url
stringlengths 14
2.42k
| text
stringlengths 100
1.02M
| date
stringlengths 19
19
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|---|
https://www.research.ed.ac.uk/en/publications/measurement-of-icpi-observables-in-the-process-bsup%CE%BFsup-dksup%CE%BFsup
|
# Measurement of CP observables in the process Bο → DK*ο with two- and four-body D decays
Peter Clarke, Robert Currie, Stephan Eisenhardt, Silvia Gambetta, Franz Muheim, Matthew Needham, Marco Pappagallo, Mark Williams, LHCb Collaboration
Research output: Contribution to journalArticlepeer-review
## Abstract
Measurements of $C\!P$ observables in $B^0 \to DK^{*0}$ decays are presented, where $D$ represents a superposition of $D^0$ and $\bar{D}^0$ states. The $D$ meson is reconstructed in the two-body final states $K^+\pi^-$, $\pi^+ K^-$, $K^+K^-$ and $\pi^+\pi^-$, and, for the first time, in the four-body final states $K^+\pi^-\pi^+\pi^-$, $\pi^+ K^-\pi^+\pi^-$ and $\pi^+\pi^-\pi^+\pi^-$. The analysis uses a sample of neutral $B$ mesons produced in proton-proton collisions, corresponding to an integrated luminosity of 1.0, 2.0 and 1.8 $\rm fb^{-1}$ collected with the LHCb detector at centre-of-mass energies of $\sqrt{s} =$ 7, 8 and 13 TeV, respectively. First observations of the decays $B^0 \to D(\pi^+ K^-)K^{*0}$ and $B^0 \to D(\pi^+\pi^-\pi^+\pi^-)K^{*0}$ are obtained. The measured observables are interpreted in terms of the $C\!P$-violating weak phase $\gamma$.
Original language English 41 Journal of High Energy Physics 2019 https://doi.org/10.1007/JHEP08(2019)041 Published - 7 Aug 2019
## Fingerprint
Dive into the research topics of 'Measurement of <i>CP</i> observables in the process B<sup>ο</sup> → DK*<sup>ο</sup> with two- and four-body <i>D</i> decays'. Together they form a unique fingerprint.
|
2022-01-21 20:11:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.7784104943275452, "perplexity": 2837.231981454129}, "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-2022-05/segments/1642320303709.2/warc/CC-MAIN-20220121192415-20220121222415-00592.warc.gz"}
|
http://mathoverflow.net/questions/72829/which-curves-have-stable-faltings-height-greater-or-equal-to-1?sort=votes
|
# Which curves have stable Faltings height greater or equal to 1
Let $Y$ be a smooth projective connected curve of genus $g>0$ over $\overline{\mathbf{Q}}$. Let $h_{\textrm{Fal}}(Y)$ be the Faltings height of $Y$.
Question 1. Can one classify or describe the curves $Y$ such that $h_{\textrm{Fal}}(Y) \geq 1$?
Question 2. For any $g>0$, does there exist a curve $Y$ of genus $g$ such that $h_{\textrm{Fal}}(Y) <1$?
Essentially, I would like to know which curves one is excluding by looking at curves $Y$ such that $h_{\textrm{Fal}}(Y) \geq 1$.
A result of Bost says that the stable Faltings height of an abelian variety $A$ over $\overline{\mathbf{Q}}$ of dimension $g$ is bounded from below by $-\frac{1}{2}\log(2\pi)g$.
By the Northcott property of the Faltings height, the set of curves of genus $g$ with $h_{\textrm{Fal}}(Y) <1$ is finite. This means that I'm looking at the finite set of curves of genus $g$ with Faltings height not in the interval $$[-\frac{1}{2}\log(2\pi)g,1)\subset[-2/5g, 1).$$
Added: To answer Junkie's question, I'm aware of only one definition of the Faltings height of a curve over $\overline{\mathbf{Q}}$. There are several equivalent definitions, though.
Let $X$ be a smooth projective curve of genus $g>0$ over $\overline{\mathbf{Q}}$. Let $K$ be a number field such that $X$ has a semi-stable regular model $p:\mathcal{X}\to \mathrm{Spec} O_K$ over the ring of integers $O_K$ of $K$. Then, the Faltings height $h_{\mathrm{Fal}}(X)$ of $X$ is the arithmetic degree $$h_{\mathrm{Fal}}(X):=\frac{\widehat{\mathrm{deg}} Rp_\ast \mathcal{O}_{\mathcal{X}}}{[K:\mathbf{Q}]},$$ where we endow the determinant of cohomology with the Arakelov-Faltings metric. This is well-defined, i.e., independent of the field $K$. By Serre duality, it coincides with $$h_{\mathrm{Fal}}(X)=\frac{\widehat{\mathrm{deg}} p_\ast \mathcal{\omega}_{\mathcal{X}/O_K}}{[K:\mathbf{Q}]}.$$ It also coincides with the Faltings height of the Jacobian. All of this is explained in Section 4.4 of
For a curve over a number field, there is also the important relative Faltings height. This invariant depends on the number field $K$, though.
-
What is "the Faltings height" to you? There are so many normalisations around, that it can be hard to juggle them. – Junkie Oct 14 '11 at 3:40
For an elliptic curve, I've seen the Faltings height defined by Mazur as $-{1\over 2}\log\Omega$, maybe with a $2\pi$. math.arizona.edu/~swc/notes/files/98MazurLN.ps Maybe this is the "logarithmic" Faltings height, as I've seen $\sqrt{2\pi/\Omega}$. I think none match Deligne's calculation (I recall going thru this many years ago, but forget what adjustments need to be made) of below. Another example is Tonghai Yang throws in factors to make $(\Lambda'/\Lambda)(0)$ come out nice. msri.org/~levy/files/Book49/09yang.pdf But it don't matter if you don't care about constants. :) – Junkie Oct 14 '11 at 11:40
In short, it is natty for me personally to take your definition, and compare it to any of the ones for an elliptic curve. Likely a tedious exercise (I can never track down a source where it is done, though Deligne might come close), but can you say what your normalisation is in terms of $\Omega$ (the fundamental volume of the parallelogram associated to the Neron model - let's keep it easy and over Q at first)? If you don't want to bother with this, I understand too, for as I say, it's just a constant. If nothing else, I've warned you to be careful when the term "Faltings height" is used. :) – Junkie Oct 14 '11 at 11:49
Hey Junkie, thanks alot for your comments. I wansn't aware of any of these ambiguities in the litarature. For an elliptic curve over K with semi-stable reduction, the Faltings height (as I defined above) can be computed explicitly. See Proposition 5.5.1 in R. de Jong's thesis. math.leidenuniv.nl/~rdejong/publications/Thesiswebversion.pdf – Ariyan Javanpeykar Oct 14 '11 at 17:32
Looking at these sources I conclude this. The unstable Faltings height is given by ${-1\over 2}\log|{i\over 2}\int\omega\wedge\bar\omega=-{1\over 2}\log(Volume)$, see (14) of Silverman. The stable Faltings height differs from this, naturally, from contributions at places of additive reduction. Deligne differs from this stable Faltings height by an addition of $\log\sqrt\pi$ somewhere. Yang uses an normalisation suitable to his analytic number theory purposes. The "Parshin-Faltings height" more probably means exp of one of the above, like $\sqrt{1/Vol}$, possibly with $\pi$. – Junkie Oct 15 '11 at 5:51
Dear Ariyan, the elliptic curve with equation $$y^2=x^3+6$$ has Faltings height $$-(3/2)\log(\Gamma(1/3)/\Gamma(2/3))+(1/4)\log(3)=-0.748752...;$$ the curve of genus $2$ with equation $$y^2+y=x^5$$ has Faltings height $$h_{\rm Fal}(C_{\bar{\bf Q}})=2\log(2\pi)- {1\over 2}\log\big(\Gamma(1/5)^5\Gamma(2/5)^3\Gamma(3/5)\Gamma(4/5)^{-1}\big)$$ $$\approx -1.452509239645644650317707042;$$ For the first example, see Deligne, "Preuve des conjectures de Tate et Shafarevich", Séminaire Bourbaki. For the second one, see Bost, Mestre, Moret-Bailly, "Sur le calcul explicite des 'classes de Chern' des surfaces arithmétiques de genre $2$", Séminaire sur les Pinceaux de Courbes Elliptiques (Paris, 1988). Astérisque No. 183 (1990), 69–105.
Another explicit formula that should allow you to produce elliptic curves of arbitrarily large Faltings height is the inequality $$|h(j_E)-12h_{\rm Fal}(E)|\leqslant 6\log(1+h(j_E))+47.15$$ See paragraph 5. of the article "Serre's uniformity..." by Bilu and Parent for references.
Something else you can do is make numerical experiments with formula in Conj. 3 of the article of Colmez, "Hauteur de Faltings..." (Compositio), which is true (without $\log(2)$ factor !, see A. Obus, arXiv:1107.0684) if the CM field is abelian over $\bf Q$. In that case, the Artin $L$-functions become Dirichlet $L$-functions and can be computed explicitly in terms of values of the Gamma function using the Hurwitz formula.
This is not a complete answer but I hope that it helps.
-
I get that the fundamental volume of $\Omega={\Gamma(1/3)^2\over \Gamma(2/3)^4}{\pi^2\over 3^{11/6}}\approx 2.8111$ for Deligne's curve, and thus from (say) Colmez's definition of the Faltings height as $-{1\over 2}\log\int \omega\wedge\omega$, a different answer. I suspect the normalisations differ, though perhaps I missing something more subtle? – Junkie Oct 14 '11 at 12:11
Taking $e^{-2D}$ where $D$ is Deligne's result, I get some thing that differs is bigger than (what I call) the fundamental volume by a factor of $3^{5/6}\over{\pi/2}$. – Junkie Oct 14 '11 at 12:28
Looking at de Jong's thesis, he has an extra $\log\sqrt{\pi}$ in the formula. He has, for $y^2=x^3-1$ a result of $-{1\over 2}\log[({\Gamma(1/3)\over\Gamma(2/3)})^3{\pi\over\sqrt 3}]$, and Deligne has this without the $\log\sqrt\pi$. – Junkie Oct 15 '11 at 5:15
Ari, the link above math.univ-toulouse.fr/~couveig/book.htm doesn't work. I am assuming this is a book of J-M. Couveignes, is that correct? Could you provide a title or update the link please. – Tony Shaska Jul 6 '14 at 12:41
|
2016-07-28 00:58:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8051590323448181, "perplexity": 334.69197661705704}, "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/1469257827781.76/warc/CC-MAIN-20160723071027-00229-ip-10-185-27-174.ec2.internal.warc.gz"}
|
https://pdglive.lbl.gov/DataBlock.action?node=S032SP4&home=MXXX035
|
# ${{\boldsymbol D}^{0}}$ $\rightarrow$ ${{\boldsymbol K}^{*}}{{\boldsymbol K}}$ AVERAGE RELATIVE STRONG PHASE $\delta {}^{ {{\boldsymbol K}^{*}} {{\boldsymbol K}} }$ INSPIRE search
The quoted value of $\delta$ is based on the same sign $\mathit CP$ phase of ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ convention.
