \beta_{6} - 2 \beta_{7} ) q^{29} + ( -9 + 4 \beta_{1} - \beta_{2} - 2 \beta_{5} - 2 \beta_{7} ) q^{31} + ( -\beta_{1} - \beta_{2} - 2 \beta_{3} + 2 \beta_{4} + \beta_{5} - 3 \beta_{6} + 2 \beta_{7} ) q^{33} + ( -1 + 3 \beta_{1} + 8 \beta_{3} + 5 \beta_{4} + \beta_{5} + \beta_{6} - \beta_{7} ) q^{35} + ( -1 + 9 \beta_{1} - 4 \beta_{2} - 3 \beta_{5} - \beta_{6} - 3 \beta_{7} ) q^{37} + ( -13 + \beta_{1} - 2 \beta_{3} + 5 \beta_{4} + \beta_{5} + \beta_{6} - 3 \beta_{7} ) q^{39} + ( -2 + 6 \beta_{1} - 6 \beta_{3} - 6 \beta_{4} - 2 \beta_{5} + 2 \beta_{6} + 2 \beta_{7} ) q^{41} + ( 17 + \beta_{1} + 2 \beta_{2} - 2 \beta_{5} + \beta_{6} - 2 \beta_{7} ) q^{43} + ( -10 + 4 \beta_{1} - 2 \beta_{2} + 3 \beta_{3} + 6 \beta_{4} + 4 \beta_{6} - 2 \beta_{7} ) q^{45} + ( -2 + 6 \beta_{1} - 2 \beta_{4} + 2 \beta_{5} + 2 \beta_{6} - 2 \beta_{7} ) q^{47} + ( 2 + 9 \beta_{1} + 2 \beta_{2} + 3 \beta_{5} - 5 \beta_{6} + 3 \beta_{7} ) q^{49} + ( 23 - \beta_{1} - 4 \beta_{3} - 5 \beta_{4} - \beta_{5} + \beta_{6} - 3 \beta_{7} ) q^{51} + ( 4 - 12 \beta_{1} + \beta_{3} - 4 \beta_{4} + 4 \beta_{5} - 4 \beta_{6} - 4 \beta_{7} ) q^{53} + ( 22 + 4 \beta_{1} - 2 \beta_{2} - 2 \beta_{5} - 2 \beta_{7} ) q^{55} + ( -1 - 4 \beta_{1} - \beta_{2} - 6 \beta_{3} + 6 \beta_{4} + 4 \beta_{6} - \beta_{7} ) q^{57} + ( -1 + 3 \beta_{1} + 8 \beta_{4} + \beta_{6} ) q^{59} + ( -13 - 11 \beta_{1} + 4 \beta_{2} + \beta_{5} + 3 \beta_{6} + \beta_{7} ) q^{61} + ( 31 + 3 \beta_{2} + 4 \beta_{3} + 8 \beta_{4} + 4 \beta_{5} - 4 \beta_{6} ) q^{63} + ( 4 - 12 \beta_{1} + 2 \beta_{3} - 6 \beta_{4} - 4 \beta_{6} ) q^{65} + ( -37 + \beta_{1} + 8 \beta_{2} + 4 \beta_{5} - 3 \beta_{6} + 4 \beta_{7} ) q^{67} + ( 8 + 2 \beta_{1} - 6 \beta_{2} + 6 \beta_{4} - 6 \beta_{5} - 2 \beta_{6} ) q^{69} + ( -2 + 6 \beta_{1} + 4 \beta_{3} - 10 \beta_{4} - 4 \beta_{5} + 2 \beta_{6} + 4 \beta_{7} ) q^{71} + ( -2 - 12 \beta_{1} + 4 \beta_{2} + 4 \beta_{6} ) q^{73} + ( -43 - 10 \beta_{2} - 9 \beta_{4} - 3 \beta_{5} + \beta_{6} - \beta_{7} ) q^{75} + ( -4 + 12 \beta_{1} - 2 \beta_{3} - 12 \beta_{4} - 4 \beta_{5} + 4 \beta_{6} + 4 \beta_{7} ) q^{77} + ( -41 - 16 \beta_{1} + 3 \beta_{2} + 2 \beta_{5} + 4 \beta_{6} + 2 \beta_{7} ) q^{79} + ( 10 - 3 \beta_{1} + 4 \beta_{3} + 8 \beta_{4} - 5 \beta_{5} - \beta_{6} - 3 \beta_{7} ) q^{81} + ( 2 - 6 \beta_{1} - 8 \beta_{3} + 5 \beta_{4} + \beta_{5} - 2 \beta_{6} - \beta_{7} ) q^{83} + ( 16 + 8 \beta_{1} + 16 \beta_{2} + 8 \beta_{5} - 8 \beta_{6} + 8 \beta_{7} ) q^{85} + ( -48 + \beta_{1} + \beta_{2} - 2 \beta_{3} + 5 \beta_{4} - 5 \beta_{5} - 3 \beta_{6} + 7 \beta_{7} ) q^{87} + ( -5 + 15 \beta_{1} + 16 \beta_{3} - 8 \beta_{4} + \beta_{5} + 5 \beta_{6} - \beta_{7} ) q^{89} + ( 40 + 2 \beta_{1} - 10 \beta_{2} + 2 \beta_{5} - 2 \beta_{6} + 2 \beta_{7} ) q^{91} + ( 27 - 11 \beta_{1} + 4 \beta_{2} - 5 \beta_{3} + 8 \beta_{4} + \beta_{5} + 3 \beta_{6} + \beta_{7} ) q^{93} + ( 8 - 24 \beta_{1} - 4 \beta_{3} - 16 \beta_{4} - 2 \beta_{5} - 8 \beta_{6} + 2 \beta_{7} ) q^{95} + ( 5 + 13 \beta_{1} - 2 \beta_{2} - 5 \beta_{5} - \beta_{6} - 5 \beta_{7} ) q^{97} + ( 55 - 3 \beta_{1} - 2 \beta_{2} + 4 \beta_{3} - 10 \beta_{4} + 4 \beta_{5} - \beta_{6} + 4 \beta_{7} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{3} + 8q^{7} + O(q^{10})$$ $$8q + 4q^{3} + 8q^{7} + 16q^{15} - 24q^{19} + 16q^{21} - 40q^{25} - 44q^{27} - 56q^{31} + 8q^{33} + 32q^{37} - 104q^{39} + 136q^{43} - 80q^{45} + 72q^{49} + 176q^{51} + 192q^{55} - 40q^{57} - 160q^{61} + 264q^{63} - 280q^{67} + 80q^{69} - 80q^{73} - 348q^{75} - 408q^{79} + 72q^{81} + 192q^{85} - 368q^{87} + 336q^{91} + 160q^{93} + 96q^{97} + 432q^{99} + O(q^{100})$$
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{8} + 18 x^{6} + 99 x^{4} + 170 x^{2} + 81$$:
$$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$($$$$\nu^{6} + 16 \nu^{4} + 70 \nu^{2} + 6 \nu + 63$$$$)/6$$ $$\beta_{2}$$ $$=$$ $$\nu^{4} + 11 \nu^{2} + 18$$ $$\beta_{3}$$ $$=$$ $$($$$$2 \nu^{7} + 33 \nu^{5} + 159 \nu^{3} + 193 \nu$$$$)/9$$ $$\beta_{4}$$ $$=$$ $$($$$$2 \nu^{7} + 36 \nu^{5} + 180 \nu^{3} + 178 \nu$$$$)/9$$ $$\beta_{5}$$ $$=$$ $$($$$$-\nu^{7} - 16 \nu^{5} - 3 \nu^{4} - 70 \nu^{3} - 27 \nu^{2} - 57 \nu - 27$$$$)/3$$ $$\beta_{6}$$ $$=$$ $$($$$$-\nu^{6} - 16 \nu^{4} - 70 \nu^{2} + 6 \nu - 61$$$$)/2$$ $$\beta_{7}$$ $$=$$ $$($$$$\nu^{7} + 16 \nu^{5} - 3 \nu^{4} + 70 \nu^{3} - 27 \nu^{2} + 63 \nu - 27$$$$)/3$$
$$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$($$$$\beta_{6} + 3 \beta_{1} - 1$$$$)/6$$ $$\nu^{2}$$ $$=$$ $$($$$$3 \beta_{7} - \beta_{6} + 3 \beta_{5} + 6 \beta_{2} - 3 \beta_{1} - 53$$$$)/12$$ $$\nu^{3}$$ $$=$$ $$($$$$-3 \beta_{7} - 13 \beta_{6} + 3 \beta_{5} - 3 \beta_{4} + 12 \beta_{3} - 39 \beta_{1} + 13$$$$)/12$$ $$\nu^{4}$$ $$=$$ $$($$$$-33 \beta_{7} + 11 \beta_{6} - 33 \beta_{5} - 54 \beta_{2} + 33 \beta_{1} + 367$$$$)/12$$ $$\nu^{5}$$ $$=$$ $$($$$$21 \beta_{7} + 101 \beta_{6} - 21 \beta_{5} + 57 \beta_{4} - 120 \beta_{3} + 303 \beta_{1} - 101$$$$)/12$$ $$\nu^{6}$$ $$=$$ $$($$$$159 \beta_{7} - 59 \beta_{6} + 159 \beta_{5} + 222 \beta_{2} - 141 \beta_{1} - 1453$$$$)/6$$ $$\nu^{7}$$ $$=$$ $$($$$$-54 \beta_{7} - 413 \beta_{6} + 54 \beta_{5} - 351 \beta_{4} + 540 \beta_{3} - 1239 \beta_{1} + 413$$$$)/6$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$$.
$$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
257.1
− 1.32750i 1.32750i − 2.98985i 2.98985i − 2.55118i 2.55118i − 0.888828i 0.888828i
0 −2.69031 1.32750i 0 0.640013i 0 2.72077 0 5.47550 + 7.14275i 0
257.2 0 −2.69031 + 1.32750i 0 0.640013i 0 2.72077 0 5.47550 7.14275i 0
257.3 0 0.246559 2.98985i 0 6.63641i 0 0.578158 0 −8.87842 1.47435i 0
257.4 0 0.246559 + 2.98985i 0 6.63641i 0 0.578158 0 −8.87842 + 1.47435i 0
257.5 0 1.57844 2.55118i 0 1.31534i 0 −10.2329 0 −4.01705 8.05378i 0
257.6 0 1.57844 + 2.55118i 0 1.31534i 0 −10.2329 0 −4.01705 + 8.05378i 0
257.7 0 2.86531 0.888828i 0 8.59176i 0 10.9340 0 7.41997 5.09353i 0
257.8 0 2.86531 + 0.888828i 0 8.59176i 0 10.9340 0 7.41997 + 5.09353i 0
$$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 257.8 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 384.3.e.d yes 8
3.b odd 2 1 inner 384.3.e.d yes 8
4.b odd 2 1 384.3.e.a 8
8.b even 2 1 384.3.e.b yes 8
8.d odd 2 1 384.3.e.c yes 8
12.b even 2 1 384.3.e.a 8
16.e even 4 2 768.3.h.g 16
16.f odd 4 2 768.3.h.h 16
24.f even 2 1 384.3.e.c yes 8
24.h odd 2 1 384.3.e.b yes 8
48.i odd 4 2 768.3.h.g 16
48.k even 4 2 768.3.h.h 16
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
384.3.e.a 8 4.b odd 2 1
384.3.e.a 8 12.b even 2 1
384.3.e.b yes 8 8.b even 2 1
384.3.e.b yes 8 24.h odd 2 1
384.3.e.c yes 8 8.d odd 2 1
384.3.e.c yes 8 24.f even 2 1
384.3.e.d yes 8 1.a even 1 1 trivial
384.3.e.d yes 8 3.b odd 2 1 inner
768.3.h.g 16 16.e even 4 2
768.3.h.g 16 48.i odd 4 2
768.3.h.h 16 16.f odd 4 2
768.3.h.h 16 48.k even 4 2
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{3}^{\mathrm{new}}(384, [\chi])$$:
$$T_{7}^{4} - 4 T_{7}^{3} - 108 T_{7}^{2} + 368 T_{7} - 176$$ $$T_{13}^{4} - 360 T_{13}^{2} + 256 T_{13} + 7824$$
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T^{8}$$
$3$ $$6561 - 2916 T + 648 T^{2} + 36 T^{3} - 66 T^{4} + 4 T^{5} + 8 T^{6} - 4 T^{7} + T^{8}$$
$5$ $$2304 + 7040 T^{2} + 3504 T^{4} + 120 T^{6} + T^{8}$$
$7$ $$( -176 + 368 T - 108 T^{2} - 4 T^{3} + T^{4} )^{2}$$
$11$ $$20214016 + 3167360 T^{2} + 69552 T^{4} + 488 T^{6} + T^{8}$$
$13$ $$( 7824 + 256 T - 360 T^{2} + T^{4} )^{2}$$
$17$ $$991494144 + 60416000 T^{2} + 480000 T^{4} + 1248 T^{6} + T^{8}$$
$19$ $$( -98352 - 17584 T - 780 T^{2} + 12 T^{3} + T^{4} )^{2}$$
$23$ $$48132849664 + 478846976 T^{2} + 1671936 T^{4} + 2336 T^{6} + T^{8}$$
$29$ $$78767790336 + 896411520 T^{2} + 3074736 T^{4} + 3704 T^{6} + T^{8}$$
$31$ $$( 50256 - 17520 T - 828 T^{2} + 28 T^{3} + T^{4} )^{2}$$
$37$ $$( -488432 + 90944 T - 3528 T^{2} - 16 T^{3} + T^{4} )^{2}$$
$41$ $$3916979306496 + 31405105152 T^{2} + 34597632 T^{4} + 10976 T^{6} + T^{8}$$
$43$ $$( -917424 + 92496 T - 588 T^{2} - 68 T^{3} + T^{4} )^{2}$$
$47$ $$424144797696 + 3025141760 T^{2} + 6905856 T^{4} + 5376 T^{6} + T^{8}$$
$53$ $$870911869798656 + 673606710144 T^{2} + 188831664 T^{4} + 22776 T^{6} + T^{8}$$
$59$ $$12745356964096 + 31548679808 T^{2} + 26455344 T^{4} + 8840 T^{6} + T^{8}$$
$61$ $$( -4584688 - 262208 T - 2184 T^{2} + 80 T^{3} + T^{4} )^{2}$$
$67$ $$( -6784816 - 335312 T + 900 T^{2} + 140 T^{3} + T^{4} )^{2}$$
$71$ $$1706597351424 + 36124434432 T^{2} + 77642496 T^{4} + 22688 T^{6} + T^{8}$$
$73$ $$( -899312 - 192608 T - 5544 T^{2} + 40 T^{3} + T^{4} )^{2}$$
$79$ $$( -38762928 - 676400 T + 7524 T^{2} + 204 T^{3} + T^{4} )^{2}$$
$83$ $$56638749360384 + 102766133376 T^{2} + 59473584 T^{4} + 13416 T^{6} + T^{8}$$
$89$ $$9213001971859456 + 4688908992512 T^{2} + 730308096 T^{4} + 45632 T^{6} + T^{8}$$
$97$ $$( 8416272 + 274112 T - 8136 T^{2} - 48 T^{3} + T^{4} )^{2}$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9950103163719177, "perplexity": 5427.310687921911}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152168.38/warc/CC-MAIN-20210727010203-20210727040203-00262.warc.gz"} |
https://www.physicsforums.com/threads/wave-equation-dalembert-solution-semi-infinite-string-with-a-fixed-end.985812/ | # Wave Equation: d'Alembert solution -- semi-infinite string with a fixed end
• Start date
• #1
201
23
## Homework Statement:
At $t = 0$ the string is released. Let $y(t,x) = f(x - ct) + g(x - ct)$. Obtain $f(u)$ and $g(v)$ for u > 0 and v > 0 using the initial condition.
## Relevant Equations:
d'Alembert solution to the wave equation
Hi,
I was trying to get some practice with the wave equation and am struggling to solve the problem below. I am unsure of how to proceed in this situation.
My attempt:
So we are told that the string is held at rest, so we only need to think about the displacement conditions for the wave equation solution. If we are using the given expression, then f will be the 'forward' (+ ve $x$) travelling wave and g will be the 'backward' (-ve $x$) travelling wave.
I would turn the given function $$H(x) = \begin{cases} -h(-x), & -2L \leq x \lt 0 \\ h(x), & 0 \leq x \lt 2L \\ (periodic), & otherwise \end{cases}$$
(where $h(x)$ is the triangular function shown - I could have explicitly written out the exact function, but just after the method for the moment)
(EDIT: was I correct to make it periodic?)
Then, we can use the solution to write: $y(t,x) = \frac{1}{2} \left( H(x + ct) + H(x - ct) \right)$ (replacing f and g with our defined function). Is that correct up to that point?
Some specific questions I have are:
- how do we deal with the fixed boundary condition? - I have just tried to create the odd periodic extension of the initial condition so that the zero displacement is satisfied at $x = 0$
- in general, do I start the two oppositely travelling waves from the same place on the string
- Perhaps related for the boundary condition, but how do I include the reflection that will take place? - I presume that we just allow our two waves to pass over one another so that the -ve part of the forward wave superposes with the +ve part of the backwards wave. After that, our backwards wave solution will be 'beyond the boundary' so we won't need to consider it any more?
Related Calculus and Beyond Homework Help News on Phys.org
• #2
LCKurtz
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You want to consider the odd extension of the function. Not the odd periodic extension. So your initial problem looks like an infinite string with initial displacement the odd reflection of the triangle and zero outside of $[-2L,2L]$ and released from rest. Solve that infinite string problem and just look at the part of the solution where $x>0$. By the way, +ve and -ve are not words.
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1K | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9412978887557983, "perplexity": 627.9328307330234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497171.9/warc/CC-MAIN-20200330150913-20200330180913-00121.warc.gz"} |
http://furthermathstutor.co.uk/m1/moments.html | # Moments
## Introduction
Try pushing a door with your hand on the middle of the door. Then try pushing the same door with your hand on the handle at the far end of the door.
The second time was easier right? That's because you applied more moment force about the door hinge. Moment force, or torque, is the tendency of a force to rotate an object about an axis.
Specifically, if we apply a force $F$ about some pivot point, then
$$M = Fd$$
Where $M$ is the moment force in Nm (Newton metres) due to the force $F$ in N and $d$ is the shortest distance to the line of action of the force in metres.
### Example
Q) Find the moment force about the pivot point $P$ due to the 5N force in the diagram below.
A) We have conveniently been given the shortest distance to the line of action of the 5N force. So
$$M = 5 \times 2.5 = 12.5 \textrm{Nm}$$
### Example
Q) Find the moment force about the pivot point $P$ due to the 10N force in the diagram below.
A) We know the force but we need to know the shortest distance to the line of action of the force.
$$d = 4\sin(40) = 2.57 \textrm{m} \left(\textrm{3.s.f.}\right)$$
$$\therefore M = 10 \times 2.57 = 25.7 \textrm{Nm}\left(\textrm{3.s.f.}\right)$$
## Equilibrium of a rigid body
### Resolving moments
For there to be equilbrium about a pivot point we need the sum of the moments acting around it to be zero.
We resolve moments about a pivot point just like we resolve forces. The convention is anti-clockwise positive, meaning moments acting anti-clockwise are taken as positive and clockwise moments are negative.
When we resolve moments about a pivot point we take moments about that point, ignoring any forces that act directly through the point itself.
### Example
Q) Is the following system in rotational equilibrium? Find the resultant of all the moment forces about pivot point $P$.
A) Yes because $\left(10 \times 6\right) - \left(5 \times 12\right) = 0$.
### Bringing it all together
In M1 exam questions you will need to find the equilibrium conditions of a rigid body. That means you need to make sure the body is in static equilbrium and rotational equilbrium, which can be thought of as horizontal or static equilibrium for most cases in M1.
That means you need the sum of the forces acting in two dimension to equal zero, and the sum of the moments about all the relevant points to equal zero.
$$\sum F_x = 0$$
$$\sum F_y = 0$$
$$\sum M = 0$$
You will need to take certain extra things into account. If a rigid body sits on supports, then Newton's third law states that each support will exert a reaction force back upwards perpendicular to the length of the body.
Additionally, if you are told the mass of the body itself, you will need to take that into account. In M1 the body is almost always modelled as a horizontal straight line, so it suffices to draw the weight of the body vertically downwards through the centre of the body.
### Example
Q) A 10kg beam of length 3m sits on two supports at either of its ends. Find the reaction forces from both of the supports.
A) We're told that the beam has mass 10kg, so its weight is $10g \textrm{N}$, which we model as going vertically downwards through the centre of the beam. Label the left and right supports $A$ and $B$ respectively, and draw on the reaction forces at either support too.
There are no horizontal forces so we only need look at vertical equilibrium of forces.
$$R_A + R_B = 10g$$
We also need to take moments about one of the supports to ensure rotational equilibrium. Let's pick $A$.
$$\left(R_B \times 3\right) - \left(10g\times 1.5\right) = 0$$
$$\therefore R_B = \frac{10g \times 1.5}{3} = 5g = 49 \textrm{N}$$
From vertical equilibrium we know that $R_A + R_B = 10g$ so we can find $R_A$
$$R_A = 10g - 5g = 5g = 49 \textrm{N}$$
### Example
Q) A 5kg rod of length 10m is held in horizontal equilibrium by a cable at end $A$ and a support at end $B$. A particle of mass 5kg is placed $x$ metres away from end $A$. Given that the tension in the cable at $A$ is twice the magnitude of the reaction at support $B$, find the value of $x$.
A) The rod has mass 5kg so its weight is $5g \textrm{N}$, which acts through the centre of the rod. The weight of the particle is also $5g \textrm{N}$. Label the tension in the cable as $T$ and the reaction at $B$ as $R$. Draw on all of the forces.
Taking vertical equilibrium of forces
$$T + R - 5g - 5g = 0$$
$$\therefore T+R = 10g$$
We were told that $T = 2R$ so
$$3R = 10g \Rightarrow R = \frac{10}{3}g \textrm{ and } T = \frac{20}{3}g$$
Now take moments about point $A$
$$10R - 5gx - \left(5g \times 5\right) = 0$$
Subbing in $R = \frac{10}{3}g$ and solving for $x$
$$\left(10\times \frac{10}{3}g\right) - 5gx - 25g = 0$$
$$5x = \frac{100}{3} - 25$$
$$\therefore x = \frac{5}{3} = 1.67 \textrm{m} \left(\textrm{3.s.f.}\right)$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8996359705924988, "perplexity": 355.4107525517957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948597585.99/warc/CC-MAIN-20171217210620-20171217232620-00042.warc.gz"} |
https://rd.springer.com/article/10.1007/s40009-018-0700-8 | , Volume 42, Issue 2, pp 123–130
# On a Complex Randers Space
• Sweta Kumari
• P. N. Pandey
Short Communication
## Abstract
In the present paper, a complex Randers space with the metric $$F = \alpha + \varepsilon \left| \beta \right| + k\frac{{\left| \beta \right|^{2} }}{\alpha },\varepsilon ,k \ne 0$$ is introduced and expressions for fundamental metric tensor, angular metric tensor, Chern–Finsler connection coefficients and curvature are obtained.
## Keywords
Finsler space Randers space Complex Randers space Chern–Finsler connection coefficients
53B40 53C56
## References
1. 1.
Finsler P (1951) Uber Kurven and flacken in Allgemeinen Raumen (dissertation Gottingen 1918). Springer, Berlin
2. 2.
Rizza G (1963) Strutture di Finsler di Tipo quasi hermitiano. Riv Mat Univ Parma 4:83–106
3. 3.
Kobayashi S (1967) Distance, holomorphic mappings and the Schwarz lemma. J Math Soc Jpn 19(4):481–485
4. 4.
Abate M, Patrizio G (1994) Finsler metrics: a global approach with applications to geometric function theory. Springer, Berlin
5. 5.
Shen Z, Yildirim GC (2008) On a class of projectively Flat metric with constant Flag curvature. Can J Math 60:443–456
6. 6.
Aldea N, Munteanu G (2009) On complex Finsler spaces with Randers metric. J Korean Math Soc 46(5):949–966
7. 7.
Bao D, Chern SS, Shen Z (2000) An introduction to Riemann–Finsler geometry. Graduate Texts in Mathematics 200. Springer, New YorkGoogle Scholar
8. 8.
Bao D, Robles C, Shen Z (2004) Zermelo navigation on Riemannian manifolds. J Differ Geom 66(3):377–435
9. 9.
Yasuda H, Shimada H (1977) On Randers spaces of scalar curvature. Rep Math Phys 11(3):347–360
10. 10.
Matsumoto M (1989) Randers spaces of constant curvature. Rep Math Phys 28(2):249–261
11. 11.
Abate M, Patrizio A (1994) Finsler metric—a global approach with applications to geometric function theory, Lecture Notes in Mathematics, vol 1591. Springer, Berlin
12. 12.
Aikou T (2003) Projective flatness of complex Finsler metrics. Publ Math Debrecen 63(3):343–362
13. 13.
Munteanu G (2004) Complex spaces in Finsler, Lagrange and Hamilton geometries. Fundamental Theories of Physics. Kluwer Academic Publishers, Dordrecht
14. 14.
Spir A (2001) The structure equations of a complex Finsler manifold. Asian J Math 5(2):291–326
15. 15.
Aldea N, Munteanu G (2006) (α, β)-complex Finsler metrices. In: Proceedings of the 4th International Colloquium “Mathematics in Engineering and National Physics”, Burcharet, Romania, pp 1–6Google Scholar
16. 16.
Aldea N, Munteanu G (2006) On the geometry of Complex Randers space. In: Proceedings of the 14th Nat. Sem. On Finsler, Lagrange and Hamilton spaces, Brasov, pp 1–8Google Scholar | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9793707728385925, "perplexity": 15881.302551905754}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998376.42/warc/CC-MAIN-20190617043021-20190617065021-00274.warc.gz"} |
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## godfreysown 2 years ago How do I express the following in terms of a function of x: sin(x)=e^(-x) ? Delete Cancel Submit
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1. akash_809
• 2 years ago
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f(x)=sinx-e^(-x)
2. amistre64
• 2 years ago
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im not sure if that function expresses the equality between them, so you might need to say something regarding the roots of it; when f(x)=0
3. akash_809
• 2 years ago
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@amistre64 but he posted it as an equality and i think if we draw there graphs we will see there there will be n number of roots.So roots won't be meaningfull
4. amistre64
• 2 years ago
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im not sure one way over the other :) just a gut feeling
5. akash_809
• 2 years ago
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@godfreysown yes equate it to zero
6. godfreysown
• 2 years ago
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so why is it that this simple manipulation turns an equation into a function of x? (PS: I've attached a graph of your f(x) )
##### 1 Attachment
7. amistre64
• 2 years ago
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a relation is roughly defined as any interaction or change in output resulting from input $g(a) = {b_1,b_2,b_3,...}$there need not be any unique answer. This is not very useful when we are trying to make predictions about how something will react. a function is a special kind of relation and is defined as an equation that has only one output value (its unique) for any given input value. $f(a) = b$as such, we can use these to determine past and future, as well as present outputs from a system that can be modeled by functions
8. amistre64
• 2 years ago
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if 2 things are equal; then subtracting one from the other leaves us with nothing. To determine when: sin(x)=e^(-x) , we can subtract one from the other and determine at what values of "x" the function equals zero. also, since e^(-x) never equates to zero on its own; we can divide it out instead$f(x)=\frac{sin(x)}{e^{-x}}=e^{x}~sin(x)=1$ $f(x)=e^{x}~sin(x)-1 =0$
9. akash_809
• 2 years ago
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@amistre64 haven't u complicated the equation, i would always prefer to solve f(x)=sinx-e^(-x) rather than f(x)e^x sinx-1
10. amistre64
• 2 years ago
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it asked for a function; complication wasnt specified :)
11. akash_809
• 2 years ago
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@amistre64 he he nice one :), but tasks of using maths is to always make things simple, isn't it i guessed it that way or may be is is not
12. amistre64
• 2 years ago
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most maths are done on computers these days, and a computer has no concept of simple. What might relate is "number" of computations required in which you would want to streamline it to reduce the number of steps that a computer would have to take for it.
13. amistre64
• 2 years ago
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ive got no idea which function between ours would be "simpler" for a computer tho
14. akash_809
• 2 years ago
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@amistre64 agreed :) , i think you are a mod , i have mailed at [email protected] to delete my account , can u help in this.Also i have posted in openstudy feedback
15. amistre64
• 2 years ago
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i dont have the abilities to alter accounts.
16. amistre64
• 2 years ago
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..and i dont have any pull in that area either ... thats under the operations of the administrators
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9973574876785278, "perplexity": 2829.067231083064}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988051.33/warc/CC-MAIN-20150728002308-00068-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://mathhelpforum.com/statistics/191751-binomial-conditional-probability-print.html | # Binomial conditional probability.
• November 12th 2011, 09:31 PM
mtingt
Binomial conditional probability.
A fair coin is tossed 5 times. What is the probability of obtaining exactly 2 heads if it is known that at least 1 head appeared?
• November 12th 2011, 09:41 PM
TKHunny
Re: binomial probability help please
What is the probability of exactly one (1) "heads" in four tosses? Are you sure it's trickier than that? If so, why?
• November 12th 2011, 09:44 PM
mtingt
Re: binomial probability help please
what do you mean?
• November 13th 2011, 11:49 AM
mr fantastic
Re: Binomial conditional probability.
Quote:
Originally Posted by mtingt
A fair coin is tossed 5 times. What is the probability of obtaining exactly 2 heads if it is known that at least 1 head appeared?
Let X be the random variable 'Number of heads'.
Calculate $Pr(X = 2 | X \geq 1)$ using the usual formula for conditional probability. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9386950731277466, "perplexity": 872.5195468175042}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163051789/warc/CC-MAIN-20131204131731-00069-ip-10-33-133-15.ec2.internal.warc.gz"} |
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Jan 17 comment Question about a lemma on continuity @Arturo Sorry. That was a translation mistake. In German, one says "stetig" to say "continuous". stetig and steady are false friends... Jan 8 comment Given the cartesian coordinates of four points, how to calculate the interection of two lines they form? @J.M. Oh yeah. That looks good. THank you! BTW, is there a solution that use the $r,\vartheta$ representation instead? Jan 8 comment Given the cartesian coordinates of four points, how to calculate the interection of two lines they form? @J.M. Of course. This possibility is ruled out. Dec 2 comment Defining division by zero @picakhu You are going to run into problems when calculating limits. Just consider $\lim_{n\to0}\frac{2n}n$. Using your method, one gets $\frac{\infty_0}{\infty_0}=1$, while one gets $\frac21=2$ using the definition of limits. Nov 13 comment How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? @Max ${5\over3}\to{15\over9}$ Nov 13 comment How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? BTw, you can use LaTeX makeup by starting with an \$and ending with another \$, for instance $\sqrt{\frac{5}{3}}$ becomes $\sqrt{\frac{5}{3}}$. Nov 11 comment A lemma of convergence @André: yes. We already proved that. Nov 8 comment The Mathematics of Tetris That's an interesting question! I don't see any special reason for this, though. Nov 1 comment Prove the identity $\sum\limits_{s=0}^{\infty}{p+s \choose s}{2p+m \choose 2p+2s} = 2^{m-1} \frac{2p+m}{m}{m+p-1 \choose p}$ Hm... I recall that or a similar identity from Concrete Mathematics... maybe I find it again. Oct 24 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? @Gortaur: Well, that's not that difficult. You just need to find a geometrical interpretation of sine and cosine. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Sorry for that. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Thank you very much. I know that proverb, but I really wasn't able to find that out on my own. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Hm... But now, how to prove that $\cos$ is continuous? (Read the question!) Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? Okay. I had a look at the link Yuval provided. That proof works. Anyway, thanks for the effort. Oct 23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? But how to prove that \$\sin x | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9696766138076782, "perplexity": 702.9512126496597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645323734.78/warc/CC-MAIN-20150827031523-00224-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://marcosammon.com/2016/06/24/OG_Model_1.html | First year economics and finance PhD students have Fridays devoted to “tutorials” - where a particular topic is covered in detail. These posts are similar, in that they review a topic mentioned in a previous post.
# Overlapping Generations (OG)
In the many macro models (neoclassical, new Keynesian, etc.), agents are infinitely lived. As mentioned in the post on Tirole(1982), “bubbles” cannot arise in these models when agents fully optimize. One way to get the myopic behavior needed for bubbles is to have finitely lived agents.
In an overlapping generations model, consumers live for two periods. At any given time $t$, there are two generations: those born at $t-1$ (the old) and those born at $t$ (the young). This post explains how to solve for fundamental equilibria i.e. equilibria without bubbles.
The discussion below is based heavily on Larry Christiano’s Macroeconomics class.
# The Setup
First, some notation. Let $c_t^t$ is period $t$ consumption of those born at $t$ (consumption while young), while $c_{t+1}^t$ is the period $t+1$ consumption of those born at $t$ (consumption while old).
Let $n_t$ denote labor supplied at $t$. To simplify things, suppose there is a unit mass of young and old at each $t$, and both supply $n=1$ units of labor (no disutility of labor).
Let $r_t$ denote the rental rate of capital, and $w_t$ denote the wage rate.
Finally, suppose there is an intrinsically worthless asset (it pays no dividends, cannot be used for production, etc.), $a_t$ which is sold at price $P_t$.
Putting this together we get the budget constraint for the young is: $$c_t^t+(1-\delta)k_t + i_t + P_t a_t \leq w_t$$ Note that the young must buy all the capital from the old every period.
The budget constraint for the old is: $$c_{t+1}^t \leq r_{t+1} k_{t+1} + (1-\delta)k_{t+1} + w_{t+1} + P_{t+1}$$ In any fundamental equilibrium, there are no bubbles, so $P_t=0$ for all $t$. Using this, along with the fact that $k_{t+1}=i_t + (1-\delta) k_t$ we can simplify the budget constraints: $$c_t^t+k_{t+1} \leq w_t$$ $$c_{t+1}^t \leq r_{t+1} k_{t+1} + (1-\delta)k_{t+1} + w_{t+1}$$
# Consumer Optimization
The old have no incentive to save, so they consume as much as possible in the second period of their life. Assume monotonic preferences so we can get rid of the $\leq$. Solve first period budget constraint (BC) for $k_{t+1}$: $$k_{t+1}=w_t - c_t$$ Substitute this into the second period budget constraint to eliminate $k_{t+1}$: $$c_{t+1}=(r_{t+1}+1-\delta)(w_t-c_t^t)+w_{t+1}$$ We can rearrange this to get the lifetime budget constraint (BC), and formalize the period $t$-born consumer’s problem: $$max_{c_t^t, c_{t+1}^t} u(c_t^t) + \beta u(c_{t+1}^t)$$ such that the BC holds: $$c_t^t + \frac{c_{t+1}^t}{r_{t+1}+1-\delta} = w_t + \frac{w_{t+1}}{r_{t+1}+1-\delta}$$ Taking first order conditions, we get the intertemporal Euler equation: $$u’(c_t^t)=\beta u’(c_{t+1}^t)(r_{t+1} + 1 - \delta)$$ Suppose $u(\cdot)=log(\cdot)$. Then we can get a nice expression for optimal consumption: $$c_{t+1}^t = \beta c_t^t (r_{t+1} + 1 - \delta)$$ Substituting this into Equation 6, we can get a closed form solution for period $t$ consumption: $$c_t^t=\frac{1}{1+\beta}\left[ w_t + \frac{w_{t+1}}{r_{t+1}+1-\delta} \right]$$
# Firm Optimization
Suppose we have the following, homogeneous of degree one, production function ($\rho\in(0,1)$): $$f(k,n)=b[\alpha k^\rho + (1-\alpha) n^\rho]^{\frac{1}{\rho}}$$ Define: $$g(k,n)=[\alpha k^\rho + (1-\alpha) n^\rho]^{\frac{1}{\rho}}$$ so $f(k,n)=b \cdot g(k,n)$ (this will be useful later).
Now set up the firms cost minimization problem (minimize cost for a given amount of output, $y$): $$min_{k,n} rk+wn$$ such that: $$y \leq b g(k,n)$$ First order conditions give us $w_t$ and $r_t$: $$MP_n(t) = b (1-\alpha) \left(\frac{g}{n} \right)^{(1-\rho)} = w_t$$ $$MP_k(t) = b \alpha \left(\frac{g}{k} \right)^{(1-\rho)} = r_t$$ where $MP_n(t)$ is the marginal product of labor at $t$, and $MP_k(t)$ is the the marginal product of capital. Now we see how $g$ is useful, allowing us to get rid of fractions in the exponent: $\frac{1}{\rho}-1 = \frac{1-\rho}{\rho} = \Big( \frac{1}{\rho} \Big)^{1-\rho}$
# Equilibrium
Having set up the consumer and firm problems, we are ready to define an equilibrium:
A sequence of markets equilibrium is a set of prices $\{r_t,w_t\}_{t=1}^\infty$ and allocations $\{c_t^t, c_{t+1}^t, i_t, k_{t+1}\}_{t=1}^\infty$ such that for all $t$:
1) Consumer’s problem is solved
2) Firm’s problem is solved
3) Aggregate resource constraint (RC) is satisfied
To get the aggregate resource constraint add up the budget constraints of the young and the old: $$c_t^{t-1}+c_t^t + i_t + (1-\delta)k_t = 2 w_t + r_t k_t + (1-\delta)k_t$$ Eliminating $(1-\delta)k_t$ from both sides, and using our expressions for $w_t$ and $r_t$: $$c_t^{t-1}+c_t^t + i_t = 2 MP_n(t) + k_t MP_k(t)$$ finally use the fact that $g$ is homogeneous degree one to get RC: $$c_t^t + c_t^{t-1} + i_t = b g(k_t,2)$$ (recall $n=2$ in equilibrium). To see this, think of a simple Cobb-Douglas production function: $y_t=k_t^\alpha n_t^{1-\alpha}$. $MP_k(t)=\alpha k_t^{\alpha-1} n_t^{1-\alpha}$ and $MP_n(t)=(1-\alpha) k_t^\alpha n_t^{-\alpha}$, so $k_t MP_k(t) + n_t MP_n(t) = \alpha k_t^\alpha n_t^{1-\alpha} + (1-\alpha) k_t^\alpha n_t^{1-\alpha} = y_t$ as desired.
# Growth
Now to show something interesting - even though growth is feasible in this economy, we won’t have it in equilibrium.
To show growth is feasible, think of the highest possible capital accumulation, this is achieved setting $c_t^{t-1}$ and $c_t^t$ to zero. This implies (recalling $i_t=k_{t+1}-(1-\delta)k_t$) $$k_{t+1}=b g(k_t,2) + (1-\delta) k_t$$ We can divide both sides by $k_t$ to get the growth rate: $$\frac{k_{t+1}}{k_t} = \frac{b}{k_t} g(k_t,2) + 1 - \delta$$ and putting in our expression for $g$ we get $$\frac{k_{t+1}}{k_t}=b\left[\alpha + (1-\alpha)\Big(\frac{2}{k_t} \Big)^\rho \right]^{\frac{1}{\rho}} + 1 - \delta$$ If we have growth, as $t \rightarrow \infty$ we will have $k_t \rightarrow \infty$, so our expression simplifies to: $$\frac{k_{t+1}}{k_t} \rightarrow b \alpha^{\frac{1}{\rho}} + 1 - \delta$$ Choosing $b$ appropriately, we can make $b \alpha^{\frac{1}{\rho}} + 1 - \delta>1$ so growth is possible.
Now, consider the share of income going to the young (who have no capital, and only earn $w_t$): $$\frac{w_t}{y_t}= \frac{b(1-\alpha)\left(\frac{g_t}{2} \right)^{1-\rho}}{b g_t} = \frac{(1-\alpha) 2^{\rho-1}}{\alpha k_t^\rho + (1-\alpha) 2^\rho} \rightarrow_{k_t\rightarrow \infty} 0$$ Where after the first equality, I just substituted directly for $w_t$ from Equation 16, and imposed $n=2$, and the second equality is implied by the definition of $g$. This implies that if we have growth (and consequently $k_t$ is going to infinity), the share of income going to the young is going to zero. We will use this to show we won’t have growth in equilibrium.
Suppose (for the sake of contradiction) that there is growth in equilibrium, so $\frac{k_{t+1}}{k_t}>1$. Recall that weak inequalities are preserved in the limit, so it must be that: $$lim_{k_t \rightarrow \infty} \frac{k_{t+1}}{k_t} \geq 1$$
Now, look at the young consumer’s budget constraint, $c_t^t + k_{t+1} = w_t$. This implies that $k_{t+1}\leq w_t$ (just set $c_t^t=0$). Divide through by $k_t$ and multiply the RHS by $y_t/y_t$: $$\frac{k_{t+1}}{k_t} \leq \frac{w_t}{y_t} \frac{y_t}{k_t}$$ We already showed that that $\frac{w_t}{y_t} \rightarrow_{k_t\rightarrow \infty} 0$. Further, $\frac{y_t}{k_t} \rightarrow_{k_t\rightarrow \infty} b \alpha^{\frac{1}{\rho}}$ (this is immediate after dividing $y_t$ by $k_t$). As $\rho\in(0,1)$, the limit is finite. Taking the limit as $k_t \rightarrow \infty$ of both sides of Equation 27: $$lim_{k_t \rightarrow \infty} \frac{k_{t+1}}{k_t} \leq lim_{k_t \rightarrow \infty} \frac{w_t}{y_t} \frac{y_t}{k_t} = 0 < 1$$ contradicting Equation 26, so there cannot be growth in equilibrium.
# Future Work
The unique fundamental equilibrium in this economy has no growth. To get growth, we need to allow for bubble equlibria, which will be the topic of a future post. | {"extraction_info": {"found_math": true, "script_math_tex": 74, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 28, "x-ck12": 0, "texerror": 0, "math_score": 0.937317967414856, "perplexity": 515.1415843581884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818695375.98/warc/CC-MAIN-20170926085159-20170926105159-00171.warc.gz"} |
https://asmedigitalcollection.asme.org/IMECE/proceedings-abstract/IMECE2020/84553/V07BT07A042/1099292 | ## Abstract
Previous ultrasonic additive manufacturing (UAM) models ignore higher-order modes or do not simulate the entire weld cycle when studying the dynamics near critical height-to-width ratios. A multi-modal model was developed to study the dynamics near critical build heights. The cause for the critical height-to-width ratio is dynamic interaction between the substrate and sonotrode. As the build height approaches the critical height-width-ratio, the current model predicts a local maxima in the transverse velocity response directly under the moving load (simulated sonotrode excitation). This is validated by experimental observations from previous studies. However, the current model predicts that as the height is further increased, a maximum in the transverse velocity response occurs at a height-to-width ratio of 1.2 due to resonance of higher-order modes. This result indicates that a single mode-approximation is insufficient to describe the dynamics near critical build heights. In studying the time response for an entire weld cycle (1.5 s), the amplitude of the velocity response in the transverse direction varies greatly. This indicates that assuming a quasi-static or analyzing a short time period in a model excludes potential dynamics during an entire weld cycle (on the order of 1 s).
This content is only available via PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9458587169647217, "perplexity": 1320.988356251864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588244.55/warc/CC-MAIN-20211027212831-20211028002831-00322.warc.gz"} |
http://mathoverflow.net/questions/20082/a-question-on-group-action-on-categories | # A question on group action on categories
Let $Gr$ be the affine Grassmannian of $G=G((t))/G[[t]]$, and let $Perv(Gr)$ be the category of perverse sheaves on $Gr$. We have action of $G((t))$ on the left-hand side of $Perv(Gr)$, also we have action of the tensor category $Rep(G^\vee)$ on the right-hand side, through geometric Satake correspondence. It is clear that we have the action of $G((t))$ on $Perv(Gr)$ as functors.
Follow Gaitsgory's paper "the notion of category over stack", he claimed that an action of algebraic group scheme $H$ on a category $\mathcal{C}$ is actually equivalent to a category $\mathcal{C}$ with the action of the tensor category "Rep(H)".
Go back to the original set-up, that means we also have an action of $G^\vee$ on $Perv(Gr)$. I think, on this $Perv(Gr)$, the actions of $G((t))$ and $G^\vee$ should have different meaning, but why they gave them the same name?
Am I confused?
-
Yes, you are confused. What is claimed by Gaitsgory is that datum of category with action of $H$ is equivalent to datum of of another category with action of $Rep(H)$. You go back and forth between these two categories using constructions of "equivariantization" and "de-equivariantization".
Thanks. Is the action of $G((t))$ on this category just as functors? Is there any more strucutre, like the action of affine group scheme on the category? An irrelevant question, what is the regular function on $G((t))$? Or maybe we have the notion of categorical Harish-chandra module? – Jiuzu Hong Apr 1 '10 at 19:18
the action of $G((t))$ comes from its action on the affine Grassmannian, so if I understood you correctly, the answer to your first question is yes. Unfortunately I don't know much about your other questions.. – Victor Ostrik Apr 2 '10 at 0:04
The $G((t))$ action and the $Rep(G^\vee)$ [or equivalently of $G^\vee$ itself after deequivariantization, as Victor explains] are of quite different natures -- the former is a "smooth" action, and the latter an "algebraic" or "analytic" actions (the adjectives smooth and analytic come from analogy with p-adic rep theory). i.e. there are many kinds of notion of group action, and they are (to me) most conveniently summarized by describing the corresponding notion of group algebra which acts. An algebraic action of a group on a category is an action of the "quasicoherent group algebra" of G, ie the monoidal category of quasicoherent sheaves wrt convolution. (though I'd feel much safer if we said all this in a derived context, makes me uneasy otherwise). A smooth action is an action of the monoidal category of D-modules on G, the "smooth group algebra" -- analog of smooth functions on a p-adic group. Such an action is the same as an algebraic action, which is infinitesimally trivialized. Such examples are studied in Chapter 7 of Beilinson-Drinfeld's Hecke manuscript and the appendix to the long paper by Gaitsgory-Frenkel, in particular.
PS the "equivariantization" dictionary between categories over BH and categories with H action is a nice simple case of descent --- you describe things over BH as things over a point with descent data, that descent data is given by the map H --> pt, the two maps H x H---> H, and so on. When you assemble this together (most efficiently using the Barr-Beck theorem) you get the desired dictionary. (Of course if you want to consider categories as forming a 2-category you'd need a 2-categorical version of Barr-Beck, but for most practical purposes I know of you can get by with the current Lurie [$(\infty,$]1-categorical version. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9606053233146667, "perplexity": 236.07203720878502}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131296456.82/warc/CC-MAIN-20150323172136-00078-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/jordan-canoncial-form.405734/ | # Jordan canoncial form
1. May 25, 2010
### tinynerdi
1. The problem statement, all variables and given/known data
It is possible for a generalized eigenvector of a linear operator T to correspond to a scalar that is not an eigenvalue of T.
2. Relevant equations
There is a definition of generalized eigenvector of T corresponding to lamda.
3. The attempt at a solution
I know that this statement is false therefore I need a counter example, but I can't think of one since this statement contradict the definition of generalize eigenvector of T corresponding to lamda if (T-lamda I)^(p) (x) = 0 for some positive integer p. Is this enough to say that statement is false?
Can you offer guidance or do you also need help?
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http://mathhelpforum.com/differential-geometry/209485-cauchy-sequence.html | # Math Help - Cauchy sequence
1. ## Cauchy sequence
Would someone help me with this problem?
Define the sequence $\{a_n\}$ in a metric space $(X,d)$ such that $d(a_{n+2},a_{n+1})\leq cd(a_{n+1},a_n)$ for $c\in (0,1)$. Show that $\{a_n\}$ is Cauchy.
2. ## Re: Cauchy sequence
See the proof of Banach fixed-point theorem. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9972755908966064, "perplexity": 732.8394908165227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783398209.20/warc/CC-MAIN-20160624154958-00005-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://en.wikibooks.org/wiki/This_Quantum_World/Implications_and_applications/Time_independent_Schr%C3%B6dinger_equation | # This Quantum World/Implications and applications/Time independent Schrödinger equation
## Time-independent Schrödinger equation
If the potential V does not depend on time, then the Schrödinger equation has solutions that are products of a time-independent function $\psi(\mathbf{r})$ and a time-dependent phase factor $e^{-(i/\hbar)\,E\,t}$:
$\psi(t,\mathbf{r})=\psi(\mathbf{r})\,e^{-(i/\hbar)\,E\,t}.$
Because the probability density $|\psi(t,\mathbf{r})|^2$ is independent of time, these solutions are called stationary.
Plug $\psi(\mathbf{r})\,e^{-(i/\hbar)\,E\,t}$ into
$i\hbar\frac{\partial\psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial}{\partial\mathbf{r}}\cdot\frac{\partial}{\partial\mathbf{r}}\psi + V\psi$
to find that $\psi(\mathbf{r})$ satisfies the time-independent Schrödinger equation
$E\psi(\mathbf{r})=-{\hbar^2\over2m}\left(\frac{\partial^2}{\partial x^2}+ \frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\right)\psi(\mathbf{r})+V(\mathbf{r})\,\psi(\mathbf{r}).$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8763455748558044, "perplexity": 664.6223140936356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657136494.66/warc/CC-MAIN-20140914011216-00236-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?t=122&p=3826 | ## Newton's Obsoleted Constant "G"
### Newton's Obsoleted Constant "G"
Gravity, in the olden days, was said to have a force f with a mysterious source. Newton called the mystery "G" and gave it the grand title "Universal Gravitational Constant".
G is obsolete in 2014.
Its value is now know to be composed of three parts:
G = HIJ
H is pi square meters per "second to the 1.5 power"
I is the cube root of the volume of a proton
J is the inverse of the square root of 5.5 nanoseconds
The value of G is equal to the new, articulated, meaningful, insight laden HIJ.
H is the Universal Herenowium Constant
I is a length
J is the square root of time
Philosophically, these three items are vastly more satisfactory than simply having "Sir" Issac Newton's mysterious
G = 6.6 x 10^-11 meters cubed per "kilogram second squared"
It is a superior knowledge of quantum gravity that allows the Folmsbee-Christian Theory of Gravity to define
HIJ = 6.6 x 10^-11 meters cubed per "kilogram second squared"
f = HIJ x Mm/r^2
Herenowium (here and now ee um) is here to stay, for now, Sir.
muon200
Posts: 67
Joined: Fri Sep 12, 2014 1:53 pm
Location: Maui Island, Pacific Ocean
### Re: Newton's Obsoleted Constant "G"
Accuracy Improvements and a Correction of Units
The force of gravity is f, as Newton says, but with G replaced by the modern HIJ.
330 years ago, there was no word for a proton, so Issac Newton could not get this level of articulation...
f = HIJMm/(r^2) Newtons
H = pi square meters per (kg second^1.5)
I = 1.41262184 x 10^-15 meters
J = 1/(sqrt(4.4180564 nanoseconds))
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
The details of some calculations, for error checking
H = pi square meters per (kg second^1.5)
pi = 3.14159265358979
proton volume = 2.8218133333 x 10^-45 meters^3
I = cube root of proton volume 1.41262184 x 10^-15 meters
J = G/HI = 1.503836155 = 1/(sqrt(tau))
tau = 4.4180564 nanoseconds
J = 15044.729 /sqrt seconds
HIJ = G = 6.6738480 x 10^-11 cubic meters per kg second^2
Most importantly 4.4180564 nanoseconds are grown for each hadron volume shrunk.
muon200
Posts: 67
Joined: Fri Sep 12, 2014 1:53 pm
Location: Maui Island, Pacific Ocean
### Re: Newton's Obsoleted Constant "G"
I like this format for the force equation
f = (pi Mm/r^2)(meter^2/kg sec^1.5)(cube root(proton space)/sqrt(4.4ns))
f is force of gravity
pi is 3.14
M and m are masses
r is radius to center of mass
proton space is known
4.4ns is the time to shrink a proton space for gravity's sake
When do I get paid? It is a rainy night on Maui. Where to spend my next million dollars? Cars! Yeah, maybe a rusty sedan outside with a big V8 under the hood! And trick exhaust for Ferrari audio illusions.
muon200
Posts: 67
Joined: Fri Sep 12, 2014 1:53 pm
Location: Maui Island, Pacific Ocean | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8632872104644775, "perplexity": 9147.400779988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999964.8/warc/CC-MAIN-20190625233231-20190626015231-00370.warc.gz"} |
http://www.llvm.org/doxygen/classllvm_1_1sampleprof_1_1SampleProfileReader.html | LLVM 10.0.0svn
#include "llvm/ProfileData/SampleProfReader.h"
[legend]
[legend]
## Public Member Functions
SampleProfileReader (std::unique_ptr< MemoryBuffer > B, LLVMContext &C, SampleProfileFormat Format=SPF_None)
Read sample profiles from the associated file. More...
void dumpFunctionProfile (StringRef FName, raw_ostream &OS=dbgs())
Print the profile for FName on stream OS. More...
virtual void collectFuncsToUse (const Module &M)
void dump (raw_ostream &OS=dbgs())
Print all the profiles on stream OS. More...
FunctionSamplesgetSamplesFor (const Function &F)
Return the samples collected for function F. More...
virtual FunctionSamplesgetSamplesFor (StringRef Fname)
Return the samples collected for function F. More...
StringMap< FunctionSamples > & getProfiles ()
Return all the profiles. More...
void reportError (int64_t LineNumber, Twine Msg) const
Report a parse error message. More...
ProfileSummarygetSummary ()
Return the profile summary. More...
SampleProfileFormat getFormat ()
Return the profile format. More...
## Static Public Member Functions
static ErrorOr< std::unique_ptr< SampleProfileReader > > create (const Twine &Filename, LLVMContext &C)
Create a sample profile reader appropriate to the file format. More...
static ErrorOr< std::unique_ptr< SampleProfileReader > > create (std::unique_ptr< MemoryBuffer > &B, LLVMContext &C)
Create a sample profile reader from the supplied memory buffer. More...
## Protected Member Functions
void computeSummary ()
Compute summary for this profile. More...
## Static Protected Member Functions
Take ownership of the summary of this reader. More...
## Protected Attributes
StringMap< FunctionSamplesProfiles
Map every function to its associated profile. More...
LLVMContextCtx
LLVM context used to emit diagnostics. More...
std::unique_ptr< MemoryBufferBuffer
Memory buffer holding the profile file. More...
std::unique_ptr< ProfileSummarySummary
Profile summary information. More...
SampleProfileFormat Format = SPF_None
The format of sample. More...
## Detailed Description
Each profile contains sample counts for all the functions executed. Inside each function, statements are annotated with the collected samples on all the instructions associated with that statement.
For this to produce meaningful data, the program needs to be compiled with some debug information (at minimum, line numbers: -gline-tables-only). Otherwise, it will be impossible to match IR instructions to the line numbers collected by the profiler.
From the profile file, we are interested in collecting the following information:
• A list of functions included in the profile (mangled names).
• For each function F:
1. The total number of samples collected in F.
2. The samples collected at each line in F. To provide some protection against source code shuffling, line numbers should be relative to the start of the function.
The reader supports two file formats: text and binary. The text format is useful for debugging and testing, while the binary format is more compact and I/O efficient. They can both be used interchangeably.
Definition at line 265 of file SampleProfReader.h.
## Constructor & Destructor Documentation
llvm::sampleprof::SampleProfileReader::SampleProfileReader ( std::unique_ptr< MemoryBuffer > B, LLVMContext & C, SampleProfileFormat Format = SPF_None )
inline
virtualdefault
## ◆ collectFuncsToUse()
virtual void llvm::sampleprof::SampleProfileReader::collectFuncsToUse ( const Module & M )
inlinevirtual
Definition at line 282 of file SampleProfReader.h.
References llvm::dbgs(), and dump().
## ◆ computeSummary()
protected
Compute summary for this profile.
Definition at line 1044 of file SampleProfReader.cpp.
## ◆ create() [1/2]
ErrorOr< std::unique_ptr< SampleProfileReader > > SampleProfileReader::create ( const Twine & Filename, LLVMContext & C )
static
Create a sample profile reader appropriate to the file format.
Create a sample profile reader based on the format of the input file.
Parameters
Filename The file to open. C The LLVM context to use to emit diagnostics.
Returns
an error code indicating the status of the created reader.
Definition at line 986 of file SampleProfReader.cpp.
References C, and setupMemoryBuffer().
## ◆ create() [2/2]
ErrorOr< std::unique_ptr< SampleProfileReader > > SampleProfileReader::create ( std::unique_ptr< MemoryBuffer > & B, LLVMContext & C )
static
Create a sample profile reader from the supplied memory buffer.
Create a sample profile reader based on the format of the input data.
Parameters
B The memory buffer to create the reader from (assumes ownership). C The LLVM context to use to emit diagnostics.
Returns
an error code indicating the status of the created reader.
Definition at line 1022 of file SampleProfReader.cpp.
## ◆ dump()
void SampleProfileReader::dump ( raw_ostream & OS = dbgs() )
Print all the profiles on stream OS.
Dump all the function profiles found on stream OS.
Definition at line 56 of file SampleProfReader.cpp.
References dumpFunctionProfile(), I, and Profiles.
Referenced by collectFuncsToUse().
## ◆ dumpFunctionProfile()
void SampleProfileReader::dumpFunctionProfile ( StringRef FName, raw_ostream & OS = dbgs() )
Print the profile for FName on stream OS.
Dump the function profile for FName.
Parameters
FName Name of the function to print. OS Stream to emit the output to.
Definition at line 50 of file SampleProfReader.cpp.
References Profiles.
## ◆ getFormat()
inline
Return the profile format.
Definition at line 327 of file SampleProfReader.h.
References Format.
## ◆ getProfiles()
inline
Return all the profiles.
Definition at line 307 of file SampleProfReader.h.
References Profiles.
## ◆ getSamplesFor() [1/2]
FunctionSamples* llvm::sampleprof::SampleProfileReader::getSamplesFor ( const Function & F )
inline
Return the samples collected for function F.
Definition at line 288 of file SampleProfReader.h.
## ◆ getSamplesFor() [2/2]
virtual FunctionSamples* llvm::sampleprof::SampleProfileReader::getSamplesFor ( StringRef Fname )
inlinevirtual
Return the samples collected for function F.
Definition at line 297 of file SampleProfReader.h.
References getFormat(), llvm::sampleprof::getRepInFormat(), and Profiles.
## ◆ getSummary()
inline
Return the profile summary.
Definition at line 324 of file SampleProfReader.h.
References Summary.
pure virtual
pure virtual
## ◆ reportError()
void llvm::sampleprof::SampleProfileReader::reportError ( int64_t LineNumber, Twine Msg ) const
inline
Report a parse error message.
Definition at line 310 of file SampleProfReader.h.
References B, Buffer, C, create(), Ctx, and llvm::LLVMContext::diagnose().
## ◆ takeSummary()
inlinestaticprotected
Take ownership of the summary of this reader.
Definition at line 348 of file SampleProfReader.h.
References computeSummary(), and Summary.
protected
## ◆ Ctx
protected
LLVM context used to emit diagnostics.
Definition at line 338 of file SampleProfReader.h.
## ◆ Format
protected
The format of sample.
Definition at line 356 of file SampleProfReader.h.
Referenced by getFormat().
## ◆ Profiles
protected
Map every function to its associated profile.
The profile of every function executed at runtime is collected in the structure FunctionSamples. This maps function objects to their corresponding profiles.
Definition at line 335 of file SampleProfReader.h. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1997227668762207, "perplexity": 21075.086639586578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315750.62/warc/CC-MAIN-20190821022901-20190821044901-00492.warc.gz"} |
http://math.stackexchange.com/questions/166199/give-an-example-of-a-measure-which-is-not-complete?answertab=active | # Give an example of a measure which is not complete
Give an example of a measure which is not complete ? A measure is complete if its domain contains the null sets.
-
See the "motivation" and "examples" sections here. – David Mitra Jul 3 '12 at 16:41
@ArturoMagidin I wonder if this is the same user. – Matt N. Jul 3 '12 at 17:12
@MattN. No way for me to know; you could flag and ask a moderator, though. – Arturo Magidin Jul 3 '12 at 17:13
@ArturoMagidin I'm not sure whether that's the right thing to do. So I won't. – Matt N. Jul 3 '12 at 17:41
The canonical example is the Borel measure on the Borel $\sigma$ algebra (the $\sigma$ algebra generated by the open intervals) on $\mathbb{R}.$ This example is often used as a motivation for the construction of the Lebesgue measure.
-
Here's one:
Define $\mu (A) = 0$ (the zero measure) for all $A$ in the sigma algebra. Then pick any set $B$ that contains a set that is not in the sigma algebra.
And here's another one, taken from "A Course in Real Analysis" by McDonald/Weiss, page 250:
Let $(\mathbb R, \Sigma, \lambda)$ denote $\mathbb R$ with the Lebesgue measure. Then this space is complete. But the product space $(\mathbb R^2, \Sigma^2, \lambda \times \lambda)$ isn't. To see this, pick any non-Lebesgue measurable set $N$ and let $A := \{0\} \times N$ and $B:=\{0\} \times \mathbb R$. Then $B$ has measure zero and $A \subset B$. But $A$ is not measurable in the product measure.
-
For a really trivial example: let $X$ be any set with at least two points, take the trivial $\sigma$-algebra $\mathcal{F} = \{X, \emptyset\}$, and define $\mu$ on $\mathcal{F}$ by $\mu(X) = \mu(\emptyset) = 0$.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9851610064506531, "perplexity": 269.97014355911284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507443062.21/warc/CC-MAIN-20141017005723-00012-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://openstudy.com/updates/5100dab8e4b03186c3f812d5 | Here's the question you clicked on:
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## anonymous 3 years ago show that the sum of the slope mf+mg=sum of the slope m(f+g) Delete Cancel Submit
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1. anonymous
• 3 years ago
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expand the RHS.
2. anonymous
• 3 years ago
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$LHS=m(f+g)$ $=(m\times f)+(m\times g)$
3. anonymous
• 3 years ago
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Finish it off and after the RHS equals the LHS, just write down =LHS at the end of your working.
4. anonymous
• 3 years ago
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It's meant to be $RHS=m(f+g)$ Not $LHS$
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9993519186973572, "perplexity": 11971.623591798356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280899.42/warc/CC-MAIN-20170116095120-00467-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://brilliant.org/discussions/thread/dr-warms-formula-for-frobenius-number/ | ×
Dr. Warm's Formula for Frobenius Number
The McNugget problem originally stated that: For three different sized boxes of 6, 9, & 20 nuggets, what is the greatest number of nuggets that can’t be ordered with these combinations? For example, if you want to order 22 nuggets, the seller may put 20 nuggets in the big box with 2 remained. They may try combining the 6 and 9 combinations, but they all end up with multiples of 3, which can’t divide 22. Now it may seem that such unreachable number will be infinite, but as a matter of fact, it is not because as the number gets larger, the modular arithmetic summation between these multiples will eventually involve all factors.
For example, if you order 101 nuggets, 101 = 99 + 2. Since 99 is a multiple of 3, we have to find the number that has a remainder of 2 when divided by 3. Well, 20 is a perfect candidate!
Thus, $$101 = 20 + 81 = 20 + (9 \times 9)$$. That means the seller can provide you with 1 big box of 20 nuggets plus 9 boxes of 9 nuggets as your order.
This number is formally called Frobenius number written as G(a, b, c), the greatest number which can’t be written in the summation of multiples of positive integers a, b, & c: $$ax_1 + bx_2 + cx_3 = G$$ G will have no solutions for non-negative integers xi.
The modified Frobenius number $$F(a, b, c) = G(a, b, c) + a + b + c$$
By using Johnson’s formula , $$F(da, db, c) = d\cdot F(a, b, c)$$
Then if $$c|lcm(a,b)$$ and $$gcd(a, b, c) = 1$$, then $$a = pr; b = qs; c = rs$$, for some integers p, q, r, s.
Thus, $$F(a, b, c) = r[F(p, qs, s)] = rs[F(p, q, 1)]$$
$$F(p, q, 1) = G(p, q, 1) + p + q + 1$$
By definition, $$G(p, q, 1) = px_1 + qx_2 + x_3$$, but since x3 can be any non-negative integer, G will always in the range from 0 to infinity. Therefore, the greatest integer, which can’t be written in non-negative summation is -1, the greatest negative integer. Hence, $$F(p, q, 1) = G(p, q, 1) + p + q + 1 = -1 + p + q + 1 = p + q$$
Then $$F(a, b, c) = rs[F(p, q, 1)] = rs(p + q) = prs + qrs$$
Note that lcm is the largest common multiple: $$lcm(a, c) = prs$$ and $$lcm(b, c) = qrs$$. Thus, $$F(a, b, c) = lcm(a, c) + lcm(b, c)$$.
Finally, $$G(a, b, c) = F(a, b, c) –a –b –c = lcm(a, c) + lcm(b, c) –a –b –c$$
I called it: Dr. Warm’s Formula.
Now let’s back to our Mcnugget question: What is the value of $$G(6, 9, 20)$$?
Then $$lcm(9, 20) = 180$$, and clearly 6 can divide 180. So let’s calculate with Dr. Warm’s formula:
$$G(6, 9, 20) = lcm(6, 20) + lcm(6, 9) –6 –9 –20 = 60 + 18 -35 = 43$$.
As a result, the 43 nuggets are the largest amount that can’t be ordered as the combinations of boxes as mentioned above.
Mystery solved!
Dr. Warm's Formula
If $$\text{gcd}(a, b, c)= 1$$ and $$c|\text{lcm}(a,b)$$, then $$G(a, b, c) = \text{lcm}(a,c) + \text{lcm}(b,c) -a -b -c$$.
Note by Worranat Pakornrat
3 months, 1 week ago | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8886919021606445, "perplexity": 582.9321077102071}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105086.81/warc/CC-MAIN-20170818175604-20170818195604-00078.warc.gz"} |
http://physics.stackexchange.com/questions/6027/projectiles-problem-solving | # Projectiles problem solving
I've only learned about to use kinematics equation when solving projectile problems but today i came across the following equations. where does they come from?
• Distance travelled
• Time of flight
• Angle of reach
-
At the introductory level they come from (1) an assumption of no air resistance (2) an assumption of constant gravitation (3) the independence of the orthogonal components (i.e. the x motion does not effect the y motion and vice versa) and (4) the basic kinematics of constant acceleration motion. But as stated this question would take two hours in the lecture hall, please be more specific. – dmckee Feb 27 '11 at 16:20
They come from Newton's laws of motion. Thats all you need, together for some assumptions about the air, gravity and the earth being locally flat. – ja72 Jun 1 '11 at 23:13
All the basic kinematic equation you've learned come from one basic equation,
$$\frac{\textrm{d}^2\vec{x}}{\textrm{d}t^2} = \vec{g}$$
This is a vector-valued second order linear differential equation. $\vec{x}$ is the position of the projectile. $m$ is its mass. $\vec{g}$ is the acceleration due to gravity.
The equation can be read in simplified form as
$$\frac{\vec{F}}{m} = \vec{a}$$
This is called Newton's Second Law. $\vec{F}$ is the force on an object, which for a projectile near Earth's surface is $m\vec{g}$, ignoring all effects besides simple gravity (air resistance is the big one). $\vec{a}$ is the acceleration, which by definition is $\frac{\textrm{d}^2\vec{x}}{\textrm{d}t^2}$.
The kinematic equations that tell you, for example, the distance traveled by a projectile or its speed as a function of height can all be derived from this differential equation using calculus and algebra.
The differential equation itself is a postulate of Newtonian mechanics. In this sense it doesn't come from anywhere; it is simply assumed, along with the assumption that the force of gravity is constant.
However, with more advanced physics it is possible to explain Newtonian mechanics in terms of other theories. This simplest example is that the assumption that the force from gravity is $m\vec{g}$ can be understood in terms of Newton's theory of gravity. What we see is that the simple gravity law is only an approximation, but a good one.
Similarly, as we bring in more and more considerations, we tend to find that almost everything we've done in the beginning is only an approximation. The kinematic equations aren't fundamental laws of nature. They're mathematical consequences of a simple differential equation that is roughly true for everyday things.
-
As dmckee, pointed out in his comment, these equations come from (or derived from) some basic assumptions. To understand how we obtain these equations from the basic assumptions, you will need to read derivations of these equations.
Watch this video for basic understanding. Then watch Khan Academy lectures on projectile motion. (only 3 lectures).
May the force be with you!
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# Answer to Question #5751 in Electric Circuits for dani
Question #5751
If you use 20 J of work to push a 2-C charge into an electric field, its voltage with respect to its starting postition is A. 10 V, B. less than 10 V, C. more than 10 V
Potential difference of 1V this is such a difference, that the charge transfer in 1C requires 1 J of energy.
By the condition we have charge of 2C, and the work of 20 J respectively leaves just 10 V.
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https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-area-of-a-45-45-90-right-isosceles-triangle | # Basic Geometry : How to find the area of a 45/45/90 right isosceles triangle
## Example Questions
← Previous 1 3 4 5
Explanation:
### Example Question #2 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
Consider an isosceles triangle with a height of 24 and a base of 12. What is the area of this triangle?
121
169
155
144
60
144
Explanation:
The formula for the area of a trianlge is A = base * height * (1/2).
We're lucky here, because the question gives us all of the values we need. We simply need to plug them in:
A = base * height * (1/2) = 12 * 24 * (1/2) = 12 * 12 = 144
### Example Question #2 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
Calculate the area of an isosceles right triangle who's hypotenuse is inches.
Explanation:
The formula for the area of a triangle, right or not, is one half the base times height.
In this case, they are both Therefore, the respective values are entered, yielding:
### Example Question #3 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
The side length of the 45-45-90 right triangle is , find the area of the right triangle.
Explanation:
The area of a triangle is:
where b=base, h=height, and A=area
### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
Find the area of the triangle below.
Explanation:
The key to finding the area of our triangle is to reaize that it is isosceles and therefore is a 45-45-90 triangle; therefore, we know the legs of our triangle are congruent and that each can be found by dividing the length of the hypotenuse by .
Rationalizing the denominator simplifies our result; however, we are interested in the area, not just the length of a leg; we remember that the formula for the area of a triangle is
where is the base and is the height; however, in our right triangle, the base and height are simply the two legs; therefore, we can calculate the area by substituting.
### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
Find the area of a triangle that has a hypotenuse of .
Explanation:
To find the area of a triangle, we must use where b=base and h=height.
In the problem, the only information given is what type the triangle is and what its hypotenuse is.
Given the area equation, the problem hasn't given any numbers that can be substituted into the equation to solve for an area. This means that the hypotenuse value must be used to determine the height and the base.
Because this is a 45/45/90 triangle, this means that it is also isosceles. Therefore, we can logic out that the base and the height must be the same.
The missing sides can be calulated in one of two ways:
1. Using the Pythagorean Theorem
2. Or using
If we were to use the Pythagorean Theorem, since we've already determined that b=h, that mean a=b in the equation. Let's say that
That means the Pythagorean Theorem can be rewritten as:
Now to substitute in the value of c to solve for the height and base.
Now that we have the base and the height, we can substitute the values into the area equation and get the triangle's area.
### Example Question #2 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
Find the area of a triangle with a hypotenuse of .
Explanation:
To find the area of a triangle, we must use where b=base and h=height.
In the problem, the only information given is what type the triangle is and what its hypotenuse is.
Given the area equation, the problem hasn't given any numbers that can be substituted into the equation to solve for an area. This means that the hypotenuse value must be used to determine the height and the base.
Because this is a 45/45/90 triangle, this means that it is also isosceles. Therefore, we can logic out that the base and the height must be the same.
The missing sides can be calulated in one of two ways:
1. Using the Pythagorean Theorem
2. Or using
If we were to use the Pythagorean Theorem, since we've already determined that b=h, that means a=b in the equation. Let's say that
That means the Pythagorean Theorem can be rewritten as:
Now to substitute in the value of c to solve for the height and base.
Now that we have the base and the height, we can substitute the values into the area equation and get the triangle's area.
### Example Question #1 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
If the hypotenuse of an isosceles right triangle is , what is the area of the triangle?
Explanation:
An isosceles right triangle is another way of saying that the triangle is a triangle.
Now, recall the Pythagorean Theorem:
Because we are working with a triangle, the base and the height have the same length. We can rewrite the above equation as the following:
Now, plug in the value of the hypotenuse to find the height for the given triangle.
Now, recall how to find the area of a triangle:
Since the base and the height are the same length, we can then find the area of the given triangle.
### Example Question #4 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
If the hypotenuse of an isosceles right triangle is , what is the area of the triangle?
Explanation:
An isosceles right triangle is another way of saying that the triangle is a triangle.
Now, recall the Pythagorean Theorem:
Because we are working with a triangle, the base and the height have the same length. We can rewrite the above equation as the following:
Now, plug in the value of the hypotenuse to find the height for the given triangle.
Now, recall how to find the area of a triangle:
Since the base and the height are the same length, we can then find the area of the given triangle.
### Example Question #4 : How To Find The Area Of A 45/45/90 Right Isosceles Triangle
If the hypotenuse of an isosceles right triangle is , what is the area of the triangle?
Explanation:
An isosceles right triangle is another way of saying that the triangle is a triangle.
Now, recall the Pythagorean Theorem:
Because we are working with a triangle, the base and the height have the same length. We can rewrite the above equation as the following:
Now, plug in the value of the hypotenuse to find the height for the given triangle.
Now, recall how to find the area of a triangle:
Since the base and the height are the same length, we can then find the area of the given triangle.
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http://eprint.iacr.org/2012/444 | ## Cryptology ePrint Archive: Report 2012/444
Factorization of a 1061-bit number by the Special Number Field Sieve
Greg Childers
Abstract: I provide the details of the factorization of the Mersenne number $2^{1061}-1$ by the Special Number Field Sieve. Although this factorization is easier than the completed factorization of RSA-768, it represents a new milestone for factorization using publicly available software.
Category / Keywords: factoring
Date: received 4 Aug 2012, last revised 6 Aug 2012
Contact author: gchilders at fullerton edu
Available format(s): PDF | BibTeX Citation
Short URL: ia.cr/2012/444
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https://blog.csdn.net/qq_39812022/article/details/102965125 | # Substance designer understanding Blend mode practice. - Add Sub -
This composite equation is unique and inexpensive as a result of mixing two height values and can derive a special shape from the median Opacity.
float4 AddSub (float4 a, float4 b , float t)
{
return lerp(a, (b-1)+(b+a) , t);
} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.407258540391922, "perplexity": 21249.69228985528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141176922.14/warc/CC-MAIN-20201124170142-20201124200142-00668.warc.gz"} |
http://mathhelpforum.com/algebra/201103-home-work.html | # Math Help - home work
1. ## home work
2/ (6+lxl)
two over 6 plus absloute value of x
i got 1/3 +2/lxl
2. ## Re: home work
$\frac{2}{6+|x|} \neq \frac{1}{3}+\frac{2}{|x|}$
Substitute 2 into both sides to confirm.
What are you trying to achieve with this problem, what did the question ask?
3. ## Re: home work
Just a try....
2 1 2
_____ = ____ + ___
6+|x| 3 |x|
2 3
____ = ____
6X 3X
3X > X | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7155323028564453, "perplexity": 21725.402516392733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398460982.68/warc/CC-MAIN-20151124205420-00242-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://kimiyuki.net/blog/2016/06/09/cf-679-b/ | Codeforces Round #356 (Div. 1) B. Bear and Tower of Cubes
,
solution
Recursion on $m$. For each $m$, how many times is the maximal block $a$ used, is $m \bmod a^3$ or $(m \bmod a^3) - 1$, using the monotonicity of the function.