VALUE ($^\circ{}$) DOCUMENT ID TECN COMMENT
$-16.6$ $\pm18.4$ 1
2012
CLEO ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at 3.77 GeV
1 Uses quantum correlations in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ at the ${{\mathit \psi}{(3770)}}$, where the signal side ${{\mathit D}}$ decays to ${{\mathit K}_S^0}$ ${{\mathit K}}{{\mathit \pi}}$ and the tag-side ${{\mathit D}}$ decays to ${{\mathit K}}{{\mathit \pi}}$ , ${{\mathit K}}{{\mathit \pi}}{{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\mathit \pi}}{{\mathit \pi}^{0}}$ , and 10 additional $\mathit CP$-even, $\mathit CP$-odd, and mixed $\mathit CP$ modes involving ${{\mathit K}_S^0}$ or ${{\mathit K}_L^0}$ .
References:
INSLER 2012
PR D85 092016 Studies of the Decays ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$
|
2021-06-19 02:24:38
|
{"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": 0.9777678847312927, "perplexity": 853.6766754202444}, "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/1623487643380.40/warc/CC-MAIN-20210619020602-20210619050602-00457.warc.gz"}
|
https://www.esaral.com/q/solve-the-following-50948
|
# Solve the following :
Question:
A sphere starts rolling down an incline of inclination $\theta$. Find the speed of its centre when it has covered a distance $\mathrm{I}$.
Solution:
By energy conservation,
$m g(l \sin \theta)=\frac{1}{2} I \omega^{2}+\frac{1}{2} m v^{2}$
$m g l \sin \theta=\frac{1}{2}\left(\frac{2}{5} m R^{2}\right)\left(\frac{v^{2}}{R^{2}}\right)+\frac{1}{2} m v^{2}$
$v=\sqrt{\frac{10}{7} g l \sin \theta}$
|
2023-02-06 19:08:52
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7415847778320312, "perplexity": 1293.554813403636}, "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/1674764500357.3/warc/CC-MAIN-20230206181343-20230206211343-00035.warc.gz"}
|
http://zbmath.org/?q=an:1235.93112
|
zbMATH — the first resource for mathematics
Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.
Operators
a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Network-based feedback control for systems with mixed delays based on quantization and dropout compensation. (English) Zbl 1235.93112
Summary: This paper deals with the problem of feedback control for networked systems with discrete and distributed delays subject to quantization and packet dropout. Both a state feedback controller and an observer-based output feedback controller are designed. The infinite distributed delay is introduced in the discrete networked domain for the first time. Also, it is assumed that system state or output signal is quantized before being communicated. Moreover, a compensation scheme is proposed to deal with the effect of random packet dropout through communication network. Sufficient conditions for the existence of an admissible controller are established to ensure the asymptotical stability of the resulting closed-loop system. Finally, a numerical example is given to illustrate the proposed design method in this paper.
MSC:
93B52 Feedback control 93A15 Large scale systems 93C55 Discrete-time control systems
References:
[1] Delchamps, D. F.: Stabilizing a linear system with quantized state feedback, IEEE transactions on automatic control 35, 916-924 (1990) · Zbl 0719.93067 · doi:10.1109/9.58500 [2] Jiang, B.; Mao, Z.; Shi, P.: H$\infty$ filter design for a class of networked control systems via T-S fuzzy model approach, IEEE transactions on fuzzy systems 18, No. 1, 201-208 (2010) [3] Liu, G.: Predictive controller design of networked systems with communication delays and data loss, IEEE transactions on circuits and systems II 57, No. 6, 481-485 (2010) [4] Liu, Y.; Yang, G.: Quantized static output feedback stabilization of discrete-time networked control systems, International journal of innovative computing information and control 7, No. 2, 719-732 (2011) [5] Seiler, P.; Sengupta, R.: An H$\infty$ approach to networked control, IEEE transactions on automatic control 50, No. 3, 356-364 (2005) [6] Shen, B.; Wang, Z.; Hung, Y. S.: Distributed consensus H-infinity filtering in sensor networks with multiple missing measurements: the finite-horizon case, Automatica 46, No. 10, 1682-1688 (2010) · Zbl 1204.93122 · doi:10.1016/j.automatica.2010.06.025 [7] Shi, P.; Mahmoud, M.; Nguang, S.; Ismail, A.: Robust filtering for jumping systems with mode-dependent delays, Signal processing 86, 140-152 (2006) · Zbl 1163.94387 · doi:10.1016/j.sigpro.2005.05.005 [8] Walsh, G. C.; Ye, H.; Bushnell, L. G.: Stability analysis of networked control systems, IEEE transactions on control systems technology 10, No. 3, 438-446 (2002) [9] Wang, Z.; Ho, D.; Liu, Y.; Liu, X.: Robust H$\infty$ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica 45, 684-691 (2009) · Zbl 1166.93319 · doi:10.1016/j.automatica.2008.10.025 [10] Wu, L.; Su, X.; Shi, P.; Qiu, J.: Model approximation for discrete-time state-delay systems in the T-S fuzzy framework, IEEE transactions on fuzzy systems 19, No. 2, 366-378 (2011) [11] Xie, L.; Fridman, E.; Shaked, U.: Robust H$\infty$ control of distributed delay systems with application to combustion controls, IEEE transactions on automatic control 46, No. 12, 1930-1935 (2001) · Zbl 1017.93038 · doi:10.1109/9.975483 [12] Yang, H.; Xia, Y.; Shi, P.: Stabilization of networked control systems with nonuniform random sampling periods, International journal of robust and nonlinear control 21, No. 5, 501-526 (2011) · Zbl 1214.93093 · doi:10.1002/rnc.1607 [13] Yin, S.; Yu, L.; Zhang, W.: Estimator-based control of networked systems with packet-dropouts, International journal of innovative computing information and control 6, No. 6, 2737-2748 (2010) [14] Zhao, Y.; Liu, G.; Rees, D.: Design of a packet-based control framework for networked control systems, IEEE transactions on control systems technology 17, No. 4, 859-865 (2009)
|
2014-04-16 07:21:30
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.6977745294570923, "perplexity": 6083.849522953801}, "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-20140416005201-00559-ip-10-147-4-33.ec2.internal.warc.gz"}
|
http://polytimenerd.blogspot.com/2012/06/multilanguage-documents-with-tex.html
|
## Sunday, June 17, 2012
### Multilanguage Documents with TeX
Today I have been working on a LaTeX document which was supposed to produce a document in two versions, one in Italian, another in English. It was a technical report, so a lot of stuff, but not so much text.
The classic way to approach this is to have the document written in one language, and then translate it into the second. This can be fair, until you have to apply changes. Editing two documents in a row can be too much effort-consuming.
Luckily enough, $\LaTeX$ is a programming language, before an office automation tool. So we can use conditional variables to fulfill this task. So, the skeleton of my source looks like this:
\documentclass[10pt]{article}
\newif\ifit
\newif\ifen
\newcommand{\langit}[1]{\ifit#1\fi}
\newcommand{\langen}[1]{\ifen#1\fi}
\entrue
%\ittrue
\ifen\usepackage[english]{babel}\fi
\ifit\usepackage[italian]{babel}\fi
\begin{document}
\langen{This is English text}
\langit{Questo è del testo in italiano}
\end{document}
Basically, I declare two conditional variables, \ifit and \ifen which select which language code must be generated. By uncommenting either \entrue or \ittrue, the source will produce the output in English or in Italian.
To ease the task of writing the TeX source, two new commands are declared: \langit and \langen which accept one parameter (i.e., the text in the corresponding language) and output it only if the corresponding conditional variable is set.
Additionally, depending on which conditional variable is set, the babel package is loaded with the corresponding language.
This allows to work on one single TeX source (which decreases the maintainability effort), but allows to produce documents in multiple languages. Adding new languages is just a matter of creating new variables and commands.
Another interesting this, which does not appear in this example, is the charset. Some languages have different charsets, so it would be interesting to set it accordingly. For the italian case, it would entail adding before the document's begin, the following code:
\ifit\usepackage[utf8]{inputenx}\fi
|
2018-07-19 11:34:21
|
{"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": 0.8580304384231567, "perplexity": 1342.388842491838}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590866.65/warc/CC-MAIN-20180719105750-20180719125750-00210.warc.gz"}
|
https://www.physicsforums.com/threads/experimental-determination-of-the-moment-inertia-of-a-sphere.951259/
|
# Experimental determination of the moment inertia of a sphere
Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the equation:
v2 = (2mgR2h)/(mR2+ I) now if we plot v2(h) we come up with a straight line through the origin and (2mgR^2)/(mR^2+ I)should be its slope. solving for I we come up with I = mR2/k(2g-k) where k is the gradient. Now if we equate this with 2/5 mR2 which is the mathematical formula for the moment inertia of the sphere we should come up with the same result, but the mass and radius cancel. This makes no sense. Please help :(
andrewkirk
|
2022-07-06 22:33:05
|
{"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": 0.8261939287185669, "perplexity": 398.7281102847733}, "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/1656104678225.97/warc/CC-MAIN-20220706212428-20220707002428-00258.warc.gz"}
|
https://socratic.org/questions/what-is-the-the-vertex-of-y-x-2-3x-6
|
# What is the the vertex of y =-x^2-3x-6 ?
Apr 10, 2018
$\left(- \frac{3}{2} , - \frac{3}{2}\right)$
#### Explanation:
$\frac{- b}{2 a}$ is the $x$ coordinate at this point
$\frac{- - 3}{2 \times - 1}$ =$\frac{3}{- 2}$
Put this value into the equation to find the $y$ value
${\left(- \frac{3}{- 2}\right)}^{2} - 3 \times \left(\frac{3}{- 2}\right) - 6$
= $\frac{9}{4} + \frac{9}{4} - 6$= $\frac{18}{4} - 6$
=$- \frac{3}{2}$
|
2021-09-18 17:28:26
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "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": 0.9068777561187744, "perplexity": 2076.095527959316}, "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-2021-39/segments/1631780056548.77/warc/CC-MAIN-20210918154248-20210918184248-00308.warc.gz"}
|
https://www.sciencemadness.org/whisper/viewthread.php?tid=19435&page=3
|
Not logged in [Login ]
Sciencemadness Discussion Board » Non-chemistry » Detritus » Don't you love the smell of chlorinated compounds in the morning? Select A Forum Fundamentals » Chemistry in General » Organic Chemistry » Reagents and Apparatus Acquisition » Beginnings » Responsible Practices » Miscellaneous » The Wiki Special topics » Technochemistry » Energetic Materials » Biochemistry » Radiochemistry » Computational Models and Techniques » Prepublication Non-chemistry » Forum Matters » Legal and Societal Issues » Detritus » Test Forum
Pages: 1 3
Author: Subject: Don't you love the smell of chlorinated compounds in the morning?
turd
International Hazard
Posts: 800
Registered: 5-3-2006
Member Is Offline
Mood: No Mood
Quote: Originally posted by White Yeti Speed dial: Clear your mind of every distraction, create complete silence, and you will hear God. God appears in the silence.
If you hear voices you should seek professional help.
In retrospect:
You don't understand chemistry in the slightest (the first post in this thread is a major facepalm moment and it just goes downhill from there).
You don't understand drugs in the slightest.
You have the world view of a 13 year old kid that isn't yet mature enough to question the silly beliefs indoctrinated by his family. (Which actually is no shame - you probably are that 13 year old immature kid.)
Quote: What dealers cut drugs with is not my problem, but I've heard that some use powdered glass.
Gosh. You're so naïve and full of it! If you'd spend one minute thinking about it instead of regurgitating unreflected fairy tales, you would realize that cutting smack with something that doesn't dissolve in water is about the stupidest thing one can do. Newsflash: Dealers generally want their clients to buy more of the stuff, not kill them.
This thread should be locked to protect you from yourself: every post makes you look more foolish than the last (if that is even possible).
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
Quote: Originally posted by turd You have the world view of a 13 year old kid that isn't yet mature enough to question the silly beliefs indoctrinated by his family.
For your information, I was an atheist at one point, I have questioned the beliefs I have been exposed to for as long as I can remember. I know the mind of an atheist very well, because I WAS one. The fact that we, as human beings, are in constant search for a higher being is innate, and universal. Stating an absolute belief that "there is no God" goes against all scientific theory, at the centre of which there is uncertainty. God has revealed himself in many ways, and failing to accept his presence is a mortal sin, for which you will pay greatly if you do not change your views.
Let me ask you a question, as an atheist, where would you put the "zero" mark for counting years? And how would you agree with your atheist friends on one year?
Quote: you would realize that cutting smack with something that doesn't dissolve in water is about the stupidest thing one can do.
Drug dealers are not the brightest people. The fact that they enter the business in the first place proves that they are pretty dull to begin with.
"Ja, Kalzium, das ist alles!" -Otto Loewi
unionised
International Hazard
Posts: 4599
Registered: 1-11-2003
Location: UK
Member Is Offline
Mood: No Mood
"Let me ask you a question, as an atheist, where would you put the "zero" mark for counting years? And how would you agree with your atheist friends on one year?"
I'd probably call for a debate on the pros and cons of these then have a vote.
http://en.wikipedia.org/wiki/Epoch_(reference_date)#Notable_epoch_dates_in_computing
ziqquratu
National Hazard
Posts: 385
Registered: 15-11-2002
Member Is Offline
Mood: No Mood
Quote: Originally posted by White Yeti I don't even think we need to go that far. Say tomorrow someone patents a cure for cancer. Let's be idealistic, no side effects and it applies to all kinds of cancer. You can only imagine the multibillion dollar market that will develop. Depending on where you live, insurance policy may be different, but if you live in the United States, only the rich can afford expensive life saving procedures. With this in mind, the poor usually do welding, are exposed to carbon monoxide from machinery and are more likely to develop cancer. Do you think they will receive the treatment they deserve? Of course not, insurance companies will cover the cheaper chemotherapy/radiotherapy alternative, and deny coverage on the new treatment. Once the technology matures, then maybe insurance will cover it
Fortunately, not all western countries have such byzantine arrangements for the funding of healthcare as does the US. Irrespective of that, however, insurance companies in the US do, in fact, fund the expensive treatments - they don't like it, and are always looking for a way out, but they DO fund it. And, to be fair, there are good reasons for restricting access to some of the more expensive, newer drugs - certainly, price limitations play a part, but often these things are better used as second- or third-line therapies, after older drugs have failed (to avoid the development of resistance, for example, or for treating already resistant illnesses).
Quote: Originally posted by White Yeti Actually, the prohibition was not a complete failure. It may not have stopped the consumption of alcohol in the United States, but it changed people's attitudes about alcohol consumption, leading to a decline in popularity: http://edgeofthewest.files.wordpress.com/2008/01/prohibition...
Your graph seems to be missing a few decades of data... a short term decrease is not sufficient to justify the consequences of prohibition.
Quote: Originally posted by White Yeti Government intervention is not all that futile. Thanks to the government, supply is held back and purity of drugs in decreasing (dealers cut the product more and more).
Rubbish. Look at it like this - police report seizing a multi-million dollar shipment of heroin. And yet, the street price of the drug is unaffected. This is evidence of the seizure having NO effect on the availability.
Quote: Originally posted by White Yeti Whether we like it or not, drugs are here to stay.
This is the smartest thing you've said in the entire thread. And it applies to obesity, heart disease, cancer, AIDS, asthma, Alzheimers.... and just about all other diseases, too (with the possible exception of a few viral diseases - such as smallpox - which we're capable of eliminating). No matter what controls - what moralistic requirements - you put in place, these things are never going away.
ripple
Harmless
Posts: 19
Registered: 19-1-2012
Member Is Offline
Mood: No Mood
So many really great debates on here get far too heated and ruined with personal attacks. We have this fairly unique hobby/interest and are fortunate enough to have a forum to share it with each other- it would be nice for that to be reflected in the tone and quality of discussion.
Its a very small pool, please stop pissing in it
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
Thanks for pointing that out.
Different views on certain topics are almost always rejected initially, and I hoped (when I first signed up) that this forum would be accepting of different points of view. I'm afraid that many topics devolve into personal attacks for no definite reason other than the fact that some people are not willing to consider things from a different point of view. This lack of open mindedness is strange, because as a community of scientists (for the most part) you should always be open to new ideas and perspectives, if they are supported in some way or another by a logical train of thought (which I believe I articulated clearly enough for laymen to understand).
For the rest of you, personal attacks show that this community is not better than any other forum on the Internet; any group of fools can start hurling insults at one another. Granted, my original post was not perfect, far from it I might add, but you guys determined in which direction this thread was headed. Never had I though this thread would go anywhere near AIDS and oncology.
I still believe that diseases should be dealt with from the ground up. First we get rid of malaria, typhoid, tuberculosis and cholera (yes these diseases still exist). Once deaths from these diseases in developing countries are low enough to be acceptable by western standards, then we can tackle cancer, AIDS, genetic disorders etcetera…
"Ja, Kalzium, das ist alles!" -Otto Loewi
497
International Hazard
Posts: 778
Registered: 6-10-2007
Member Is Offline
Mood: HSbF6
I totally agree with ripple. No need for personal attacks. But how surprised can you really be when people react strongly to you showing up and posting posting stuff like this
Quote: The war on drugs in another issue. The problem with drugs is that there are many different kinds and chemists are worsening the situation by making derivatives which are not "illegal" per se. This makes restriction and regulation a nightmare. Government intervention is not all that futile. Thanks to the government, supply is held back and purity of drugs in decreasing (dealers cut the product more and more).
And then you say everyone else is refusing to be open to new perspectives? Anyone even vaguely familiar with the black market will tell you just how effective government intervention is... But you would prefer to listen the prison gaurd's story instead? Find some real indepent evidence that prohibitions are so great for us. Data from after 1930.
How did Portugal's prohibition work out?
"If only we could figure out the right set of federal regulations, the mexican cartel wars would be solved!" That's just not how it works.
http://www.downsizedc.org/blog/drug-prohibition-your-childre...
Quote: The Mexican government reports that its War on Drugs has killed 28,000 people over the past four years. This ongoing tragedy is undermining Mexico's stability, which is bad news for the United States. But that's not the only way drug prohibition is hurting us. I urge you to watch this interview with Neill Franklin, the Executive Director of Law Enforcement Against Prohibition (under 9 minutes) http://www.youtube.com/watch?v=DzOHQdKRANA The video reveals that the Mexican drug cartels have expanded into 230 U.S. cities. Unsurprisingly, the overwhelming majority of police 911 calls are related to this illegal drug trade. And yet, as our police go from one drug-related 911 call to the next, most violent crimes go unsolved, including . . . * 60% of rapes * 73% of robberies * 88% of auto thefts * And 37% of murders Whereas, in 1963, before the War on Drugs, only 9% of murders went unsolved! Repealing drug prohibition would put an end to narcotics units and place more cops on the street to "do the work that is supposed to be done." But unsolved crime is not the only danger caused by the Drug War. Our children are particularly at risk . . . * Criminals don't ask for ID's to verify the age of their customers * This means that powerful drugs are more available to kids than cigarettes and alcohol * Criminals don't care about quality control, so the black market substances that lure our kids are more dangerous than they would be if prohibition didn't exist * And urban, African-American children are at special risk. They are heavily recruited to the drug trade because juvenile offenders get lesser sentences Whereas in Portugal, which legalized personal drug possession ten years ago . . . * There was a double-digit drop in drug use by school-age children * As well as a double-digit drop in AIDS cases * The stigma has been removed for people seeking treatment * And there is MORE MONEY for treatment Even so, President Obama still wants to increase funding for the War on Drugs! But the facts are clear. Drug prohibition doesn't work. Repeal the federal drug laws. Our communities will be safer and our children will be better off.