Let $a = \max \{ a \mid a^3 \le m \}$, the maximal block. Think whether the block $a$ is used or not. Assume it is not used, the result is equivalent to one for $m’ = a^3 -1$. But under this assumption, you can also use $p - 1$ blocks of $a$ if $m = p \dot a^3 + q$, and use the same blocks for $m’ = a^3 -1$. So you always use at least $(m \bmod a^3) - 1$ blocks with side $a$, and also use blocks for $m’ = a^3-1$ or use blocks for $m’ = m \bmod a^3$ and one block of $a$.
implementation
#include <iostream>
#include <unordered_map>
#include <tuple>
#include <cmath>
#define repeat(i,n) for (int i = 0; (i) < (n); ++(i))
typedef long long ll;
using namespace std;
template <class T> bool setmax(T & l, T const & r) { if (not (l < r)) return false; l = r; return true; }
ll cube(ll a) { return a * a * a; }
ll cbrt(ll x) {
ll y = pow(x, 1/3.) - 3;
while (cube(y+1) <= x) ++ y;
return y;
}
unordered_map<ll,pair<ll,ll> > memo;
pair<ll,ll> f(ll m) {
if (m == 0) return { 0, 0 };
if (memo.count(m)) return memo[m];
ll a = cbrt(m);
auto use = [=](ll k) {
ll y, x; tie(y, x) = f(min(cube(a)-1, m - k * cube(a)));
y += k;
x += k * cube(a);
return make_pair(y, x);
};
pair<ll,ll> ans = { 0, 0 };
setmax(ans, use(m / cube(a)));
setmax(ans, use(m / cube(a) - 1));
return memo[m] = ans;
}
int main() {
ll m; cin >> m;
ll y, x; tie(y, x) = f(m);
cout << y << ' ' << x << endl;
return 0;
} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7802196741104126, "perplexity": 6295.634538669801}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934808935.79/warc/CC-MAIN-20171124195442-20171124215442-00020.warc.gz"} |
http://plansinmotion.net/prince-albert-clumsp/49e56a-avalanche-photodiode-application | DOI: 10.5772/intechopen.81294 The transit times (both electrons and holes) increase with increasing thickness, implying a tradeoff between capacitance and transit time for performance. An Avalanche Photodiode (APD) provides higher sensitivity than a standard photodiode and is for extreme low-level light (LLL) detection and photon counting. The avalanche photodiode (APD) was invented by Japanese engineer Jun-ichi Nishizawa in 1952. {\displaystyle \kappa } APD noise is given by the formula: As the APD gain increases the output signal increases linearly, but the noise increases as shown in the graph below. The internal gain of an avalanche photodiode makes it a key ... sensitivity and can be a key enabler in the manufacturing of high-sensitivity optical receivers for 10-Gbit/sec applications. An avalanche photodiode is a photovoltaic device with internal gain that utilizes the directional motion of photogenerated carriers in a strong electric field to produce an avalanche effect to obtain the gain of the photocurrent. APD applicability and usefulness depends on many parameters. This InGaAs APD has a planer structure for high reliability. Nakamura et al, An InGaAs/InAlAs Superlattice Avalanche Photodiode with Thin Well Width for 10Gb/s Optical Transmission Systems , ECOC, TuC5 4, 1991, pp. General Sales Manager Hamamatsu Photonics UK Ltd. Avalanche Photodiodes ( APDs ) are high sensitivity, high speed semi-conductor "light" sensors. Providing the noise of the APD device is low enough, then it is also possible to operate an APD is Geiger mode as opposed to analogue operation, described above, to detect individual incident photons. Silicon will detect in the visible and near infrared, with low multiplication noise (excess noise). Due to their performance advantages APDs are then used widely in applications such as distance measurement, data transmission ( over fibre or through free space ), range finding, high speed industrial inspection ( including colour measurement ) and in various other medical and scientific instrumentation. In this regime, carriers (electrons and holes) excited by absorbed photons are strongly accelerated in the strong internal electric field, so that they can generate secondary carriers. In other words, an "ideal" semiconductor would convert the energy of the charged particle into an exact and reproducible number of electron hole pairs to conserve energy; in reality, however, the energy deposited by the charged particle is divided into the generation of electron hole pairs, the generation of sound, the generation of heat, and the generation of damage or displacement. Avalanche Photodiodes ( APDs ) are high sensitivity, high speed semi-conductor "light" sensors. The ENF is defined for any device, such as photomultiplier tubes, silicon solid-state photomultipliers, and APDs, that multiplies a signal, and is sometimes referred to as "gain noise". It is a multiplicative correction applied to the noise that describes the increase in the statistical noise, specifically Poisson noise, due to the multiplication process. Electronic dark-noise components are series and parallel noise. Two of the larger factors are: quantum efficiency, which indicates how well incident optical photons are absorbed and then used to generate primary charge carriers; and total leakage current, which is the sum of the dark current, photocurrent and noise. Highlights of Marubeni's Si Avalanche photodiodes are as follow: Marubeni Si Avalanche Photodiode (APDs) have a higher signal-to-noise ratio (SNR), fast time response, low dark current, and high sensitivity. SPADs that operate in this high-gain regime are sometimes referred to being in Geiger mode. 261 264. For an electron multiplication device it is given by the hole impact ionization rate divided by the electron impact ionization rate. . Most commonly available APDs are fabricated from silicon and employ a so called "reach through" structure where light is incident from the N-side of the silicon. This means for any APD there is an optimum operating gain, usually well below the actual maximum gain for that APD, where the maximum signal to noise performance can be obtained. As with regular photodiodes the maximum wavelength than can be detected is determined by the semi-conductor band gap energy using the formula: Among the various expressions for the APD multiplication factor (M), an instructive expression is given by the formula. Compared to regular PIN construction photodiodes, APDs, have an internal region where electron multiplication occurs, by application of an external reverse voltage, and the resultant "gain" in the output signal means that low light levels can be measured at high speed. Applications of Avalanche Diode The applications of an avalanche diode include the following. Contact Laser Components USA, Inc. 116 South River Road Building C Bedford, NH 03110 USA Phone: +1 603 821 7040 E-Mail:[email protected] [1] However, study of avalanche breakdown, microplasma defects in Silicon and Germanium and the investigation of optical detection using p-n junctions predate this patent. The result is the optimized series of high Responsivity devices, exhibiting excellent sensitivity. Deeper depletion silicon APD structures are then available for operation in the 900 nm to 1100 nm waveband range, such as the S8890 series from Hamamatsu Photonics, but these generally have the disadvantage of requiring a much higher reverse voltage to create the high electric fields needed and consequently they have much higher dark currents. We should add a note of caution here however as such highly stable, highly sensitive APD systems are often more expensive than a comparable PMT based system, and such low noise APDs are generally only hundreds of microns ( or smaller ) in size, thus very often more light is lost in the optical collection system than may be gained from the higher quantum efficiency of the detector itself ! Get the latest industry news and expert insights delivered straight to your inbox. Avalanche Diode Mode. The internal gain increases the device response. Electronic dark-noise components are series and parallel noise. By applying a high reverse bias voltage (typically 100â200 V in silicon), APDs show an internal current gain effect (around 100) due to impact ionization (avalanche effect). Photodetector Noise â Optical Fiber Communication. Reach-through avalanche photodiode structure and the electric fields in the depletion and multiplication regions. Wavelength Opto-Electronic offers quality Avalanche Photodiode (APD) in different specifications. Connecting a Photodiode in an External Circuit The Avalanche diode is used to protect the circuit. Manufacturers then supply APD modules where the performance of each individual APD is optimised and set-up at the factory prior to supply, such as the Hamamatsu C5331 and C5460 devices. The imaging detectors of choice today are electron-multiplied charge-coupled devices (EMCCDs), not to be confused with the âavalanche processâ in avalanche photodiodes (APDs). At a gain M, it is denoted by ENF(M) and can often be expressed as. Enquire on our Avalanche Photodiode (APD) now. New applications include positron emission tomography and particle physics. In order for a regular photodiode to detect lower light levels it is usual to increase the gain in the operating circuit by increasing the feedback resistor value. Global âAvalanche Photodiode Detector Market 2021-2026â Research Report categorizes the global Avalanche Photodiode Detector by key players, product type, applications and regions,etc. In an APD dark current is generated both from leakage at the surface of the diode and also from electron – holes thermally generated within the bulk of the silicon which are then multiplied in the gain region. As it is a relatively thin layer within the APD structure that gives rise to the "gain", the peak wavelength for silicon APDs tends to be from 600 nm to 800 nm, somewhat shorter than the 900 nm to 1000 nm peak wavelength for a regular photodiode. PN photodiode- two doped regions, positive and negative; PIN photodiode- has an additional intrinsic layer increasing its sensitivity. Avalanche Photodiode - Low noise APD receivers, Excelitas Technologies Photonic Detectors, This page was last edited on 8 January 2021, at 15:19. In principle, any semiconductor material can be used as a multiplication region: APD applicability and usefulness depends on many parameters. κ It is apparent that the shot noise of an APD is higher than that for a comparable performance photodiode, so even though the APD gives an amplified output the overall signal to noise performance ( SNR ) is not necessarily improved. Sometimes it is also called as photo-detector, a light detector, and photo-sensor. Consequently increasing the gain of the APD, by increasing the external bias, also increases this dark current. Avalanche diode- heavily reverse-biased operation; Scotty photodiode; APPLICATION. Avalanche photodiode detectors (APD) have and will continue to be used in many diverse applications such as laser range finders, data communications or photon correlation studies. {\displaystyle \alpha } APD gain is typically in the range from x10 to x300 for most commercial devices, but there are APDs available from specialist manufacturers with gains of thousands. Optocoupler- offers electrical circuit isolation for the safety of sensitive equipment. The existence of these other channels introduces a stochastic process, where the amount of energy deposited into any single process varies from event to event, even if the amount of energy deposited is the same. Submitted: April 10th 2018 Reviewed: September 4th 2018 Published: November 5th 2018. Active and passive current-quenching techniques have been used for this purpose. This is due to the low noise characteristics of CSPs, as well as the integrating nature of the output signal which provides an output proportional to the total charge flowing from the APD detector during the pulse event. The underlying physics associated with the excess noise factor (gain noise) and the Fano factor (conversion noise) is very different. 1. The correction factor describes the decrease in the noise, relative to Poisson statistics, due to the uniformity of conversion process and the absence of, or weak coupling to, bath states in the conversion process. This means that for some applications such photon counting APDs are these days also starting to be used over more established Photomultiplier Tube ( PMT ) technology, due to the higher quantum efficiencies of the semi-conductor device. The avalanche multiplication time times the gain is given to first order by the gain-bandwidth product, which is a function of the device structure and most especially Applications of avalanche diodes. Avalanche photodiode breaks performance record for LiDAR receivers Team's fabrication process achieves long-wavelength sensitivity, ultra-low noise and design flexibility In practice then the shot noise associated with this dark current ultimately will limit the minimum amount of light that any device can detect. By: Tim Stokes The APD multiplication process also produces an additional noise component, known as "excess noise" since the ionization of any individual carrier has a certain probability of occurance, the overall gain from the device being the statistical average of all of these individual ionization events. Go!Fotonâs Avalanche Photodiode (APD), front-illuminate type is suitable for 2.5 Gbps applications in G-PON/Ge-PON. The report also covers the latest industry data, key players analysis, market share, growth rate, opportunities and trends, investment strategy for your reference in analyzing the global Avalanche Photodiode ⦠Avalanche photodiodes (APDs) are widely utilized in laser based fiberoptic systems to convert optical data into electrical form. where L is the space-charge boundary for electrons, and Incident photons create electron – hole pairs in the depletion layer of a silicon photodiode structure and these move towards the respective PN junctions at a speed of up to 105 metres per second, depending on the electric field strength. (UNKNOWN) Avalanche Photodiode Focal Plane Arrays and Their Application to Laser Detection and Ranging. In fiber optic communication systems, the photodiode is generally required to detect very weak optical signals. Hence, this produces internal gain within photodiode. If the external bias increases this localised electric field to above about 105 V / cm then the carriers in the semi-conductor collide with atoms in the crystal lattice, and the resultant ionization creates more electron – hole pairs, some of which then go on to cause further ionization giving a resultant gain in the number of electron – holes generated for a single incident photon (See schematic below). where Series noise, which is the effect of shot noise, is basically proportional to the APD capacitance, while the parallel noise is associated with the fluctuations of the APD bulk and surface dark currents. In imaging applications, a two-dimensional (2-D) detector with very high quantum efficiency is desirable to optimize sensitivity. Series noise, which is the effect of shot noise, is basically proportional to the APD capacitance, while the parallel noise is associated with t⦠{\displaystyle \kappa \,} At longer wavelengths then an alternative semi-conductor material with smaller band gap is required, such as Germanium, or much more commonly these days due to its higher performance, InGaAs is chosen. In this case, the photodetector needs to have its signal current limited and quickly diminished. Typical applications for APDs are laser rangefinders, long-range fiber-optic telecommunication, and quantum sensing for control algorithms. For the period 2015-2025, the growth among segments provide accurate calculations and forecasts for ⦠By Hai-Zhi Song. The noise term for an APD may also contain a Fano factor, which is a multiplicative correction applied to the Poisson noise associated with the conversion of the energy deposited by a charged particle to the electron-hole pairs, which is the signal before multiplication. 57(7), 13 Aug., 1990, pp. However, some silicon APDs employ alternative doping and beveling techniques compared to traditional APDs that allow greater voltage to be applied (> 1500 V) before breakdown is reached and hence a greater operating gain (> 1000). This paper discusses APD structures, critical performance parameters and the excess noise factor. An avalanche photodiode is a semiconductor-based photodetector which is operated with a relatively high reverse voltage (typically tens or even hundreds of volts), sometimes just below breakdown. Silicon Avalanche Photodiodes make use of internal multiplication to achieve gain due to impact ionization. Another noise source is the excess noise factor, ENF. It is desirable to have a large asymmetry between these rates to minimize ENF(M), since ENF(M) is one of the main factors that limit, among other things, the best possible energy resolution obtainable. In this module, you will learn about another very important detector technology: p-n junctions. As the name implies, the avalanche photodiode uses the avalanche process to provide additional performance, although the avalanche process does have some disadvantages. This diode is very complex to light s⦠Avalanche photodiodes therefore are more sensitive compared to other semiconductor photodiodes. which is 1.12 eV for silicon at room temperature, giving a cut-off at 1100 nm. In this mode, avalanche diode operates at a high reverse bias condition. The range of commercial Infrared APDs available is however much smaller than for silicon; InGaAs APDs, such as the Hamamatsu Photonics G8931, having small area ( 30 micron diameter ) since they are used predominantly for fibre applications such as telecommunications. ... With the evaluation board, the SPAD sensor for high-resolution imaging applications can be tested quickly and easily. (SEA) Tarof et al, "Planar InP/InGaAs Avalanche Photodetectors with Partial Charge Sheet in Device Periphery", Appl. An avalanche photodiode (APD) is a highly sensitive semiconductor photodiode that exploits the photoelectric effect to convert light into electricity. Electron-multiplied CCDs are very sensitive, and if cooled, can approach single-photon sensitivities. Photodiodes operate by absorption of photons or charged particles and generate a flow of current in an external circuit, proportional to the incident power. From a functional standpoint, they can be regarded as the semiconductor analog of photomultipliers. Avalanche Photodiodes fabricated from these materials are then available in the market for operation in the 900 nm to 1700 nm wavelength range. It has been discovered in 2020 that adding graphene layer can prevent degradation over time to keep avalanche photodiodes like new, which is important in shrinking their size and costs for many diverse applications & brining devices out of vacuum tubes into digital age. All semi-conductor devices have such an associated dark current caused by thermal ( rather than optical ) generation of electron – holes. [2] The capacitance increases with increasing device area and decreasing thickness. When the reverse bias voltage begins to enhance, the diode purposely starts an avalanche effect at a fixed voltage. It allows multiplication of an avalanche breakdown to each photo-produced electron-hole pair. With 650 nm to 850 nm for high cut-off frequencies, this avalanche photodiode is a perfect match for many devices and industrial applications such as laser ⦠This has the unwanted consequence of reducing the speed of response and increasing the thermal noise associated with the operating circuit. For the period 2015-2025, the growth among segments provide accurate calculations and forecasts for ⦠If very high gain is needed (105 to 106), detectors related to APDs (single-photon avalanche diodes) can be used and operated with a reverse voltage above a typical APD's breakdown voltage. Photodiode Characteristics and Applications 5 Silicon photodiodes are semiconductor devices responsive to high-energy particles and photons. Avalanche diode Photodiode Light Emitting Diode Laser diode Tunnel diode Schottky diode Varactor diode P ... Increasing the doping density will decreases the breakdown voltage of the avalanche diode. The use of APDs instead of PIN photodetectors will result in improved sensitivity in many applications. is the ratio of the hole impact ionization rate to that of electrons. This mode is particularly useful for single-photon detection, provided that the dark count event rate and afterpulsing probability are sufficiently low. In general, the higher the reverse voltage, the higher the gain. In addition to excess noise, there are limits to device performance associated with the capacitance, transit times and avalanche multiplication time. These diodes are particularly designed to work in reverse bias condition, it means that the P-side of the photodiode is associated with the negative terminal of the battery and n-side is connected to the positive terminal of the battery. 670-672. In contrast, operation with an APD allows for the gain to be increased to improve the SNR whilst maintaining the speed of response, until the shot noise reaches a level equivalent to the thermal noise. Phys. α Avalanche Photodiode Arrays is split by Type and by Application. Since APD gain varies strongly with the applied reverse bias and temperature, it is necessary to control the reverse voltage to keep a stable gain. Avalanche photodiodes can be used in a number of applications to provide performance that other types of photodiode may mot be able to attain. Compared to regular PIN construction photodiodes, APDs, have an internal region where electron multiplication occurs, by application of an external reverse voltage, and the resultant "gain" in the output signal means that low light levels can be measured at high speed. Its spectral response range is 400 â 150 nm. For the majority of instrumentation based applications, the larger detection area, higher gain and superior SNR of the PMT make it still the detector of choice for many years to come. However, the timing r⦠This website uses cookies to ensure you get the best experience on our website. An APD receiver module and attendant circuitry appears in Figure 1. Silicon Avalanche Photodiodes (APD) are useful in applications with low optical power levels. Lett. This coefficient has a strong dependence on the applied electric field strength, temperature, and doping profile. Video created by University of Colorado Boulder for the course "Nanophotonics and Detectors". Avalanche photodiode is a less common detector, which was typically used in fiber optic telecommunication until it recently experienced a resurgence in flow cytometry. Avalanche Photodiode Detector is split by Type and by Application. Have been used for this purpose this diode is very different that the. As photo-detector, a light detector, and photo-sensor devices show useful sensitivity in the 450 to... Thermal noise associated with this dark current caused by thermal ( rather than optical ) generation of electron holes. Of electrons expressions for the course Nanophotonics and detectors '' in imaging applications, two-dimensional... ) is very complex to light s⦠avalanche photodiode ( APD ) can be measured and.. \Displaystyle \kappa } is the ratio of the hole impact ionization rate is very complex to sâ¦... High reliability performance parameter and excess noise ) is very different to produce electric.... Photodiode may mot be able to attain mode is particularly useful for single-photon detection, provided that dark! To produce electric current the evaluation board, the SPAD sensor for high-resolution imaging applications can be in. Offers quality avalanche photodiode Focal Plane Arrays and Their Application to laser detection and Ranging can... The following, temperature, and doping profile September 4th 2018 Published: November 2018! For high reliability offers electrical circuit isolation for the course Nanophotonics and detectors '' in Figure 1 sensitive and! ; Scotty photodiode ; Application of avalanche diode include the following and thus improve the of. 10Th 2018 Reviewed: September 4th 2018 Published: November 5th 2018 uses cookies to ensure you get latest... Very complex to light s⦠avalanche photodiode detector is split by type and by Application in principle, semiconductor... Are more sensitive compared to other semiconductor photodiodes the operating circuit invented by Japanese Jun-ichi... For control algorithms devices show useful sensitivity in many applications capacitance increases with thickness! Useful in applications with low multiplication noise ( excess noise factor ( gain noise ) include following. To light s⦠avalanche photodiode ( APD ) can be used in many.. This purpose purposely starts an avalanche effect at a high reverse bias voltage begins to enhance, the Application these... Cookies to ensure you get the latest industry news and avalanche photodiode application insights straight... Is a PN-junction diode that consumes light energy to produce electric current instead! Exploits the photoelectric effect to convert light into electricity a highly sensitive semiconductor photodiode that exploits the effect! Diode operates at a high reverse bias condition the speed of response and increasing the thermal noise associated with dark... Called as photo-detector, a light detector, and if cooled, approach. Evaluation board, the SPAD sensor for high-resolution imaging applications, a light detector and! By the electron impact ionization a functional standpoint, they can be used many. Used for this purpose photodiode may mot be able to attain this purpose: APD and! And Their Application to laser detection and Ranging are laser rangefinders, long-range fiber-optic,. Various expressions for the safety of sensitive equipment detector is split by type and by Application avalanche diode- reverse-biased... Material can be regarded as the S6045 series from Hamamatsu Photonics as a multiplication region: APD and! Optimized series of high Responsivity devices, exhibiting excellent sensitivity wavelength range such... Gain noise ) and can often be expressed as speed of response and increasing the external,... And will continue to be used in many applications detector, and if cooled, can single-photon. Figure 1 the market for operation in the visible and near infrared with. Are more sensitive compared to other semiconductor photodiodes photodiode may mot be able to attain region. The 450 nm to 1700 nm wavelength range excess noise factor light s⦠avalanche photodiode APD. Devices, exhibiting excellent sensitivity gain due to impact ionization rate to that of electrons in different specifications important. That operate in this module, you will learn about another very important technology... Expert insights delivered straight to your inbox offers electrical circuit isolation for the course Nanophotonics detectors., by increasing the external bias, also lightning detection and Ranging and! From Hamamatsu Photonics silicon avalanche photodiodes therefore are more sensitive compared to semiconductor. From an avalanche photodiode detectors have and will continue to be used as multiplication! Silicon photodiodes are semiconductor devices responsive to high-energy particles and photons a multiplication region: APD avalanche photodiode application and usefulness on. Boulder for the APD multiplication factor ( conversion noise ) and the excess noise factor ( M ) an! Starts an avalanche effect avalanche photodiode application a gain M, it is also called as photo-detector, two-dimensional. Sensitive equipment detector is split by type and by Application source is the ratio of APD... Expected Poisson noise is similar and thus improve the range of incident that! To device performance associated with the capacitance, transit times ( both electrons and holes ) increase with thickness. Light detector, and analysis delivered to avalanche photodiode application inbox detector, and photo-sensor semiconductor.! Of the APD multiplication factor ( M ) and can often be expressed as ] capacitance... That exploits the photoelectric effect to convert light into electricity for performance excess factor... To achieve gain due to avalanche photodiode application ionization rate a photodiode is generally required to detect very weak signals. Apds instead of PIN photodetectors will result in improved sensitivity in many diverse applications such the... Addition to excess noise ) is very different afterpulsing probability are sufficiently.! Straight to your inbox market for operation in the 900 nm to 1000 nm wavelength range, as... Each photo-produced electron-hole pair et al, Planar InP/InGaAs avalanche photodetectors with charge... The hole impact ionization rate to that of electrons in imaging applications a... Circuitry appears in Figure 1 sometimes referred to being in Geiger mode straight to your inbox... the! Applications, a two-dimensional ( 2-D ) detector with very high quantum efficiency is desirable to optimize sensitivity the sensor. Detector will run away '' by Japanese engineer Jun-ichi Nishizawa in 1952 industry news insights. News, insights, and doping profile achieve gain due to impact ionization rate divided by the formula very.. And detectors '' are then available in the depletion and multiplication regions these factors as corrections! Consumes light energy to produce electric current corrections to the expected Poisson noise is similar signal current limited quickly! Area and decreasing thickness ) Tarof et al, Planar InP/InGaAs avalanche photodetectors with Partial Sheet! Applications with low multiplication noise ( excess noise factor, ENF to your inbox available in the market for in! Diode include the following high-gain regime are sometimes referred to being in Geiger mode mot be able to attain instructive... Very important detector technology: p-n junctions the hole impact ionization rate divided by the hole impact rate. This high-gain regime are sometimes referred to being in Geiger mode may be future applications source! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7281137704849243, "perplexity": 2178.1147308307077}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362589.37/warc/CC-MAIN-20211203030522-20211203060522-00311.warc.gz"} |
https://www.physicsforums.com/threads/deriving-the-moment-of-inertia-of-solid-sphere.912961/ | # I Deriving the moment of inertia of solid sphere
1. Apr 28, 2017
### Arisylia
So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like
$$\frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dl*m}{l} \\ \int_{0}^{L}r^2\frac{dl*m}{l} \\ \frac{ml^2}{3}$$
thats for a rod on its end point.
i tried doing something similar with a sphere
$$\frac{d_m}{m} = \frac{4\pi r^2 dr}{\frac{4}{3}\pi R^3} \\ d_m = \frac{4 r^2 dr*m}{\frac{4}{3} R^3} \\ \int_{0}^{R}r^2\frac{4 r^2 dr*m}{\frac{4}{3} R^3} \\ \frac{3mR^2}{5}$$
but its supposed to be 2/5mr^2
i dont know if its because i cant apply this method or because i screwed something up. I looked at the derivation using the slices but I'm still curious about this.
Thanks for the help.
(its my first post here, sorry if im missing some part of etiquette or anything ! not sure if this is intermediate or basic?)
2. Apr 29, 2017
### andrewkirk
The moment of inertial is not $\int_0^R r^2dm$, as implied by the above. The incremental mass $dm$ is a thin spherical shell, which is not all at the same distance (radius) from the axis of rotation. Hence the integrand does not represent the momentum of inertia of that shell.
You need to set up an integration in which the solid sphere is split up into a series of incremental masses for which you know the moment of inertia. If you know the moment of inertia of a spherical shell, you can use the above approach and replace the integrand by the MoI of a spherical shell of radius $r$ (which is in the list here). Otherwise you need to split the sphere up a different way, eg as a stack of discs.
Last edited: Apr 29, 2017
3. Apr 29, 2017
### scottdave
Draft saved Draft deleted
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http://mathhelpforum.com/pre-calculus/228788-parallel-vectors.html | 1. ## Parallel Vectors
Hi,
The question I am working on is:
given vectors u = (t, t+1) and v = (3, -4),
Find all values of t if the given vectors are parallel.
I have had a go at this but not sure if I have done the right thing.
I have set (t, t+1) = k(3,-4) since they are parallel.
This gives me t=3k and t+1 =-4k
I have then solved simultaneously and got an answer of t=-3/7
Can anyone give me an idea if I have done the right thing here, I am thinking maybe there is more to this and I have missed something, especially since the question asks for all values of t.
Thanks
2. ## Re: Parallel Vectors
That's exactly what I would do.
3. ## Re: Parallel Vectors
Thanks, would there only be one answer for t that could make a parallel vector?
cheers
4. ## Re: Parallel Vectors
Well surely the negative of the one given is also parallel... | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9352393746376038, "perplexity": 874.5680747252029}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560283689.98/warc/CC-MAIN-20170116095123-00101-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://scitation.aip.org/content/aip/journal/apl/88/10/10.1063/1.2181652 | • journal/journal.article
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Pinning in -axis oriented films studied with angular dependent magnetoresistivity
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10.1063/1.2181652
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Affiliations:
1 Department of Physics, University of Alberta, Edmonton T6G 2J1, Canada
2 ELTECH, 5 Prof. Popov Strasse, St. Petersburg 197376, Russia
a) Present address: Physics Department, King Fahd University of Petroleum and Minerals, Hail Community College, Hail, Saudi Arabia.
b) Electronic mail: [email protected]
Appl. Phys. Lett. 88, 102501 (2006)
/content/aip/journal/apl/88/10/10.1063/1.2181652
http://aip.metastore.ingenta.com/content/aip/journal/apl/88/10/10.1063/1.2181652
## Figures
FIG. 1.
Angular dependence of magnetoresistivity measured in a magnetic field at different temperatures close to on YBCO film 6. Inset: the depinning angle and normalized magnitude of the minimum at [defined as ] measured as a function of temperature. The lines are guides to the eye.
FIG. 2.
Angular dependence of magnetoresistivity measured at a temperature of for different magnetic fields on YBCO film 6. Inset: the depinning angle and normalized magnitude of the minimum at [defined as ] measured as a function of magnetic field. The lines are guides to the eye.
FIG. 3.
Temperature dependence of the pinning energy per unit length of a planar defect in YBCO films 6 and 8 in a constant magnetic field. was calculated from Eq. 11 derived by Paulius et al. (see Ref. 5), using the experimental values of the depinning angle .
## Tables
Table I.
Parameters that describe YBCO thin films Nos. 1–8. is the transition temperature at and . is the midpoint transition temperature at , taken as the temperature at which has a maximum. is the critical current density at . It was determined from the self-field of the persistent current at the critical level, induced in ring-shaped samples (see Ref. 4). FWHM is the full-width-half-maximum of a (005) x-ray diffraction peak. is the depinning angle defined as described in the text. is the normalized magnitude of the minimum at . Both and are listed for and . Only films 6, 7, and 8 on this list exhibit a minimum in the angular dependence of magnetoresistivity close to (PLD: pulsed laser deposition; rf-MAG; radio frequency (rf) magnetron sputter depositions; and dc-MAG: direct current (rf) magnetron sputter depositions).
/content/aip/journal/apl/88/10/10.1063/1.2181652
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This is a required field | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8918171525001526, "perplexity": 4036.1052875890073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00092-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/college-physics-7th-edition/chapter-3-motion-in-two-dimensions-learning-path-questions-and-exercises-exercises-page-96/3 | ## College Physics (7th Edition)
(a) (3) Magnitude of the acceleration vector is between $4\,\mathrm{m/s^2}$ and $7\,\mathrm{m/s^2}$. (b) The acceleration has a magnitude of $5\,\mathrm{m/s^2}$, directed at angle of $53^{\circ}$ to the x-axis.
The magnitude of a vector is given by - $|a|=\sqrt{a_x^2+a_y^2}$ (a) This is analogous to the magnitude being the hypotenuse of a triangle with x- and y-components as the two other sides. Thus, the magnitude of the vector must be greater than the larger of the two components, which is 4 here. And, the magnitude must also be less than the sum of the components, which is 7 here. (b) Using the values of the components, $a_x=3$ and $a_y=4$ - $|a|=\sqrt{9+16}=5$. for direction at an angle $\theta$ to x-axis - $\tan{\theta}=\frac{a_y}{a_x}=\frac{4}{3}$ or, $\theta=53^{\circ}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8820390105247498, "perplexity": 144.28462314301277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588246.79/warc/CC-MAIN-20211028003812-20211028033812-00131.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/134581-exponential-random-variable-random-mean.html | # Math Help - exponential random variable with a random mean?
1. ## exponential random variable with a random mean?
Hi all,
I'm wondering how could I model a r.v. $B$ which is exponentially distributed (i.e. with pdf $f(b)=kexp(-kb)u(b)$ with $u(b)$ = the step function) but whose parameter $k$ is itself a random variable, not a fixed deterministic value.
Since:
$f(b|k)=f(b,k)/f(k)$
I think I can write:
$f(b,k)=f(b|k)f(k)=kexp(-kb)u(b)f(k)$
is this correct?
Thanks!
2. Hello,
You don't know whether k has a pdf or not. So it's not really correct to write f(k). If you assume so, it's ok.
And your whole formula is ok (actually, u(b)=1 iff b>0)
3. Hi,
I assume that k is a r.v. so as you say everything is ok.
Thanks for confirming it! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.951632022857666, "perplexity": 834.3725654812961}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657137948.80/warc/CC-MAIN-20140914011217-00166-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://www.brucelindbloom.com/Eqn_RGB_to_XYZ.html | # RGB to XYZ
A companded RGB color [RGB], whose components are in the nominal range [0, 1], is converted to XYZ in two steps.
## 1. Inverse Companding
First, the companded RGB channels (denoted with upper case $(R,G,B)$, or generically $V$) are made linear with respect to energy (denoted with lower case $(r,g,b)$, or generically $v$).
$$v \in \{r, g, b\}$$ $$V \in \{R, G, B\}$$
The same operation is performed on all three channels, but the operation depends on the companding function associated with the RGB color system.
### Inverse Gamma Companding
$$v = V^\gamma$$
### Inverse sRGB Companding
$$v = \cases{ V/12.92 & \text{if }V \leq 0.04045 \\ {((V+0.055)/1.055)}^{2.4} & \text{otherwise} }$$
### Inverse L* Companding
$$v = \cases{ 100v/\kappa & \text{if }V \leq 0.08 \\ {((V+0.16)/1.16)}^{3} & \text{otherwise} }$$ $$\kappa = \cases{ {903.3} & \text{Actual CIE standard} \\ {24389 / 27} & \text{Intent of the CIE standard} }$$
## 2. Linear RGB to XYZ
$$\left[ \matrix{X \\ Y \\ Z} \right] = [M] \left[ \matrix{r \\ g \\ b}\right]$$
Implementation Notes:
1. The transformation matrix $[M]$ is calculated from the RGB reference primaries as discussed here.
2. The gamma values for many common RGB color spaces may be found here.
3. Your input RGB values may need to be scaled before using the above. For example, if your values are in the range [0, 255], you must first divide each by 255.0.
4. The output XYZ values are in the nominal range [0.0, 1.0].
5. The XYZ values will be relative to the same reference white as the RGB system. If you want XYZ relative to a different reference white, you must apply a chromatic adaptation transform to the XYZ color to convert it from the reference white of the RGB system to the desired reference white.
6. Sometimes the more complicated special case of sRGB shown above is replaced by a "simplified" version using a straight gamma function with $\gamma = 2.2$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7058344483375549, "perplexity": 1386.8519332557617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00730.warc.gz"} |
https://encyclopediaofmath.org/wiki/Matrix_of_transition_probabilities | # Matrix of transition probabilities
The matrix $P _ {t} = \| p _ {ij} ( t) \|$ of transition probabilities in time $t$ for a homogeneous Markov chain $\xi ( t)$ with at most a countable set of states $S$:
$$p _ {ij} ( t) = {\mathsf P} \{ \xi ( t) = j \mid \xi ( 0) = i \} ,\ \ i, j \in S.$$
The matrices $\| p _ {ij} ( t) \|$ of a Markov chain with discrete time or a regular Markov chain with continuous time satisfy the following conditions for any $t > 0$ and $i, j \in S$:
$$p _ {ij} ( t) \geq 0,\ \ \sum _ {j \in S } p _ {ij} ( t) = 1,$$
i.e. they are stochastic matrices (cf. Stochastic matrix), while for irregular chains
$$p _ {ij} ( t) \geq 0,\ \ \sum _ {j \in S } p _ {ij} ( t) \leq 1,$$
such matrices are called sub-stochastic.
By virtue of the basic (Chapman–Kolmogorov) property of a homogeneous Markov chain,
$$p _ {ij} ( s+ t) = \sum _ {k \in S } p _ {ik} ( s) p _ {kj} ( t),$$
the family of matrices $\{ {P _ {t} } : {t > 0 } \}$ forms a multiplicative semi-group; if the time is discrete, this semi-group is uniquely determined by $P _ {1}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9502400755882263, "perplexity": 389.0623682764327}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334579.46/warc/CC-MAIN-20220925132046-20220925162046-00328.warc.gz"} |
https://kbwiki.ercoftac.org/w/index.php?title=CFD_Simulations_AC1-08 | # CFD Simulations AC1-08
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# L1T2 3 element airfoil
Application Challenge 1-08 © copyright ERCOFTAC 2004
## Overview of CFD Simulations
Numerical simulations for the L1T2 test case have been made by QinetiQ using the BAE SYSTEMS RANSMB code. This code solves the Reynolds-Averaged-Navier-Stokes equations (RANS) with a ${\displaystyle k-g}$ turbulence model [2]. The ${\displaystyle k-g}$ turbulence model is formally equivalent to Wilcox’s k-ω model [3], with g related to ω through the relation:
${\displaystyle g={\sqrt {1 \over \omega }}}$
Thus, g reduces linearly to zero at a wall, avoiding the singularity in ω. The RANSMB CFD simulations were carried out using a multi block structured grid.
## QINETIQ CFD Simulation
### Solution strategy
The code used for the CFD simulations was the BAE SYSTEMS RANSMB flow solver, version 9.6, which solves the RANS equations. The calculations reported here were made with a ${\displaystyle k-g}$ turbulence model. RANSMB is a cell centred finite volume code with a central, Jameson type, flux approximation. Convergence to a steady-state solution is achieved by means of a four stage Runge-Kutta scheme with multigrid acceleration. Three levels of grid were available for the multigrid algorithm – fine, medium and coarse. The medium and coarse grids were obtained from the fine grid by deleting every other point in each of the co-ordinate directions. In addition, using a grid-sequencing algorithm increased the rate of solution convergence. That is, solutions were first obtained on the coarse and then medium grids to provide good initial solutions on the next finer mesh.
### Computational Domain
The mesh used in the computations was generated by QinetiQ using the SAUNA multi-block mesh generation system and consisted of 76848 cells. The mesh was of pseudo-2D type. It consisted of two identical 2D meshes in the spanwise (Y) direction, separated by one mesh unit. In mesh units, the retracted chord length of the L1T2 section was equal to 1.0. The far-field boundaries in the X and Z directions were located at ±15 retracted chord lengths. The flow solution was assumed to be entirely two-dimensional. This is achieved by RANSMB by setting fluxes in the spanwise direction to zero and enforcing symmetry boundary conditions on the two planes of constant Y.
### Boundary Conditions
A no-slip and adiabatic boundary condition was applied on the slat, main-element and flap solid surfaces. The simulation was performed in “free-air”. Default far-field boundary conditions based on 1D Riemann invariant theory were used. The effects of lift-dependent circulation at the far-field boundary were accounted for by perturbing the far-field solution by a compressible point vortex model centred in the near field of the aerofoil. Symmetry boundary conditions were applied on the two constant Y computational planes to enforce two-dimensionality. No sensitivity tests were carried out to determine the effects on the solution of the effects of far-field boundary location. However, experience within QinetiQ has shown that the chosen far-field boundary extent and compressible vortex boundary conditions represent best practice.
### Application of Physical Models
A low Reynolds number formulation was employed for the ${\displaystyle k-g}$ turbulence model. A y+ at the first grid point from the wall was chosen to be of O(1) for the slat, main-element and flap surfaces. Transition was fixed on the main-element upper and lower surfaces at 12.5 % retracted chord. This set the turbulent viscosity to zero ahead of the transition points on the main element as well as turning off the source terms in the turbulent kinetic energy transport equation in this region.
### Numerical Accuracy
No studies were undertaken to investigate the effects of grid refinement on solution accuracy. However, the grid design has been based on long experience at QinetiQ and conforms to best practice.
For the two CFD solutions presented here, the number of time-step iterations on the coarse, medium and fine grids were 200, 1000 and 20000 respectively. This achieved a reduction in the average density residual of approximately three orders of magnitude. By contrast, only two orders of magnitude reduction were obtained for the turbulent kinetic energy (k) residual and one order of magnitude reduction for the g variable. The calculation was terminated when further convergence had effectively stalled i.e. the residuals were exhibiting a limit cycle behaviour.
### CFD Results
The CFD data consists of surface pressure coefficients Cp on the slat, main-element and flap; and total pressure coefficients Cptot through the boundary layer and wakes at four locations. These were extracted in a direction normal to the local surface, with the exception of the profile at the wing shroud trailing edge. The profile here was extracted just downstream of the main-element trailing edge as shown in Figure 2. There was some uncertainty in the location of the zero traverse position from the experiment. To allow a reasonable comparison of the CFD and experimental results, the CFD data was shifted along this line so that the location of the main element maximum wake deficit coincided with that from the experiment.
Figure 2 Location of wing shroud trailing edge traverse
NAME Re Mach Incidence (deg.) Position of traverse Detailed data GNDPs PDPs SPs 3.52x106 0.197 4.01° 35% wing element chord; shroud t/e; 50%flap chord; Cp on surface Cptot normal to surface 20.18° flap t/e
MP1 MP2 L1T2 Cp Cptot 4.01° CFD_Cp_a040_slat.dat CFD_Cptot_a040_BL01.dat CFD_Cp_a040_wing.dat CFD_Cptot_a040_BL02.dat CFD_Cp_a040_flap.dat CFD_Cptot_a040_BL03.dat CFD_Cptot_a040_BL04.dat 20.18° CFD_Cp_a202_slat.dat CFD_Cptot_a202_BL01.dat CFD_Cp_a202_wing.dat CFD_Cptot_a202_BL02.dat CFD_Cp_a202_flap.dat CFD_Cptot_a202_BL03.dat CFD_Cptot_a202_BL04.dat
## References
[2] G. Kalitzin, A.R.B. Gould, J.J. Benton. Application of Two-Equation Turbulence Models in Aircraft Design, AIAA 96-0327.
[3] Wilcox, D.C., Turbulence Modelling for CFD, DCW Industries Inc., La Canada, Ca., 1998.
© copyright ERCOFTAC 2004
Contributors: Antony Hutton; Jan Vos - QinetiQ; CFS Engineering SA | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8031281232833862, "perplexity": 3360.396243889758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988882.94/warc/CC-MAIN-20210508151721-20210508181721-00144.warc.gz"} |
https://www.varsitytutors.com/5th_grade_math-help/operations | # 5th Grade Math : Operations
## Example Questions
### Example Question #4 : 5th Grade Math
Solve:
Explanation:
When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.
can be reduced to by dividing both sides by
### Example Question #5 : 5th Grade Math
Solve:
Explanation:
When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then the division.
### Example Question #6 : 5th Grade Math
Heather collected of a bag of leaves. Matt collected times as many bags as Heather. How many bags did Matt collect?
Explanation:
When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over Then we multiply like normal.
Because can go into only time and is left over.
Matt collected bags of leaves.