A few people out there are even starting to notice...
http://newsnetscotland.com/index.php/scottish-opinion/4570-m...
This is a good way to illustrate the heart of the problem:
Quote: People laugh when politicians talk about their drug use. The audience laughed during a 2003 CNN Democratic presidential primary debate when John Kerry, John Edwards and Howard Dean admitted smoking weed. Yet those same politicians oversee a cruel system that now stages SWAT raids on people’s homes more than 100 times a day. People die in these raids –some weren’t even the intended targets of the police. Neill Franklin once led such raids. The 33-year Maryland police veteran, now executive director of Law Enforcement Against Prohibition, locked up hundreds of people for drugs and felt good about it. “We really thought that these drugs made people evil,” he told me. But 10 years ago Franklin decided that drugs –even hard drugs –do much less harm to Americans than does the drug war. “Drugs can be –and are in many cases –problematic. But the policies that we have in place to prohibit their use are 10 times more problematic.” The raids helped change his mind. “We end up with kids being shot … search warrants being served on the wrong home, innocent people on the other side of the door thinking that they are protecting their home.” And the level of drug use remains about the same. Still, most Americans support the drug war. Paul Chabot, White House drug adviser to Presidents George W. Bush and Clinton, told me: “We should be kicking down more doors. … They’re kicking the door of somebody who’s a violent person.” Violent?People who get high are rarely violent. The violence occurs because when something’s illegal, it is sold only on the black market. And that causes crime. Drug dealers can’t just call the cops if someone tries to steal their supply. So they form gangs and arm themselves to the teeth. “We have the violence of these gangs competing for market share, and people get hurt,” said Franklin. Especially kids. Drug gangs constantly look for new recruits. “Some of these gangs have better recruitment programs than Fortune 500 companies. They know what to say to kids.” People think that if drugs were legal, there would be more recruiting of kids. Franklin says the opposite is true. “Prohibition causes that. We don’t have kids on the corner (saying), ‘Pssst, I got a fifth of Jack Daniel’s.’” Kids rarely peddle liquor, and there’s little violence around liquor sales because alcohol is legal. There was lots of violence before 1933, but that was because Prohibition forbade liquor sales. Prohibition gave us Al Capone. “Organized crime existed well before Prohibition,” Chabot replied. That’s true. But much less of it. The murder rate rose when alcohol was banned. It dropped when Prohibition was repealed. “If we were to do away with our drug laws … we know drug usage numbers will skyrocket,” Chabot said. But we don’t know that. It’s logical to assume that, were it not for drug prohibition, drug abuse would be rampant. But 10 years ago, Portugal decriminalized every drug –crack, heroin, you name it. The number of abusers actually declined. Joao Goulao, Portugal’s top drug official, said that before decriminalization “we had a huge problem with drug use … around 100,000 people hooked on heroin.” Then they started treating drug use more like a parking ticket. People caught with drugs get a slap on the wrist, sometimes a fine. Independent studies have found the number of people in Portugal who say they regularly do drugs stayed about the same. And the best news, said Goulao: “Addiction itself decreased a lot.” At first, police were skeptical of the law, but Joao Figueira, chief inspector of Lisbon’s drug unit, told me that decriminalization changed lots of minds. “The level of conflicts on the street are reduced. Drug-related robberies are reduced. And now the police are not the enemies of the consumers!” And teen drug use is down. All good news. But in America and in most of the world, the drug war continues, thousands are murdered, and in ghettos the police are enemies of the people. Governments should wake up and learn something from the Portuguese.
http://www.wnd.com/2012/02/on-pot-prohibition-and-portugal/
[Edited on 4-4-2012 by 497]
A word to the wise: NEUROFEEDBACK
http://citizenworks.org/corp/dg/s2r1.pdf
http://www.newscientist.com/mobile/article/mg21228354.500-re...
"To expose a 15 Trillion dollar ripoff of the American people by the stockholders of the 1000 largest corporations over the last 100 years will be a tall order of business."
Buckminster Fuller
"No problem can be solved from the same level of consciousness that created it."
Albert Einstein
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
Quote: Originally posted by 497 Anyone even vaguely familiar with the black market will tell you just how effective government intervention is... But you would prefer to listen the prison gaurd's story instead? Find some real indepent evidence that prohibitions are so great for us. Data from after 1930. How did Portugal's prohibition work out?
Very well then, let me elaborate.
The drug war is mostly ineffective because it's focused on the wrong drugs and the wrong people. Instead of focusing attacks on hard drugs, the government is cracking down on all drugs when it should be focusing on crack, meth and (to a decreasing extent) heroin. The reason why echoes to the fundamental belief that the government should do everything in its power to protect public welfare and keep crime rates down to a minimum.
I have never heard of a pot head revert to bouts of violence to get his fix, some even say that cannabis calms people down to a certain extent. The same is not true of meth and crack. In my opinion, meth is the hardest drug of them all, it's the most addictive, it gives the user the highest and longest high of all drugs and it's also the one and only drug that seems to "possess" people into bouts of unjustified violence. In some ways, crack pales in comparison, but it's still a major cause of urban violence and crime. Another major cause of crime is poverty, but there's not much the government can do about that, hence why it didn't declare a war on poverty.
I put heroin in parentheses because its use is declining, instead, people are using prescription painkillers. This makes the drug war on this front impossible to fight because what is usually used as legitimate medicine is now used as a cleaner and purer alternative to heroin. The medicinal and therapeutical properties of certain drugs makes outlawing them an impossible feat, which is why the government should lift its nonsensical ban on shrooms, LSD, cannabis, DMT, ibogane and all the others I can't name off the top of my head.
So, a complete end to prohibition wouldn't be the best decision either. If you legalised meth and crack you would not be solving the problem, you'd make the black market and even larger and more dangerous market. Since the current situation is that enforcement is too spread out over all the drugs, a different approach should be adopted. The government should base their decisions on whether or not to outlaw a drug based on statistics on public violence that consumption of the drug brings with it. With this outlook, crackdown would theoretically be more focused on there it is needed rather than dispersed over every and any drug in existence. Organised crime over the distribution of cannabis would disappear. In that sense, we would already improve public safety by simply legalising cannabis.
[Edited on 4-4-2012 by White Yeti]
"Ja, Kalzium, das ist alles!" -Otto Loewi
Bot0nist
International Hazard
Posts: 1559
Registered: 15-2-2011
Location: Right behind you.
Member Is Offline
Mood: Streching my cotyledons.
Hate to say it, bit im with The Dark Lord Sauron on this one... Legalize all drugs and make the FREELY available to anyone (of age) that wants them, at the pharmaceutical companies expense (since they founded the mainstream use of many of these drugs at one time). Removing monetary value and lack of availability will reduce most, if not all drug related violence and crime. The governments role could then be purely focused on education, harm reduction, and treatment. A role they are much better suited too, IME
"fundamental belief that the government should do everything in its power to protect public"
But not to protect.me from myself. When the Pure Food and Drugs Act was passed this is not what was in mind. The G men have no more right to persecute me for the chemicals I intake than it does four the literature I read! Stupid Nanny State!
[Edited on 5-4-2012 by Bot0nist]
U.T.F.S.E. and learn the joys of autodidacticism!
Don't judge each day only by the harvest you reap, but also by the seeds you sow.
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
Quote: Originally posted by Bot0nist Legalize all drugs and make the FREELY available to anyone (of age)
That "of age" part is difficult to enforce, when youths want to get messed up, they will, and by any means necessary. There is an age restriction for the consumption of alcohol, it may be enforced, but is it always obeyed? The problem will only be magnified when you legalise hard drugs that go hand in hand with addiction and violence. If you give an age restriction to some drugs and provide a good reason, then people might follow it. The reason being that the brain is adversely affected by all drugs (especially psychedelics) and more profoundly so, when it is initially developing during the first 20 years of life.
There is no black and white when it comes to politics, but I think it's obvious that drugs like meth and crack should remain illegal.
"Ja, Kalzium, das ist alles!" -Otto Loewi
497
International Hazard
Posts: 778
Registered: 6-10-2007
Member Is Offline
Mood: HSbF6
Bot0nist has it right this time. The monetary value (sometimes combined with drug effects) is the only thing that results in violence. Drugs are sooo cheap to manufacture, the costs should never be an issue.
So, tell me how subjectively different amphetamine is from meth? It's pretty damn close based on all the people I've talked to. The route of administration makes a much bigger difference. So if these are such a scourge on us, why are there 5 million prescriptions for it, plus almost 10 million for methylphenidate as of 10 years ago..
Meth is not that different than any other drug. It's ability to keep you awake for many days does result in more rapid damage if heavily abused, but it is most definitely not on the same level as opiates in terms of addiction.
The point is, if you tell people they are incapable of using something responsibly, they won't use it responsibly. That's a fact. People only treat drugs like a big deal because society makes a big deal about them, and they're worth their weight in gold. You're trying to argue that demonic possession chemicals are the driving force behind the black market's destructive effects, while it is clearly economics.
The of age issue will plague us in many ways until a real "rite of passage" is used to delineate where childhood ends and adulthood begins. Treating it as huge taboo when kids experiment with drugs only increases their interest. There is ample evidence for that concept if you look at the way some Europeans treat alcohol vs the way Americans often treat it... The same applies to all drugs. 18 is such arbitrary bullshit, how can we expect anyone to act like an adult when we won't even allow them to, until years after they would have had a family just a few centuries ago.
And what about those wars? http://en.m.wikipedia.org/wiki/War_on_Poverty
A word to the wise: NEUROFEEDBACK
http://citizenworks.org/corp/dg/s2r1.pdf
http://www.newscientist.com/mobile/article/mg21228354.500-re...
"To expose a 15 Trillion dollar ripoff of the American people by the stockholders of the 1000 largest corporations over the last 100 years will be a tall order of business."
Buckminster Fuller
"No problem can be solved from the same level of consciousness that created it."
Albert Einstein
turd
International Hazard
Posts: 800
Registered: 5-3-2006
Member Is Offline
Mood: No Mood
Quote: Originally posted by White Yeti This lack of open mindedness is strange, because as a community of scientists (for the most part) you should always be open to new ideas and perspectives, if they are supported in some way or another by a logical train of thought (which I believe I articulated clearly enough for laymen to understand).