Solve: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9864861965179443, "perplexity": 1303.0755515755163}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794870082.90/warc/CC-MAIN-20180527190420-20180527210420-00279.warc.gz"} |
https://www.arxiv-vanity.com/papers/cond-mat/0502374/ | # Characteristic BEC scaling close to Quantum Critical Point in BaCuSi2O6
S. E. Sebastian, P. A. Sharma, M. Jaime, N. Harrison, V. Correa, L. Balicas, N. Kawashima, C. D. Batista, I. R. Fisher Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford, CA 94305 MST-NHMFL, Los Alamos National Laboratory, Los Alamos, NM 87545 National High Magnetic Field Laboratory, Tallahassee, FL 32310 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545
May 19, 2021
###### Abstract
We report an experimental determination of the phase boundary approaching the quantum critical point separating a quantum paramagnetic state and the proposed spin Bose-Einstein condensate of triplons in the spin gap compound BaCuSiO. The ordering temperature is related to the proximity to a quantum critical point at the lower critical magnetic field T by a power law parameterized by critical exponent . We obtain an experimental estimate of down to a temperature of 0.61K, which is in good agreement with the mean field prediction of for the Bose-Einstein condensation universality class.
###### pacs:
75.50.-y, 75.30.-m
preprint: This line only printed with preprint option
Several spin gap compounds, including BaCuSiO[1,2], TlCuCl[3-7] and SrCu(BO)[8], have a singlet ground state in zero magnetic field with a gap to the lowest excited triplet state. The spin gap can be closed by an applied magnetic field, such that a quantum critical point (QCP) at a magnetic field separates the quantum paramagnetic state from a state characterized by long range magnetic order. The order parameter for this transition is , the creation operator for a triplet state. In the absence of U(1) symmetry-breaking anisotropy, the transition from the quantum paramagnetic state () to an ordered state with broken U(1) symmetry ( where and are the and components of the staggered magnetization in the plane perpendicular to the applied field) may be interpreted as a Bose Einstein condensation (BEC) of triplons [9]. The magnetic field functions as a chemical potential, thereby providing a convenient means to tune a BEC to criticality at the QCP.
The spin gap system BaCuSiO is unique because it provides experimental access to a quantum phase transition of this nature in a spin lattice that can be described by a U(1) rotationally symmetric spin Hamiltonian [1]. A quantum phase transition that belongs to the same universality class is observed in superfluid He[10-12], but with a phase diagram that is comparatively inaccessible for experimentation [13].
The proximity to the QCP is expected to be related to the ordering temperature () by a power law [14], which can be expressed in reduced form
t = f(h)×(1−h)ν (1)
where , ( and represent the point on the phase boundary halfway between and , the field at which the magnetization saturates) and is finite. The mean field critical exponent is characteristic of the Bose-Einstein condensation universality class, and describes the scaling behavior of a 3D dilute interacting Bose gas near the QCP. The mean field estimate is appropriate since the upper critical space dimension of 2 ( because for this universality class) is exceeded [9, 15-17].
In this paper, we present a set of experiments on BaCuSiO that examine the critical scaling of this phase transition in the vicinity of the quantum critical point. The experimental results are consistent with the BEC critical exponent, and agree with Monte Carlo simulations in the lowest experimentally accessible temperature window.
BaCuSiO has a well characterized quasi 2D structure [1,2,18] consisting of vertical Cu dimers arranged on a square bilayered lattice staggered between bilayers. The inter-layer, interdimer and interbilayer exchange couplings have been estimated from high field magnetization data [1] to be meV, meV, meV respectively [1,2]. Representing each dimer by a pseudospin with two possible states (lowest energy states singlet and triplet), and using appropriate transformations [1], the effective Hamiltonian describes a 3D gas of hardcore bosons with in-plane nearest neighbor hopping and repulsive interactions. At low temperatures, the system undergoes a second order phase transition, which has been interpreted as triplon condensation [1].
Here, magnetic torque, magnetocaloric effect and specific heat measurements are performed to obtain points on the phase boundary into the ordered state. Features in these thermodynamic quantities characterise the classical 3D-XY phase transition into the ordered state at finite temperatures.
Single crystal samples of BaCuSiO grown by a flux-growth technique [19] are used for these experiments, whereas previous measurements on this material [1,2,18] used single crystals grown by a floating zone technique. Flux grown crystals are chosen because of a lower impurity content, a clearly defined Schottky anomaly in the zero field heat capacity, and narrower nuclear magnetic resonance lines. The characteristic features of the magnetic ordering transition observed previously are identical in these samples, indicating sample independence.
The specific heat of the sample is measured at T in a He cryostat in the hybrid magnet at Tallahassee. The inset to figure 1a shows the characteristic lambda anomaly observed in specific heat, indicating a second order phase transition into the ordered state. The shape is identical to that in [1], which has been fit using directed-loop Monte Carlo simulations. The ordering temperature at T is plotted on the phase diagram in figure 1a.
Magnetic torque measurements enable a sensitive probe of the magnetic ordering transition at low temperatures. They are performed in static magnetic fields up to T in a He refrigerator in Tallahassee. Samples are mounted on the moving plate of a phosphor bronze capacitance cantilever, attached to a rigid plate rotatable about an axis parallel to the axis of torque and perpendicular to the applied magnetic field. The sample is mounted with a small angle (< ) between the applied field and the normal to the sample plane (easy axis ), such that the applied field exerts a torque on the crystal due to the difference in -factor between the and orientations with and [19]. The anisotropy in results in an anisotropy in (where is the spin gap)[19]. Hence, on entering the magnetically ordered phase with increasing magnetic field, the anisotropy in magnetization causes a sudden increase in torque, as the field attempts to align the axis more closely with the applied magnetic field. Torque measurements are made during magnetic field sweeps across the ordering transition at different temperatures.
The signature of the ordering transition is seen in field dependent torque curves in a temperature range K - K (sample curves shown in figure 1b). The field at which the phase transition occurs is obtained from the position of a sharp feature in the second derivative of the torque (example shown in the inset to figure 1b) [20]. The feature becomes weaker at higher temperatures, but can be extracted up to K. Examples of the ordering transitions thus obtained are indicated by solid symbols on the torque curves in figure 1b. Points on the phase diagram obtained from torque measurements are shown as solid circles in the phase diagram plotted in figure 1a.
The magnetocaloric effect describes the temperature change of a magnetic material associated with an external magnetic field change in an adiabatic process. An abrupt change in the temperature with changing magnetic field indicates a large field variation of the isothermal magnetic entropy, and is associated with an ordering transition. These measurements are a good probe of ordering transitions in a rapidly changing magnetic field, so can be used to trace the phase boundary [21]. Magnetocaloric effect measurements are carried out in fields up to T in a He cryostat in the hybrid magnet in Tallahassee. Temperature changes are detected during magnetic field sweeps across the ordering transition at different temperatures (shown in fig 1b). The peak in lattice temperature at () in a rising (falling) field indicates a drop in magnetic entropy with ordering. Similarly, a dip in temperature in a falling (rising) field indicates the transition out of the ordered phase at (). The position of the ordering transition for is obtained from the onset of the peak (as defined by the maximum in the first derivative) in a rising field and for from the onset of the dip in a falling field. The ordering transition thus obtained for a representative field sweep is shown in figure 1b. Points on the phase diagram obtained from magnetocaloric effect measurements are shown by open symbols in the phase diagram plotted in figure 1a.
The Monte Carlo simulations for this system are performed using the directed-loop algorithm [22] (results are represented by symbols in figure 1a). Estimates of interdimer exchange coupling are refined from [1], with revised values of meV and meV yielding better agreement of the Monte Carlo simulations with experimental points on the phase diagram.
Experimental access to the particle-hole symmetric region in BaCuSiO enables us to extend the region near the QCP in which the power law can be fit. Eqn. 1 describes scaling near while describes scaling near . In other words, the particle-hole symmetry of the system implies that is a function of :
t=g(h2)×[(1−h)(1+h)]ν ≡ g(h2)×(1−h2)ν (2)
where varies more slowly than in the vicinity of the QCP.
In this set of experiments, points on the particle-hole symmetric phase diagram first reported in [1] are refined using measurements on a flux-grown single crystal and extended to low temperatures close to the QCP (figure 1a). Critical scaling near the QCP is described by eqn. 2. Importantly, we have access to sufficient data points in the low temperature region near to obtain an estimate of the critical scaling exponent by fitting a power law dependence in that region.
The power law dependence in the quantum critical region is extremely sensitive to both the fit temperature range, and to the estimate of [17]. We use an empirical convergence approach to determine the best estimate of . Figure 2a shows the trend in the estimate of (denoted as ) obtained by fitting the lowest few experimental points on the phase boundary in figure 1a in a window of increasing size to eqn. 2 (where is assumed to be constant to a first approximation) for different fixed values of . Near the QCP, it is empirically observed from linear extrapolation to , that estimates of become less dependent on , and converge to a single value irrespective of the value of (figure 2a). Similar convergence to is observed for the Monte Carlo simulation results (figure 2a). The convergence is due to the fact that the QCP is at , independent of the path along which it is approached (characterized by ). From convergence, we obtain an estimate of T. The uncertainty in this value of is estimated to be T, arising from the experimental uncertainty in measuring . The value of T thus obtained is then used to estimate the critical exponent .
The critical exponent is estimated from fitting eqn.2 (with const.) to the narrowest temperature range near the QCP with a statistically significant number of experimental datapoints. Figure 2b shows the variation in with the size of the temperature window that is fit to eqn. 2 (points on the phase boundary are fit from the lowest value of to a highest value of ). As the critical region near the QCP is approached with narrowing window size, approaches the theoretical mean field value of . In the lowest experimentally accessible temperature window down to 0.61K, we obtain a value of Performing a similar analysis for data points from the Monte Carlo simulation reveals the expected increase in to the theoretical mean field value as the temperature window is further reduced below currently accessible experimental temperatures (figure 2b). The experimental estimate of based on measurements down to temperature is consistent with the theoretical mean field prediction of to within experimental error.
Figure 3 shows the comparison between the Monte Carlo simulation and the experimental data for T. The lines represent the power law (eqn. 2) with . The Monte Carlo simulation and experimental data are in good agreement in the lowest experimentally accessible temperature window. We empirically observe that the deviation from the power law at higher temperatures is less in the case of the experimental data than for the Monte Carlo simulation.
In summary, we performed magnetic torque and magnetocaloric effect experiments to map out the phase diagram in the vicinity of the QCP in the spin gap system BaCuSiO. Points down to 0.61K are fit to the power law (with const.) to give a value . The estimate we obtain for near the QCP is close to the theoretical value = , whereas previous experimental measurements of in the spin gap system TlCuCl have resulted in lower values in the range [3-7]. The other known experimental measurements of the BEC critical exponent have been on He adsorbed in aerogel [10-12], which is a realisation of a dilute Bose gas, but is experimentally limited by the presence of a random external potential. BaCuSiO is a unique U(1) symmetric spin gap material that enables experimental access to a QCP separating a quantum paramagnet from a Bose-Einstein condensate [1]. It provides a novel experimental realization of a BEC in a grand canonical ensemble in the absence of an external potential, with the region around the QCP accessible by a tuneable external magnetic field.
This work is supported by the National Science Foundation (NSF), DMR-0134613. Experiments performed at the NHMFL were supported by the NSF, Florida State, and the Department of Energy. Monte Carlo computations presented here were performed with the SGI 2800/384 at the Supercomputer Center, Institute for Solid State Physics, University of Tokyo. The numerical work was supported by a Grant-in-Aid (Program No. 14540361) from Monkasho, Japan. S. E. S. thanks D. I. Santiago for helpful discussions. I. R. F. acknowledges support from the Alfred P. Sloan Foundation and S. E. S. from the Mustard Seed Foundation.
## References
• (1) M. Jaime et al., Phys. Rev. Lett. 93, 087203 (2004).
• (2) Y. Sasago et al., Phys. Rev. B. 55, 8357 (1997).
• (3) T. Nikuni et al., Phy. Rev. Lett. 84, 5868 (2000).
• (4) Ch. Ruegg et al., Nature 423, 62 (2003).
• (5) H. Tanaka et al., J. Phys. Soc. Jpn. 70, 939 (2001).
• (6) A. Oosawa et al., Phys. Rev. B. 63, 134416 (2001).
• (7) Y. Shindo and H. Tanaka, J. Phys. Soc. Jpn. 73, 2642 (2004).
• (8) S. E. Sebastian et al., condmat/0403334.
• (9) T. Giamarchi and A. M. Tsvelik, Phys. Rev. B. 59, 11398 (1999).
• (10) B. C. Crooker et al., Phys. Rev. Lett. 51, 666 (1983).
• (11) P.A. Crowell et al., Phys. Rev. B 55, 12620 (1997).
• (12) P.A. Crowell et al., Phys. Rev. Lett. 75, 1106 (1995).
• (13) Tuning the particle hole density to provide access to the QCP requires absorption of He in an external media, which introduces a random external potential and effects due to surface absorption that influence system behaviour.
• (14) S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 1999)
• (15) M. P. A. Fisher et al., Phys. Rev. B. 40, 546 (1989).
• (16) N. Kawashima, J. Phys. Soc. Jpn. 73, 3219 (2004).
• (17) O. Nohadani et al., Phys. Rev. B. 69, 220402(R) (2004).
• (18) K.M. Sparta and G. Roth, Act. Crys. B. 60, 491 (2004).
• (19) S. E. Sebastian et al., in preparation.
• (20) The non-analytic behavior of the free energy is dominated by a single relevant exponent. Hence, the singular behavior of when and are close to a critical point on the line does not depend on the direction of approach to the critical point, as long as it is not tangent to the critical line. In particular, for we have . Choosing , we obtain . Since -0.015 [Campostrini et al, Phys. Rev. B 63, 214503 (2001)] for a 3D XY-like transition, the second derivative of the magnetization is divergent at the critical point: .
• (21) M. Jaime et al., Phys. Rev. Lett. 89, 287201 (2002).
• (22) O.E.Syljuåsen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002). | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9151433110237122, "perplexity": 825.6665726409539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488249738.50/warc/CC-MAIN-20210620144819-20210620174819-00489.warc.gz"} |
https://deepai.org/publication/deep-model-based-reinforcement-learning-via-estimated-uncertainty-and-conservative-policy-optimization | # Deep Model-Based Reinforcement Learning via Estimated Uncertainty and Conservative Policy Optimization
Model-based reinforcement learning algorithms tend to achieve higher sample efficiency than model-free methods. However, due to the inevitable errors of learned models, model-based methods struggle to achieve the same asymptotic performance as model-free methods. In this paper, We propose a Policy Optimization method with Model-Based Uncertainty (POMBU)—a novel model-based approach—that can effectively improve the asymptotic performance using the uncertainty in Q-values. We derive an upper bound of the uncertainty, based on which we can approximate the uncertainty accurately and efficiently for model-based methods. We further propose an uncertainty-aware policy optimization algorithm that optimizes the policy conservatively to encourage performance improvement with high probability. This can significantly alleviate the overfitting of policy to inaccurate models. Experiments show POMBU can outperform existing state-of-the-art policy optimization algorithms in terms of sample efficiency and asymptotic performance. Moreover, the experiments demonstrate the excellent robustness of POMBU compared to previous model-based approaches.
## Authors
• 10 publications
• 60 publications
• 65 publications
• ### Uncertainty-aware Model-based Policy Optimization
Model-based reinforcement learning has the potential to be more sample e...
06/25/2019 ∙ by Tung-Long Vuong, et al. ∙ 0
• ### Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models
Model-based reinforcement learning (RL) algorithms can attain excellent ...
05/30/2018 ∙ by Kurtland Chua, et al. ∙ 0
• ### Model-free and Bayesian Ensembling Model-based Deep Reinforcement Learning for Particle Accelerator Control Demonstrated on the FERMI FEL
Reinforcement learning holds tremendous promise in accelerator controls....
12/17/2020 ∙ by Simon Hirlaender, et al. ∙ 0
• ### Bidirectional Model-based Policy Optimization
Model-based reinforcement learning approaches leverage a forward dynamic...
07/04/2020 ∙ by Hang Lai, et al. ∙ 8
• ### Reinforcement Learning for Robotics and Control with Active Uncertainty Reduction
Model-free reinforcement learning based methods such as Proximal Policy ...
05/15/2019 ∙ by Narendra Patwardhan, et al. ∙ 0
• ### Guided Uncertainty-Aware Policy Optimization: Combining Learning and Model-Based Strategies for Sample-Efficient Policy Learning
Traditional robotic approaches rely on an accurate model of the environm...
05/21/2020 ∙ by Michelle A. Lee, et al. ∙ 33
• ### Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning
Model-based reinforcement learning algorithms with probabilistic dynamic...
06/15/2020 ∙ by Sebastian Curi, et al. ∙ 23
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## 1 Introduction
Model-free reinforcement learning has achieved remarkable success in sequential decision tasks, such as playing Atari games [21, 11] and controlling robots in simulation environments [19, 10]
. However, model-free approaches require large amounts of samples, especially when using powerful function approximators, like neural networks. Therefore, the high sample complexity hinders the application of model-free methods in real-world tasks, not to mention data gathering is often costly. In contrast, model-based reinforcement learning is more sample efficient, as it can learn from the interactions with models and then find a near-optimal policy via models
[14, 8, 17, 22]. However, these methods suffer from errors of learned models, which hurt the asymptotic performance [31, 1]. Thus, compared to model-free methods, model-based algorithms can learn more quickly but tend to learn suboptimal policies after plenty of trials.
Early model-based methods achieve impressing results using simple models, like linear models [2, 18] and Gaussian processes [16, 8]. However, these methods have difficulties in high-dimensional and non-linear environments due to the limited expressiveness of models. Recent methods use neural network models for better performance, especially for complicate tasks [29, 22]. Some methods further characterize the uncertainty in models via neural network ensembles [30, 15], or Bayesian neural networks [9]. Although the uncertainty in models improves the performance of model-based methods, recent research shows that these methods still struggle to achieve the comparable asymptotic performance to state-of-the-art model-free methods robustly [35].
Inspired by previous work that improves model-free algorithms via uncertainty-aware exploration [23], we propose a theoretically-motivated algorithm to estimate the uncertainty in Q-values and apply it to the exploration of model-based reinforcement learning. Moreover, we propose to optimize the policy conservatively by encouraging a large probability of performance improvement, which is also informed by the estimated uncertainty. Thus, we use the uncertainty in Q-values to enhance both exploration and policy optimization in our model-based algorithm.
Our contributions consist of three parts.
First, we derive an upper bound of the uncertainty in Q-values and present an algorithm to estimate it. Our bound is tighter than previous work [23], and our algorithm is feasible for deep model-based reinforcement learning, while many previous methods only focus on model-free cases [25, 26], or assume simple models [7].
Second, we propose to optimize the policy conservatively based on an estimated probability of performance improvement, which is estimated via the uncertainty in Q-values. We found the conservative policy optimization is useful to prevent the overfitting to the biased models.
Third, we propose a Policy Optimization method with Model-Based Uncertainty (POMBU), which combines our uncertainty estimation algorithm with the conservative policy optimization algorithm. Experiments show that POMBU achieves excellent robustness and can outperform state-of-the-art policy optimization algorithms.
## 2 Background
A finite-horizon Markov decision process (MDP)
is defined by the tuple . Here, is a finite set of states, is a finite set of actions,
is a third-order tensor that denotes the transition probabilities,
is a matrix that denotes the rewards, denotes the distribution of initial states and is the horizon length. More specifically, at the state and selecting the action , is the probability of transitioning to the state , and is the obtained reward. We represent a posterior of MDPs as , where is the sample space containing all possible MDPs, is a -field consisting of subsets of , and
measures the posterior probability of MDPs. We assume that each MDP in
is different from others only in terms of and . In this case, is a random tensor and
is a random matrix. For any random variable, matrix or tensor
, and
denotes its expectation and variance respectively. When without ambiguity, we write
as for short. For example, denotes and denotes .
Let denotes a policy. denotes the probability of taking the action at the state . Considering the posterior of MDPs, the expected return is a random variable, which is defined by
Jπ=Eτ∼(M,π)[H∑h=1Rshah].
Here is a trajectory. means that the trajectory is sampled from the MDP under policy . That is, is sampled from the initial state distribution of , is sampled with the probability and is sampled with the probability in . Our goal is to find a policy maximizing in real environment.
Given an MDP , we define the corresponding state-action value function , the state value function and the advantage function as follow:
Vhπ(s)=Eτ∼(M,π)[H∑l=hRslal∣∣sh=s], Qhπ(s,a)=Eτ∼(M,π)[H∑l=hRslal∣∣sh=s,ah=a], Ahπ(s,a)=Qhπ(s,a)−Vhπ(s).
When the policy is fixed, we write , and as , and respectively for short. In this case, for any time-step , , and are random variables mapping to . Hence,
is a random vector.
and are random matrices.
## 3 Uncertainty Estimation
In this section, we consider a fixed policy . Similarly to the uncertainty Bellman equation (UBE) [23]
, we regard the standard deviations of Q-values as the uncertainty. In this section, we derive an upper bound of
for each , and prove that our upper bound is tighter than that of UBE. Moreover, we propose an uncertainty estimation algorithm for deep model-based reinforcement learning and discuss its advantages. We provide related proofs in Appendix A.1-A.4.
### Upper Bound of Uncertainty in Q-values
To analyze the uncertainty, we first make two assumptions.
###### Assumption 1
Each MDP in is a directed acyclic graph.
This assumption is common [27, 23]. It means that the agent cannot visit a state more than twice within the same episode. This assumption is weak because each finite horizon MDP violating the assumption can be converted into a similar MDP that satisfying the assumption [23].
###### Assumption 2
The random vector and the random matrix are independent of and if .
This assumption is used in the derivation of UBE [23]. It is consistent with the trajectory sampling strategies used in recent model-based algorithms [5, 15], which sample a model from the ensemble of models independently per time step to predict the next state and reward.
First, we derive an inequation from these assumptions.
###### Lemma 1
Under Assumption 1 and 2, for any and , we have
DM[Qhsa]≤uhsa+∑s′,a′πs′a′¯Psas′DM[Qh+1s′a′], where uhsa=DM[Rsa+∑s′Psas′¯Vh+1s′].
We consider as a local uncertainty, because we can compute it locally with .
Then, we can derive our main theorem from this lemma.
###### Theorem 1
Under Assumption 1 and 2, for any policy , there exists a unique solution satisfying the following equation:
Uhsa=uhsa+∑s′,a′πs′a′¯Psas′Uh+1s′a′ (1)
for any and , where , and furthermore pointwise.
Theorem 1 means that we can compute an upper bound of by solving the Bellman-style equation (1).
Moreover, we provide the following theorem to show the convergence when computing iteratively.
###### Theorem 2
For arbitrary , if
(Uhsa)i+1=(uhsa)i+∑s′,a′πs′a′¯Psas′(Uh+1s′a′)i,
for any , and , where and converges to pointwise, we have converges to pointwise.
Theorem 2 shows that we can solve the equation (1) iteratively if the estimated local uncertainty is inaccurate per update but converges to the correct value, which is significant when we use an estimated to compute the uncertainty.
As is an upper bound of , is an upper bound of the uncertainty in . We use the upper bound to approximate the uncertainty in our algorithm similarly to UBE. We need to analyze the accuracy of our estimates.
Here, we compare our upper bound with that of UBE under the same assumptions, and hence we need to make an extra assumption used in UBE.
###### Assumption 3
is independent of for any .
This assumption is not used to derive our upper bound of the uncertainty but is used in UBE. Under the assumption 2 and 3, we have is independent of .
The upper bound derived in UBE satisfies
Bhsa=νhsa+∑s′,a′πs′a′¯Psas′Bh+1s′a′,
where . Here, is an upper bound of all for any and MDP. For example, we can regard as .
###### Theorem 3
Under the assumption 1, 2 and 3, is a tighter upper bound of than .
This theorem means that our upper bound is a more accurate estimate of the uncertainty in Q-values than the upper bound derived in UBE.
### Uncertainty Estimation Algorithm
First, we characterizes the posterior of MDPs approximatively using a deterministic model ensemble (please refer to the Section 5 for the details of training models). A deterministic ensemble is denoted by . Here, for any , is a single model that predicts the next state and the reward, and is its parameters. We define a posterior probability of MDPs by
Pr{Psas′=1,Rsa=x}=1KK∑i=1eq((s′,x),fwi(s,a)),
where eq is defined by
eq((s1,x1),(s2,x2))={1,if s1=s2 and x1=x2,0,otherwise.
Then, we can construct an MDP defined according to the posterior of MDPs, such that its transition tensor is equal to and its reward matrix is equal to . Hence, the state value matrix of the MDP is equal to .
Moreover, we use a neural network to predict for any state and time step , which is equivalent to predicting . We train by minimizing loss function
Lv(ϕ)=Eτ∼(^M,π)⎡⎣1HH∑h=1∥∥ ∥∥~Vϕ(sh)−H∑l=h^Rslal∥∥ ∥∥22⎤⎦. (2)
Finally, given an imagined trajectory sampled from under , we can estimate the uncertainty in Q-values via the algorithm 1. Note that for long-horizon tasks, we can introduce a discount factor similarly to previous work [23]. The modified uncertainty estimation method can be found in Appendix B.
### Discussion
In this part, we discuss some advantages of our algorithm to estimate the uncertainty in Q-values.
#### Accuracy
Based on the Theorem 3, our upper bound of the uncertainty is tighter than that of UBE, which means a more accurate estimation. Intuitively, our local uncertainty depends on while that of UBE depends on . Therefore, our local uncertainty has a weaker dependence on and can provide a relatively accurate estimation for long-horizon tasks (see an example in Appendix C). Moreover, considering an infinite set of states, our method ensures the boundedness of the local uncertainty because and are bounded. Therefore, our method has the potential to apply to tasks with continuous action spaces.
#### Applicability for Model-Based Methods
Our method to estimate the uncertainty in Q-values is effective for model-based reinforcement learning. In model-based cases, estimated Q-values are highly dependent on the models. Our method considers the model when computing the local uncertainty, while most of the existing methods estimate the uncertainty directly via the real-world samples regardless of the models. Ignoring models may lead to bad estimates of uncertainty in model-based cases. For example, the uncertainty estimated by a count-based method [3, 28] tends to decrease with the increase of the number of samples, while the true uncertainty keeps high even with a large amount of samples when modeling a complicate MDP using a simple model.
#### Computational Cost
Our method is much more computationally cheap compared with estimating the uncertainty via the empirical standard deviation of . When MDP is given, estimating requires plenty of virtual samples. Estimating the empirical standard deviation requires estimating for several MDPs. Previous work reduces the computational cost by learning an ensemble of Q functions [4]. However, training an ensemble of Q functions requires higher computational overhead than training a single neural network .
#### Compatibility with Neural Networks
Previous methods that estimate uncertainty for model-based methods always assume simple models, like Gaussian processes [8, 7]. Estimating uncertainty using Theorem 1 only requires that the models can represent a posterior. This makes our method compatible with neural network ensembles and Bayesian neural networks. For instance, we propose Algorithm 1 with an ensemble of neural networks.
#### Propagation of Uncertainty
As discussed in previous work [24], Bellman equation implies the high dependency between Q-values. Ignoring this dependence will limit the accuracy of the estimates of uncertainty. Our method considers the dependency and propagates the uncertainty via a Bellman-style equation.
## 4 Conservative Policy Optimization
In this section, we first introduce surrogate objective and then modify it via uncertainty. The modified objective leads to conservative policy optimization because it penalizes the update in the high-uncertainty regions. denotes a parameterized policy, and is its parameters. is the probability of taking action at state .
### Surrogate Objective
Recent reinforcement learning algorithms, like Trust Region Policy Optimization (TRPO) [32], Proximal Policy Optimization (PPO) [33], optimize the policy based on surrogate objective. We rewrite the surrogate objective in TRPO and PPO as follow:
Lsr(θ)=Eτ∼(M,πθold)[H∑h=1rθ(sh,ah)Ahold(sh,ah)],
where are the old policy parameters before the update, is the advantage function of and
rθ(s,a)=πθ(a|s)πθold(a|s).
Previous work has proven the surrogate objective is the first order approximation to when is around [32, 12]. That is, for any , we have the following theorem:
###### Theorem 4
Lsr(θ)|θ=θold =J(πθ)−J(πθold)∣∣θ=θold, ∇θLsr(θ)|θ=θ% old =∇θ(J(πθ)−J(πθ% old))∣∣θ=θold
(see proof in Appendix A.5). Therefore, maximizing can maximize approximately when is around .
### Uncertainty-Aware Surrogate Objective
To prevent the overfitting of the policy to inaccurate models, we introduce the estimated uncertainty in Q-values into the surrogate objective.
First, we need to estimate , which means the probability that the new policy outperforms the old one. Because of Theorem 4, can approximate . We assume that a Gaussian can approximate the distribution of . Thus, is approximately equal to , where
is the probability distribution function of standard normal distribution.
Then, we need to construct an objective function for optimization. Here, we aims to find a new with a large . As is monotonically increasing, we can maximize while minimize . Therefore, we can maximize
EM[Lsr(θ)]−α√DM[Lsr(θ)], (3)
where
is a hyperparameter.
Moreover, we need to estimate the expectation and the variance of the surrogate objective. Because is equal to
Eτ∼(M,πθold)[H∑h=1(rθ(sh,ah)−1)Qhold(sh,ah)],
we can approximate and as and respectively, where
Lexp(θ)=Eτ∼(^M,πθold)[H∑h=1rθ(sh,ah)¯Ahold(sh,ah)], (4) Lstd(θ)=Eτ∼(^M,πθold)[H∑h=1∣∣rθ(sh,ah)−1∣∣√Dh]. (5)
Here is defined in Section 3 using a learned ensemble, can be approximated by , and is computed by Algorithm 1.
However, policy optimization without trust region may lead to unacceptable bad performance [32]. Thus, we clip similarly to PPO. That is,
Lclip(θ)=Eτ∼(^M,πθold)[H∑h=1^rθ(sh,ah)¯Ahold(sh,ah)]. (6)
Here, we define as
{max(1−ϵ,rθ(sh,ah)),if ¯Ahold(sh,ah)≤0,min(1+ϵ,rθ(sh,ah)),if ¯Ahold(sh,ah)>0,
in which is a hyperparameter.
Finally, we obtain the modified surrogate objective
Lπ(θ)=Lclip(θ)−αLstd(θ).
Note that, the main difference of our objective from PPO is the uncertainty penalty . This penalty limits the ratio changes in high-uncertainty regions. Therefore, this objective is uncertainty-aware and leads to a conservative update.
## 5 Algorithm
In this section, we propose a Policy Optimization method with Model-Based Uncertainty (POMBU) in Algorithm 2. We detail each stage of our algorithm as following.
#### Exploration Policy
We train a set of exploration policies by maximizing the . Different policies are trained with different virtual trajectories. To explore the unknown, we replace with in the equation (6). Here, controlling the exploration to high-uncertainty regions.
#### Model Ensemble
To predict the next state, a single neural network in the ensemble outputs the change in state and then adds the change to the current state [15, 22]. To predict the reward, we assume the reward in real environment is computed by a function such that , which is commonly true in many simulation control tasks. Then, we can predict the reward via the predicted next state. We train the model by minimizing loss similarly to previous work [15, 22] and optimize the parameter using Adam [13]. Different models are trained with different train-validation split.
#### Policy Optimization
We use a Gaussian policy whose mean is computed by a forward neural network and standard deviation is represented by a vector of parameters. We optimizing all parameters by maximizing via Adam.
## 6 Experiments
In this section, we fist evaluate our uncertainty estimation method. Second, we compare POMBU to state-of-the-arts. Then, we show how does the estimated uncertainty work by ablation study. Finally, we analyze the robustness of our method empirically. In the following experiments, we report the performance averaged over at least three random seeds. Please refer to Appendix D for the details of experiments. The source code and appendix of this work is available at https://github.com/MIRALab-USTC/RL-POMBU.
### Effectiveness of Uncertainty Estimation
We evaluate the effectiveness of our uncertainty estimation method in two environments: 2D-point and 3D-point. These environments have continuous state spaces and continuous action spaces. First, we train an ensemble model of the environment and sample state-action pairs from the model using a deterministic policy. Then, we estimate the Q-values of these pairs via the means of virtual returns (computed using the models), and estimate the uncertainty using the algorithm 1. Finally, we compute the real Q-values using the return in real world, compute the ratios of errors to the estimated uncertainties, and count the frequencies of these ratios to draw Figure 1. This figure shows the distribution of ratios is similar to a standard normal distribution after sufficient training of , which demonstrates the accuracy of the estimated uncertainty.
### Comparison to State-of-the-Arts
We compare POMBU with state-of-the-art policy optimization algorithms in four continuous control tasks of Mujoco [34]: Swimmer, HalfCheetah, Ant, and Walker2d. Our method and our baselines optimize a stochastic policy to complete the tasks. Our baselines include: soft actor critic (SAC) [10]; proximal policy optimization (PPO); stochastic lower bounds optimization (SLBO) [20]; model-ensemble trust region policy optimization (METRPO) [15]. To show the benefits of using uncertainty in model-based reinforcement learning, we also compare POMBU to model-ensemble proximal policy optimization (MEPPO), which is equivalent to POMBU when and . We evaluate POMBU with and for all tasks.
The result is shown in Figure 2. The solid curves correspond to the mean and the shaded region corresponds to the empirical standard deviation. It shows that POMBU achieves higher sample efficiency and better final performance than baselines, which highlights the great benefits of using uncertainty. Moreover, POMBU achieves comparable asymptotic performances with PPO and SAC in all tasks.
We also provide Table 1 that summarizes the performance, estimated wall-clock time and the number of used imagined samples and real-world samples in the HalfCheetah task (H=200). Compared to MEPPO, the extra time used in POMBU is small (time: ), while the improvement is significant (mean: ; standard deviation: ). Compared to SAC, POMBU achieve higher performance with about 5 times less real-world samples. Moreover, in our experiments, the total time to compute the uncertainty (not include the time to train ) is about 1.4 minutes, which is ignorable compared with the overall time.
We further compare POMBU with state-of-the-art model-based algorithms in long-horizon tasks. The compared algorithms include model-based meta policy optimization (MBMPO) [6], probabilistic ensemble with trajectory sampling (PETS) [5] and stochastic ensemble value expansion (STEVE) [4] in addition. We directly use some of the results given by Tingwu Wang [35], and summarize all results in Table 2. The table shows that POMBU achieves comparable performance with STEVE and PETS, and outperforms other model-based algorithms. It demonstrates that POMBU is also effective in long-horizon tasks.
### Ablation Study
We provide an ablation study to show how the uncertainty benefits the performance. In our algorithm, we employ the uncertainty in policy optimization (controlled by ) and exploration (controlled by ). Therefore, we compare the performance with different and .
The results are shown in Figure 3 and 4. Setting as or achieves the best final performance and the best robustness with 200K samples. Note that a large may result in poorer performance in the early stage, because the uncertainty is high in the early stage and a large tends to choose a small step size when uncertainty is high. Using can improve the performance (larger mean and smaller standard deviation), which demonstrate the effectiveness of uncertainty-aware exploration.
### Robustness Analyses
We demonstrate the excellent robustness of POMBU in two ways. First, we evaluate algorithms in noisy environments. In these environments, we add Gaussian noise to the observation with the standard deviation . This noise will affect the accuracy of the learned models. Second, we evaluate algorithms in long-horizon tasks. In these tasks, models need to generate long trajectories, and the error is further exacerbated due to the difficulty of longterm predictions.
We report the results in Figure 5. Experiments show that our algorithm achieves similar performance with different random seeds, while the performance of METRPO varies greatly with the random seeds. Moreover, in Figure 5, the worst performance of POMBU beats the best of METRPO. This implies that our method has promising robustness, even in noisy environments and long-horizon environments.
## 7 Conclusion
In this work, we propose a Policy Optimization method with Model-Based Uncertainty (POMBU), which is a novel uncertainty-aware model-based algorithm. This method estimates uncertainty using a model ensemble and then optimizes policy Conservatively considering the uncertainty. Experiments demonstrate that POMBU can achieve comparable asymptotic performance with SAC and PPO while using much fewer samples. Compared with other model-based methods, POMBU is robust and can achieve better performance. We believe that our approach will bring new insights into model-based reinforcement learning. An enticing direction for further work is the combination of our uncertainty estimation method with other kinds of models like Bayesian neural networks. Another exciting direction is to modify other advanced model-based algorithms like STEVE and PETS using our uncertainty estimation method.
## A Proof
In this suction, We provide all the proof mentioned in the body of our paper.
### Proof of Lemma 1
###### Lemma 1
Under Assumption 1 and 2, for any and , we have
DM[Qhsa]≤uhsa+∑s′,a′πs′a′¯Psas′DM[Qh+1s′a′], where uhsa=DM[Rsa+∑s′Psas′¯Vh+1s′].
Proof. Let and each is a random variable. By using Jensen’s inequality , we have
D[∑iaiXi] =E⎡⎣(∑iaiXi−E[∑iaiXi])2⎤⎦ =E⎡⎣(∑iai(Xi−E[Xi]))2⎤⎦ ≤E[∑iai(Xi−E[Xi])2] =∑iaiD[Xi]. (7)
By applying the inequation (7) to the Bellman equation, we have
(8)
By using the law of total variance, we have
DM[Qhsa] =DM[Rsa+∑s′Psas′Vh+1s′] =DPsa,Rsa[E[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]]+EPsa,Rsa[D[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]] (9)
Because Assumption 1 and 2 implies that when , we have
DPsa,Rsa[E[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]] =DPsa,Rsa[Rsa+∑s′Psas′E[Vh+1s′∣∣Psa,Rsa]] =DPsa,Rsa[Rsa+∑s′Psas′¯Vh+1s′]=ulsa (10)
By using the inequation (7), we have
EPsa,Rsa[D[Rsa+∑s′Psas′Vh+1s′∣∣ ∣∣Psa,Rsa]] ≤EPsa,Rsa[∑s′Psas′D[Vh+1s′∣∣Psa,Rsa]] =∑s′¯Psas′D[Vh+1s′∣∣Psa,Rsa] =∑s′¯Psas′DM[Vh+1s′], (11)
where the last step holds because is independent of when according to Assumption 1 and 2. Combining 8, 9, 10 and 11, we obtain the Lemma 1.
### Proof of Theorem 1
###### Theorem 1
Under Assumption 1 and 2, for any policy , there exists a unique solution satisfying the following equation:
Uhsa=uhsa+∑s′,a′πs′a′¯Psas′Uh+1s′a′ (12)
for any and , where , and furthermore pointwise.
Proof. First, the solution of exists and is unique because and is a linear combinations of . Moreover, we know that
Then, there exists a unique solution of if there exists a unique solution of because is a linear combinations of and . Additionally, by using Lemma 1, we have
DM[QH−(i+1)sa]≤uH−(i+1)sa+∑s′,a′πs′a′¯Psas′DM[QH−is′a′]≤uH−(i+1)sa+∑s′,a′πs′a′¯Psas′UH−is′a′=UH−(i+1)sa
if pointwise.
Finally, we obtain Theorem 1 by induction.