Nothing what you said in this thread (and mostly elsewhere) is even remotely based on scientific method. Science is not:
- There's invisible pink unicorns everywhere because you can't prove the opposite. (Extraordinary claims require extraordinary evidence)
- There's a life after death because it makes me feel better. (Wishful thinking, one of the biggest sins of a scientist)
- Repeating fairy tales without questioning them
Again and again, you show absolute ignorance on the topic of drugs (and physics and chemistry) and act if you were some kind of authority. You are too lazy to use Google for two minutes before spouting your nonsense. Otherwise, you would for example realize how ridiculous the claim "methamphetamine is the most addictive drug" is. No wonder people react with irritation.
https://en.wikipedia.org/wiki/Amphetamine
Quote: Data from The Lancet suggests amphetamine is ranked the 8th most addictive and 6th most harmful of 20 popular recreational drugs.
The same for your religious tirades: There's no theologically of philosophically interesting content to them. It's like the caricature of religion filtered through the mind of an immature kid. If I were Christian I would be deeply embarrassed by the contemptuous, inhumane drivel you are posting. But there's hoping that you grow up one day.
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
Quote: Originally posted by 497 The route of administration makes a much bigger difference. So if these are such a scourge on us, why are there 5 million prescriptions for it, plus almost 10 million for methylphenidate as of 10 years ago.. [...]but it is most definitely not on the same level as opiates in terms of addiction.
I definitely agree that the method of administration is a huge factor, hence why you can abuse pills by simply injecting them. What was (somewhat) safe to begin with becomes a powerful narcotic when administered in a different fashion.
But I still think that amphetamines are just as, if not more addictive than opiates. Here's why, even though withdrawal from amphetamines is not as dangerous as opiate withdrawal, it lasts longer and is more severe than withdrawal from cocaine (wikipedia). Methamphetamine triggers the release of dopamine and you all know the rest, the reward cycle etc... The brain is depleted of dopamine for years after the user discontinues the use of meth. Think about how crumby an existence that would be and how strong the pull must be towards the drug. You're effectively depressed for the rest of your life and that can be changed if you take more meth.
Apparently, ibogaine can be used to treat opioid dependence and it can treat methamphetamine dependence as well, but the craving for the drug makes treatment very difficult because although the physical aspect of the dependence can be eliminated, the mental craving for the drug is not eliminated.
@turd, you might think I act like an immature kid, but you're the one hurling senseless insults, and you're the one acting like a fool. You know very well that personal attacks are not welcome on this forum.
"Ja, Kalzium, das ist alles!" -Otto Loewi
watson.fawkes
International Hazard
Posts: 2793
Registered: 16-8-2008
Member Is Offline
Mood: No Mood
Quote: Originally posted by White Yeti [...] but you're the one hurling senseless insults
You must have no idea, then, how insulting you have already been in this thread:
Quote: Originally posted by White Yeti [...] but sex was intended to strengthen the relationship between one man and one woman, not two men, not two women and not any number of each either.
Take your private metaphysical beliefs and keep them out of this science board. Asserting the universality of such beliefs is at best unseemly, and become insulting when you insist upon it, which you have, and particularly so when with even a fragment of thought you would have realized how many people disagree with you. Doubly so when this is not a general-topic discussion board, but one about science.
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
"Asserting the universality of such beliefs is at best unseemly, and become insulting when you insist upon it."
Although what I said may be offensive to some, my comments are impersonal. You may choose to take my comments any way you like. If you choose to take offence, go right ahead, that's not my problem.
"with even a fragment of thought you would have realized how many people disagree with you. Doubly so when this is not a general-topic discussion board, but one about science."
Firstly, I don't care whether or not people agree with me. I don't judge myself based on what others think. This is a forum, what's the point of having a forum where everyone agrees on everything? There would be no discussion. This is already a very monochrome forum some of these threads are pathetic because everyone agrees on the same subject.
Secondly, yes my original post was flawed, but I was hoping for a reasonable, unheated discussion on scientific ground. The problem was that this topic overlapped into politics and society, something I didn't realise until the discussion started to degenerate. I even posted an apology to the moderators:
"I appologise to the moderators for having posted something so close to politics. I didn't realise it at the time. I still think this is a subject worthy of discussion, so long as it doesn't get out of hand."
[Edited on 4-5-2012 by White Yeti]
"Ja, Kalzium, das ist alles!" -Otto Loewi
watson.fawkes
International Hazard
Posts: 2793
Registered: 16-8-2008
Member Is Offline
Mood: No Mood
Quote: Originally posted by White Yeti my comments are impersonal.
Doesn't matter. Still insulting.
White Yeti
International Hazard
Posts: 816
Registered: 20-7-2011
Location: Asperger's spectrum
Member Is Offline
Mood: delocalized
Quote: Originally posted by watson.fawkes Doesn't matter. Still insulting.
It depends solely on your personal judgement, what one might find offensive, another might find in line. What homosexuals do is insulting and out of line, especially when they do it on front of the world, for everyone to see.
"Ja, Kalzium, das ist alles!" -Otto Loewi
Bot0nist
International Hazard
Posts: 1559
Registered: 15-2-2011
Location: Right behind you.
Member Is Offline
Mood: Streching my cotyledons.
Your a bigot and a homophobe, that is my impersonal opinion. Maybe you should spend some more time worrying about your own life, and stop trying to dictate others, you fascist! If gays make you so uncomfortable, then I guarantee that you have some issues with your own sexuality that needs attention...
Go beat your bible elsewhere! Dick.
Quote: Originally posted by turd This thread should be locked to protect you from yourself: every post makes you look more foolish than the last (if that is even possible).
Too late...
EDIT: Just so you know where that came from, not that you deserve or care; My younger brother is a homosexual and has had to deal with people like you his whole life. It makes me sick. He is a much better and "moral" human being than you could ever pretend to be with all your self righteous rhetoric. WTF makes you think you have the right to tell others who to love or how to live there life?
*TheBot leaves this thread, along with any respect he had for Yeti, behind.
[Edited on 5-4-2012 by Bot0nist]
U.T.F.S.E. and learn the joys of autodidacticism!
Don't judge each day only by the harvest you reap, but also by the seeds you sow.
watson.fawkes
International Hazard
Posts: 2793
Registered: 16-8-2008
Member Is Offline
Mood: No Mood
Quote: Originally posted by White Yeti What homosexuals do is insulting and out of line, especially when they do it on front of the world, for everyone to see.
You really don't think that overt homophobia, as you have well illustrated here for everyone to see, isn't insulting to homosexuals, even if you claim it's impersonal. Wow.
Just so that I'm clear, I entered in after you accused turd of being insulting. Hint: the parable of the mote and the beam is in Matthew 7.
497
International Hazard
Posts: 778
Registered: 6-10-2007
Member Is Offline
Mood: HSbF6
So can you or anyone else present any evidence at all that drugs even begin to approach alcohol in destructive effects? Why should we be pouring more and more money in to stopping people from gaining new perspectives (a proven result of some drugs, unlike alchol) while alcohol is treated in this way?
Quote: Some might say there is a beneficial effect of the growing incidence of FAS: it's good for prison business. According to some research, as many as half of the young offenders appearing in court have FAS. (8) Besides having poor judgment and lack of impulse control, many persons with FAS are destined to become alcohol abusers, all of which makes them vulnerable to committing crimes. Alcohol alone is involved in seven times more violent crimes than all illegal substances combined. (9) Education and treatment is seven times more cost effective than arrest and incarceration for substance addiction, yet we continue to spend more tax dollars on prisons than treatment. (9) The Justice Department reports that the cost per prisoner per year is $13,500. (10) In the US, over two million people are now locked up. In Canada, the cost of FAS now exceeds that of that country's national debt. Bonnie Buxton, founder of FASworld based in Toronto, states, "Just caring for people now alive with fetal alcohol syndrome and fetal alcohol effects will cost us at least$600 billion, which is the approximate size of the national debt." (7)
http://www.acbr.com/fas/\$5Mbaby.htm
It is common for older individuals to have trouble accepting that the world is changing... Based on your drug knowledge base, I would guess you learned most of it at least 20-30 years ago. Things have changed, and are accelerating towards even more change. Deal with it.
A word to the wise: NEUROFEEDBACK
http://citizenworks.org/corp/dg/s2r1.pdf
http://www.newscientist.com/mobile/article/mg21228354.500-re...
|
2021-05-07 04:56:10
|
{"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": 0.2505418658256531, "perplexity": 3670.163497754651}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.96/warc/CC-MAIN-20210507025943-20210507055943-00373.warc.gz"}
|
http://mathhelpforum.com/calculus/74690-sequence-convergence.html
|
# Math Help - sequence, convergence
1. ## sequence, convergence
Suppose that $(x_n)$ is a sequence in $\mathbb{R}$. Define a sequence $(y_n)$ by $y_n=\frac{x_1+x_2+\cdots+x_n}{n}$, $\forall n \in \mathbb{N}$. Prove that if $(x_n)$ converges to $x \in \mathbb{R}$ then $(y_n)$ converges to $x$.
2. Hello,
Originally Posted by xboxlive89128
Suppose that $(x_n)$ is a sequence in $\mathbb{R}$. Define a sequence $(y_n)$ by $y_n=\frac{x_1+x_2+\cdots+x_n}{n}$, $\forall n \in \mathbb{N}$. Prove that if $(x_n)$ converges to $x \in \mathbb{R}$ then $(y_n)$ converges to $x$.
This is Cesaro's mean. And you want to prove Cesaro's lemma.
There is a proof in the French Wikipedia (Lemme de Cesàro - Wikipédia), but not in the English one.
I'll translate and adapt it here...