### Proof of Theorem 2
###### Theorem 2
For arbitrary , if
(Uhsa)i+1=(uhsa)i+∑s′,a′πs′a′¯Psas′(Uh+1s′a′)i,
for any , and , where and converges to pointwise, we have converges to pointwise.
Proof. is converges to because converges to and .
For any , if converges to , converges to with the assumption converges to because is a linear combinations of and .
Then, we obtain the conclusion by induction.
### Proof of Theorem 3
###### Theorem 3
Under the assumption 1, 2 and 3, is a tighter upper bound of than .
Proof. Here, we only show that pointwise (see UBE [23] for the proof that is an upper bound of uncertainty).
Because , by using inequation (8), we have
DM[∑s′Psas′¯Vh+1s′] =DM[∑s′¯Psas′¯Psas′Psas′¯Vh+1s′] ≤∑s′¯Psas′DM[Psas′¯Psas′¯Vh+1s′] =∑s′DM[¯Psas′¯Vh+1s′]/¯Psas′ ≤∑s′DM[¯Psas′Qmax]/¯Psas′ =(Qmax)2∑s′DM[Psas′]/¯Psas′. (13)
Under the Assumption 1, 2 and 3, we have
uhsa =DM[Rsa+∑s′Psas′¯Vh+1s′] ≤DM[Rsa]+(Q% max)2∑s′DM[Psas′]/¯P | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9441003203392029, "perplexity": 1024.7521120642948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243990419.12/warc/CC-MAIN-20210511214444-20210512004444-00057.warc.gz"} |
https://www.proctor-it.com/category/uncategorized/ | # Ibid.
During my interview with Gene Kim on for Functional Geekery, Episode 128, Gene talked about how he had a problem he was asking different people for how they would solve it nicely with a functional approach, to see how to improve his Clojure solution to be more idiomatic.
His problem was on “rewriting” Ibid. entries in citation references, to get the authors names instead of the Ibid. value, as Ibid. is a shorthand that stands for “the authors listed in the entry before this”.
As he was describing this problem, I was picturing the general pseudo-code with a pattern match in my head. To be fair, this has come from a number of years of getting used to thinking in a functional style as well as thinking in a pattern matching style.
The following Erlang code is a close representation to the pseudo-code that was in my head.
-module(ibid).
-export([ibid/1]).
ibid(Authors) ->
ibid(Authors, []).
ibid([], UpdatedAuthors) ->
{ok, lists:reverse(UpdatedAuthors)};
ibid(["Ibid." | _], []) ->
{error, "No Previous Author for 'Ibid.' citation"};
ibid(["Ibid." | T], UpdatedAuthors=[H | _]) ->
ibid(T, [H | UpdatedAuthors]);
ibid([H | T], UpdatedAuthors) ->
ibid(T, [H | UpdatedAuthors]).
Running this in the Erlang shell using erl results in the following
> ibid:ibid(["Mike Nygard", "Gene Kim", "Ibid.", "Ibid.", "Nicole Forsgren", "Ibid.", "Jez Humble", "Gene Kim", "Ibid."]).
{ok,["Mike Nygard","Gene Kim","Gene Kim","Gene Kim",
"Nicole Forsgren","Nicole Forsgren","Jez Humble","Gene Kim",
"Gene Kim"]}
> ibid:ibid(["Ibid."]).
{error,"No Previous Author for 'Ibid.' citation"}
Throughout the editing of the podcast, I continued to think about his problem, and how I would approach it in Clojure without built-in pattern matching, and came up with the following using a cond instead of a pure pattern matching solution:
(defn
update_ibids
([authors] (update_ibids authors []))
([[citation_author & rest_authors :as original_authors] [last_author & _ :as new_authors]]
(let [ibid? (fn [author] (= "Ibid." author))]
(cond
(empty? original_authors) (reverse new_authors)
(and (ibid? citation_author) (not last_author))
(throw (Exception. "Found Ibid. with no previous author"))
:else (recur
rest_authors
(cons
(if (ibid? citation_author)
last_author
citation_author)
new_authors))))))
And if we run this in the Clojure REPL we get the following:
user=> (def references ["Gene Kim", "Jez Humble", "Ibid.", "Gene Kim", "Ibid.", "Ibid.", "Nicole Forsgren", "Micheal Nygard", "Ibid."])
user=> (update_ibids [])
()
user=> (update_ibids ["Ibid."])
Execution error at user/update-ibids (REPL:8).
Found Ibid. with no previous author
user=> (update_ibids references)
("Gene Kim" "Jez Humble" "Jez Humble" "Gene Kim" "Gene Kim" "Gene Kim" "Nicole Forsgren" "Micheal Nygard" "Micheal Nygard")
That solution didn’t sit well with me (and if there is a more idiomatic way to write it I would love some of your solutions as well), and because of that, I wanted to see what could be done using the core.match library, which moves towards the psuedo-code I was picturing.
(ns ibid
(:require [clojure.core.match :refer [match]]))
(defn
update_ibids
([authors] (update_ibids authors []))
([orig updated]
(match [orig updated]
[[] new_authors] (reverse new_authors)
[["Ibid." & _] []] (throw (Exception. "Found Ibid. with no previous author"))
[["Ibid." & r] ([last_author & _] :seq) :as new_authors] (recur r (cons last_author new_authors))
[[author & r] new_authors] (recur r (cons author new_authors)) )))
And if you are trying this yourself, don’t forget to add to your deps.edn file:
{:deps
{org.clojure/core.match {:mvn/version "0.3.0"}}
After the first couple of itches were scratched, Gene shared on Twitter Stephen Mcgill’s solution and his solution inspired by Stephen’s.
(Edit 2022-05-02 : I took out the Twitter embed and changed the embed to be an HTML link to Twitter if you are interested in seeing the post as it was pointed out that tracking cookies were being dropped by Twitter, in an effort to reduce cookies being dropped by this site.)
And then, just for fun (or “just for defun” if you prefer the pun intended version), I did a version in LFE (Lisp Flavored Erlang) due to it being a Lisp with built in pattern matching from being on the Erlang runtime.
(defmodule ibid
(export (ibid 1)))
(defun ibid [authors]
(ibid authors '[]))
(defun ibid
([[] updated]
(tuple 'ok (: lists reverse updated)))
(((cons "Ibid." _) '[])
(tuple 'error "No Previous Author for 'Ibid.' citation"))
([(cons "Ibid." authors) (= (cons h _) updated)]
(ibid authors (cons h updated)))
([(cons h rest) updated]
(ibid rest (cons h updated))))
Which if we call it in LFE’s REPL gives us the following:
lfe> (: ibid ibid '["Mike Nygard" "Gene Kim" "Ibid." "Ibid." "Nicole Forsgren" "Ibid." "Jez Humble" "Gene Kim" "Ibid."])
#(ok
("Mike Nygard"
"Gene Kim"
"Gene Kim"
"Gene Kim"
"Nicole Forsgren"
"Nicole Forsgren"
"Jez Humble"
"Gene Kim"
"Gene Kim"))
lfe> (: ibid ibid '["Ibid."])
#(error "No Previous Author for 'Ibid.' citation")
If you have different solutions shoot them my way as I would love to see them, and if there looks to be interest, and some responses, I can create a catalog of different solutions similar to what Eric Normand does on his weekly challenges with his PurelyFunctional.tv Newsletter.
# Ruby Tuesday – Proc#call
Today’s Ruby Tuesday is Proc#call.
Procs are blocks of code that are bound to local variables, and as such, we need a way to be able to invoke them at a later time. Enter Proc#call.
Proc#call takes a list of arguments which are then used as the arguments to the Proc that call is being invoked on.
Proc.new {|x| x * x }.call 9
# => 81
Kernel.proc{|x| x * x }.call 11
# => 121
lambda {|x| x * x }.call 7
# => 49
->(x){x * x}.call 5
# => 25
->(x){x * x}.call 5
# => 25
If Proc#call is invoked with extra arguments, it will either discard the extra arguments, or raise an error if it was created as a lambda.
Proc.new {|x| x * x }.call 9, 3
# => 81
Kernel.proc{|x| x * x }.call 11, 15
# => 121
lambda {|x| x * x }.call 7, 13
# ArgumentError: wrong number of arguments (2 for 1)
# from (pry):94:in block in __pry__'
->(x){x * x}.call 5, 3
# ArgumentError: wrong number of arguments (2 for 1)
# from (pry):93:in block in __pry__'
Proc#call also has some other syntactic sugar providing alias for calling the method. You can use [], .(), or even the method Proc#yield as variations of Proc#call.
Proc.new {|x| x * x }[9]
=> 81
Proc.new {|x| x * x }.(9)
=> 81
Proc.new {|x| x * x }.yield 9
=> 81
As an extra bonus, there is also the method Method#call that can be used when you have an named method and you have a Method object for it. This call method behaves in the manner of lambda in that it expects the correct number of arguments to be passed to it.
def square(x)
x * x
end
method(:square).call 2
# => 4
method(:square).call 2, 4
# ArgumentError: wrong number of arguments (2 for 1)
# from (pry):78:in square'
–Proctor
# LaTeX in WordPress
Writing up my post Project Euler in Clojure – Problem 15 I wanted to represent the formulation for combinations in a nice manner. As I previously had found the [sourecode] tags, I figured it was worth a shot at doing some searching to see if WordPress.com supported any forumla formatting plug ins out of the box.
I have known of LaTeX for formulas but as I use a wordpress.com site, I knew it only ships with a limited number of plug ins, so I did a search about mathematical formula formatting in WordPress.com. Through the blog post Math for the Masses, I discovered that WordPress.com does indeed support LaTeX.
In my previous post mentioned above, I had the following formula for combinations:
$\frac{n}{\big((n-k)!*k!\big)}$
So to break that down and outline how I display that lets give the WordPress markup I used to get that:
$\frac{n}{\big((n-k)!*k!\big)}&s=3$
So to start with we have $latex which begins our LaTex statement, and if you notice we have a $ that signifies the end of the expression. The example on for the LaTeX in LaTeX is coded:
$LaTeX$
Which results in the following:
$LaTeX$
The next part in the LaTex statement begins the expression, which is the fraction part of the expression where
\frac{numerator}{denominator}
giving:
$\frac{numerator}{denominator}$
The parenthesis are done using big( and big). The last part of the expression is parameters to update the size of the display in WordPress. The WordPress support page for LaTeX discusses the different parameters available for the LaTeX. The parameter s is the parameter to specify the size of the LaTeX, of which I set as 3 which is the numeric representation of LARGE`.
The posts mentioned above contained links to other resources for LaTeX. The two additional ones I used were: a LaTeX wiki on The Student Room and The Not So Short Introduction to LATEX 2ε.
# Welcome
Hello and welcome. I have recently realized that I should start chronicling my journey to becoming a better software developer and honing my skills and my craft. Sometime around the first quarter of 2009, I began to realize that my career growth had started to slow, and that if I was not vigilant, my career would stagnate.
Since that time, I have been reading software development books as well as blogs, and trying to understand, absorb and apply that knowledge to writing better code, making better software, and making the software better. I was also fortunate to have come across a user group in the area that somehow manages to get software development luminaries, such as Martin Fowler, Dave Thomas (PragDave), Kent Beck, and others, in the software development field to come out and speak to them for free, and have since started to attend those. I have also just come back from the Software Craftsmanship North America 2010 conference and CodeRetreat, and as a result have plenty of ideas and half-formed thoughts in my head which need to be captured.
As such, is finally time to stop wondering if I have anything worth saying, and time to just start journaling, even if no-one else will ever come across this blog; for even just trying to record those thoughts will clarify them. With that, here is looking forward to being able to document, and reflect, on my journey of continuous improvement as a software developer. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4346802830696106, "perplexity": 6304.831349500547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499857.57/warc/CC-MAIN-20230131091122-20230131121122-00048.warc.gz"} |
https://brilliant.org/problems/a-mechanics-problem-by-akansha-saxena/ | # A classical mechanics problem by Akansha Saxena
Classical Mechanics Level pending
A ball is thrown upwards from the ground with an initial speed of u. The ball is at a height of 80m at two times. The time interval being 6s .Find u. (take g=10m/s)
× | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9546260237693787, "perplexity": 1451.6923817390234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280266.9/warc/CC-MAIN-20170116095120-00258-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://math.hecker.org/2013/08/04/linear-algebra-and-its-applications-exercise-2-6-12/ | ## Linear Algebra and Its Applications, Exercise 2.6.12
Exercise 2.6.12. If $H$ is the reflection matrix in the $x$$y$ plane, show that $H^2 = I$ using the trigonometric identity $\cos^2 \theta + \sin^2\theta = 1$ ($c^2+s^2=1$ for short).
$H = \begin{bmatrix} 2c^2 -1&2cs \\ 2cs&2s^2-1 \end{bmatrix}$
so that
$H^2 = \begin{bmatrix} 2c^2 -1&2cs \\ 2cs&2s^2-1 \end{bmatrix} \begin{bmatrix} 2c^2 -1&2cs \\ 2cs&2s^2-1 \end{bmatrix}$
$= \begin{bmatrix} (2c^2 -1)(2c^2 -1)+(2cs)(2cs)&2cs(2c^2-1)+2cs(2s^2-1) \\ 2cs(2c^2-1)+2cs(2s^2-1)&(2cs)(2cs)+(2s^2 -1)(2s^2 -1) \end{bmatrix}$
$= \begin{bmatrix} 4c^4-4c^2+1+4c^2s^2&2cs(2c^2+2s^2-2) \\ 2cs(2c^2+2s^2-2)&4c^2s^2+4s^4-4s^2+1 \end{bmatrix}$
$= \begin{bmatrix} 4c^2(c^2+s^2-1)+1&4cs(c^2+s^2-1) \\ 4cs(c^2+s^2-1)&4s^2(c^2+s^2-1)+1 \end{bmatrix}$
Since $c^2+s^2 =1$ this can be simplified to
$H^2 = \begin{bmatrix} 4c^2(1-1)+1&4cs(1-1) \\ 4cs(1-1)&4s^2(1-1)+1 \end{bmatrix}$
$= \begin{bmatrix} 4c^2 \cdot 0+1&4cs \cdot 0 \\ 4cs \cdot 0&4s^2 \cdot 0+1 \end{bmatrix} = \begin{bmatrix} 1&0 \\ 0&1 \end{bmatrix} = I$
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.
This entry was posted in linear algebra. Bookmark the permalink. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 14, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 6496.076815713015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541157498.50/warc/CC-MAIN-20191214122253-20191214150253-00107.warc.gz"} |
https://casaguides.nrao.edu/index.php?title=EVLA_Wide-Band_Wide-Field_Imaging:_G55.7_3.4-CASA4.0&direction=prev&oldid=13774 | # EVLA Wide-Band Wide-Field Imaging: G55.7 3.4-CASA4.0
## Overview
This CASA Guide describes the imaging of the supernova remnant G55.7+3.4.. The data were taken on August 23, 2010, in the first D-configuration for which the new wide-band capabilities of the WIDAR correlator were available. The 8-hour-long observation includes all available 1 GHz of bandwidth in L-band, from 1-2 GHz in frequency.
## Obtaining the data
Note that this dataset is rather large: ~14GB
As a start, unzip and untar the data:
tar -xzvf G55.7+3.4_10s.ms.tar.gz
This will take a minute, but once it's complete, you will have a directory called G55.7+3.4_10s.ms which is the data. Online flags have been applied (which delete known bad data), some uninteresting scans removed, and the data time-averaged to 10 seconds. (The data were taken in D-configuration, where maximum baselines are 1 km, so one can safely average to 3s or even 10s to reduce data set size.) This is equivalent to what you would download from the archive if you requested time-averaging, scans 16~313, and online flag application.
You can also find the dataset in the NRAO archive. Note that it is 170 GB in raw form.
Averaging to 10 seconds and the removal of some scans which are not used in this tutorial reduces the size of the data set to around 14 GB; the addition of columns for model and corrected data (known as "scratch columns") inflates it to 43 GB, which is the size of the MS we will be using here.
## Start and confirm your version of CASA
Start CASA by typing casapy on the command line. If you have not used CASA before, some helpful tips are available on the Getting Started in CASA page.
This guide has been written for CASA release 4.0.0. Please confirm your version before proceeding.
# In CASA
version = casalog.version()
print "You are using " + version
if (int(version.split()[4][1:-1]) < 21724):
print "\033[91m YOUR VERSION OF CASA IS TOO OLD FOR THIS GUIDE."
print "\033[91m PLEASE UPDATE IT BEFORE PROCEEDING."
else:
print "Your version of CASA is appropriate for this guide."
## Preliminary data evaluation
As a first step, use listobs to have a look at the MS:
# In CASA
listobs('G55.7+3.4_10s.ms')
Note that throughout this tutorial, we will run tasks using the task(parameter=value) syntax. When called in this manner, all parameters not explicitly set will use their default values.
The logger output will look like this:
##########################################
listobs(vis="G55.7+3.4_10s.ms",selectdata=True,spw="",field="",
antenna="",uvrange="",timerange="",correlation="",scan="",
intent="",feed="",array="",observation="",verbose=True,
listfile="")
================================================================================
MeasurementSet Name: /scr2/casa/evla_G55/G55.7+3.4_10s.ms MS Version 2
================================================================================
Observer: Dr. Sanjay Sanjay Bhatnagar Project: T.B.D.
Observation: EVLA
Data records: 7343848 Total integration time = 26691.5 seconds
Observed from 23-Aug-2010/01:00:25.0 to 23-Aug-2010/08:25:16.5 (UTC)
ObservationID = 0 ArrayID = 0
Date Timerange (UTC) Scan FldId FieldName nRows Int(s) SpwIds ScanIntent
23-Aug-2010/01:00:25.0 - 01:01:00.5 16 1 J1925+2106 8008 7.79 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_PHASE.UNSPECIFIED
01:01:10.0 - 01:02:30.0 17 1 J1925+2106 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_PHASE.UNSPECIFIED
01:02:40.0 - 01:04:00.0 18 1 J1925+2106 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_PHASE.UNSPECIFIED
01:04:10.0 - 01:05:29.5 19 1 J1925+2106 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_PHASE.UNSPECIFIED
01:05:39.0 - 01:06:59.0 20 1 J1925+2106 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_PHASE.UNSPECIFIED
01:07:12.0 - 01:08:29.0 21 2 G55.7+3.4 25064 9.33 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:08:39.0 - 01:09:59.0 22 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:10:09.0 - 01:11:29.0 23 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:11:39.0 - 01:12:58.5 24 2 G55.7+3.4 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:13:08.0 - 01:14:28.0 25 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:14:38.0 - 01:15:58.0 26 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:16:08.0 - 01:17:28.0 27 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:17:38.0 - 01:18:57.5 28 2 G55.7+3.4 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:19:07.0 - 01:20:27.0 29 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
01:20:37.0 - 01:21:57.0 30 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
<snip>
08:04:31.0 - 08:05:50.5 300 2 G55.7+3.4 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:06:00.0 - 08:07:20.0 301 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:07:30.0 - 08:08:50.0 302 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:09:00.0 - 08:10:20.0 303 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:10:30.0 - 08:11:49.5 304 2 G55.7+3.4 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:11:59.0 - 08:13:19.0 305 2 G55.7+3.4 25272 10 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:13:29.0 - 08:14:48.5 306 2 G55.7+3.4 25272 9.89 [0, 1, 2, 3, 4, 5, 6, 7] OBSERVE_TARGET.UNSPECIFIED
08:17:50.5 - 08:17:50.5 308 3 0542+498=3C147 80 4 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_AMPLI.UNSPECIFIED,UNSPECIFIED.UNSPECIFIED,CALIBRATE_BANDPASS.UNSPECIFIED
08:17:59.0 - 08:19:18.5 309 3 0542+498=3C147 17152 9.36 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_AMPLI.UNSPECIFIED,UNSPECIFIED.UNSPECIFIED,CALIBRATE_BANDPASS.UNSPECIFIED
08:19:28.0 - 08:20:48.0 310 3 0542+498=3C147 18216 10 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_AMPLI.UNSPECIFIED,UNSPECIFIED.UNSPECIFIED,CALIBRATE_BANDPASS.UNSPECIFIED
08:20:58.0 - 08:22:18.0 311 3 0542+498=3C147 18216 10 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_AMPLI.UNSPECIFIED,UNSPECIFIED.UNSPECIFIED,CALIBRATE_BANDPASS.UNSPECIFIED
08:22:28.0 - 08:23:47.5 312 3 0542+498=3C147 18216 9.89 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_AMPLI.UNSPECIFIED,UNSPECIFIED.UNSPECIFIED,CALIBRATE_BANDPASS.UNSPECIFIED
08:23:57.0 - 08:25:16.5 313 3 0542+498=3C147 18216 9.89 [0, 1, 2, 3, 4, 5, 6, 7] CALIBRATE_AMPLI.UNSPECIFIED,UNSPECIFIED.UNSPECIFIED,CALIBRATE_BANDPASS.UNSPECIFIED
(nRows = Total number of rows per scan)
Fields: 3
ID Code Name RA Decl Epoch SrcId nRows
1 D J1925+2106 19:25:59.60537 +21.06.26.1622 J2000 1 1004816
2 NONE G55.7+3.4 19:21:40.00000 +21.45.00.0000 J2000 2 6248936
3 N 0542+498=3C147 05:42:36.13792 +49.51.07.2336 J2000 3 90096
(nVis = Total number of time/baseline visibilities per field)
Spectral Windows: (8 unique spectral windows and 1 unique polarization setups)
SpwID #Chans Frame Ch1(MHz) ChanWid(kHz) TotBW(kHz) Corrs
0 64 TOPO 1000 2000 128000 RR RL LR LL
1 64 TOPO 1128 2000 128000 RR RL LR LL
2 64 TOPO 1256 2000 128000 RR RL LR LL
3 64 TOPO 1384 2000 128000 RR RL LR LL
4 64 TOPO 1520 2000 128000 RR RL LR LL
5 64 TOPO 1648 2000 128000 RR RL LR LL
6 64 TOPO 1776 2000 128000 RR RL LR LL
7 64 TOPO 1904 2000 128000 RR RL LR LL
Sources: 24
ID Name SpwId RestFreq(MHz) SysVel(km/s)
1 J1925+2106 0 - -
1 J1925+2106 1 - -
1 J1925+2106 2 - -
1 J1925+2106 3 - -
1 J1925+2106 4 - -
1 J1925+2106 5 - -
1 J1925+2106 6 - -
1 J1925+2106 7 - -
2 G55.7+3.4 0 - -
2 G55.7+3.4 1 - -
2 G55.7+3.4 2 - -
2 G55.7+3.4 3 - -
2 G55.7+3.4 4 - -
2 G55.7+3.4 5 - -
2 G55.7+3.4 6 - -
2 G55.7+3.4 7 - -
3 0542+498=3C147 0 - -
3 0542+498=3C147 1 - -
3 0542+498=3C147 2 - -
3 0542+498=3C147 3 - -
3 0542+498=3C147 4 - -
3 0542+498=3C147 5 - -
3 0542+498=3C147 6 - -
3 0542+498=3C147 7 - -
Antennas: 27:
ID Name Station Diam. Long. Lat.
0 ea01 W09 25.0 m -107.37.25.2 +33.53.51.0
1 ea02 E02 25.0 m -107.37.04.4 +33.54.01.1
2 ea03 E09 25.0 m -107.36.45.1 +33.53.53.6
3 ea04 W01 25.0 m -107.37.05.9 +33.54.00.5
4 ea05 W08 25.0 m -107.37.21.6 +33.53.53.0
5 ea06 N06 25.0 m -107.37.06.9 +33.54.10.3
6 ea07 E05 25.0 m -107.36.58.4 +33.53.58.8
7 ea08 N01 25.0 m -107.37.06.0 +33.54.01.8
8 ea09 E06 25.0 m -107.36.55.6 +33.53.57.7
9 ea10 N03 25.0 m -107.37.06.3 +33.54.04.8
10 ea11 E04 25.0 m -107.37.00.8 +33.53.59.7
11 ea12 E08 25.0 m -107.36.48.9 +33.53.55.1
12 ea13 N07 25.0 m -107.37.07.2 +33.54.12.9
13 ea15 W06 25.0 m -107.37.15.6 +33.53.56.4
14 ea16 W02 25.0 m -107.37.07.5 +33.54.00.9
15 ea17 W07 25.0 m -107.37.18.4 +33.53.54.8
16 ea18 N09 25.0 m -107.37.07.8 +33.54.19.0
17 ea19 W04 25.0 m -107.37.10.8 +33.53.59.1
18 ea20 N05 25.0 m -107.37.06.7 +33.54.08.0
19 ea21 E01 25.0 m -107.37.05.7 +33.53.59.2
20 ea22 N04 25.0 m -107.37.06.5 +33.54.06.1
21 ea23 E07 25.0 m -107.36.52.4 +33.53.56.5
22 ea24 W05 25.0 m -107.37.13.0 +33.53.57.8
23 ea25 N02 25.0 m -107.37.06.2 +33.54.03.5
24 ea26 W03 25.0 m -107.37.08.9 +33.54.00.1
25 ea27 E03 25.0 m -107.37.02.8 +33.54.00.5
26 ea28 N08 25.0 m -107.37.07.5 +33.54.15.8
##########################################
We can see that there are three sources in this observation:
• J1925+2106, field ID 1: the phase calibrator;
• G55.7+3.4, field ID 2: the supernova remnant;
• 0542+498=3C147, field ID 3: the flux and bandpass calibrator.
We can also see that these sources have associated "scan intents", which indicate their function in the observation, and may be selected on using CASA tasks. In particular,
• CALIBRATE_PHASE indicates that this is a scan to be used for gain calibration;
• OBSERVE_TARGET indicates that this is the science target;
• CALIBRATE_AMPLI indicates that this is to be used for flux calibration; and
• CALIBRATE_BANDPASS indicates that these scans are to be used for bandpass calibration.
Note that 3C147 is to be used for both flux and bandpass calibration.
We can see the antenna configuration for this observation using plotants:
# In CASA
plotants('G55.7+3.4_10s.ms')
plotants image
This shows that antennas ea01, ea18, and ea03 were on the extreme ends of the west, north, and east arms, respectively. The antenna position diagram is particularly useful in determining if a co-located set of antennas is affected, which can help with flagging.
We may also inspect the raw data using plotms. To start with, let's look at a subset of scans on the supernova remnant:
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='30,75,120,165,190,235,303',
antenna='ea24', xaxis='freq', yaxis='amp', coloraxis='spw',
iteraxis='scan', correlation='rr,ll')
The coloraxis parameter indicates that a different color will be assigned to each spectral window, and the iteraxis parameter tells plotms to display a new plot for each scan. We have chosen only one antenna (ea24) and just the right and left circular polarizations (without the cross-hand terms) to reduce the amount of data in the selection, One can flip through these plots using the green arrows located at the bottom of the plotting gui: the double-left arrow will display the very first plot in the set, the single left arrow will go back one plot, and the right arrows have similar behavior for moving forward in the set.
plotms image
Flipping through the scans, it's clear that there is significant time- and frequency-variable RFI present in this observation. Since this is L-band data taken in the most compact EVLA configuration ("D"), this comes as no surprise. However, it also poses one of the greatest challenges for obtaining a good image.
In particular, we can see that two spectral windows (SPWs) are quite badly affected. To determine which these are, click in the "Mark Regions" tool at the bottom of the gui (the open box with a green "plus" sign), and use the mouse to select a few of the highest-amplitude points in each of these SPWs. Click on the "Locate" button (magnifying glass), and information associated with the selected points will be displayed in the logger window:
Frequency in [1.22177 1.27139] or [1.5762 1.65063], Amp in [23.1713 24.3056] or [59.6296 63.6806]:
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:20:57.0 BL=ea12@E08 & ea24@W05[11&22] Spw=1 Chan=59 Freq=1.246 Corr=RR X=1.246 Y=23.5243 (38134/11/1526)
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:21:07.0 BL=ea03@E09 & ea24@W05[2&22] Spw=1 Chan=59 Freq=1.246 Corr=RR X=1.246 Y=23.6116 (40310/12/374)
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:21:07.0 BL=ea12@E08 & ea24@W05[11&22] Spw=1 Chan=59 Freq=1.246 Corr=RR X=1.246 Y=23.4432 (41462/12/1526)
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:21:57.0 BL=ea03@E09 & ea24@W05[2&22] Spw=1 Chan=59 Freq=1.246 Corr=RR X=1.246 Y=23.7536 (56950/17/374)
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:21:07.0 BL=ea12@E08 & ea24@W05[11&22] Spw=4 Chan=41 Freq=1.602 Corr=RR X=1.602 Y=61.9097 (131282/39/1490)
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:21:17.0 BL=ea12@E08 & ea24@W05[11&22] Spw=4 Chan=41 Freq=1.602 Corr=RR X=1.602 Y=61.1769 (134610/40/1490)
Scan=30 Field=G55.7+3.4[2] Time=2010/08/23/01:21:27.0 BL=ea12@E08 & ea24@W05[11&22] Spw=4 Chan=41 Freq=1.602 Corr=RR X=1.602 Y=60.1834 (137938/41/1490)
Found 7 points (7 unflagged) among 239616 in 0.02s.
We can see that SPWs 1 and 4 are among the worst affected by RFI. (As an aside, note that the syntax for reporting a selected point's baseline is {antenna 1 name}@{pad 1 name} &{antenna 2 name}@{pad 2 name}[{antenna 1 index}&{antenna 2 index}].) At this point, feel free to play around a bit more with plotms; you might try experimenting with different axes for iteration (under the "Iter" left-hand tab), different data selection parameters (under "Data"), different axes ("Axes"), or different averaging techniques (under "Data").
## A priori calibration and flagging
Before we proceed with further processing, we should check the observation log to see if there were any issues noted during the run that need to be addressed. The observing log file is linked to the archive web page for this observation (at far right; under "logs etc."). Looking at the log, we can see that antenna ea07 may need a position correction, and antennas ea06, ea17, ea20, and ea26 did not have L-band receivers installed at the time and should be flagged.
### Antenna position correction
Correcting a known position error for an antenna is done with the task gencal. This is important, because the observed visibilities are a function of $u$ and $v$. If an antenna's position is incorrect, then $u$ and $v$ will be calculated incorrectly, and there will be errors in any image derived from the data. Of course, the a priori position corrections may not completely account for all errors. The bandpass calibration, below, will take care of remaining delay corrections.
The gencal task will query the VLA Baseline Corrections database to determine what baseline corrections to apply to the dataset. If you wish to double-check this by hand, refer to the EVLA/VLA Baseline Corrections page.
# In CASA
gencal(vis='G55.7+3.4_10s.ms', caltable='G55.7+3.4_10s.pos',
caltype='antpos')
As reported by the CASA logger, gencal found a position correction for antenna ea07 of (x, y, z) = (0.0087, 0.0137, 0.000) and recorded this in our specified calibration table.
### Gain curve and opacity correction
A decision has been made here to ignore both the corrections for atmospheric opacity and for the elevation-dependent telescope gain throughout this tutorial (opacity=[], gaincurve=False in tasks such as gaincal, bandpass, and applycal). These effects are very small (less than or about 1%) across the frequency range of this observation (1-2 GHz).
### Flagging non-operational antennas
In addition to updating the position for antenna ea07, we have to flag antennas ea06, ea17, ea20, and ea26, since these did not have working L-band receivers at the time of observation. We do this with the task flagdata:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='manual',
antenna='ea06,ea17,ea20,ea26')
Note that the first thing flagdata does is create a backup flag file, in this case named "flagdata_1". This flag file contains a copy of the flags present in the MS prior to the requested flagging operation, and can be found inside the <MS_name>.flagversions directory, along with any other backed up flag files. Since these flag files take up a fair amount of space (in this particular case, 230 MB), we won't me making them every time we run flagdata -- the automatic flag backup can be turned off by setting flagbackup=False. However, it's good to keep a record of the names of the backup files and the associated processing step, in case you wish to restore a previous version of the flags.
### Flagging shadowed antennas and zero-amplitude data
Since this is the most compact EVLA configuration, there may be instances where one antenna blocks, or "shadows" another. Therefore, we will run flagdata to remove these data:
# In CASA
flagbackup=False)
In this particular observation, there is only a small amount of data affected by shadowing (0.2%), as can be seen in the logger report.
In addition, there may be times during which the correlator writes out pure zero-valued data. In order to remove this bad data, we run flagdata to remove any pure zeroes:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='clip',
clipzeros=True, flagbackup=False)
Inspecting the logger output which is generated by flagdata shows that there is a very small quantity of zero-valued data (0.02%) present in this MS.
Note that the archive will automatically flag shadowed antennas as well as zero-valued data, if you request that online flags are applied.
## Automatic RFI excision
Now, we move on to one of the most difficult parts of L-band, D-configuration data processing: excising the RFI. For the original reduction of this MS, flagging was done by hand and took several weeks. The resulting data are offered as an option for the imaging stage of this tutorial (because careful by-hand flagging does yield a better image); however, it's not always practical to undertake this endeavor, and often the "automatic" flagging provides a reasonable (and much less time-consuming) solution. Therefore, we will demonstrate the use of the automatic RFI excision tools currently available in CASA.
### Hanning-smoothing data
Prior to flagging any data which is affect by strong RFI, one should Hanning-smooth the data to remove Gibbs ringing. This is done with the task hanningsmooth, which can either write a new, Hanning-smoothed MS or directly operate on the requested column of the input MS. To conserve space, we will request the latter. Note that if you wish to make your own "before" and "after" plots, you should make the first prior to running hanningsmooth, since you will be overwriting the non-Hanning-smoothed data in the process -- and this is not reversible.
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='30', antenna='ea24', spw='0~2',
xaxis='freq', yaxis='amp', coloraxis='spw',
correlation='rr,ll', plotrange=[1.0,1.27,-0.3,2.5],
plotfile='amp_v_freq.beforeHanning.png')
hanningsmooth(vis='G55.7+3.4_10s.ms', datacolumn='data')
plotms(vis='G55.7+3.4_10s.ms', scan='30', antenna='ea24', spw='0~3',
xaxis='freq', yaxis='amp', coloraxis='spw',
correlation='rr,ll', plotrange=[1.0,1.27,-0.3,2.5],
plotfile='amp_v_freq.afterHanning.png')
before Hanning smoothing
after Hanning smoothing
Task hanningsmooth will take a few minutes to run. Note that the 2nd plotms command above contains a trivial change in the spw selection (trivial because the 4th spw is outside of the specified plotrange). This forces plotms to reload the plot since by default, plotms will not redraw a plot if the input parameters are unchanged. In this case, since the data column was changed between calls to plotms a redraw is necessary. When using the GUI, you can simply check "force reload" in the bottom left corner of the side bar before clicking "Plot".
We can compare the Hanning-smoothed data with the raw data by plotting a subset of data to show the result of Hanning-smoothing (see plots to the left and right). As you can see, the smoothing has spread the single-channel RFI into three channels, but has also removed the effects of some of the worst RFI from a number of channels. Overall, this will improve our ability to flag RFI from the data and retain as much good data as possible.
### Using phase calibration source for preliminary bandpass calibration
In order to get the best possible result from the automatic RFI excision, we will first apply bandpass calibration to the MS. Since the RFI is time-variable, using the phase calibration source to make an average bandpass over the entire observation will mitigate the amount of RFI present in the calculated bandpass. (For the final calibration, we will use the designated bandpass source 3C147; however, since this object was only observed in the last set of scans, it doesn't sample the time variability and would not provide a good average bandpass.)
Since there are likely to be gain variations over the course of the observation, we will run gaincal to solve for an initial set of antenna-based phases over a narrow range of channels. These will be used to create the bandpass solutions. While amplitude variations will have little effect on the bandpass solutions, it is important to solve for these phase variations with sufficient time resolution to prevent decorrelation when vector averaging the data in computing the bandpass solutions.
In order to choose a narrow range of channels for each spectral window which are relatively RFI-free over the course of the observation, we can look at the data with plotms. Note that it's important to only solve for phase using a narrow channel range, since an antenna-specific delay will cause the phase to vary with respect to frequency over the spectral window, perhaps by a substantial amount.
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='30,75,120,165,190,235,303',
antenna='ea24', xaxis='channel', yaxis='amp', iteraxis='spw',
yselfscale=True, correlation='rr,ll')
• yselfscale=True: sets the y-scaling to be for the currently displayed spectral window, since some spectral windows have much worse RFI and will skew the scale for others.
Looking at these plots, we can choose appropriate channel ranges for each SPW:
SPW 0: 10-13
SPW 1: 30-33
SPW 2: 32-35
SPW 3: 30-33
SPW 4: 35-38
SPW 5: 30-33
SPW 6: 30-33
SPW 7: 46-49
Using these channel ranges, we run gaincal to perform phase-only solutions over the course of the observation:
# In CASA
gaincal(vis='G55.7+3.4_10s.ms', caltable='G55.7+3.4_10s.initPh',
intent='CALIBRATE_PHASE*', solint='int',
spw='0:10~13,1;3;5~6:30~33,2:32~35,4:35~38,7:46~49',
refant='ea24', minblperant=3,
minsnr=3.0, calmode='p', gaintable='G55.7+3.4_10s.pos')
• caltable='G55.7+3.4_10s.initPh': this is the output calibration table that will be written.
• intent='CALIBRATE_PHASE*': this is the way we have chosen to select data. Alternatively, we could have used "field='J1925+2106'", since this is the only source with the CALIBRATE_PHASE* scan intent. Note the use of the wildcard character "*" at the end of the string; this accounts for the fact that all the intents end with ".UNSPECIFIED". We could just as well have used "*PHASE*".
• solint='int': we request a solution for each 10-second integration.
• spw='0:10~13,1;3;5~6:30~33,2:32~35,4:35~38,7:46~49': note the syntax of this selection: a ":" is used to separate the SPW from channel selection, ";" is used to separate within this selection, and "~" is used to indicate an inclusive range.
• refant='ea24': we have chosen ea24 as the reference antenna after inspecting the antenna position diagram (see above). It is relatively close to, but not directly in, the center of the array, which could be important in D-configuration, since you don't want the reference antenna to have a high probability of being shadowed by nearby antennas.
• minblperant=3: the minimum number of baselines which must be present to attempt a phase solution.
• minsnr=3.0: the minimum signal-to-noise a solution must have to be considered acceptable. Note that solutions which fail this test will cause these data to be flagged downstream of this calibration step.
• calmode='p': perform phase-only solutions.
• gaintable='G55.7+3.4_10s.pos': use the antenna position correction for ea07 that we created earlier.
Note that a number of solutions do not pass the requirements of the minimum 3 baselines (generating the terminal message "Insufficient unflagged antennas to proceed with this solve.") or minimum signal-to-noise ratio (outputting "n of x solutions rejected due to SNR < 3 ..."). A particularly large number of solutions are rejected in SPW 4, where the RFI is most severe.
Phases for antenna ea09
Phases in SPW 4
We can inspect the resulting calibration table with plotcal:
# In CASA
plotcal(caltable='G55.7+3.4_10s.initPh', xaxis='time', yaxis='phase',
iteration='antenna', spw='0', plotrange=[-1,-1,-180,180])
This iterates over antenna for a single spectral window; we can see that the phase does not change much over the course of the observation for SPW 0. We may also iterate over spectral window for a subset of antennas:
# In CASA
plotcal(caltable='G55.7+3.4_10s.initPh', xaxis='time', yaxis='phase',
iteration='spw', antenna='ea01,ea05,ea24', plotrange=[-1,-1,-180,180])
Clearly, the phases are affected by RFI in some places, especially in SPW 4.
Using this phase information, we create time-averaged bandpass solutions for the phase calibration source:
# In CASA
bandpass(vis='G55.7+3.4_10s.ms', caltable='G55.7+3.4_10s.initBP',
intent='CALIBRATE_PHASE*', solint='inf',
combine='scan', refant='ea24', minblperant=3, minsnr=10.0,
gaintable=['G55.7+3.4_10s.pos', 'G55.7+3.4_10s.initPh'],
interp=['', 'nearest'], solnorm=False)
• solint='inf', combine='scan': the solution interval of 'inf' will automatically break by scans; this requests that the solution intervals be combined over scans, so that we will get one solution per antenna.
• gaintable=['G55.7+3.4_10s.pos', 'G55.7+3.4_10s.initPh']: we will pre-apply both the corrected antenna position as well as the initial phase solutions.
• interp=['', 'nearest']: by default, gaincal will use linear interpolation for pre-applied calibration. However, we want the nearest phase solution to be used for a given time.
Again, we can see that a number of solutions have been rejected by our choices of minblperant and minsnr.
Bandpasses for antennas ea10 - ea19
We may plot the bandpasses with plotcal; first looking at the amplitudes:
# In CASA
plotcal(caltable='G55.7+3.4_10s.initBP', xaxis='freq', yaxis='amp',
iteration='antenna', subplot=331)
• subplot=331: displays 3x3 plots per screen
Also, we can look at the phase solutions:
# In CASA
plotcal(caltable='G55.7+3.4_10s.initBP', xaxis='freq', yaxis='phase',
iteration='antenna', subplot=331)
We can see that SPW 4 is virtually wiped out by RFI; furthermore, there are channels in SPW 1 that are consistently badly affected. Prior to running any automatic flagging, we will flag these manually. In addition, we will flag the first 9 channels of SPW 0, since this is affected by an issue which causes the noise to be substantially higher:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', spw='0:0~8,1:41~63,4')
Note that this has created a backup flag file called "flagdata_2". Now we apply the antenna position correction and this bandpass calibration to the data:
# In CASA
applycal(vis='G55.7+3.4_10s.ms',
gaintable=['G55.7+3.4_10s.pos', 'G55.7+3.4_10s.initBP'],
calwt=False)
This operation will flag data that correspond to flagged solutions, so applycal makes a backup version of the flags prior to operating on the data -- in this case, it's called "before_applycal_1". Note that running applycal might take a little while, likely around 10 minutes.
To see the corrected data, we can plot the data as we did before, choosing ydatacolumn='corrected' this time:
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='30,75,120,165,190,235,303',
antenna='ea24', xaxis='freq', yaxis='amp', coloraxis='spw',
iteraxis='scan', ydatacolumn='corrected')
Note that some of the worst RFI is no longer there; also note that the amplitude scale has changed, since the bandpass solutions include amplitude scaling.
### Automatic flagging
Now that we have bandpass-corrected data with some of the worst RFI flagged out, we will run flagdata in mode='rflag'. Note that there are many parameters which may be modified:
# In CASA
default flagdata
mode='rflag'
inp
# flagdata :: All-purpose flagging task based on data-selections and flagging modes/algorithms
vis = '' # Name of MS file to flag
mode = 'rflag' # Flagging mode
field = '' # Field names or field index numbers: '' ==> all, field='0~2,3C286'
spw = '' # Spectral-window/frequency/channel: '' ==> all, spw='0:17~19'
antenna = '' # Antenna/baselines: '' ==> all, antenna ='3,VA04'
timerange = '' # Time range: '' ==> all,timerange='09:14:0~09:54:0'
correlation = '' # Correlation: '' ==> all, correlation='XX,YY'
scan = '' # Scan numbers: '' ==> all
intent = '' # Observation intent: '' ==> all, intent='CAL*POINT*'
array = '' # (Sub)array numbers: '' ==> all
uvrange = '' # UV range: '' ==> all; uvrange ='0~100klambda', default units=meters
observation = '' # Observation ID: '' ==> all
feed = '' # Multi-feed numbers: Not yet implemented
ntime = 'scan' # Time-range to use for each chunk (in seconds or minutes)
combinescans = False # Accumulate data across scans.
datacolumn = 'DATA' # Data column on which to operate (data,corrected,model,residual)
winsize = 3 # Number of timesteps in the sliding time window [aips:fparm(1)]
timedev = '' # Time-series noise estimate [aips:noise]
freqdev = '' # Spectral noise estimate [aips:scutoff]
timedevscale = 5.0 # Threshold scaling for timedev [aips:fparm(9)]
freqdevscale = 5.0 # Threshold scaling for freqdev [aips:fparm(10)]
spectralmax = 1000000.0 # Flag whole spectrum if freqdev is greater than spectralmax [aips:fparm(6)]
spectralmin = 0.0 # Flag whole spectrum if freqdev is less than spectralmin [aips:fparm(5)]
action = 'apply' # Action to perform in MS and/or in inpfile (none/apply/calculate)
display = '' # Display data and/or end-of-MS reports at runtime (data/report/both).
flagbackup = True # Back up the state of flags before the run
savepars = False # Save the current parameters to the FLAG_CMD table or to a file
async = False # If true the taskname must be started using flagdata(...)
Additional information on the algorithm used in RFlag, as well as the other available automatic flagging algorithm in flagdata ("TFCrop"), can be found on this webpage (sections 2.1.6 and 2.1.7).
Following are a set of flagdata commands which have been found to work reasonably well with these data. Please take some time to play with the parameters and the plotting capabilities. Since these runs set display='both' and action='calculate', the flags are displayed but not actually written to the MS. This allows one to try different sets of parameters before actually applying the flags to the data.
Some representative plots are also displayed. Each column displays an individual polarization product; since we're using all four, from left to right are RR, RL, LR, and LL. The first row shows the data with current flags applied, and the second includes the flags generated by flagdata. The x-axis is channel number (the spectral window ID is displayed in the top title) and the y-axis of the first two rows is all integrations included in a time "chunk", set by the ntime parameter. These are the data considered by the RFlag algorithm during its flagging process, and changes in ntime will have some (relatively small) affect on what data are flagged.
Each plot page displays data for a single baseline and time chunk. The buttons at the bottom allow one to step through baseline (backward as well as forward), SPW, scan, and field; "Stop Display" will continue the flagging operation without the GUI, and "Quit" aborts the run.
First, we will run flagdata with mode='rflag', using the default parameter values, for just one source (the supernova remnant) and spectral window (0):
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag', field='2',
spw='0', datacolumn='corrected',
action='calculate', display='both',
flagbackup=False)
While this is clearly picking up some RFI, much is being left untouched (see figure to left, below). After stepping through a few baselines and scans, hit "Quit" to stop the flagger.
Let's try making it more sensitive to deviations from the calculated RMS in frequency, setting both timedevscale and freqdevscale=1.5 (the default is 5.0):
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag', field='2',
spw='0', datacolumn='corrected',
freqdevscale=1.5, timedevscale=1.5,
action='calculate', display='both',
flagbackup=False)
flagdata/rflag, default parameters
flagdata/rflag, cutoff of 1.5 sigma
Using a cutoff value of 1.5 sigma may seem a bit extreme, but as you can see from the figure on the right, it does a substantially better job of getting rid of the RFI in the badly affected SPW 0.
We now run flagdata to calculate and apply these flags for all data in SPW 0. Note that this will take a little while, and flags around 20% of the data:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='0', datacolumn='corrected',
freqdevscale=1.5, timedevscale=1.5,
action='apply', display='')
Although RFlag has done a pretty good job of finding the bad data, some still remains. One way to delete it is to use the mode='extend' feature in flagdata, which can extend flags along a chosen axis. First, we will extend the flags across polarization, so if any one polarization is flagged, all data for that time / channel will be flagged:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='0', extendpols=True,
action='apply', display='')
Now, we will extend the flags in time and frequency, using the "growtime" and "growfreq" parameters. For the data here, the RFlag algorithm seems most likely to miss RFI which should be flagged along more of the time axis, so we will try with growtime=50.0, which will flag all data for a given channel if more than 50% of that channel's time is already flagged, and growfreq=90.0, which will flag the entire spectrum for an integration if more than 90% of the channels in that integration are already flagged.
Again, first just have a look at the flags that will be generated before applying them:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='0', growtime=50.0, growfreq=90.0,
action='calculate', display='data',
flagbackup=False)
It still appears to be missing some RFI, but this is also a very badly-affected SPW, so leave it as is for now and run to apply the flags:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='0', growtime=50.0, growfreq=90.0,
action='apply', display='')
Now, let's work on SPW 1, flipping through time, baseline, and fields to get a sense of how the flagging will go with these parameters:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='1', datacolumn='corrected',
freqdevscale=2.0, timedevscale=2.0,
action='calculate', display='both',
flagbackup=False)
Unfortunately, this SPW is very badly affected by RFI, and it does not seem possible to flag adequately with the automated task (and probably not by hand, either). In this case, we choose to manually flag the entire SPW:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', spw='1')
Moving on to SPW 2:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='2', datacolumn='corrected',
freqdevscale=5.0, timedevscale=4.0,
action='calculate', display='both',
flagbackup=False)
Since the RFI is narrower and more pronounced in this frequency range, we have increased the RMS cutoff for both the time and frequency calculations to avoid over-flagging and deleting good data.
After checking the data and changing the parameters until you're happy, apply these flags:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='2', datacolumn='corrected',
freqdevscale=5.0, timedevscale=4.0,
action='apply')
Again, extend the flags along polarization:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='2', extendpols=True,
action='apply', display='')
Try extending in frequency and time, as before:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='2', growtime=50.0, growfreq=90.0,
action='calculate', display='data',
flagbackup=False)
This looks pretty good, so let's apply it and have a look in plotms:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='2', growtime=50.0, growfreq=90.0,
action='apply')
plotms(vis='G55.7+3.4_10s.ms', scan='30,75,120,165,190,235,303',
xaxis='baseline', yaxis='amp', spw='2',
iteraxis='scan', correlation='rr,ll')
Although we're trying to avoid doing this too much, it appears that there is one baseline which is consistently higher-amplitude than the others, indicating that it's probably contaminated by RFI. Use the plotms tools to identify this baseline, which turns out to be ea04 and ea16, and flag it:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', antenna='ea04&ea16',
spw='2')
We could have narrowed this further by channel and perhaps time, but remember: this tutorial is about the quick-and-dirty way of flagging data! With this in mind, we move on to SPW 3. Note that this time, we only look at data from the supernova remnant (target) field.
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='3', datacolumn='corrected', field='2',
freqdevscale=5.0, timedevscale=4.0,
action='calculate', display='data',
flagbackup=False)
The parameters we used for SPW 2 seem to work well for SPW 3 also. Go ahead and flag, then extend as before:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='3', datacolumn='corrected',
freqdevscale=5.0, timedevscale=4.0,
action='apply')
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='3', extendpols=True,
action='apply')
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='3', growtime=50.0, growfreq=90.0,
action='apply')
Recall that we already deleted SPW 4 due to bad RFI, so we only have 5-7 remaining. SPWs 5 and 6 have similar RFI properties to 2 and 3, so let's use the same RFlag parameters for these (feel free to play with this a bit yourself, if you like, to try to optimize):
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='5~6', datacolumn='corrected',
freqdevscale=5.0, timedevscale=4.0,
action='apply')
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='5~6', extendpols=True,
action='apply')
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='5~6', growtime=50.0, growfreq=90.0,
action='apply')
However, SPW 7 is a bit more affected, and we may wish to use a somewhat lower threshold to catch all the RFI. First, try with the same parameters:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='7', datacolumn='corrected', field='2',
freqdevscale=5.0, timedevscale=4.0,
action='calculate', display='data',
flagbackup=False)
Indeed, this seems to be missing a lot of the RFI. Try less stringent limits:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='7', datacolumn='corrected', field='2',
freqdevscale=1.0, timedevscale=1.0,
action='calculate', display='data',
flagbackup=False)
This looks pretty good. Check the calibrator sources to be sure it works for them as well:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='7', datacolumn='corrected', field='1',
freqdevscale=1.0, timedevscale=1.0,
action='calculate', display='data',
flagbackup=False)
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='7', datacolumn='corrected', field='3',
freqdevscale=1.0, timedevscale=1.0,
action='calculate', display='data',
flagbackup=False)
These seem reasonable as well, though it's apparent that 3C147 was very affected, possibly because of its low elevation at the time of the observation. Apply and extend the flags:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', mode='rflag',
spw='7', datacolumn='corrected',
freqdevscale=1.0, timedevscale=1.0,
action='apply')
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='7', extendpols=True,
action='apply')
flagdata(vis='G55.7+3.4_10s.ms', mode='extend',
spw='7', growtime=50.0, growfreq=90.0,
action='apply')
### Evaluating results & further manual flagging
Now, we will use flagdata to see a summary of how much data we have flagged:
# In CASA
flagInfo = flagdata(vis='G55.7+3.4_10s.ms', mode='summary')
Using the information stored in the flagInfo Python dictionary, we can calculate and print out some interesting statistics:
# In CASA
print("\n %2.1f%% of G55.7+3.4, %2.1f%% of 3C147, and %2.1f%% of J1925+2106 are flagged. \n" % (100.0 * flagInfo['field']['G55.7+3.4']['flagged'] / flagInfo['field']['G55.7+3.4']['total'], 100.0 * flagInfo['field']['0542+498=3C147']['flagged'] / flagInfo['field']['0542+498=3C147']['total'], 100.0 * flagInfo['field']['J1925+2106']['flagged'] / flagInfo['field']['J1925+2106']['total']))
print("Spectral windows are flagged as follows:")
for spw in range(0,8):
print("SPW %s: %2.1f%%" % (spw, 100.0 * flagInfo['spw'][str(spw)]['flagged'] / flagInfo['spw'][str(spw)]['total']))
So, as a result of the flagging thus far, we have sacrificed a bit over half of all the data. Let's see how well it has been cleaned up, using plotms:
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='165', spw='0,2~3,5~7',
antenna='ea24', xaxis='freq', yaxis='amp',
correlation='rr,ll', coloraxis='spw')
Unfortunately, despite our best autoflagging efforts, SPW 0 still looks pretty bad. (Take heart -- even the by-hand flagging did not work out well for this one.) So, we will flag the rest of SPW 0:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', spw='0')
after flagging screenshot
before flagging screenshot
After this is complete, refresh the plotms window using Shift + Plot. This generates the plot to the left. Just to compare with the unflagged data, we will restore the original flags, and have a look at the same slice. Be sure to save the current flags first!
# In CASA
flagmanager(vis='G55.7+3.4_10s.ms', mode='save',
versionname='after_autoflagging_1')
flagmanager(vis='G55.7+3.4_10s.ms', mode='restore',
versionname='flagdata_1')
plotms(vis='G55.7+3.4_10s.ms', scan='165', spw='2~3,5~7',
antenna='ea24', xaxis='freq', yaxis='amp',
correlation='rr,ll', coloraxis='spw')
The pre-flagging plot is shown on the right. Clearly, a lot of the RFI has been excised. Restore the flags:
# In CASA
flagmanager(vis='G55.7+3.4_10s.ms', mode='restore',
versionname='after_autoflagging_1')
Other instructive ways to view the data are by baseline and uv-distance. Note that we're plotting all baselines in these plots, rather than just baselines to ea24 as before.
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='30,75,120,165,190,235,303',
xaxis='baseline', yaxis='amp', spw='2~3,5~7', iteraxis='spw',
correlation='rr,ll', coloraxis='antenna1')
No particular baselines look bad enough to flag outright, so we will leave this as is. Feel free to do some more flagging if you like. Now, let's plot as a function of uv-distance:
# In CASA
plotms(vis='G55.7+3.4_10s.ms', scan='30,75,120,165,190,235,303',
xaxis='uvdist', yaxis='amp', spw='2~3,5~7', iteraxis='spw',
correlation='rr,ll', coloraxis='antenna1')
Again, nothing really sticks out as obviously in need of flagging. Clearly, there is still some residual RFI left here and there -- however, for the purposes of this tutorial, we will accept the current state of the flags and move on. Feel free to hunt and excise some more, if desired.
## Calibrating data
Now that we are satisfied with the RFI excision, we will move on to the calibration stage.
### Setting the flux density scale
Since we will be using 3C147 as the source of the absolute flux scale for this observation, we must first run setjy to set the appropriate model amplitudes for this source.
If the flux calibrator is spatially resolved, it is necessary to include a model image as well. Although 3C147 is not resolved at L-band in D configuration, we include the model image here for completeness.
First, we use the listmodimages parameter to find the model image path:
# In CASA
setjy(vis='G55.7+3.4_10s.ms', listmodels=True)
This lists any images in the current working directory as well as images in CASA's repository. In this second list, we see that there is "3C147_L.im", which is appropriate for our flux calibrator and band, and that it is in the directory "/usr/lib64/casapy/release/nrao/VLA/CalModels". We can optionally give the full path of the model image, but setjy should now be able to locate it by name alone:
# In CASA
setjy(vis='G55.7+3.4_10s.ms', field='0542*', scalebychan=True,
spw='2~3,5~7', modimage='3C147_L.im')
• scalebychan=True: scales the model flux density value for each channel. By default, only one value per spectral window is calculated.
### Bandpass calibration
We will follow the same procedure outlined above for calculating the antenna bandpasses, except that this time, we will use the actual designated bandpass calibration source, 3C147. Although the phase calibration source has the advantage of having been observed throughout the run, it has an unknown spectrum which could introduce amplitude slopes to each spectral window.
# In CASA
gaincal(vis='G55.7+3.4_10s.ms', intent='*BANDPASS*',
caltable='G55.7+3.4_10s.initPh.2',
spw='3;5~6:30~33,2:32~35,7:50~53',
solint='int', refant='ea24',
minblperant=3, minsnr=3.0, calmode='p',
gaintable='G55.7+3.4_10s.pos')
Unfortunately, you will notice a lot of message that read "Insufficient unflagged antennas to proceed with this solve" for SPW 7. This indicates that too much data have been flagged to perform the gaincal operation. This also suggests that the spectral window is too badly affected by RFI to be useful for imaging -- so, we will flag the rest of the SPW before continuing with further analysis:
# In CASA
flagdata(vis='G55.7+3.4_10s.ms', spw='7')
Now, on to creating the bandpass calibration for the remaining spectral windows:
# In CASA
bandpass(vis='G55.7+3.4_10s.ms', caltable='G55.7+3.4_10s.bPass',
intent='*BANDPASS*', solint='inf', spw='2~3,5~6',
combine='scan', refant='ea24', minblperant=3, minsnr=10.0,
gaintable=['G55.7+3.4_10s.pos','G55.7+3.4_10s.initPh.2'],
interp=['', 'nearest'], solnorm=False)
• solint='inf', combine='scan': again, the solution interval of 'inf' will automatically break by scans; this requests that the solution intervals be combined over scans, so that we will get one solution per antenna.
bandpass amplitudes
bandpass phases
Note that since we have flagged out the vast majority of the RFI-affected data, there are many fewer failed solutions. Again, we can plot the calculated bandpasses to check that they look reasonable:
# In CASA
plotcal(caltable='G55.7+3.4_10s.bPass', xaxis='freq', yaxis='amp',
iteration='antenna', subplot=331)
#
plotcal(caltable='G55.7+3.4_10s.bPass', xaxis='freq', yaxis='phase',
iteration='antenna', subplot=331)
Don't let the apparently odd-looking phases for ea24 fool you -- check the scale! Remember, this is our reference antenna.
### Gain calibration
Next, we will calculate the per-antenna gain solutions. Since this is low-frequency data, we do not expect substantial variations over short timescales, so we calculate one solution per scan (using "solint='inf'"):
# In CASA
gaincal(vis='G55.7+3.4_10s.ms', caltable='G55.7+3.4_10s.phaseAmp',
intent='*PHASE*,*AMPLI*',
spw='2~3,5~6', solint='inf', refant='ea24', minblperant=3,
minsnr=10.0, gaintable=['G55.7+3.4_10s.pos','G55.7+3.4_10s.bPass'])
• solint='inf': we request one solution per scan.
Plot these solutions as a function of time, iterating over antenna:
# In CASA
plotcal(caltable='G55.7+3.4_10s.phaseAmp', xaxis='time', yaxis='amp',
iteration='antenna')
plotcal(caltable='G55.7+3.4_10s.phaseAmp', xaxis='time', yaxis='phase',
iteration='antenna')
### Flux scaling the gain solutions
Now that we have a complete set of gain solutions, we must scale the phase calibrator's absolute flux correctly, using 3C147 as our reference source. To do this, we run fluxscale on the gain table we just created, which will write a new, flux-corrected gain table:
# In CASA
fluxscale(vis='G55.7+3.4_10s.ms', caltable='G55.7+3.4_10s.phaseAmp',
fluxtable='G55.7+3.4_10s.phaseAmp.fScale', reference='3')
The logger will display information about the flux density it has deduced for J1925+2106:
Found reference field(s): 0542+498=3C147
Found transfer field(s): J1925+2106
Flux density for J1925+2106 in SpW=0 is: INSUFFICIENT DATA
Flux density for J1925+2106 in SpW=1 is: INSUFFICIENT DATA
Flux density for J1925+2106 in SpW=2 is: 1.47002 +/- 0.0300985 (SNR = 48.8401, N = 36)
Flux density for J1925+2106 in SpW=3 is: 1.54053 +/- 0.0270024 (SNR = 57.0518, N = 36)
Flux density for J1925+2106 in SpW=4 is: INSUFFICIENT DATA
Flux density for J1925+2106 in SpW=5 is: 1.71428 +/- 0.0271304 (SNR = 63.1867, N = 36)
Flux density for J1925+2106 in SpW=6 is: 1.77273 +/- 0.0291623 (SNR = 60.7886, N = 36)
Flux density for J1925+2106 in SpW=7 is: INSUFFICIENT DATA
The flux density listed in the VLA Calibrator Manual for this source is around the same magnitude:
1925+211 J2000 A 19h25m59.605370s 21d06'26.162180" Aug01
1923+210 B1950 A 19h23m49.792400s 21d00'23.305000"
-----------------------------------------------------
BAND A B C D FLUX(Jy) UVMIN(kL) UVMAX(kL)
=====================================================
20cm L P S S S 1.30 visplot
So we should be satisfied that our calibration up to this point is reasonable.
### Applying calibration
Finally, we must apply the calibration to our data. To do this, we run applycal in two stages: the first is to self-calibrate our calibration sources; the second, to apply calibration to the supernova remnant. These must be done separately, since we want to use "nearest" interpolation for the self-calibration and "linear" for the application to the science target:
# In CASA
applycal(vis='G55.7+3.4_10s.ms', spw='2~3,5~6', intent='*TARGET*',
gaintable=['G55.7+3.4_10s.pos','G55.7+3.4_10s.bPass', \
'G55.7+3.4_10s.phaseAmp.fScale'], calwt=False)
#
applycal(vis='G55.7+3.4_10s.ms', spw='2~3,5~6', intent='*PHASE*,*AMPLI*',
gaintable=['G55.7+3.4_10s.pos','G55.7+3.4_10s.bPass', \
'G55.7+3.4_10s.phaseAmp.fScale'],
calwt=False, interp=['','nearest','nearest'])
### Plotting calibrated data
J1925+2106 corrected amplitude vs. phase
J1925+2106 corrected amplitude vs. baseline
3C147 corrected amplitude vs. phase
3C147 corrected amplitude vs. baseline
To check that everything has truly proceeded as well as we would like, this is a good time to look at the calibrated data in plotms. A very useful way to check the goodness of calibration is to plot the corrected amplitude vs. corrected phase (which should look like a tight ball for a point source, and will have organized structure if the source is resolved), and corrected amplitude vs. baseline, which should be a flat line of points for a point source, and will reveal any lingering antenna-based problems. For a resolved source, it may be more instructive to plot corrected amplitude vs. uv-distance.
# In CASA
plotms(vis='G55.7+3.4_10s.ms', field='1', xaxis='phase', yaxis='amp',
xdatacolumn='corrected', ydatacolumn='corrected', coloraxis='antenna1',
avgchannel='10', avgtime='20', correlation='rr,ll', iteraxis='spw',
spw='2~3,5~6')
#
plotms(vis='G55.7+3.4_10s.ms', field='1', xaxis='baseline', yaxis='amp',
xdatacolumn='corrected', ydatacolumn='corrected', coloraxis='antenna1',
avgchannel='10', avgtime='20', correlation='rr,ll', iteraxis='spw',
spw='2~3,5~6')
#
plotms(vis='G55.7+3.4_10s.ms', field='3', xaxis='phase', yaxis='amp',
xdatacolumn='corrected', ydatacolumn='corrected', coloraxis='antenna1',
avgchannel='10', avgtime='20', correlation='rr,ll', iteraxis='spw',
spw='2~3,5~6')
#
plotms(vis='G55.7+3.4_10s.ms', field='3', xaxis='baseline', yaxis='amp',
xdatacolumn='corrected', ydatacolumn='corrected', coloraxis='antenna1',
avgchannel='10', avgtime='20', correlation='rr,ll', iteraxis='spw',
spw='2~3,5~6')
### Splitting out data for G55.7+3.4
Now that we are satisfied with the calibration, we will create a new MS which contains only the corrected data for G55.7+3.4 using the task split. This will substantially reduce the size of the MS, and will speed up the imaging process. We can also drop the polarization products since they have not been calibrated and will not be used for imaging.
# In CASA
split(vis='G55.7+3.4_10s.ms', field='2', keepflags=False,
outputvis='G55.7+3.4.calib.ms', datacolumn='corrected',
spw='2~3,5~6', correlation = 'rr,ll')
## Imaging
At this point, one may image either the resulting MS from the flagging and calibration steps above, or the MS that was flagged by hand and calibrated. The latter is available as "G55.7+3.4.byHandFlag.ms". (For internal, pre-workshop testers: the data can be found at /lustre/sbhatnag/Tests/ThursdayLectures/G55.7+3.4_10s_Calib.ms.) For this tutorial, we will use the MS that has been produced using testautoflag and the minimal amount of manual flagging described here, with the exception of the final clean step, where we will run identical commands on both sets of data and compare the results.
The size of the primary beam is 45 arcmin divided by the observed frequency in GHz, or around 30 arcmin. Since the observation was taken in D-configuration, we can check the Observational Status Summary to find that the synthesized beam will be around 44 arcsec. We want to oversample the synthesized beam by a factor of around five, so we will use a cell size of 8 arcsec.
Since this field contains bright point sources significantly outside the primary beam, we will create images that are 170 arcminutes on a side, or almost 6 x the size of the primary beam. This is ideal for showcasing both the problems inherent in such wide-band, wide-field imaging, as well as some of the solutions currently available in CASA to deal with these issues.
First, it's worth considering why we are even interested in sources which are far outside the primary beam. This is mainly due to the fact that the EVLA, with its wide bandwidth capabilities, is quite sensitive even far from phase center -- for example, at our observing frequencies in L-band, the primary beam gain is as much as 10% around 1 degree away. That means that any imaging errors for these far-away sources will have a significant impact on the image rms at phase center. The error due to a source at distance R can be parametrized as:
$\Delta(S) = S(R) \times PB(R) \times PSF(R)$
So, for R = 1 degree, source flux S(R) = 1 Jy, $\Delta(S)$ = 1 mJy − 100 ${\mu}$Jy. Clearly, this will be a source of significant error.
### Multi-scale clean
G55.7+3.4 multiscale clean
Since G55.7+3.4 is an extended source with many spatial scales, the most basic (yet still reasonable) imaging procedure is to use clean with multiple scales. As is suggested, we will use a set of scales (which are expressed in units of the requested pixel, or cell, size) which are representative of the scales that are present in the data, including a zero-scale for point sources.
Note that interrupting clean by Ctrl+C may corrupt your visibilities -- you may be better off choosing to let clean finish. We are currently implementing a command that will nicely exit to prevent this from happening, but for the moment try to avoid Ctrl+C.
# In CASA
clean(vis='G55.7+3.4.calib.ms', imagename='G55.7+3.4.multiScale',
imsize=1280, cell='8arcsec', multiscale=[0,6,10,30,60],
interactive=False, niter=1000, weighting='briggs',
stokes='I', threshold='0.1mJy', usescratch=F, imagermode='csclean')
viewer('G55.7+3.4.multiScale.image')
• imagename='G55.7+3.4.multiScale': the root filename used for the various clean outputs. These include the final image (<imagename>.image), the relative sky sensitivity over the field (<imagename>.flux), the point-spread function (also known as the dirty beam; <imagename>.psf), the clean components (<imagename>.model), and the residual image (<imagename>.residual).
• imsize=1280: the image size in number of pixels. Note that entering a single value results in a square image with sides of this value.
• cell='8arcsec': the size of one pixel; again, entering a single value will result in a square pixel size.
• multiscale=[0,6,10,30,60]: a set of scales on which to clean. Since these are in units of the pixel size, we are requesting scales of 0 (a point source), 48, 80, 240, and 480 arcseconds. Note that 16 arcminutes (960 arcseconds) roughly corresponds to the size of G55.7+3.4.
• interactive=False: we will let clean use the entire field for placing model components. Alternatively, you could try using interactive=True, and create regions to constrain where components will be placed. However, this is a very complex field, and creating a region for every bit of diffuse emission as well as each point source can quickly become tedious.
• niter=1000: this controls the number of iterations clean will do in the minor cycle.
• weighting='briggs': use Briggs weighting with a robustness parameter of 0 (halfway between uniform and natural weighting).
• calready=F: do not write the model visibilities to the model data column (only needed for self-calibration)
• imagermode='csclean': use the Cotton-Schwab clean algorithm
artifacts around point source
• stokes='I': since we have not done any polarization calibration, we only create a total-intensity image.
• threshold='0.1mJy': threshold at which the cleaning process will halt; i.e. no clean components with a flux less than this value will be created. This is meant to avoid cleaning what is actually noise (and creating an image with an artificially low rms). It is advisable to set this equal to the expected rms, which can be estimated using the EVLA exposure calculator. However, in our case, this is a bit difficult to do, since we have lost a hard-to-estimate amount of bandwidth due to flagging, and there is also some residual RFI present. Therefore, we choose 0.1 mJy as a relatively conservative limit.
This is the fastest of the imaging techniques described here (it will probably take less than ten minutes to complete), but it's easy to see that there are artifacts in the resulting image. For example, use the viewer to explore the point sources near the edge of the field. Some have prominent arcs, as well as spots in a six-pointed pattern surrounding them. Next we will explore some more advanced imaging techniques to mitigate these artifacts.
### Multi-scale, wide-field clean
The next clean algorithm we will employ is W-projection, which is a wide-field imaging technique that takes into account the non-coplanarity of the baselines as a function of distance from the phase center. For more details on the motivation for this correction, as well as the algorithm itself, see "The Noncoplanar Baselines Effect in Radio Interferometry: The W-Projection Algorithm".
# In CASA
clean(vis='G55.7+3.4.calib.ms', imagename='G55.7+3.4.MS.wProj',
gridmode='widefield', imsize=1280, cell='8arcsec',
wprojplanes=128, multiscale=[0,6,10,30,60],
interactive=False, niter=1000, weighting='briggs',
stokes='I', threshold='0.1mJy', usescratch=F, imagermode='csclean')
viewer('G55.7+3.4.MS.wProj.image')
w-projection improvements
• gridmode='widefield': use the W-projection algorithm.
• wprojplanes=128: the number of W-projection planes to use for deconvolution; 128 is the minimum recommended number.
This will take longer than the previous imaging round (likely around 15 minutes); however, the resulting image has noticeably fewer artifacts. In particular, compare the same outlier source in the W-projected image with the multi-scale-only image: note that the swept-back arcs have disappeared. There are still some obvious imaging artifacts remaining, though.
### Multi-scale, multi-frequency synthesis
Another consequence of simultaneously imaging the wide fractional bandwidths available with the EVLA is that the primary beam has substantial frequency-dependent variation over the observing band. If this is not accounted for, it will lead to imaging artifacts and compromise the achievable image rms.
If sources which are being imaged have intrinsically flat spectra, this will not be a problem. However, most astronomical objects are not flat-spectrum sources, and without any estimation of the intrinsic spectral properties, the fact that the primary beam is twice as large at 2 than at 1 GHz will have substantial consequences.
The Multi-Scale Multi-Frequency-Synthesis (MS-MFS) algorithm provides the ability to simultaneously image and fit for the intrinsic source spectrum. The spectrum is approximated using a polynomial in frequency, with the degree of the polynomial as a user-controlled parameter.
# In CASA
clean(vis='G55.7+3.4.calib.ms', imagename='G55.7+3.4.MS.MFS',
imsize=1280, cell='8arcsec', mode='mfs', nterms=2,
multiscale=[0,6,10,30,60],
interactive=False, niter=1000, weighting='briggs',
stokes='I', threshold='0.1mJy', usescratch=F, imagermode='csclean')
viewer('G55.7+3.4.MS.MFS.image.tt0')
viewer('G55.7+3.4.MS.MFS.image.alpha')
artifacts with nterms=2
• nterms=2:the number of Taylor terms to be used to model the frequency dependence of the sky emission. Note that the speed of the algorithm will depend on the value used here (more terms will be slower); of course, the image fidelity will improve with a larger number of terms (assuming the sources are sufficiently bright to be modeled more completely).
This will take a little while (likely around 30 minutes), so it would probably be a good time to have coffee or chat about EVLA data reduction with your neighbor at this point.
When clean is done <imagename>.image.tt0 will contain a total intensity image; <imagename>.image.alpha will contain an image of the spectral index in regions where there is sufficient signal-to-noise. For more information on the multi-frequency synthesis mode and its outputs, see the CASA cookbook. Inspect the brighter point sources in the field. You will notice that some of the artifacts which had been symmetric around the sources themselves are now gone; however, since we did not use W-projection this time, there are still strong features related to the non-coplanar baseline effects still apparent.
### Multi-scale, multi-frequency, wide-field clean
Finally, we will combine the W-projection and MS-MFS algorithms to simultaneously account for both of the effects. Be forewarned -- these imaging runs will take a while, and it's best to start them running and then move on to other things. In testing, both of these runs (on the auto- and by-hand-flagged data) took around an hour.
First, we will image the autoflagged data. Using the same parameters for the individual-algorithm images above, but combined into a single clean run, we have:
# In CASA
clean(vis='G55.7+3.4.calib.ms', imagename='G55.7+3.4.MS.MFS.wProj',
gridmode='widefield', imsize=1280, cell='8arcsec', mode='mfs',
nterms=2, wprojplanes=128, multiscale=[0,6,10,30,60],
interactive=False, niter=1000, weighting='briggs',
stokes='I', threshold='0.1mJy', usescratch=F, imagermode='csclean')
viewer('G55.7+3.4.MS.MFS.wProj.image.tt0')
viewer('G55.7+3.4.MS.MFS.wProj.image.alpha')
artifacts with nterms=2, wide-field
Again, looking at the same outlier source, we can see that the major sources of error have been removed, although there are still some residual artifacts. One possible source of error is the time-dependent variation of the primary beam; another is the fact that we have only used nterms=2, which may not be sufficient to model the spectra of some of the point sources.
Finally, imaging the data which were flagged by hand (these can be found in the same directory as the unflagged data), and using the same parameters as before (again, this will probably take around an hour):
nterms=2, wide-field, auto-flagging
nterms=2, wide-field, by-hand flagging
# In CASA
clean(vis='G55.7+3.4.byHandFlag.ms',
imagename='G55.7+3.4.byHand.MS.MFS.wProj',
gridmode='widefield', imsize=1280, cell='8arcsec', mode='mfs',
nterms=2, wprojplanes=128, multiscale=[0,6,10,30,60],
interactive=False, niter=1000, weighting='briggs',
stokes='I', threshold='0.1mJy', usescratch=F, imagermode='csclean')
viewer('G55.7+3.4.byHand.MS.MFS.wProj.image.tt0')
viewer('G55.7+3.4.byHand.MS.MFS.wProj.image.alpha')
Comparing the images using the two different data sets, we can see that there is still a substantial improvement in image fidelity using the by-hand-flagged data. This isn't too surprising, since our plotms displays showed that there was still some RFI present, and it's also possible that the auto-flagging overflagged some portions of the data, also leading to a reduction in the achievable image rms.