$x_n \to x$ can be translated this way :
$\forall \varepsilon >0,~ \exists N \in \mathbb{N},~ \forall n>N,~ |x_n-x|< \varepsilon/2$
Let $S_N=\sum_{k=1}^N |x_k-x|$
Let's assume n>N :
$|y_n-x|=\left|\frac 1n \sum_{k=1}^n (x_k-x)\right|$
By the triangle inequality, we have :
$|y_n-x| \leqslant \frac 1n \sum_{k=1}^N |x_k-x|+\frac 1n \sum_{k=N+1}^n |x_k-x|$
$|y_n-x| \leqslant \frac{S_N}{n}+\frac{n-N}{n} (\varepsilon/2)=\frac{S_N}{n}+\varepsilon/2 -\frac{N}{n} (\varepsilon/2) \leqslant \frac{S_N}{n}+\varepsilon/2$
(because N/n (epsilon/2) >0)
But $S_N$ doesn't depend on n. So $\lim_{n \to \infty} \frac{S_N}{n}=0$
This means that for any $\varepsilon >0$, there exists an integer N' such that for all n>N', we have :
$\left|\frac{S_N}{n}\right|\leqslant \varepsilon/2$
By combining this latter inequality to the previous one, we have, for $n>\max\{N,N'\}$ :
$|y_n-x| \leqslant \varepsilon/2+\varepsilon/2=\varepsilon \qquad \square$
|
2016-07-23 10:15:52
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 30, "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": 0.9948354959487915, "perplexity": 409.4262900642875}, "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/1469257821671.5/warc/CC-MAIN-20160723071021-00046-ip-10-185-27-174.ec2.internal.warc.gz"}
|
https://mathoverflow.net/questions/315837/reference-request-for-fractional-poincare-inequality
|
# Reference request for fractional Poincare inequality
Suppose we consider in $$\mathbb R^n$$, then how to show $$\Vert f \Vert_{L^{p}} \leq C\Vert \nabla^{s}f \Vert_{L^{q}}^{\alpha}$$, where $$s>0$$ is noninteger and $$\alpha \in (0,1)$$?
• Can you be more precise: what are $p$ and $q$ and what do you mean by $\nabla^s f$? – Piotr Hajlasz Nov 21 '18 at 14:31
Such an inequality cannot be true unless $$f=0$$. That can be proved by a standard homogeneity argument. Suppose that $$\Vert \nabla^sf\Vert_p<\infty$$. Replacing $$f$$ by $$tf$$, where $$t>0$$ we have $$t\Vert f\Vert_p=\Vert tf\Vert_p\leq C\Vert \nabla^s(tf)\Vert_p^\alpha=t^\alpha C\Vert \nabla^sf\Vert_p^\alpha, \quad \Vert f\Vert_p\leq t^{\alpha-1} C\Vert \nabla^sf\Vert_p^{\alpha},$$ Since $$\alpha-1<0$$, letting $$t\to\infty$$, the right hand side will converge to $$0$$ and hence $$\Vert f\Vert_p=0$$, $$f=0$$.
I guess that your question is ill-formulated: you have to respect the homogeneity on both sides of the inequality. Let us say that for $$f$$ in the Schwartz space you always have $$\Vert f\Vert_{W^{t,q}(\mathbb R^n)}\lesssim \Vert \vert D\vert^s f \Vert_{L^{p}(\mathbb R^n)}\quad\text{(and also}\quad \Vert f\Vert_{L^{n/(n-1)}(\mathbb R^n)}\lesssim \Vert D f\Vert_{L^{1}(\mathbb R^n)}),$$ provided $$\frac{s-t}{n}=\frac{1}{p}-\frac{1}{q},\quad 1 Applying the second inequality above to $$f=u^2$$, you obtain for $$p>1$$, $$\Vert u\Vert_{L^{2n/(n-1)}(\mathbb R^n)}^2\lesssim \Vert uD u\Vert_{L^{1}(\mathbb R^n)}\lesssim \Vert u\Vert_{L^{p'}(\mathbb R^n)} \Vert D u\Vert_{L^{p}(\mathbb R^n)} \lesssim \Vert u\Vert_{L^{p'}(\mathbb R^n)} \Vert \vert D\vert u\Vert_{L^{p}(\mathbb R^n)},$$ so that $$\Vert u\Vert_{L^{2n/(n-1)}(\mathbb R^n)} \lesssim \Vert u\Vert_{L^{p'}(\mathbb R^n)}^{1/2} \Vert \vert D\vert u\Vert_{L^{p}(\mathbb R^n)}^{1/2},$$ an inequality resembling yours. Choosing $$f= u^\alpha$$ leads to more general interpolation inequalities.
|
2019-01-17 16:05:34
|
{"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": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9893296957015991, "perplexity": 782.7327461406568}, "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-2019-04/segments/1547583658988.30/warc/CC-MAIN-20190117143601-20190117165601-00637.warc.gz"}
|
https://collegephysicsanswers.com/openstax-solutions/car-sliding-down-hill-slope-20circ-mass-car-965-kg-when-cable-used-pull-car
|
Question
A car is sliding down a hill with a slope of $20^\circ$. The mass of the car is 965 kg. When a cable is used to pull the car up the slope, a force of 4215 N is applied. What is the car’s acceleration, ignoring friction?
$1.02 \textrm{ m/s}^2$ up the slope.
|
2019-12-13 15:13:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.25400394201278687, "perplexity": 306.56479854764586}, "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-2019-51/segments/1575540564599.32/warc/CC-MAIN-20191213150805-20191213174805-00375.warc.gz"}
|
https://socratic.org/questions/how-do-you-write-y-16x-2-40x-4-into-vertex-form
|
# How do you write y = -16x^2+40x+4 into vertex form?
May 7, 2015
Vertex form for a parabola is
$y = m {\left(x - a\right)}^{2} + b$
with the vertex at $\left(a , b\right)$
Re-arranging $y = 16 {x}^{2} + 40 x + 4$ into vertex form:
$y = - 16 \left({x}^{2} - \frac{5}{2} x\right) + 4 \text{ extract the "m" factor}$
$y = - 16 \left({x}^{2} - \frac{5}{2} x + {\left(\frac{5}{4}\right)}^{2}\right) + 25 + 4 \text{ complete the square}$
$y = - 16 {\left(x - \frac{5}{4}\right)}^{2} + 29$
|
2020-07-15 06:23:19
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.6225049495697021, "perplexity": 5831.345649705759}, "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/1593657155816.86/warc/CC-MAIN-20200715035109-20200715065109-00025.warc.gz"}
|
https://cs184.eecs.berkeley.edu/sp21/docs/proj4-part-5
|
In projects 3-1 and 3-2, we were doing all of our raytracing computation on CPU. You've likely felt the effects of this already, waiting minutes to render a single frame with any realistic lighting, even with threading. For real-time and interactive applications, which often have framerates of 60 fps (that's 60 frames per second), this is just impossibly slow. In this part, you will get a glimpse of how things may be accelerated by writing a few basic GLSL shader programs. Shaders are isolated programs that run in parallel on GPU, executing sections of the graphics pipeline, taking in an input, and outputing a single 4 dimensional vector. Recall the brief overview of shader programs given in lecture.
First let's get acquainted with GLSL, a C like language in which we will write our shaders. This is a great highlevel overview of the basic constructs of the language. Take a minute to look through the definitions. TLDR:
• A GLSL shader can have functions just like C
• An attribute is an input to a vertex shader (position, normal, uv coordinates)
• A uniform is shared by all instances of the running program (light position, textures, transform matrices)
• A varying is typically written into by the vertex shader for use in the fragment shader (transformed positions, normals, uv coordinates)
• GLSL has built-in types and operations that make vector math simpler like vec3, vec4, mat4, dot, length
We will be dealing with two basic OpenGL shader types:
• vertex shaders: These shaders generally apply transforms to vertices, modifying their geometric properties like position and normal vectors, writing the final position of the vertex to gl_Position in addition to writing varyings for use in the fragment shader.
• fragment shaders: After rasterization, we end up with fragments, which these shaders process. These shaders generally take in geometric attributes of the fragment calculated by the vertex shader to compute and write a color into out_color.
NB: Because we didn't want to make a high-end GPU part of CS 184's required hardware, our shaders only use up to OpenGL 3.3 features. Shaders post OpenGL 3.3 have some much nicer features and syntax, but operate on entirely the same principles. If you're interseted, learnopengl.com is an excellent guide for modern openGL programming.
## Getting Started
The skeleton will automatically search for and load shader programs contained in the shaders directory. A simple shader program is made of two parts:
• A .vert file, which specifies a vertex shader. The vertex shader is responsible for reading and writing all per-vertex values. These per-vertex values are then interpolated via barycentric coordinates across the polygon's face.
• A .frag file, which specifies a fragment shader. The fragment shader is responsible for writing all per-pixel* values. It takes as input the interpolated per-vertex values from the vertex shader and outputs the final color of that pixel.
The skeleton will scan the shaders directory for <NAME>.frag shaders, and link it to the corresponding <NAME>.vert, defaulting to Default.vert if none exists. (Shader-based final projects might want to take advantage of this behavior!)
When writing your shaders, be sure to pay extra attention to the types you are using. GLSL 1.0 will not automatically promote ints to floats or demote floats to ints. Function calls must match their declared types exactly as well, so something like max(2, 3.0) will cause the shader to fail compilation. In addition, the built ins gl_Position and gl_FragColor are both of type vec4, the first expecting homogenous coordinates and the second expecting an rgba vector. Many of our calculations will be done using vec3's, so don't forget to convert back to a vec4 (an easy way is simply use vec4(my_vec_3, w_coordinate)).
*Note: technically, a fragment shader writes "per-fragment" not "per-pixel" values. An OpenGL fragment is much closer to our notion of a sample than a pixel. Recall that in super-sampling anti-aliasing, a single pixel might represent the averaged color of multiple individual sample points. Additionally, we might take samples that are overwritten or occluded by those of other polygons. Nevertheless, for most purposes, we can think of a fragment as equivalent to a pixel.
Relevant Files:
• shaders/Default.vert
• shaders/Diffuse.frag
In project 3-1, you saw how diffuse objects appear under light in the world. Let's try to recreate this in a shader program. In Default.vert, we can see an example of a simple vertex shader. It takes in as input the model-space attributes of in_position and in_normal, both of type vec4, in addition to the uniforms u_model, u_view_projection, which are the matrices used to transform a point from model space into world space, and from world space to view space to screen space respectively. We output two values for use in the fragment shader: v_position and v_normal.
Taking a look at the main function, we see that the world space position and normal vector are written into the corresponding varyings v_position and v_normal and the screen space position is written into gl_Position.
Recall the formula for diffuse lighting from the lecture:
$\mathbf{L}_d = \mathbf{k}_d\ (\mathbf{I} / r^2)\ \max(0, \mathbf{n} \cdot \mathbf{l})$
Now in Diffuse.frag, output into out_color the color of the fragment. The light intensity and position are provided as uniforms to the fragment shader. You may choose your own diffuse coefficient vector (you probably just want 1).