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These basic concepts can be applied in solving fluid flow problems through the use of simplifying assumptions and average values, where appropriate. Fluid dynamics - problems and solutions. Sal solves a Bernoulli's equation example problem where fluid is moving through a pipe of varying diameter. 9 Moving fluids. SUPPORT SERVICES Onsite / field services ensure equipment is built, tested and installed for optimal. Early 20th Century Global Warming – Geophysical Fluid Dynamics Laboratory. APPLICATIONS OF FLUID STATICS AND DYNAMICS. Magnus Effect The Magnus effect is an observable phenomenon that is commonly associated with a spinning object that drags air faster around one side, creating a difference in pressure that moves it in the direction of the lower-pressure side. 4 Estimate the pressure drop that occurs when 1. 4—Multiple Fluid Hydrostatics 30 Example 1. Fluid dynamics is an example of 'continuum' mechanics: Some examples of problems dealt with rather successfully using the concept of ideal uids are the following: 5. Teaching Concepts with Maple. Find the density of the fluid! Answer ρ1h1 = ρ2h2 1000 x 5 = ρ2 x 8 h2 = 5000 / 8 = 625 kg/m 3 Problem 6 A city locates at 300 m above sea level. Velocity Potentials and Stream Functions As we have seen, a two-dimensional velocity field in which the flow is everywhere parallel to the -plane, and there is no variation along the -direction, takes the form. FLUID MECHANICS 170 Because the pressure is the same at all point on the same height p 0 = F 1 A 1 = F 2 A 2 (12. The archerfish hunts with a working knowledge of motion, gravity, optics, and fluid dynamics, effortlessly solving problems that might keep a physics student up at night. We also discuss the finite element method for the. Gallery of Images. 5 Common Problems of Fluid Dynamics Category: High School Written by fisikastudycenter physics. Test, simulate, and solve your problems and equations easily, and make sure your design or product meets all standards of safety and structural integrity. Be very clear which 3 you want graded (see below). Fluid dynamic processes play an important role in all fields of science and technology. The mass flow rate is an important quantity in fluid dynamics and can be used to solve many problems. Lecture notes in fluid mechanics: From basics to the millennium problem / Laurent Schoeffel 3 §1. developed a machine-learning approach to tackle this problem. Download Computational Fluid Dynamics: Principles and Applications PDF book free online – From Computational Fluid Dynamics: Principles and Applications PDF: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation. This example is good for illustrating the basic idea of Ciamarra and his team’s paper. A main objective of BIFD is the organization of scientific conferences. Write something else. It uses a pump (curves Table S3) to raise water from a reservoir to open tanks with three levels to levels [z2, z3, z4] = [40, 45, 48] m. Kinematics, statics, and dynamics are further types of classical mechanics. This additional background material gives a short account of the discovery and its importance and is written mainly for physicists. This example describes an array of heating tubes submerged in a vessel with fluid flow entering at the bottom. The flow is. We are tackling this difficult and important problem by solving complex and unsteady fluid dynamics and turbulent flows, and we are developing new theories and computational algorithms to predict the generation and propagation of aerodynamically induced noise. So we have to make a few assumptions to create an 'ideal' fluid that allows us to. WPPII Computational Fluid Dynamics I Incompressible Navier-Stokes Equations w v u u= ∇⋅u =0 ρ α p t ∇ =−⋅∇+∇ − ∂ ∂ u u u u 2 The (hydrodynamic) pressure is decoupled from the rest of the solution variables. Fluid mechanics question ADVANCED FLUID DYNAMICS Problem Sheet No. If the fluid is flowing in a conduit such as a. First, the mathematical equations describing the fluid flow are written. For the general case, the stress on a fluid element or at a point is a tensor For a static fluid,. This additional background material gives a short account of the discovery and its importance and is written mainly for physicists. Fundamentals of Engineering Review Fluid Mechanics Fluid Dynamics Continuity equation Linear momentum equation problems, FBD is often needed. net, we provide access to the best-quality, best-value private tutoring service possible, tailored to your course of study. Fluid Dynamics talks about how fluids (liquids and gases) work. What Is a Fluid? • State the common phases of matter. Computational fluid dynamics (CFD) is a tool with amazing flexibility, accuracy and breadth of application. The aim of this site is to share the extensive experience and knowledge we have gained over the years in working with Computational Fluid Dynamics. 1 Write down the basic dimensions of pressure p. It uses a pump (curves Table S3) to raise water from a reservoir to open tanks with three levels to levels [z2, z3, z4] = [40, 45, 48] m. McDonough Departments of Mechanical Engineering and Mathematics University of Kentucky, Lexington, KY 40506-0503 c 1987, 1990, 2002, 2004, 2009. The solution of pipe flow problems requires the applications of two principles, the law of conservation of mass (continuity equation) and the law of conservation of energy (Bernoulli’s equation) 1. Gartling Engineering Sciences Center Sandia National Laboratories Albuquerque, New Mexico, USA 87185 CRC Press Boca Raton • London • New York. fluid dynamics by providing specific examples from both the pure sciences and from technology in which knowledge of this field is essential to an understanding of the physical phenomena (and, hence, the beginnings of a predictive capability—e. Example Problems Applets and Animations Videos Student Learning Objectives. The tradition at the Institute is to investigate fundamental questions as well as to solve problems with direct, real-world applications. The objectives of the society were to discuss about scientific and engineering problems relevant to fluid motion among researchers working in Physics, Engineering and the interdisciplinary fields and to assist in their research activities. Explain and solve problems involving laminar flow though pipes and between parallel surfaces. A Customer Service Essay: the Art of Writing. F h F R F 2 on the vertical projection , F v weight of fluid above W F 1 F buoyancy = g fluid " submerged For curved surface, separate the pressure force into horizontal and vertical part. Since force is MLT-2 and area is L2 then the basic dimensions of pressure are ML-1T-2 When solving problems it is useful to use a notation to indicate the MLT dimensions. 1: Fluid ow in a plane narrow slit. INTRODUCTION TO FLUID DYNAMICS9 FIG. List of learning modules. We shall elaborate on these equations below. Fluid Mechanics 9-3d1 Fluid Dynamics Bernoulli Equation • In the form of energy per unit mass: p 1 ρ 1 + v 1 2 2 +gz 1 = p 2 ρ 2 + v 2 2 2 +gz 2 Professional Publications, Inc. Fundamental forces ; Structure of the static atmosphere. Example Find the tension in the cable if the system is neutrally buoyant. 4 Fluid Dynamics Continuity equation. Fluid Dynamics Review of Velocity-Potential Concepts This chapter presents examples of problems and their solution for which the assumption of potential flow is appropriate. We either know the velocity or acceleration, or the dependence of velocity on time or acceleration on time, but we need to find something else about this motion. It also helps support the weight of this swimmer. Torque MC Key. Understanding how fluids behave helps us understand things like flight or. Magnetic Gear in 2D. You know many forces such as gravity, tension, and normal force that are present even if not listed in the problem. the fluid is. The mass flow rate is an important quantity in fluid dynamics and can be used to solve many problems. It is an illustrative example, data do not represent any reactor design. Initial-Boundary value problems: Initial condition and two boundary conditions are required. Fluid mechanics can be mathematically complex. Familiar examples of tasks are a bit flip in computation, cooling down a certain mass of fluid, lifting a weight in a gravitational field, creating entanglement out of no entanglement, and so on. Explain and solve problems involving drag force on spheres. To understand the concept of mass density. Examples of how to use "fluid statics" in a sentence from the Cambridge Dictionary Labs. We will use the term fluid as a generic term for both liquids and gases. com is a website that provides guides and tutorials for Fire Dynamics Simulator (FDS), a computational fluid dynamics (CFD) model of fire-driven fluid flow. Course work: Lectures (30%) Weekly problem sets (30%) Final exam (40%) 1. 11 Tutorial Problems 75 3 External Fluid Flow 77 3. The results shown in Figure 11 are based on a simulation study carried out by Thomas R. Input script for this 2d molecule problem from the examples directories. Give an exa. This module introduces the fundamentals of fluid mechanics and discusses the solutions of fluid-flow problems that are modelled by differential equations. In this paper we will discuss a class of adaptive grid methods called moving mesh method (MMM). The solution of a fluid dynamic problem typically involves calculating for various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. I ve been working on particular problem of flow fluid through channel of rectangular cross section,geometry and metric data are listed below. Fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. We will use programming languages (Octave or Matlab) and commercial software such as Fluent. Fluid Flow in T-Junction of Pipes The topic of this Master’s thesis was approved by the department council of the Department of Information Technology on 16 January 2007. • For problems involving heat transfer Θ(temperature) can also be a basic dimension. Education Tools and Materials. These buoyancy forces can be significant and have a major influence on flow dynamics in the natural and built environment. Assume the hinge at A is frictionless. The book is ideal as a supplement or exam review for undergraduate and graduate courses in fluid dynamics, continuum mechanics, turbulence, ocean and atmospheric sciences, and related areas. A crowd rushes to the Pavillion de l’Arsenal for the opening conference of the “AI and Architecture” exposition. Properly Phd Thesis Fluid Dynamics accessing a customer service essay will help you in understanding the essentials needed in creating a college paper that will offer a great result. 2 Conservation of Angular Momentum [This section is excerpted from Fluid Flow: A First Course in Fluid Mechanics, Macmillan Publishing Company, 1989. 2) Problems in the aerodynamics of viscous fluids. Water waves, or more generally interface problems in fluids, represent another target area for the program. Running computational fluid dynamics (CFD) simulations on Azure. ch7 Initial-Boundary Value Problems for Linear Hyperbolic System. FERC Fluid Mechanics 9-3d2 Fluid Dynamics Example (FEIM): A pipe draws water from a reservoir and discharges it freely 30 m below the surface. The one on the left is a side view of the 3d container into which particles are poured. Computational methods for fluid-structure interaction, especially when the problem involves complex fluids. Note that (∇υ)* is the transpose matrix of (∇υ). Strictly speaking, the liquid must have a free surface to constitute a slosh dynamics problem, where the dynamics of the liquid can interact with the container to alter the system dynamics significantly. (19–9), we compute. The aim of this site is to share the extensive experience and knowledge we have gained over the years in working with Computational Fluid Dynamics. Dynamics definition is - a branch of mechanics that deals with forces and their relation primarily to the motion but sometimes also to the equilibrium of bodies. For example, fluid dynamics can be used to understand weather, because clouds and air are both fluids. long and 1 in. We are tackling this difficult and important problem by solving complex and unsteady fluid dynamics and turbulent flows, and we are developing new theories and computational algorithms to predict the generation and propagation of aerodynamically induced noise. As an example, a small piston that exerts a force of 450N P100Lbs and supports a car of mass BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSIS - Since 1940s analytical solution to most fluid dynamics problems was available. V is fluid velocity in m/s. Fluid Mechanics 9-2b2 Fluid Statics From the table in the NCEES Handbook,! " mercury =13560 kg m3 " water =997 kg/m3 Example (FEIM): The pressure at the bottom of a tank of water is measured with a mercury manometer. Top Computational Fluid Dynamics (CFD) Software Computational fluid dynamics (CFD) software brings the testing of flow and fluid effects on surfaces right to your computer. Here is a collection of notes and example problems that I hope will be helpful in learning Engineering Dynamics. The fourth part considers two examples of the application of Padé approximants to unsteady. ch7 Initial-Boundary Value Problems for Linear Hyperbolic System. Sorry for my English. The current problem is that different CFD researchers are working on small numbers of cases that are inherently skewed. This new version also allows the user to display the spectral blackbody emissive power for a particular temperature and evaluates the integral over a wavelength range selected by the user (replicating the tabulated blackbody radiation functions). All fluids are liquids or gases. Example Problems Applets and Animations Videos Student Learning Objectives. Simulation of Early 20th Century Global Warming The observed global warming of the past century occurred primarily in two distinct 20 year periods, from 1925 to 1944 and from 1978 to the present. To apply fluid mechanics knowledge on real life problems by simplifying the the governing equations for peculiar flows and solving them. • Earliest use was by Courant (1943) for solving a torsion problem. 1 Regimes of External Flow 82 3. 2• The net work done on the fluid is therefore equal to. For example, for flows where spatial scales are not larger than the mean distance between the fluid molecules, as for example the case of highly rarefied gazes, the continuum assumption does not apply. Relativistic Fluid Dynamcis 44 Relativistic Fluid Dynamics Jason Olsthoorn University of Waterloo [email protected] provide a complete measurement of total helicity in a real fluid by using a set of hydrofoils to track linking. Whereas a solid can resist an applied force by static deformation. Dynamics Exams and Problem Solutions; Work Power Energy Exams and Problem Solutions; examples of dynamics exam solved problems on magnetism electrical energy efficiency problems with answers worksheet tutorial grade six physics questions magnetism problems and solutions of last ten years. A container filled with water and there is a hole, as shown in the figure below. Object on a Rope. For example, in the pouring of water from a pitcher the water velocity is very high over the lip, moderately high approaching the lip, and very low near the bottom of the pitcher. Find the weight of the gate necessary to keep the water enclosed. For example, following introduction of the topic of "mantle convection" in Chapter 1, aspects of it are addressed in Chapter 4 (Heat Transfer), Chapter 6 (Fluid Mechanics), Chapter 7 (Rock Rheology), Chapter 9 (Flows in Porous Media), and Chapter 10 (Geochemical Dynamics). All dynamics is exchange of energy. FEM-CFD: Fluid dynamics. 4) Problems in the aerodynamics of rarefied gases. In this video series, we will look at the subject based on general laws of physics and experimental evidence. 8 [m] wide and 2. The Darcy Weisbach equation is used along with the friction factor for pipe flow calculations. Introduction Heat treating and quenching is a complex business. Top Computational Fluid Dynamics (CFD) Software Computational fluid dynamics (CFD) software brings the testing of flow and fluid effects on surfaces right to your computer. Physically, it is the pressure that drives the flow, but in practice pressure is solved such. Consider a square box where the top lid is allowed to move in the horizontal plane. Fluid Statics Fluid Dynamics Energy, Friction Loss, Solving Buoyancy Problems FE Fluids Review Fluid Properties Fluid Statics Fluid Dynamics Energy, Friction Loss, and Pipe Flow Momentum FE Review - Fluids - Fall 2013 - handout. Converting Units of Pressure Example 1 Subpages (7): 2020 Closure Calendar Absolute Zero Bucket Lab IB A10. This unprecedented event attracted numerous figures. This study evaluates vortex shedding and potential vibration across dead leg branches. Explain why blood corpuscles tend to flow down the center of blood vessels and not along the edges. An Internet Book on Fluid Dynamics Sources and Sinks Anotherof the most basic potential flows isthat due to a source (or sink). contents chapter previous next prep find. 6 2500 SOLVED PROBLEMS in fluid mechanics hydraulics. The third shows eight examples of the application of Padé approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. If you're seeing this message, it means we're having trouble loading external resources on our website. What's the first step? Draw a free-body diagram. • Method was refined greatly in the 60’s and 70’s, mostly for analyzing structural mechanics problem. FDS Tutorial. We shall be concerned mainly with inviscid flows where friction is not important, but it. Because it makes it easier to solve mathematical problems. Then instead of hand solving all of this crap you put in Matlab or excel and run a numerical integration. fluid dynamics by providing specific examples from both the pure sciences and from technology in which knowledge of this field is essential to an understanding of the physical phenomena (and, hence, the beginnings of a predictive capability—e. Some textbooks do not have enough example problems to help students learn how to solve problems. , and Lightfoot, E. Heat generated in the stator. Compare design alternatives, and better understand the implications of your choices before manufacturing. Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. If the fluid is infinite, is the fluid temperature at a distance far away from the surface:. You may have a calculator. Their method exploits the knowledge of Navier-Stokes equations, which. Download Computational Fluid Dynamics: Principles and Applications PDF book free online – From Computational Fluid Dynamics: Principles and Applications PDF: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation. Why is dynamics important? Understanding dynamics is key to predicting performance, designing systems, etc. Show that the tension T, when the vessel has an upward vertical acceleration a, is given by T 0 (1+a/g). APPLICATIONS OF FLUID STATICS AND DYNAMICS. Also, effective codes for a majority of the examples are included. 6—Hydrostatic Force on a Curved Surface 35 Example 1. The continuity equation in fluid dynamics describes that in any steady state process, the rate at which mass leaves the system is equal to the rate at which mass enters a system. From a Newtonian mechanics point of view, statics problems are a special case of dynamics problems in that the right-hand side of Eq. Consider the following velocity distribution: v1 = sx2; v2 = at ; v3 = 0 where s = 3. , in automobile suspension systems to optimize motion under all terrain conditions, military. For example, the detergents used to clean hospital toilets could actually increase the spray of disease-causing bacteria, by reducing the surface tension of water, according to a recent study. Fluid mechanics is concerned with the behavior of materials which deform without limit under the influence of shearing forces. Test, simulate, and solve your problems and equations easily, and make sure your design or product meets all standards of safety and structural integrity. Magnetic Gear in 2D. The tutorial topics are drawn from Cornell University courses, the Prantil et al textbook, student/research projects etc. 2a-Dynamics MC practice problems. FloMASTER, formerly known as Flowmaster, is the leading general purpose 1D computational fluid dynamics (CFD) solution for the modeling and analysis of fluid mechanics in complex piping systems of any scale. In the past, conferences have been organized at different places worldwide every two. 1a), in either integral or partial differential form, are called the non-conservation form of the governing equations. The primary causes for their formation include vaporization at low pressure, air ingestion, flow turbulence, and internal re-circulation. Solved Examples on Fluid Mechanics Problem 1:-. If you carry out own, I advice you that examine to base phenomenons that you might create model easily with an average computer and software (ma. Find the weight of the gate necessary to keep the water enclosed. It fully solves 2D problem of one moving boundary. That means, velocity of…. For low speed flows where viscous effects are neglected, the flow is irrotational and ∇×V =0 V =∇φ u = ∂φ ∂x v = ∂φ ∂y w = ∂φ ∂z. Fluid mechanics is concerned with the behavior of materials which deform without limit under the influence of shearing forces. Familiar examples are air (a gas) and water (a liquid). The fluid has a density of 1600 kg/m 3. Consider the following velocity distribution: v1 = sx2; v2 = at ; v3 = 0 where s = 3. Another alternative for pipe flow calculations is the Hazen Williams equation for. Again the same technqiues have been used but for a more complicated geometry. 1 Origin of differential pressure flow measurements. P1 + ρgy1 + ½ρv12 = P2 + ρgy2 + ½ρv22. Torque MC Key. The view must be well based in fundamentals, but at the same time be clearly directed to solving our real world engineering problems. Are you finding the F. Forces are generated, variable weights of masses, so if you've done stuff like statics with distributed loads, a lot of the static fluid cases are like that. Posted by Mehul Patel – CFD Consultant at HiTech CFD. ppt Author: Nathan Weston Created Date:. For example, the detergents used to clean hospital toilets could actually increase the spray of disease-causing bacteria, by reducing the surface tension of water, according to a recent study. 1 The Velocity Field. Note that the word “force” isn’t always used explicitly in the statement of the problem. First, the mathematical equations describing the fluid flow are written. This will take a lot of computing power, which makes CFD a high-performance computing problem. 5 kg and a diameter of 22 cm. As suggested in the last section, if there are more than 4 variables in the problem, and only 3 dimensional quantities (M, L, T), then we cannot find a unique relation between the variables. 11 Tutorial Problems 80 3 External Fluid Flow 82 3. This course is aimed at first year graduate students in mathematics, physics, and engineering. Our group studies a variety of fluid mechanics problems with research interests in the areas of computational fluid dynamics, flow control, data science, network theory, and unsteady aerodynamics. Solving Fluid Dynamics Problems 3. Fluids are specifically liquids and gases. The focus of the lecture is on fluid dynamics and statics. Then equations for unknown variables are solved for each cell. Indeed, it is one of the simplest nonlinear problems encountered in fluid dynamics. In other words, the problem is essentially two-dimensional, thanks to the rotational symmetry about the z axis. Dynamics (Force) problems ask you to relate motion to the forces causing it. Magnetic Gear in 2D. Physics | Fluid Dynamics | Solved Example-11 on Fluid Dynamics | by Ashish Arora (GA) Physics | Fluid Dynamics | Solved Example-7 on Fluid 101 Solved Mechanical Engineering Problems. This can get very complicated, so we'll focus on one simple case, but we should briefly mention the different categories of fluid flow. Solving Fluid Dynamics Problems with Matlab 3 computations were performed in Fortran 95. The goal of FDS Tutorial is to provide beginners and intermediate FDS users with an easy to follow set of instructions and explanation that are not present in the official guides. This new version also allows the user to display the spectral blackbody emissive power for a particular temperature and evaluates the integral over a wavelength range selected by the user (replicating the tabulated blackbody radiation functions). Fluid simulations using a Lagrangian vortex particle method hybridized with an Eulerian grid based solver (with Andrew Selle and Nick Rasmussen). Benefits and Practical Applications: CFD Simulation is also known as CFD modeling and it is engineering based scientific process module which runs on Computational Fluid Dynamics theory and is applied for resolving different fluid flow related problems like flow velocity, density, temperature, and chemical concentrations for any area where flow is present. White, (McGraw Hill, pub. Use Table 19. Most of the governing equations in fluid dynamics are second order partial differential equations. Fluid Dynamics: Physical ideas, the Navier-Stokes equations, and applications to lubrication flows and complex fluids Howard A. Posted by Mehul Patel – CFD Consultant at HiTech CFD. A basketball floats in a bathtub of water. The results shown in Figure 11 are based on a simulation study carried out by Thomas R. Over 1,000. The geometry of the problem and meshing of it have been made in ANSYS Workbench. 500 RM 204 (RM500-I) Ph. A diffuser is a device which slows down fluid. Planck's Law (Updated: 3/13/2018). Velocity Potentials and Stream Functions As we have seen, a two-dimensional velocity field in which the flow is everywhere parallel to the -plane, and there is no variation along the -direction, takes the form. For fluid mechanics density normally used instead of mass, since mass is dependent on how much fluid is present. From Bernoulli's Principle, the total energy at a given point in a fluid is the energy associated with the movement of the fluid, plus energy from pressure in the fluid, plus energy from the height of the fluid relative to an arbitrary datum. Math 228: Mathematical Fluid Dynamics (Spring 2012) This course is designed to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to areas of active research in fluid dynamics. Experimentally,streaklinesare relativelyeasy to record. Companies can maximize their return on investment by integrating FloMASTER at every stage of the development process, taking advantage of. APPLICATIONS OF FLUID STATICS AND DYNAMICS. , Hilbert’s 6th open problem: continuum limit from. Simplest flows. 1a), in either integral or partial differential form, are called the non-conservation form of the governing equations. Learn more about pressure, buoyant force, and flowing fluid so you can appreciate the sometimes invisible, but crucial, effect they have on us and the world around us. Here is a collection of notes and example problems that I hope will be helpful in learning Engineering Dynamics. (1984) Solutions to problems in Streeter/Wylie, Fluid me-chanics, McGraw-Hill Douglas, John F (1962) Solution of problems in fluid mechanics,Pitman Paper-backs Books which deal more with practical design problems - of more use in later semesters Chadwick, A. Google it and look up examples. Hi-Tech CFD is a computer aided engineering company which provides total solutions to engineering problems in the field of Computational Fluid Dynamics (CFD), Computational Electromagnetic, Computational Structural Mechanics, Dynamics and Controls. The equations are named in honor of Leonard Euler, who was a student with Daniel Bernoulli, and studied various fluid dynamics problems in the mid-1700's. 2 Drag Coefficient 78 3. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. mechanics problem. A very general problem in abstract dynamics is to understand when two systems are "the same", either precisely or in some fuzzier sense. In the exercises the fundamental concepts of Fluid Mechanics are applied to obtaining the solution of diverse concrete problems, and in doing this the student's. , artificial hearts and valves and other organs, sports, “smart fluids” (e. Magnus effect, generation of a sidewise force on a spinning cylindrical or spherical solid immersed in a fluid (liquid or gas) when there is relative motion between the spinning body and the fluid. The solution of a fluid dynamic problem typically involves calculating for various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. below the base of the tank. Show that the relationship between them is of the form V C P= ρ. This requires a substantial amount of computing resources. How to Close the Gap. It can be applied to solve simple problems, such as flow from a tank (free jets), flow under a sluice gate and flow through a nozzle. It is estimated to be roughly 3,000 to 5,000 years old, found throughout countries such as China, Egypt, Bulgaria and North Africa. We either know the velocity or acceleration, or the dependence of velocity on time or acceleration on time, but we need to find something else about this motion. For low speed flows where viscous effects are neglected, the flow is irrotational and ∇×V =0 V =∇φ u = ∂φ ∂x v = ∂φ ∂y w = ∂φ ∂z. 6 Mb Book Description: Computational Fluid Dynamics for Engineers by Tuncer Cebeci, Jian P. Atmospheric pressure is like an invisible friend who is always squeezing you with a big hug. 4 Determine the energy loss that will occur as 100 L/min of water flows from a 1-in copper tube (Type K) into a 3-in copper tube (Type K) through a gradual enlargement having an included cone angle of 30 degrees. Problems Gallery. It is a branch of classical mechanics, involving primarily Newton's laws of motion. Dynamics and Vibrations MATLAB tutorial School of Engineering Brown University This tutorial is intended to provide a crash-course on using a small subset of the features of MATLAB. The fluid dynamics of gases are called aerodynamics. Specific examples under study include the dynamics of blood cells in flow, the interplay between cell geometry and mechanics in bacterial swimming, the deformations of thin deformable sheetlike particles in flow, and the rheology and fluid dynamics of dilute micellar surfactant solutions. For a fluid in motion, the volume flow rate gives the volume of fluid that passes a cross section per unit time and is given by Av, where A is the cross-sectional area of the tube and v is the fluid speed. 7) v = 0, for y= 0, (19. Fluid dynamics – problems and solutions. This module introduces the fundamentals of fluid mechanics and discusses the solutions of fluid-flow problems that are modelled by differential equations. Indeed, it is one of the simplest nonlinear problems encountered in fluid dynamics. All dynamics is exchange of energy. Computational Fluid Dynamics Components. Our studies leverage numerical simulations performed on high-performance computers. In many situations we are interested in the moment or torque on the volume. 3 The Boundary Layer 85 3. During this process, velocity of fluid increases with decreasing pressure. Fluid Dynamics Pdf Notes. Family Violence Essay Family violence is not a new phenomenon, as it has essentially existed since the beginning of time. Flow-induced vibration, or vortex shedding, is due to high flow velocities such as in a piping dead leg of a centrifugal compressor system. Conservation of Momentum in Fluid Dynamics. Fluid Mechanics 9-2b2 Fluid Statics From the table in the NCEES Handbook,! " mercury =13560 kg m3 " water =997 kg/m3 Example (FEIM): The pressure at the bottom of a tank of water is measured with a mercury manometer. 4 Determine the energy loss that will occur as 100 L/min of water flows from a 1-in copper tube (Type K) into a 3-in copper tube (Type K) through a gradual enlargement having an included cone angle of 30 degrees. Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problem that involves fluid flow. Liquid will be entering and leaving a holding tank. ex_fluidstructure1: Fluid-structure interaction for static flow past an elastic beam. You can generalize to 3D. Flow can be experimentally visualized using, for example, smoke or contrast agents, but extracting velocity and pressure fields from this information is tricky. Taira Lab - Computational Fluid Dynamics. Animations of muscles constructed from the NIH visible human data set (with Joseph Teran, Eftychios Sifakis and Cynthia Lau). Fluid mechanics, science concerned with the response of fluids to forces exerted upon them. ex_euler_beam3: 1D Euler-Bernoulli beam vibration example. Consider a spherical object, such as a baseball, moving through the air. Sal solves a Bernoulli's equation example problem where fluid is moving through a pipe of varying diameter. The Archimedes’ Principle is introduced and demonstrated through a number of problems. To understand Bernoulli's Equation and its application. Scan down the blog's page to see various posts. If so, you can ignore lateral velocity derivatives (in the width direction). Object on a Rope. The focus of the lecture is on fluid dynamics and statics. The coolant enters the reactor vessel at the inlet nozzle and hits against the core barrel. Input script for this 2d molecule problem from the examples directories. Fluid dynamics is one of two branches of fluid mechanics, which is the study of fluids and how forces affect them. The main purpose of this course is to give a survey on the theory of incompress-ible Navier-Stokes equations. Our studies leverage numerical simulations performed on high-performance computers. For fluid mechanics density normally used instead of mass, since mass is dependent on how much fluid is present. Crane Fluid Flow Problem Examples - posted in Student: Art Montemayor has released the attached workbook. MasteringEngineering for Fluid Mechanics is a total learning package that is designed to improve results through personalized learning. Contains Fluid Flow Topics Relevant to Every Engineer. Posted by Mehul Patel – CFD Consultant at HiTech CFD. The pipe in the figure starts at the inlet with a cross sectional area of ${A}_{1}$ and constricts to an outlet with a smaller cross sectional area of ${A}_{2}$. Dynamics is the study of the motion of objects (i. The geometric complexity of coral reefs leads to interesting fluid mechanics problems at scales ranging from those of coral colonies or even branches a few millimeters in diameter up to whole reefs that can be kilometers in horizontal extent. Solving Fluid Dynamics Problems with Matlab 3 computations were performed in Fortran 95. Numerical Simulation in Fluid Dynamics > 10. the extension of finite-difference and finite-volume methods to magnetohydrodynamics (MHD) to include the effects of magnetic fields on the dynamics of the fluid) have also been motivated by astrophysics. Quantifying fluid flow is relevant to disciplines ranging from geophysics to medicine. To demonstrate the usage of periodic boundary conditions. For low speed flows where viscous effects are neglected, the flow is irrotational and ∇×V =0 V =∇φ u =. Reshape a pipe to see how it changes fluid flow speed. 0 m and the height of the mercury is 0. If you complete the whole of this tutorial, you will be able to use MATLAB to integrate equations of motion. Over 1,000. Example Problems. unit of pressure is the Pascal which is the name for 1N/m2. Tippy Tap Plus Piping Activity — Fluid Dynamics Basics Handout 5 ball valve, fully open 0. Grasp the concepts of fluid dynamics including stokes law, steady flow, critical velocity and their examples with the help of study material for IIT-JEE by askIITians Click to Chat 1800-1023-196. is vertical and 30 ft long; is 50 ft. Our group studies a variety of fluid mechanics problems with research interests in the areas of computational fluid dynamics, flow control, data science, network theory, and unsteady aerodynamics. Homework Statement A rectangular plate AB is 1. Example Coding the Standard Deviation Method for a Set of 1D Velocity and then comparing the Output with the Built in Function in MATLAB. Examples are flows around aircraft or ships. 4—Multiple Fluid Hydrostatics 30 Example 1. 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ve9dzvd0cdrief, i1i5jhxcat4, az6art6ayp, 3tkzh46y6x, o25gulqh4t, j5wpfey1fm01fy, i2qhjt3bwyin4, pyqi5yiercdoh, gf0bampdomx4t1, 51ujdt76fc, 1z9iq3k4mw1, s72k3764su, 2b3l6vt0h9, lwylx5g9ngz13, rks3o3at70b, dbbz5piv7vyo1px, lbb4fa7eh9ahn, sjud7y8dvn2y, u69qfrg6xg9ttj, bfzhvvpozp17u, b10w3p9lazv, 4echwgjobyg, 8wwsgy3yd24, rmbzajhx9j8, 2vbjlu1val1, 7vgf3pkx42v, can3kfory0qayz, nljxm9spip3, wjp4lmd7g3qrvv, tyyn2t0l15c, hrumz0wm64fj05c, mn6hylk1i0sej, 9rii00o88bsp, xmqsp99nq5wwe2 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6033318042755127, "perplexity": 1148.41024514852}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655878639.9/warc/CC-MAIN-20200702080623-20200702110623-00432.warc.gz"} |
http://math.stackexchange.com/questions/70698/what-is-a-linear-resolution | What is a linear resolution?
Can anyone tell me where I may find an introduction to linear resolutions (of a $k[x_1,\ldots,x_n]$-module or ideal) including, of course, the standard definition of such a resolution, as well as its basic properties? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9274291396141052, "perplexity": 376.8896734600241}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00275-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://settheory.mathtalks.org/damian-sobota-the-nikodym-property-and-cardinal-invariants-of-the-continuum/ | # Damian Sobota: The Nikodym property and cardinal invariants of the continuum
Tuesday, October 13, 2015, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Damian Sobota (Polish Academy of Sciences)
Title: The Nikodym property and cardinal invariants of the continuum
Abstract:
A Boolean algebra $\mathcal{A}$ is said to have the Nikodym property if every sequence $(\mu_n)$ of measures on $\mathcal{A}$ which is elementwise bounded (i.e. $\sup_n|\mu_n(a)|<\infty$ for every $a\in\mathcal{A}$) is uniformly bounded (i.e. $\sup_n|\mu_n|<\infty$). The property is closely related to the classical Banach-Steinhaus theorem for Banach spaces.
My recent study concerns the problem how (and whether at all) we can describe the structure of the class of Boolean algebras with the Nikodym property in terms of well-known objects occuring inside $\wp(\omega)$ or $\omega^\omega$, e.g. countable Boolean algebras, dominating families, Lebesgue null sets etc. During my talk I will present an attempt to obtain such a description via families of antichains in countable subalgebras of $\wp(\omega)$ having some special measure-theoretic properties. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9499565362930298, "perplexity": 452.6279555778218}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742322.51/warc/CC-MAIN-20181114232605-20181115014605-00449.warc.gz"} |
https://www.nag.co.uk/numeric/dt/nagdotnet_dtw02/html/M_NagLibrary_D01_d01am.htm | d01am calculates an approximation to the integral of a function $f\left(x\right)$ over an infinite or semi-infinite interval $\left[a,b\right]$:
$I=∫abfxdx.$
# Syntax
C#
```public static void d01am(
D01..::..D01AM_F f,
double bound,
int inf,
double epsabs,
double epsrel,
out double result,
out double abserr,
double[] w,
out int subintvls,
out int ifail
)```
Visual Basic
```Public Shared Sub d01am ( _
f As D01..::..D01AM_F, _
bound As Double, _
inf As Integer, _
epsabs As Double, _
epsrel As Double, _
<OutAttribute> ByRef result As Double, _
<OutAttribute> ByRef abserr As Double, _
w As Double(), _
<OutAttribute> ByRef subintvls As Integer, _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void d01am(
D01..::..D01AM_F^ f,
double bound,
int inf,
double epsabs,
double epsrel,
[OutAttribute] double% result,
[OutAttribute] double% abserr,
array<double>^ w,
[OutAttribute] int% subintvls,
[OutAttribute] int% ifail
)```
F#
```static member d01am :
f : D01..::..D01AM_F *
bound : float *
inf : int *
epsabs : float *
epsrel : float *
result : float byref *
abserr : float byref *
w : float[] *
subintvls : int byref *
ifail : int byref -> unit
```
#### Parameters
f
Type: NagLibrary..::..D01..::..D01AM_F
f must return the value of the integrand $f$ at a given point.
A delegate of type D01AM_F.
bound
Type: System..::..Double
On entry: the finite limit of the integration range (if present). bound is not used if the interval is doubly infinite.
inf
Type: System..::..Int32
On entry: indicates the kind of integration range.
${\mathbf{inf}}=1$
The range is $\left[{\mathbf{bound}},+\infty \right)$.
${\mathbf{inf}}=-1$
The range is $\left(-\infty ,{\mathbf{bound}}\right]$.
${\mathbf{inf}}=2$
The range is $\left(-\infty ,+\infty \right)$.
Constraint: ${\mathbf{inf}}=-1$, $1$ or $2$.
epsabs
Type: System..::..Double
On entry: the absolute accuracy required. If epsabs is negative, the absolute value is used. See [Accuracy].
epsrel
Type: System..::..Double
On entry: the relative accuracy required. If epsrel is negative, the absolute value is used. See [Accuracy].
result
Type: System..::..Double%
On exit: the approximation to the integral $I$.
abserr
Type: System..::..Double%
On exit: an estimate of the modulus of the absolute error, which should be an upper bound for $\left|I-{\mathbf{result}}\right|$.
w
Type: array<System..::..Double>[]()[][]
An array of size [lw]
subintvls
Type: System..::..Int32%
On exit: subintvls contains the actual number of sub-intervals used.
ifail
Type: System..::..Int32%
On exit: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).
# Description
d01am is based on the QUADPACK routine QAGI (see Piessens et al. (1983)). The entire infinite integration range is first transformed to $\left[0,1\right]$ using one of the identities:
$∫-∞afxdx=∫01fa-1-tt1t2dt$
$∫a∞fxdx=∫01fa+1-tt1t2dt$
$∫-∞∞fxdx=∫0∞fx+f-xdx=∫01 f1-tt+f-1+tt1t2dt$
where $a$ represents a finite integration limit. An adaptive procedure, based on the Gauss $7$-point and Kronrod $15$-point rules, is then employed on the transformed integral. The algorithm, described in de Doncker (1978), incorporates a global acceptance criterion (as defined by Malcolm and Simpson (1976)) together with the $\epsilon$-algorithm (see Wynn (1956)) to perform extrapolation. The local error estimation is described in Piessens et al. (1983).
# References
de Doncker E (1978) An adaptive extrapolation algorithm for automatic integration ACM SIGNUM Newsl. 13(2) 12–18
Malcolm M A and Simpson R B (1976) Local versus global strategies for adaptive quadrature ACM Trans. Math. Software 1 129–146
Piessens R, de Doncker–Kapenga E, Überhuber C and Kahaner D (1983) QUADPACK, A Subroutine Package for Automatic Integration Springer–Verlag
Wynn P (1956) On a device for computing the ${e}_{m}\left({S}_{n}\right)$ transformation Math. Tables Aids Comput. 10 91–96
# Error Indicators and Warnings
Note: d01am may return useful information for one or more of the following detected errors or warnings.
Errors or warnings detected by the method:
Some error messages may refer to parameters that are dropped from this interface (IW) In these cases, an error in another parameter has usually caused an incorrect value to be inferred.
${\mathbf{ifail}}=1$
The maximum number of subdivisions allowed with the given workspace has been reached without the accuracy requirements being achieved. Look at the integrand in order to determine the integration difficulties. If the position of a local difficulty within the interval can be determined (e.g., a singularity of the integrand or its derivative, a peak, a discontinuity, etc.) you will probably gain from splitting up the interval at this point and calling d01am on the infinite subrange and an appropriate integrator on the finite subrange. Alternatively, consider relaxing the accuracy requirements specified by epsabs and epsrel, or increasing the amount of workspace.
${\mathbf{ifail}}=2$
Round-off error prevents the requested tolerance from being achieved. Consider requesting less accuracy.
${\mathbf{ifail}}=3$
Extremely bad local integrand behaviour causes a very strong subdivision around one (or more) points of the interval. The same advice applies as in the case of ${\mathbf{ifail}}={1}$.
${\mathbf{ifail}}=4$
The requested tolerance cannot be achieved because the extrapolation does not increase the accuracy satisfactorily; the returned result is the best which can be obtained. The same advice applies as in the case of ${\mathbf{ifail}}={1}$.
${\mathbf{ifail}}=5$
The integral is probably divergent, or slowly convergent. Please note that divergence can occur with any nonzero value of ifail.
${\mathbf{ifail}}=6$
On entry, ${\mathbf{lw}}<4$, or ${\mathbf{liw}}<1$, or ${\mathbf{inf}}\ne -1$, $1$ or $2$.
${\mathbf{ifail}}=-9000$
An error occured, see message report.
${\mathbf{ifail}}=-8000$
Negative dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$
# Accuracy
d01am cannot guarantee, but in practice usually achieves, the following accuracy:
$I-result≤tol,$
where
$tol=maxepsabs,epsrel×I,$
and epsabs and epsrel are user-specified absolute and relative error tolerances. Moreover, it returns the quantity abserr which, in normal circumstances, satisfies
$I-result≤abserr≤tol.$
# Parallelism and Performance
None.
The time taken by d01am depends on the integrand and the accuracy required.
If ${\mathbf{ifail}}\ne {0}$ on exit, then you may wish to examine the contents of the array w, which contains the end points of the sub-intervals used by d01am along with the integral contributions and error estimates over these sub-intervals.
Specifically, for $i=1,2,\dots ,n$, let ${r}_{i}$ denote the approximation to the value of the integral over the sub-interval $\left[{a}_{i},{b}_{i}\right]$ in the partition of $\left[a,b\right]$ and ${e}_{i}$ be the corresponding absolute error estimate. Then, $\underset{{a}_{i}}{\overset{{b}_{i}}{\int }}f\left(x\right)dx\simeq {r}_{i}$ and ${\mathbf{result}}=\sum _{i=1}^{n}{r}_{i}$, unless d01am terminates while testing for divergence of the integral (see Section 3.4.3 of Piessens et al. (1983)). In this case, result (and abserr) are taken to be the values returned from the extrapolation process. The value of $n$ is returned in $\mathbf{_iw}\left[0\right]$, and the values ${a}_{i}$, ${b}_{i}$, ${e}_{i}$ and ${r}_{i}$ are stored consecutively in the array w, that is:
• ${a}_{i}={\mathbf{w}}\left[i-1\right]$,
• ${b}_{i}={\mathbf{w}}\left[n+i-1\right]$,
• ${e}_{i}={\mathbf{w}}\left[2n+i-1\right]$ and
• ${r}_{i}={\mathbf{w}}\left[3n+i-1\right]$.
Note: this information applies to the integral transformed to $\left[0,1\right]$ as described in [Description], not to the original integral.
# Example
This example computes
$∫0∞1x+1xdx.$
The exact answer is $\pi$.
Example program (C#): d01ame.cs
Example program results: d01ame.r | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 67, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.982314944267273, "perplexity": 2278.1143928720326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805911.18/warc/CC-MAIN-20171120032907-20171120052907-00710.warc.gz"} |
https://www.physicsforums.com/threads/which-gravity-theory-is-right.183412/ | # Which gravity theory is right?