After completing this part, you should be able to render the cloth like below:
Relevant Files:
• shaders/Default.vert
• shaders/Phong.frag
Now let's create a shader capable of performing Blinn-Phong shading. Recall the equation for Blinn-Phong shading from lecture:
$\mathbf{L} = \mathbf{k}_a\ \mathbf{I}_a\ + \mathbf{k}_d\ (\mathbf{I} / r^2)\ \max(0, \mathbf{n} \cdot \mathbf{l})\ + \mathbf{k}_s\ (\mathbf{I} / r^2)\ \max(0, \mathbf{n} \cdot \mathbf{h})^p$
Notice we add both an ambient light component and specular reflection component to the diffuse lighting from the previous part to calculate the output light. As before, the light intensity and position are passed as uniforms to the shader. Complete the main function in Phong.frag to implement the Blinn-Phong shading model. You may decide on $k_a, k_d, k_s, I_a, p$ to suite your tastes. After completion, you should be able to see some nice specular lighting effects:
Relevant Files:
• shaders/Default.vert
• shaders/Texture.frag
Looking at Default.vert, we can notice that this shader also takes in a in_uv coordinate associated with the instance's vertex and writes it into v_uv for use in the fragment shader.
We can sample from the u_texture_1 uniform using the built-in function texture(sampler2D tex, vec2 uv), which samples from a texture tex at the texture space coordinate uv. In Texture.frag, complete the shader so that the sampled spectrum is output as the fragment's color.
## Task 4: Displacement and Bump Mapping
Relevant Files:
• shaders/Bump.frag
• shaders/Displacement.vert
• shaders/Displacement.frag
We can use textures for more than just determining the color on a mesh. With displacement and bump mapping, we can encode a height map in a texture to be processed and applied by a shader program. NOTE: You don't have to generate exactly the same results as we have in our reference images, just make sure the results are plausible.
### 4.1: Bump Mapping
In bump mapping, we modify the normal vectors of an object so that the fragment shader gives the illusion of detail (such as bumps) on an object. How can we calculate the new normals given the height map?
To make our calculations easier, we can work in object space, where all normal vectors initially point directly out of the local vertex and have a z-coordinate of 1. Given a vector in object space, we can transform it into back into model space by multiplying by the tangent-bitangent-normal (TBN) matrix.
We already know the original model-space normal vector $\mathbf{n}$ as this is an input to our vertex shader. We can pre-compute the tangent vector $\mathbf{t}$ from the mesh geometry, and this will also be passed as an attribute to the vertex shader. The bitangent should be orthogonal to both the tangent and normal and can be found using the cross product $\mathbf{b} = \mathbf{n} \times \mathbf{t}$. We then have:
$TBN = [ \mathbf{t}\ \ \mathbf{b}\ \ \mathbf{n}]$
Because we have access to the entire height map, we can compute the local space normals by looking at how the height changes as we make small changes in $u$ or $v$. Let $h(u, v)$ be a function that returns the height encoded by a height map at texture coordinates $u$ and $v$ and $w$ and $h$ be the width and height of our texture.
$dU = (h(u + 1 / w, v) - h(u, v)) * k_h * k_n$
$dV = (h(u, v + 1 / h) - h(u, v)) * k_h * k_n$
$k_h$ is a height scaling factor and $k_n$ is a normal scaling factor represented in our shader by the u_height_scaling and u_normal_scaling variables. The local space normal is then just $\mathbf{n}_o = (-dU, -dV, 1)$. Our displaced model space normal is then $\mathbf{n}_d = TBN\ \mathbf{n}_o$.
Complete the main function in Bump.frag to calculate the displaced world space normal. The height map is stored in the u_texture_2 texture and the resolution of the texture is stored in vec2 u_texture_2_size. One such $h(u, v)$ you could use would be the r component of the color vector stored in the texture at coordinates $(u, v)$. On completion, you should be able to see some realistic lighting effects on the mapped bumps:
### 4.2: Displacement Mapping
In displacement mapping, we modify the position of vertices to reflect the height map in addition to modifying the normals to be consistent with the new geometry. First, copy your fragment shader from Bump.frag into Displacement.frag. Modify Displacement.vert so that it also displaces the vertex positions in the direction of the original model space vertex normal scaled by the u_height_scaling variable:
$\mathbf{p}' = \mathbf{p} + \mathbf{n} * h(u, v) * k_h$
On completion, you should be able to notice the change in geometry:
Relevant Files:
• shaders/Mirror.frag
In the pathtracer project, we saw a simple model for a mirror material. We took the incoming eye-ray, reflected it across the surface normal to get the outgoing direction, and then sampled the environment for that direction's incoming radiance.
Here, we will approximate the incoming radiance sample using an environment map, which is a pre-computed store of the direction-to-radiance mapping we previously calculated explicitly via monte carlo integration. We do this by enclosing our scene inside of an infinitely-large room with the environment's appearance painted on the inside. If this sounds like the environment lights from the previous project, you're right! However, as a part of the approximation, we will sample the environment map without shadow rays (assumes no intersections with other parts of the scene).
Using the camera's position u_cam_pos and the fragment's position v_position, compute the outgoing eye-ray, $w_o$. Then reflect $w_o$ across the surface normal given in v_normal to get $w_i$. Finally, sample the environment map u_texture_cubemap for the incoming direction $w_i$.
We can sample from the u_texture_cubemap uniform again using the built-in function texture(samplerCube tex, vec3 dir) overload, which samples from a texture tex at looking down the direction dir.
(For the cubemap used above and other great cubemap textures, check out Emil Persson's site.)
## Extra Credit Opportunity:
Relevant Files:
• shaders/Custom.vert
• shaders/Custom.frag
Make your own shader or scene! If you need more space to work, you can edit loadObjectsFromFile() in main and add a new object type. It can be as complex as you desire.
Add color controls to a previous shader, add a time uniform to generate procedural scenes, add a new object type or texture and see how your shaders work with them! Try combining together all 5 shader types and see what you can make!
|
2021-04-14 16:10:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 27, "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": 0.2354578971862793, "perplexity": 2142.292159004861}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077843.17/warc/CC-MAIN-20210414155517-20210414185517-00261.warc.gz"}
|
https://settheory.mathtalks.org/logic-seminar-wednesday-11-march-2015/
|
# Dilip Raghavan: A bound for the weak covering number of the density 0 ideal
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 March 2015, 17:00 hrs
Room: S17#05-11, Department of Mathematics, NUS
Speaker: Dilip Raghavan
Title: A bound for the weak covering number of the density 0 ideal.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
We prove a ZFC bound for cov*(Z_0) where Z_0 is the ideal of sets of
asymptotic density 0. This answers a question about diagonalizing
F_{sigma delta} ideals without adding unbounded reals.
This is joint work with Saharon Shelah.
|
2017-08-22 09:17:00
|
{"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": 0.9702757596969604, "perplexity": 3163.9276811482437}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886110573.77/warc/CC-MAIN-20170822085147-20170822105147-00249.warc.gz"}
|
https://sysmath.cjoe.ac.cn/jssc/EN/10.1007/s11424-023-1144-x
|
### An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs
ELSAWAH A M1,2,3, VISHWAKARMA G K4, MOHAMED H S5, FANG Kai-Tai1,2,6
1. 1. Department of Statistics and Data Science, Faculty of Science and Technology, Beijing Normal UniversityHong Kong Baptist University United International College, Zhuhai 519087, China;
2. Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China;
3. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt;
4. Department of Mathematics & Computing, Indian Institute of Technology Dhanbad, Dhanbad 826004, India;
5. College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350002, China;
6. The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing 100190, China
• Received:2021-05-07 Revised:2021-08-22 Online:2023-01-25 Published:2023-02-09
• Supported by:
Elsawah’s work was supported by the UIC Research Grants with No. of (R201912 and R202010); the Curriculum Development and Teaching Enhancement with No. of (UICR0400046-21CTL); the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College with No. of (2022B1212010006); and Guangdong Higher Education Upgrading Plan (2021-2025) with No. of (UICR0400001-22).
ELSAWAH A M, VISHWAKARMA G K, MOHAMED H S, FANG Kai-Tai. An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs[J]. Journal of Systems Science and Complexity, 2023, 36(1): 433-456.
A uniform experimental design (UED) is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs, limited resources and unknown underlying models. A UED enjoys the following two significant advantages: (i) It is a robust design, since it does not require to specify a model before experimenters conduct their experiments; and (ii) it provides uniformly scatter design points in the experimental domain, thus it gives a good representation of this domain with fewer experimental trials (runs). Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed. Constructing large UEDs using the existing techniques is an NP-hard problem, an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed. This paper presents a new effective and easy technique, adjusted Gray map technique (AGMT), for constructing (nearly) UEDs with large numbers of four-level factors and runs by converting designs with $s$ two-level factors and $n$ runs to (nearly) UEDs with $2^{t-1}s$ four-level factors and $2^tn$ runs for any $t\geq0$ using two simple transformation functions. Theoretical justifications for the uniformity of the resulting four-level designs are given, which provide some necessary and/or sufficient conditions for obtaining (nearly) uniform four-level designs. The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large (nearly) UEDs with four-level factors.