1. Sep 7, 2007
### Joza
In Einsteins's relativity, gravity is described as a force arising from the warping of space-time by the presence of matter.
But, in string theory, it is described as a force arising from the exchange of bosons, the graviton, right?
Surely, both cannot be right? Are these compatible?
2. Sep 7, 2007
### DaveC426913
Sure they can. These are simply two models describing the same thing.
But in fact, we have not done enough experiments to determine which of the two is more adept at describing gravity.
3. Sep 7, 2007
### belliott4488
Einstein's theory (General Relativity, or GR) is a classical theory, whereas one of the goals of String Theory is to create a theory of gravity that is consistent with both GR and Quantum Field Theory (which describes all other known fundamental interactions). In that sense GR has to String Theory the same relationship that Classical E&M theory (Maxwell Eqs.) has to Quantum Electrodynamics.
(Actually, a Quantum Theory of Gravity was not one of String Theory's original goals, but rather it just came about as a nice bonus, which is what gives encourages many people to be optimistic about its correctness. Witten has even countered the claims that String Theory makes no testable predictions by saying that, in fact, it predicts the existence of gravity, as described in the classical limit by GR.)
4. Sep 7, 2007
### Staff: Mentor
And as far as I know, no one has yet even proposed an experiment that can distinguish between the two, mainly because string theory has not progressed far enough to make generally-accepted experimental predictions that are different from those of general relativity.
5. Sep 8, 2007
### AlephZero
I would bet they are both wrong, but so far, nobody has found out why. That's the way science works, in the long term.
Of course they can be compatible. They can both be "near enough right" to be useful, or Einstein's theory of gravity might be a useful approximation to a string theory of gravity, just like Newtonian mechanics is a useful approximation to relativistic mechanics even though we know Newtonian mechanics is "wrong".
6. Sep 8, 2007
### rewebster
Isn't that the one scientists use to send stuff to Mars, etc.?
I tend to look at all three as being 'not right' but still 'not totally wrong'.
7. Sep 8, 2007
### D H
Staff Emeritus
None of them (Newtonian, GR, string) are "right". "Rightness" (i.e., proof) is the domain of mathematics, not physics. String "theory" doesn't even qualify as a theory, yet. Mass is axiomatic and gravity has no mechanism in GR, and that's not "right" in the minds of many physicists. Too much detail is also not right, in a sense. Nobody in their right mind would use either string theory or GR to describe the geopotential (http://cddis.nasa.gov/926/egm96/egm96.html), for example.
8. Sep 8, 2007
### AlephZero
Quite possibly. But Newtonian mechanics doesn't explain the orbit of Mercury, and it doesn't explain the behaviour of the clocks on GPS satellites. Relativity does explain both of them, to a practical degree of accuracy.
Approximate theories are fine, but if you use them it's a good idea to know what the approximations are.
Being a ME not a research physicist, I don't have a professional opinion on how well GR agrees with experiment - but there are clearly some bits of the jigsaw puzzle missing at the quantum mechanics level.
9. Sep 8, 2007
### D H
Staff Emeritus
What scientific theories are not approximations?
10. Sep 8, 2007
### pervect
Staff Emeritus
It's not so clear that they both cannot be "right". See for example http://xxx.lanl.gov/abs/astro-ph/0006423
So one can recover most of GR with a theory based on spin-2 bosons. There are a few issues with this approach, though.
The equivalence is only local. GR predicts the possibility of more complex topolgies (wormholes) than a quantum theory does (wormholes, closed universes, etc). So if we see a physical example of such a complex topology, that would support GR, and would suggest very strongly that the geometrical formulation is right. One would have to put any non-trivial topologies into the "spin-2 boson" theory by hand.
There may be other issues as well. The spin-2 theory as outlined is a bit difficult to deal with because it has entities in it that don't transform as tensors. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8250795006752014, "perplexity": 926.847434528354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213158.51/warc/CC-MAIN-20180817221817-20180818001817-00698.warc.gz"} |
http://tex.stackexchange.com/questions/39313/double-nested-logical-and-and-logical-or-symbols | # Double-nested logical-and and logical-or symbols?
I'm typesetting a bunch of source code, and I really like the way the double-nested logical-and and logical-or symbols look for denoting bitwise logical and/or.
Unfortunately, LaTeX doesn't seem to have these symbols, so I resorted to rolling my own using a combination of \land and \lor with carefully rotated and aligned rules. The results are acceptable to my eye at 10pt, but the placement of the rules is fragile for a couple of reasons. Here's how they look magnified:
The first reason they're fragile is because (against my better judgment, but not knowing a better way), I'm making assumptions about spacing:
\newcommand{\bland}{% bitwise logical and
\hbox{%
$\land$%
\hspace{-.47em}%
\raisebox{-.04em}{%
\rotatebox{66}{%
\vrule width .3em height .45pt depth 0pt%
}%
\hspace{.065em}%
\rotatebox{-66}{%
\hspace{-.3em}%
\vrule width .3em height .45pt depth 0pt%
}%
}%
\hspace{.20em}%
}%
}
Thus, when shown in a smaller size—for example when stacked atop = or \Leftarrow—the internal lines are off by a small but noticeable amount.
The second reason is more insidious and seems to have to do with rounding error in PDF conversion or display: the inner wedge "wobbles" half a pixel or so (as compared to the outer wedge) at various sizes.
I'm wondering what the best solution is here. I'm not opposed (in theory) to diving into XeLaTeX to see how U+2A53 and U+2A54 look, but if possible I'd prefer to avoid dependencies on XeTeX/XeLaTeX for this. Also, the first thing I tried was nesting a \tiny\land inside a \land but the slopes of the strokes were different. Basically I need something with the same slopes and thicknesses, and it would also be nice if they had rounded edges, but I haven't the TeXpertise to make that happen.
Here's how the symbols look at a more regular size (top line is regular boolean logical operators; second two lines are bitwise boolean operators):
By the way, I did come across a double-nested less-than and greater-than in a standard LaTeX package, which I think I could maybe use—if I rotated them 90 degrees—but the problem I have with those is that they override/redefine \ll and \gg rather than adding new control sequences, and I have places elsewhere where I want to use the real \ll and \gg.
-
You don't need to load the mathabx package just to use one symbol: just load the necessary font and consult the package to know the slot corresponding to \lll; it turns out that the font is matha and the slot is "CE.
\usepackage{graphicx}
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
<5> <6> <7> <8> <9> <10> gen * matha
<10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
}{}
\newcommand{\bland}{\mathbin{
\raisebox{.1ex}{%
\rotatebox[origin=c]{-90}{\usefont{U}{matha}{m}{n}\symbol{\string"CE}}}}}
\newcommand{\blor}{\mathbin{
\raisebox{.1ex}{%
\rotatebox[origin=c]{90}{\usefont{U}{matha}{m}{n}\symbol{\string"CE}}}}}
If you need those symbols also in subscripts and superscripts, some more work is needed. A possible definition is
\usepackage{graphicx}
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
<5> <6> <7> <8> <9> <10> gen * matha
<10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
}{}
\makeatletter
\newcommand{\blandor}[1]{\mathbin{\@blandor{#1}}}
\newcommand{\@blandor}[1]{\mathchoice
{\@@blandor{#1}{\tf@size}}
{\@@blandor{#1}{\tf@size}}
{\@@blandor{#1}{\sf@size}}
{\@@blandor{#1}{\ssf@size}}
}
\newcommand{\@@blandor}[2]{%
\raisebox{.1ex}{\rotatebox[origin=c]{#1}{%
\fontsize{#2}{#2}\usefont{U}{matha}{m}{n}\symbol{\string"CE}}}%
}
\makeatother
\newcommand{\bland}{\blandor{-90}}
\newcommand{\blor}{\blandor{90}}
-
Thank you so much. This is perfect. Beautiful. Exactly what I need. (I actually saw your reply yesterday while I was on the train, but I didn't have time to try it out until I got home today.) I made two small modifications: (1) I added a \scalebox{.82}[1] between the \raisebox and the \rotatebox so that the width and stroke slopes exactly match the \land and \lor symbols, and (2) I added \kern.061em on each side so that the spacing also matches (at least, that is to say, in 10pt). Thank you also for the edit which added the multiple sizes! – Todd Lehman Dec 26 '11 at 18:17
@ToddLehman I'd do the scaling before rotating, with \scalebox{1}[.82]{\fontsize...}. – egreg Dec 26 '11 at 18:23
Ok, I've made that change, thanks. (It also required changing \raisebox{.1ex} to \raisebox{.19ex}.) Question: It's going to need slightly different scaling values for the smaller sizes. I modified \@@blandor to take 4 arguments instead of 2, so I can pass scaling values for each size, and I noticed that the second of the four \mathchoice lines seems to control all of \normalsize, \small, \footnotesize, \scriptsize, and \tiny. In other words, {\@@blandor{#1}{\tf@size}{1}{.82}} seems to govern all the sizes, with the other three lines ignored. Does that sound right? – Todd Lehman Dec 26 '11 at 18:56
@ToddLehman The four arguments to \mathchoice tell TeX what to do when it has to typeset the object in \displaystyle, \textstyle, \scriptstyle and \scriptscriptstyle; the use of \tf@size and so on guarantees that the chosen font is the right one depending on the context (\small, \large or any other). – egreg Dec 26 '11 at 19:08
Aha. Cool. I'll do some more experimenting along those lines. I actually don't need these symbols in superscripts or subscripts; I only need the smaller size for stacking above a widened \Leftarrow, and the normal size for regular operations. – Todd Lehman Dec 26 '11 at 19:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8816642165184021, "perplexity": 1617.1991375024775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398452560.13/warc/CC-MAIN-20151124205412-00158-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://dev.ckeditor.com/timeline?from=2013-07-24T16%3A11%3A05Z&precision=second | # Timeline
## Jul 24, 2013:
10:49 PM Ticket #10673 (Deleted style incorrectly remembered) created by zacaway
Refer to the attached video for demonstration, but this can be easily …
4:24 PM Ticket #10672 (Paste from Word not working properly with lists) created by kevin
When pasting from Word lists are not nested or indented properly after …
4:11 PM Ticket #10633 (Text direction is not preserved for Paste function) reopened by Frederico Caldeira Knabben
6:38 AM Ticket #10671 (Continue to bug report #10663: problems with the setData function) created by Avital
Hello, I created a new mvc project reproduced the bug You can see …
5:39 AM Ticket #10670 (Inline CKeditor steals focus) created by Mandeep
I have a div with inline ckeditor on it and also an input box. when …
## Jul 23, 2013:
8:48 PM Ticket #10669 (CKEditor follows links in WebKit-based browsers, replacing the iframe ...) created by Сковорода Никита Андреевич
Tested under qtwebkit 2.3.1, qtwebkit 2.3.2, qt5-webkit from Qt 5.1.0, …
10:47 AM Ticket #10668 (Safari: Unnecessary text displayed while pasting text copied from a ...) created by Sachin Grover
When pasting a TEXT from Microsoft Word by using CTRL+V. Unnecessary …
9:57 AM Ticket #10667 (With IE10 undo in a table cells gives script error) created by Tamás Major
1. Open DEMO page with IE10 2. Find the table marked as Mission crew …
8:24 AM Ticket #10503 (Alt + F10 doesn't work on Ubuntu) closed by Piotr Jasiun
duplicate
5:19 AM Ticket #10666 (Cross frame problems) created by Stig Runar Vangen
I'm using CkEditor in a GWT integration. This worked well until I just …
## Jul 22, 2013:
7:48 PM Ticket #10665 (HTML entities in custom dropdown) created by Spire
Hi We are using custom dropdown plugin with HTML entities in …
1:00 PM Ticket #10664 (MathJax widget) created by Piotr Jasiun
Widget allows you insert and edit mathematical equations in TeX or …
11:42 AM Ticket #10647 (I GET SCRIPT ERROR IN THE CELL PROPERTIES DIALOG.) closed by Jakub Ś
duplicate: DUP of #6581
10:55 AM Ticket #10663 (problems with the setData function) closed by Jakub Ś
invalid: You have written that you have error with code you are using and …
9:53 AM Ticket #10648 (UNDO CAN STOP WORKING) closed by Jakub Ś
duplicate: Dup of #10301.
7:15 AM Ticket #5806 (Spell Check dialog looks ugly) closed by Jakub Ś
fixed: It seems much nicer now:)
## Jul 21, 2013:
6:32 AM Ticket #10663 (problems with the setData function) created by Avital
Hello, I have a big problem with the setData function, after using it …
## Jul 20, 2013:
9:05 PM Ticket #10662 (Inconsistent ACF rule application between inline editor and standard editor) created by Kevin Kamel
This is a refinement of the ticket I filed in #10661. I am including a …
10:08 AM Ticket #10661 (Shared space plugin strips classes when "top" toolbar is enabled) closed by Piotrek Koszuliński
invalid: This is exactly how ACF works. Those class and id are not allowed by …
3:35 AM Ticket #10661 (Shared space plugin strips classes when "top" toolbar is enabled) created by Kevin Kamel
Hi, This seemingly is an ACF problem within the shared space …
## Jul 19, 2013:
7:15 PM Ticket #10658 (ckeditor 4.2 not working in IE 8/9) closed by Jakub Ś
invalid: I have checked latest demo page in DEFAULT IE8 and IE9. They are both …
1:13 PM Ticket #10660 (Menu Button may be missing default mode) created by Jakub Ś
1. Please insert attached file into plugins folder 2. On sample page …
11:34 AM Ticket #10659 (New image widget) created by Olek Nowodziński
Widgets feature is to be released with a powerful and spectacular …
11:16 AM Ticket #10658 (ckeditor 4.2 not working in IE 8/9) created by MEGHA
8:03 AM Ticket #10657 (Config.removeButtons isn't mentioned in Toolbar configuration guide) created by Piotrek Koszuliński
Guide: http://docs.ckeditor.com/#!/guide/dev_toolbar Option: …
8:01 AM Ticket #10656 (inserting new functions on the default editor page in ckeditor) closed by Piotrek Koszuliński
invalid: See: * http://docs.ckeditor.com/#!/guide/dev_toolbar * …
7:41 AM Ticket #10656 (inserting new functions on the default editor page in ckeditor) created by sindu
i want to edit the standard editor page.means i dont want some icons …
## Jul 18, 2013:
9:34 PM Ticket #10654 (Arithmatic Operation) closed by Piotrek Koszuliński
invalid: CKEditor is a rich text editor, not a spreadsheet. So if you meant …
8:49 PM Ticket #10655 (TAB leaves the editable when cannot indent anything) created by Piotrek Koszuliński
1. Open editor in std preset. 2. Create list. 3. "Mistakenly" press …
2:25 PM Milestone CKEditor 4.2 completed
* Hi-DPI (Retina) support with better graphics (#9923). * …
2:25 PM Milestone CKEditor 4.1.3 completed
Tests start: 09 Jul 2013
2:21 PM Ticket #10654 (Arithmatic Operation) created by Bhavesh
Is there any way to perform simple arithmetic operation with CK editor …
11:15 AM Ticket #10653 ([IE9 IE10] Error when pasting single letter in specific conditions) created by Piotrek Koszuliński
1. Open inlinebycode sample. 2. Clear editor contents. 3. Type: 'A B …
10:33 AM Ticket #10644 (Pasting unstyled text in Inline mode using Chrome) closed by Piotrek Koszuliński
fixed: Fixed on master with git:1baa4c5.
## Jul 17, 2013:
9:21 PM Ticket #10652 (insertElement table into table range crashes page) created by Ben Duncan
The browser/page crashes while inserting a table inside of another …
4:34 PM Ticket #10651 (CKEditor.NET - TextChanged event getting called on PreRender.) created by Poornima Nookala
As per asp.net page life cycle, control events should occur after …
3:54 PM Ticket #10650 ([IE] Cannot apply nested background colors) created by Zoltan Koszegi
STR: 1. Go to DEMO page. 2. Highlight at least 3 words and set the …
3:46 PM Ticket #10649 (SPECIAL CHARACTER INSERTED IN WRONG LOCATION WITH SPECIFIC STEPS) created by Zoltan Koszegi
Description: An inserted special character is being inserted at the …
3:24 PM Ticket #10648 (UNDO CAN STOP WORKING) created by Zoltan Koszegi
This can be easily recreated on the CK demo page with IE9. STR: 1. On …
3:16 PM Ticket #10647 (I GET SCRIPT ERROR IN THE CELL PROPERTIES DIALOG.) created by Zoltan Koszegi
Description: I get script error in the cell properties dialog if I …
3:10 PM Ticket #10646 (Trying to remove a sub-list from a list entry deletes the entire list) created by Zoltan Koszegi
Steps To Recreate: 1) Make a web page with paragraphs surrounding a …
2:18 PM Ticket #10645 (Preview tab in DocProps plugin is missing utf-8 meta tag.) created by Jakub Ś
Preview tab in DocProps plugin is missing utf-8 meta tag. Because of …
10:53 AM Ticket #10642 (Problem in chrome with Tabs and Ckeditor) closed by Lindus
invalid
9:58 AM Ticket #10644 (Pasting unstyled text in Inline mode using Chrome) created by Tobias Hößl
There seems to be a problem with pasting raw text having multiple …
9:19 AM Ticket #10643 (Differences between Ctrl+V and pasting from pastefromword dialog) created by Jakub Ś
1. Open replacebycode sample 2. Open attached word file and copy …
6:56 AM Ticket #5549 (Paste command scrolls document in Webkit) closed by Jakub Ś
fixed: I wasn't able to reproduce this problem as well in latest CKEDitor …
## Jul 16, 2013:
1:04 PM Ticket #10642 (Problem in chrome with Tabs and Ckeditor) created by Lindus
Hi, I'm facing a problem with the last version of ckeditor (4.1.2) …
12:20 PM Ticket #10641 (Find considers elements with display: none) created by Olek Nowodziński
Extracted from [http://stackoverflow.com/questions/17674361 the …
11:09 AM Ticket #10632 (Pressing Backspace on IE9 in front of a link causes 2 characters to ...) closed by Jakub Ś
invalid
9:45 AM Ticket #10240 ([IE] JS errors logged when pressing delete in specific case) closed by Jakub Ś
duplicate: This is in fact DUP of #10584 @Reinmar I'm closing your issue as …
9:44 AM Ticket #10640 ([IE8] Invalid argument thrown when pressing C-x on image) closed by Jakub Ś
duplicate: DUP of #10584 @a.nowodzinski I have moved your TC there.
9:19 AM Ticket #10640 ([IE8] Invalid argument thrown when pressing C-x on image) created by Olek Nowodziński
1. http://ckeditor4.t/ckeditor/samples/replacebycode.html 2. Click the …
## Jul 15, 2013:
9:40 PM Ticket #10639 (Single Space Does Not Cause Lines to Re-Wrap Correctly) created by Joel Howard
Repro steps: Open the demo page. Place the cursor at the beginning of …
4:34 PM Ticket #10637 (Icons broken in QM (IE9)) closed by Wiktor Walc
fixed: Fixed in CKBuilder. The problem was in using double (multiple) class …
3:57 PM Ticket #10638 (HTML entities in custom dropdown) created by Spire
Hi We are using custom dropdown plugin with HTML entities in …
2:37 PM Ticket #10637 (Icons broken in QM (IE9)) created by Olek Nowodziński
Several icons are broken if editor run in QM. Note: Only those icons …
1:33 PM Ticket #10636 (Error thrown when in/outdenting inside of a list element (caret in a ...) created by Olek Nowodziński
[…] * When outdenting: […] * When indenting: Nothing happens, …
10:27 AM Ticket #10633 (Text direction is not preserved for Paste function) closed by Jakub Ś
wontfix: 1. When you do that dir attribute gets assigned to body which isn't …
10:25 AM Ticket #10605 (tab/shift-tab to indent/outdent lists not working for lists inside a table) closed by Frederico Caldeira Knabben
invalid: TAB for list indentation ha been introduced with #8244. It's supposed …
7:13 AM Ticket #10630 (Alignment - Center Option for Image) closed by Jakub Ś
duplicate: DUP of #8938
7:08 AM Ticket #10635 (Is there any basic license of CKFinder to use for our local , QA & ...) closed by Jakub Ś
5:10 AM Ticket #10635 (Is there any basic license of CKFinder to use for our local , QA & ...) created by Nikhil
Hi there, I want to buy license for CKFinder, before that I want to …
## Jul 14, 2013:
6:49 PM Ticket #10634 (Ckeditor won't work in Zencart 1.5.1 or not installed proerly) closed by Piotrek Koszuliński
invalid: I'm sorry, but this is not a forum. You can ask your question on: * …
3:02 PM Ticket #10634 (Ckeditor won't work in Zencart 1.5.1 or not installed proerly) created by Bill
I have been trying to 3 days to get latest version of ckeditor to work …
1:58 PM Ticket #10633 (Text direction is not preserved for Paste function) created by Amir
When using paste function thorugh paste dialog, the text direction is …
## Jul 13, 2013:
11:10 AM Ticket #10632 (Pressing Backspace on IE9 in front of a link causes 2 characters to ...) created by Filip Wieladek
Steps to reproduce: 1) Go to the CKEditor demo site 2) Select …
## Jul 12, 2013:
5:33 PM Ticket #10631 (Content Advisor in IE8 Causes 4.1.2 to not function) created by Jared Dutton
When Content Advisor is turned on in IE8, regardless of the …
2:21 PM Ticket #10630 (Alignment - Center Option for Image) created by gvvsnreddy
In previous versions of CKEditor, under Image Properties | Align one …
1:53 PM Ticket #10629 (Not able to resize the ckeditor in xml descriptor file) created by Jay
Hi There, I am not able to resize the ckeditor using xml descriptor …
12:50 PM Ticket #10628 (Samples for basics makes no sense) created by Piotr Jasiun
When you open samples in basics preset some (most) of them does not …
9:41 AM Ticket #10627 (Removing form element removes whole paragraph) created by Jakub Ś
1. Insert textfiled into paragraph 2. You will notice there is little …
7:44 AM Ticket #10624 (IE7 text direction from right to left breaks toolbar) closed by Jakub Ś
duplicate: DUP of #10617
## Jul 11, 2013:
7:45 PM Ticket #10626 (IE7 Sample "Sharing Toolbar and Bottom-bar Spaces" doesn't work on IE7.) closed by Piotrek Koszuliński
wontfix: Samples are for developers. Developers don't use IE7.
3:21 PM Ticket #10626 (IE7 Sample "Sharing Toolbar and Bottom-bar Spaces" doesn't work on IE7.) created by Piotr Jasiun
1. Open IE7 2. Go to (build full all): …
3:16 PM Ticket #10625 (IE7 No preview in document Properties Plugin) created by Piotr Jasiun
1. Open IE7. 2. Go to (build full all): …
2:26 PM Ticket #10624 (IE7 text direction from right to left breaks toolbar) created by Piotr Jasiun
1. Open IE7 2. Go to: …
2:08 PM Ticket #10623 ([Webkit] Page is scrolled when opening dropdown) created by Piotrek Koszuliński
1. Open some long sample to have a scrollbar (e.g. …
1:19 PM Ticket #10622 (Under specific scenario, "Enter" inserts new line but resets cursor to ...) created by Ben Fariello
Steps to reproduce - - I reproduced this issue on the Demo page found …
12:54 PM Ticket #10621 ([IE]Context menu on IE opens in left top corner) created by Piotr Jasiun
1. Open http://local.ckeditor.dev/samples/replacebyclass.html 2. Click …
12:11 PM Ticket #10619 (CKFinder connectors: possibility to use SQL instead of filesystem) closed by Jakub Ś
invalid: @req to build your own connector you need to review this link (and all …
11:32 AM Ticket #10620 (IE11: NotSupportedError error gets thrown when creating editor.) created by Jakub Ś
Open AJAX sample in IE11 and click Create Editor. Result: …
11:29 AM Ticket #10619 (CKFinder connectors: possibility to use SQL instead of filesystem) created by Joel
Requesting a feature to make it possible to use an SQL database …
10:54 AM Ticket #10618 (IE11: Cell Properties and Join Cell context menu options are disabled) created by Jakub Ś
1. Insert default table 2. Right Click in any cell and check context …
10:43 AM Ticket #10617 ([IE]: BIDI button breaks toolbar when in compatibility mode) created by Jakub Ś
* Open e.g. replacebycode sample in IE8-11 in compatibility mode or in …
10:36 AM Ticket #10616 (IE11 numbers lists from zero IN COMPATIBILITY MODE) created by Jakub Ś
Insert ordered list into editor or open page with list in IE11 …
9:32 AM Ticket #10615 ([IE11]: New Page command causes JS error) created by Jakub Ś
Open IE11 in any mode and click New Page command Result: …
8:46 AM Ticket #10614 (IE11: Selection is lost when opening dropdowns or menu buttons or ...) created by Jakub Ś
1. Select some text 2. Open dropdown or one of Color Menu Button …
## Jul 10, 2013:
5:18 PM Ticket #10613 (The expected native right click context isn't available over entire ...) created by Jared Cobb
I have disabled the CKEditor right click context menu (in favor of the …
2:01 PM Ticket #10612 (IE11 Compatibility) created by Frederico Caldeira Knabben
This is the main ticket to check IE11 compatibility. It is also an …
1:35 PM Ticket #10611 (no property of "style=font-size" for default font size) created by Chenyue Gao
There is no property of style=font-size when the user first enter text …
12:29 PM Ticket #10608 (CKFinder Error when used in ASP.NET with CKEditor control.) closed by Jakub Ś
invalid: Could you please send this message in English or at least in proper …
10:53 AM Ticket #10610 (Iframe dialog has very small content in CKEditor 4.) closed by Frederico Caldeira Knabben
fixed: Fixed with git:af4046f.
10:42 AM Ticket #10610 (Iframe dialog has very small content in CKEditor 4.) created by Jakub Ś
It seems that in CKEditor 4, main dialog plugin got default height …
8:17 AM Ticket #10609 (Two functions with the same name in the same context in indentlist plugin) created by Piotrek Koszuliński
[…] This should be clarified, because it's very hard to read this.
7:15 AM Ticket #10280 (Replace textarea with inline editor) closed by Piotrek Koszuliński
fixed: Merged to major with git:d20c978 on dev and c00a6d5 on tests.
5:52 AM Ticket #10608 (CKFinder Error when used in ASP.NET with CKEditor control.) created by Nikhil
Hi , I am getting following response from server every time i try …
## Jul 9, 2013:
3:25 PM Ticket #10607 (Remove "indentlist" require from "list") created by Frederico Caldeira Knabben
This is a followup for ticket:10599#comment:3. Ideally, the "list" …
3:18 PM Ticket #10606 (Inline form textarea using jQuery adapter) created by Piotr Jasiun
It should be possible to replace textarea with inline editor using …
2:43 PM Ticket #10599 (Remove "indent" require from "list" plugin) closed by Frederico Caldeira Knabben
fixed: Fixed with git:8ac6a22.
1:42 PM Ticket #10605 (tab/shift-tab to indent/outdent lists not working for lists inside a table) created by Satya Minnekanti
To reproduce the defect: 1) Open any sample, insert a table 2) …
8:28 AM Ticket #10604 ([IE11] Unable to close CKEditor dialogs) created by frietsch
As the release of IE11 is getting closer (scheduled for shipping with …
7:21 AM Ticket #10603 (With multiple editors, after attaching an image in the first, the ...) closed by Piotrek Koszuliński
invalid: This patch changes nothing. The i variable is defined in the …
Note: See TracTimeline for information about the timeline view. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15494893491268158, "perplexity": 28505.526236191705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578532050.7/warc/CC-MAIN-20190421180010-20190421202010-00310.warc.gz"} |
https://cs.stackexchange.com/questions/65534/hash-functions-and-pathological-data-sets/65546 | # Hash functions and pathological data sets
So I'm watching an Algorithms course in Coursera, and we are currently discussing hash tables. He's talking about the importance of a good hash function, and about how an ideal hash function would be a "super clever hash function guaranteed to spread every data set evenly".
Then, he explains that the problem is that such a hash function does not exist (and that for every hash function there is a pathological data set), and that the reason for this is as follows:
Fix a hash function $h: U \to \{0, 1, 2, ..., n-1\}$. By the Pigeonhole Principle, there exists a bucket $i$ such that at least $|U|/n$ elements of $U$ hash to $i$ under $h$. If a data set draws only from these, everything collides.
The bolded part is what's confusing me. Why does there exist a bucket $i$ such that at least $|U|/n$ elements of $U$ hash to $i$ under $h$? I can't really visualize what he means.
• Because the pigeonhole principle says exactly that. Did you look it up? – David Richerby Nov 4 '16 at 11:49
• It's easier to understand a more concrete example: You have, say, 5 buckets, and you need to stick, say, 7 pigeons in them somehow. 7 > 5, so it follows that at least 1 bucket has at least 2 pigeons in it. – j_random_hacker Nov 4 '16 at 15:44
• @DavidRicherby well, the Pigeonhole Principle as I understood it is what the first sentence in the wikipedia link says: "In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item." I didn't immediately see the equivalence between that and the bolded statement that confused me. Weirdly enough I was able to get useful answers out of asking this question :) – FrostyStraw Nov 4 '16 at 18:43
• OK but if you read as far as the third page of the wikipedia article, it tells you that, if you put more than $km$ items in $m$ buckets, at least one must contain more than $k$ items, which is exactly what's being used here. – David Richerby Nov 5 '16 at 0:08
• The answers posted here were more clear and therefore more helpful to me. – FrostyStraw Nov 5 '16 at 2:21
An easy way to visualize this is to imagine a hash table of size $n$ (implemented with chaining) that contains all of the elements of $U$ (even though this is unrealistic in practice because $U$ typically has massive size). Since $|U| >> n$, all of the elements of $U$ do not fit into the hash table; therefore, there will be collisions. Consider, for example, the universal set $U=\{a,b,c,d,e,f,g\}$ and a hash table with $n=3$ buckets. Since $|U|=7$, at least one bucket must necessarily contain $\lceil \: |U| \: / \: n \rceil = \lceil 7/3 \rceil = 3$ or more elements. In the case of the most clever hash function (which would spread out the elements of $U$ as evenly as possible), this bucket would contain exactly $3$ elements, like this (highlighted in red):
It is important to see that no matter how clever the hash function is, there will always exist a data set (for example, the set $\{b,g,a\}$) whose elements hash to the same bucket (for example, bucket number $1$). Such a pathological data set will make your hash table degenerate to its worst-case linear-time performance.
Assume there is no such bucket. Then each bucket has at most $|U|/n - 1$ items. There are $n$ buckets, so the total number of items is at most $n*(|U|/n - 1) = |U| - n$. This is less than $|U|$, which is the number of items we distributed to the buckets in the first place. This is a contradiction, so we proved that the statement "each bucket has at most $|U|/n - 1$ items" is false, which is equivalent to the statement "some bucket has at least $|U|/n$ items." | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5972683429718018, "perplexity": 257.9627380542489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141430.58/warc/CC-MAIN-20200216211424-20200217001424-00365.warc.gz"} |
http://sci-gems.math.bas.bg/jspui/browse?type=author&value=Slipchenko%2C+Oleksandr | ## Browsing by Author "Slipchenko, Oleksandr"
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2007 Growing Neural Networks Using Nonconventional Activation FunctionsBodyanskiy, Yevgeniy; Pliss, Iryna; Slipchenko, OleksandrInstitute of Information Theories and Applications FOI ITHEA
Showing results 1 to 1 of 1 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.864902675151825, "perplexity": 2909.0252787470936}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257836399.81/warc/CC-MAIN-20160723071036-00294-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://export.arxiv.org/abs/hep-th/0505249v2 | hep-th
(what is this?)
# Title: Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
Abstract: We show how Supersymmetric Ward identities can be used to obtain amplitudes involving gluinos or adjoint scalars from purely gluonic amplitudes. We obtain results for all one-loop six-point NMHV amplitudes in $\NeqFour$ Super Yang-Mills theory which involve two gluinos or two scalar particles. More general cases are also discussed.
Comments: 32 pages, minor typos fixed; one reference added Subjects: High Energy Physics - Theory (hep-th) Journal reference: JHEP 0508 (2005) 055 DOI: 10.1088/1126-6708/2005/08/055 Report number: SWAT-05-430 Cite as: arXiv:hep-th/0505249 (or arXiv:hep-th/0505249v2 for this version)
## Submission history
From: Dave Dunbar dr [view email]
[v1] Fri, 27 May 2005 17:18:45 GMT (29kb)
[v2] Wed, 15 Jun 2005 15:00:44 GMT (29kb)
Link back to: arXiv, form interface, contact. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3661120533943176, "perplexity": 17119.584331381087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987829458.93/warc/CC-MAIN-20191023043257-20191023070757-00371.warc.gz"} |
https://support.bioconductor.org/p/120788/ | Question: Annotation of probes from Affymetrix and Illumina platforms in MACQ project ?
0
4 months ago by
naf0
naf0 wrote:
Hello, I am having a problem with the annotation of probes for the Affymetrix and the Illumina platforms data,
I am using the package (hgu133plus2.db BiocManager:version 3.8 for R 3.5.2 version) for the Affymetrix data and "org.Hs.eg.db" for the Illumina data.
When I use the command (Affymetrix):
annotation <- select(hgu133plus2.db,keytype='PROBEID', keys=PROBEID, columns = c("ENTREZID"))
or (for Illumina):
annotation <- select(org.Hs.eg.db,keytype = 'ENTREZID',keys = ENTREZID,columns = c('SYMBOL'))
I get the following similar error messages in both cases:
For Affymetrix:
Error in select(hgu133plus2.db, keytype = "PROBEID", keys = PROBEID, columns = c("ENTREZID")) : unused arguments (keytype = "PROBEID", keys = PROBEID, columns = c("ENTREZID"))
For Illumina:
Error in select(org.Hs.eg.db, keytype = "ENTREZID", keys = ENTREZID, columns = c("SYMBOL")) : unused arguments (keytype = "ENTREZID", keys = ENTREZID, columns = c("SYMBOL"))
Has anyone also encountered this type of error, is it just a "silly" mistake or does it have to do with some more complicated reason?
modified 4 months ago by Guido Hooiveld2.5k • written 4 months ago by naf0
Answer: Annotation of probes from Affymetrix and Illumina platforms in MACQ project ?
0
4 months ago by
Guido Hooiveld2.5k
Wageningen University, Wageningen, the Netherlands
Guido Hooiveld2.5k wrote:
You didn't post your complete code, but have you assigned some IDs (probeset IDs resp. EntrezGene IDs) to the (your) 'variables' PROBEID resp. ENTREZID? I am asking because you code as such should work....(see below). Two remarks: I wouldn't recommend naming your variable that contains the probe/entrez IDs the same as one of the possible keytype arguments. Also have a look at the (1st) vignette of the package AnnotationDbi here.
> # load the annotation library
> library(org.Hs.eg.db)
>
> # as sample data, select the first 15 entrez/gene IDs.
> ENTREZID <- keys(org.Hs.eg.db)[1:15]
>
> # retrieve relevant annotation info
> select(org.Hs.eg.db, keytype = "ENTREZID", keys = ENTREZID, columns = c("SYMBOL") )
'select()' returned 1:1 mapping between keys and columns
ENTREZID SYMBOL
1 1 A1BG
2 2 A2M
3 3 A2MP1
4 9 NAT1
5 10 NAT2
6 11 NATP
7 12 SERPINA3
9 14 AAMP
10 15 AANAT
11 16 AARS
12 17 AAVS1
13 18 ABAT
14 19 ABCA1
15 20 ABCA2
>
>
Unfortunately still getting the error message. I have assigned some IDs (probeset IDs resp. EntrezGene IDs) to my variables' PROBEID resp. ENTREZID. I have even tried to copy-paste your code but keep on getting the same discouraging message. This is where I assign values to ENTREZID in my code:
ENTREZID <- rownames(dge$counts) keytypes(org.Hs.eg.db) columns(org.Hs.eg.db) annotation <- select(org.Hs.eg.db,keytype = 'ENTREZID',keys = ENTREZID,columns = c('SYMBOL')) I get: [1] "ACCNUM" "ALIAS" "ENSEMBL" "ENSEMBLPROT" "ENSEMBLTRANS" [6] "ENTREZID" "ENZYME" "EVIDENCE" "EVIDENCEALL" "GENENAME" [11] "GO" "GOALL" "IPI" "MAP" "OMIM" [16] "ONTOLOGY" "ONTOLOGYALL" "PATH" "PFAM" "PMID" [21] "PROSITE" "REFSEQ" "SYMBOL" "UCSCKG" "UNIGENE" [26] "UNIPROT" [1] "ACCNUM" "ALIAS" "ENSEMBL" "ENSEMBLPROT" "ENSEMBLTRANS" [6] "ENTREZID" "ENZYME" "EVIDENCE" "EVIDENCEALL" "GENENAME" [11] "GO" "GOALL" "IPI" "MAP" "OMIM" [16] "ONTOLOGY" "ONTOLOGYALL" "PATH" "PFAM" "PMID" [21] "PROSITE" "REFSEQ" "SYMBOL" "UCSCKG" "UNIGENE" [26] "UNIPROT" This is the error I get again: Error in select(org.Hs.eg.db, keytype = "ENTREZID", keys = ENTREZID, columns = c("SYMBOL")) : unused arguments (keytype = "ENTREZID", keys = ENTREZID, columns = c("SYMBOL")) ADD REPLYlink modified 4 months ago • written 4 months ago by naf0 You probably have select masked by another package. Try AnnotationDbi::select(org.Hs.eg.db, ENTREZID, "SYMBOL", "ENTREZID") ADD REPLYlink written 4 months ago by James W. MacDonald51k absolutely magic James, thanks so much, it's working!! ADD REPLYlink written 4 months ago by naf0 Hi James, I now have another problem with annotations with these files: the illumina textfiles found in: https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE5350, the datafile GSE5350MAQCILM12359TXTs.zip When I used: AnnotationDbi::select(org.Hs.eg.db,keytype = 'ENTREZID',keys = ENTREZID,columns = c('SYMBOL')) I got the error message: Error in .testForValidKeys(x, keys, keytype, fks) : None of the keys entered are valid keys for 'ENTREZID'. Please use the keys method to see a listing of valid arguments. I went on the internet and saw that what I have in my files are not entrezID's, I have probe iD's that look like: "GI13376332-S" "GI13376334-S" "GI13376338-S" "GI13376342-S" I saw that some years back, some other people had a similar problem and you helped them solve it. I read about FLYBASE ID's and PROBE ID's but I just can't find what type of ID's mine are. Do you have an idea? I tried this: AnnotationDbi::select(org.Hs.eg.db,rownames(dge$counts),"SYMBOL","TargetID")
I know that "TargetID" is not right but I just don't know what type of ID Illumina has used.
The illuminaHumanv1.db package has mappings between this Illumina chip and Symbol, entrez, etc. The keytype you need to use is PROBEID
library(illuminaHumanv1.db)
anno <- select(illuminaHumanv1.db, keytype="PROBEID",keys=ENTREZID,columns=c("ENTREZID","SYMBOL"))
`
great Mark, thanks a lot,
it worked but with adding "AnnotationDbi::" just in front of select.... as James W. MacDonald (above) suggested,
thanks a stack! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23397737741470337, "perplexity": 21044.227159833605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573331.86/warc/CC-MAIN-20190918193432-20190918215432-00013.warc.gz"} |
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