[1] Fang K T, The uniform design:Application of number-theoretic methods in experimental design, Acta Math. Appl. Sinica, 1980, 3:363-372.[2] Wang Y and Fang K T, A note on uniform distribution and experimental design, Chin. Sci. Bull., 1981, 26:485-489.[3] Hickernell F J, A generalized discrepancy and quadrature error bound, Math. Comp., 1998, 67:299-322.[4] Hickernell F J, Lattice Rules:How Well Do They Measure Up? Random and Quasi-Random Point Sets, Eds. by Hellekalek P and Larcher G, Springer, New York, 1998.[5] Zhou Y D, Ning J H, and Song X B, Lee discrepancy and its applications in experimental designs, Statist. Probab. Lett., 2008, 78:1933-1942.[6] Elsawah A M, Designing uniform computer sequential experiments with mixture levels using Lee discrepancy, Journal of Systems Science and Complexity, 2019, 32(2):681-708.[7] Elsawah A M, An appealing technique for designing optimal large experiments with three-level factors, J. Computational and Applied Mathematics, 2021, 384:113164.[8] Lan W G, Wong M K, Chen N, et al., Four-level orthogonal array design as a chemometric approach to the optimization of polarographic reaction system for phosphorus determination, Talanta, 1994, 41(11):1917-1927.[9] Edmondson R N, Agricultural response surface experiments in view of four-level factorial designs, Biometrics, 1991, 47(4):1435-1448.[10] Ankenman B E, Design of experiments with two-and four-level factors, J. Quality Technol., 1999, 31(4):363-375.[11] Phadke M S, Design optimization case studies, AT & T Techn. J., 1986, 65:51-68.[12] Elsawah A M, Constructing optimal router bit life sequential experimental designs:New results with a case study, Commun. Statist. Simul. Comput., 2019, 48(3):723-752.[13] Elsawah A M, Designing optimal large four-level experiments:A new technique without recourse to optimization softwares, Communications in Mathematics and Statistics, 2022, 10:623-652.[14] Bettonvil B and Kleijnen J P C, Searching for important factors in simulation models with many factors:Sequential bifurcation, European J. Oper. Res., 1996, 96:180-194.[15] Kleijnen J P C, Ham G V, and Rotmans J, Techniques for sensitivity analysis of simulation models:A case study of the CO2 greenhouse effect, Simulation, 1992, 58(6):410-417.[16] Kleijnen J P C, Bettonvil B, and Persson F, Screening for the important factors in large discreteevent simulation:Sequential bifurcation and its applications, Screening Methods for Experimentation in Industry, Drug Discovery, and Genetics, Eds. by Dean A and Lewis S, Springer, New York, 2006.[17] Morris M D, Factorial sampling plans for preliminary computational experiments, Technometrics, 1991, 33:161-174.[18] Phoa F K H and Xu H, Quarter-fraction factorial designs constructed via quaternary codes, Ann. Statist., 2009, 37:2561-2581.[19] Phoa F K H, A code arithmetic approach for quaternary code designs and its application to (1/64)th fraction, Ann. Statist., 2012, 40:3161-3175.[20] Chatterjee K, Ou Z, Phoa F K H, et al., Uniform four-level designs from two-level designs:A new look, Statist. Sinica, 2017, 27:171-186.[21] Elsawah A M and Fang K T, New results on quaternary codes and their Gray map images for constructing uniform designs, Metrika, 2018, 81(3):307-336.[22] Hu L, Ou Z, and Li H, Construction of four-level and mixed-level designs with zero Lee discrepancy, Metrika, 2020, 83:129-139[23] Winke P and Fang K T, Optimal U-Type Designs. Monte Carlo and Quasi-Monte Carlo Methods, Eds. by Niederreiter H, Hellekalek P, Larcher G, and Zinterhof P, Springer, New York, 1997.[24] Fang K T, Ke X, and Elsawah A M, Construction of uniform designs via an adjusted threshold accepting algorithm, J. Complexity, 2017, 43:28-37.[25] Elsawah A M and Qin H, Optimum mechanism for breaking the confounding effects of mixed-level designs, Computational Statistics, 2017, 32(2):781-802.[26] Yang F, Zhou Y D, and Zhang X R, Augmented uniform designs, J. Statist. Plan. Infer., 2017, 182:61-73.[27] Elsawah A M, Constructing optimal asymmetric combined designs via Lee discrepancy, Statist. Probab. Lett. 2016, 118:24-31.[28] Tang Y and Xu H, An effective construction method for multi-level uniform designs, J. Statist. Plan. Infer., 2013, 143:1583-1589.[29] Elsawah A M, Fang K T, and Ke X, New recommended designs for screening either qualitative or quantitative factors, Statistical Papers, 2021, 62:267-307.[30] Yang F, Zhou Y D, and Zhang A J, Mixed-level column augmented uniform designs, J. Complexity, 2019, 53:23-39.[31] Elsawah A M, Fang K T, He P, et al., Optimum addition of information to computer experiments in view of uniformity and orthogonality, Bulletin of the Malaysian Math. Sci. Soc., 2019, 42(2):803-826.[32] Fang K T and Hickernell F J, The uniform design and its applications, Bull. Inst. Int. Stat., 1995, 1:333-349.[33] Elsawah A M and Qin H, A new strategy for optimal foldover two-level designs, Statist. Probab. Lett., 2015, 103:116-126.[34] Elsawah A M, Multiple doubling:A simple effective construction technique for optimal two-level experimental designs, Statistal Papers, 2021, 62(6):2923-2967.[35] Mukerjee R and Wu C F J, On the existence of saturated and nearly saturated asymmetrical orthogonal arrays, Ann. Statist., 1995, 23(6):2102-2115.[36] Cheng C S, Deng L Y, and Tang B, Generalized minimum aberration and design efficiency for nonregular fractional factorial designs, Statist. Sinica, 2002, 12:991-1000.[37] Elsawah A M, Building some bridges among various experimental designs, J. Korean Statist. Soc., 2020, 49:55-81.[38] Xu H, Minimum moment aberration for nonregular designs and supersaturated designs, Statist Sinica, 2003, 13:691-708.[39] Elsawah A M, Fang K T, He P, et al., Sharp lower bounds of various uniformity criteria for constructing uniform designs, Statistal Papers, 2021, 62:1461-1482.[40] Cheng C S, Projection Properties of Factorial Designs for Factor Screening Screening, Eds. by Dean A and Lewis S, Springer, New York, 2006.[41] Sun F, Wang Y, and Xu H, Uniform projection designs, Ann. Statist., 2019, 47(1):641-661.[42] Elsawah A M, Tang Y, and Fang K T, Constructing optimal projection designs, Statistics, 2019, 53(6):1357-1385.[43] Elsawah A M and Qin H, An effective approach for the optimum addition of runs to three-level uniform designs, J. Korean Statist. Soc., 2016, 45(4):610-622.[44] Weng L C, Elsawah A M, and Fang K T, Cross-entropy loss for recommending efficient fold-over technique, Journal of Systems Science and Complexity, 2021, 34(1):402-439.
[1] Hong QIN, Na ZOU, Shangli ZHANG. DESIGN EFFICIENCY FOR MINIMUM PROJECTION UNIFORMITY DESIGNS WITH TWO LEVELS [J]. Journal of Systems Science and Complexity, 2011, 24(4): 761-768. [2] Shixin ZHU;Xiaoshan KAI. THE HAMMING DISTANCES OF NEGACYCLIC CODES OF LENGTH $2^s$ OVER \$GR( {2^a,m}) [J]. Journal of Systems Science and Complexity, 2008, 21(1): 60-066. [3] Zhao Zhi ZHANG. FURTHER RESULTS ON THE ASYMPTOTIC BEHAVIOUR OF MINIMUM AVERAGE HAMMING DISTANCE FOR BINARY CODES [J]. Journal of Systems Science and Complexity, 1999, 12(4): 335-337.
Viewed
Full text
Abstract
|
2023-03-20 12:20:22
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5670276880264282, "perplexity": 12646.256983885607}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943483.86/warc/CC-MAIN-20230320114206-20230320144206-00679.warc.gz"}
|
https://stats.stackexchange.com/questions/45381/is-fx-extx-a-suitable-kernel-to-be-choosen
|
# Is $f(x)=e^{x^Tx'}$ a suitable kernel to be choosen?
Is $f(x)=e^{x^Tx'}$ a suitable kernel to be choosen? If so, to what dimension does it transform the data?
• Kernel for what? "Kernel" means many different things in mathematics and statistics. Even the data-transformation tag doesn't narrow the scope much!
– whuber
Dec 7, 2012 at 20:52
• @whuber: Right, sorry that I wasn't clear enough. I meant this one where $k(x,x')$ is referred to as a kernel or a kernel function. Dec 7, 2012 at 21:00
• What's the difference between $x^T$ and $x'$? Dec 7, 2012 at 21:08
• He means there's two different variables, $x$ and $x'$, and he's just taking their dot product. Dec 7, 2012 at 21:17
• I think he means $K(x,y)=e^{x^Ty}$. Is that correct? Dec 7, 2012 at 21:19
If you are referring to the kernel as a kernel in machine-learning literature, then yes, it is a kernel.
More generally, we can consider the family of Gaussian kernels, parametrized by $\sigma$:
$$K(x,x') = e^{x^Tx'/\sigma^2 }$$
Using the power series expansion of the function exponential, we can rewrite the expression of $K$ as:
$$K(x, x') = \sum_{n=0}^{\infty} \frac{(x^T \cdot x' )^n}{\sigma^{2n}n!}$$
Recall kernels are closed under summation, even infinite sums. $K$ then is sum of other (polynomial) kernels , thus is still kernel. The polynomial kernel, $(x\cdot x')^d$ can be shown to map $x$ to monomials of degree $d$. Thus the Gaussian kernel maps $x$ to all the polynomial kernels.
Example: In two dimensions, $x = (x_1,x_2), \; x' = (x_1', x_2')$, the secord order polynomial kernel $(x \cdot x')^2$ maps the data to look like a new inner product:
$$( x_1^2, x_2^2, x_1 x_2 ) \cdot (x_1'^2, x_2'^2, x_1' x_2')$$ The polynomial kernel is actually computing the above, which looks like it mapped $(x_1, x_2)$ to all monomials of degree 2. The Gaussian kernel does the same thing but for degree 1, degree 2, degree 3...
## Side Note
Often in ML literature, the Gaussian kernel is defined as
$$K'(x,x') = \exp{\Big( \frac{||x - x'||^2}{2\sigma^2} \Big) }$$
But this is actually the normalized Gaussian kernel. A normalized kernel, $K'$, is defined:
$$K'(x,x') = \frac{K(x,x')}{\sqrt{ K(x,x) K(x',x') } }$$
If we use $K(x,x') = \exp{\Big( \frac{x^Tx'}{\sigma^2 } \Big) }$, we get:
$$K'(x,x') = \frac{e^{x^Tx'/\sigma^2 }}{ \exp{ \Big(\frac{||x||^2}{2\sigma^2} \Big)} \exp{\Big(\frac{||x'||^2}{2\sigma^2}\Big) } }$$
$$= \exp{ \Big( -\frac{||x' - x||^2}{2\sigma^2} \Big) }$$
• Thank you for your answer. Could you please explain yourself a little more - what do you mean by "maps x to all powers of x"? Dec 7, 2012 at 21:28
• I edited my answer a bit to include a better explaination Dec 7, 2012 at 21:44
|
2022-10-01 00:52:57
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8231838941574097, "perplexity": 522.9710992750468}, "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/1664030335514.65/warc/CC-MAIN-20221001003954-20221001033954-00545.warc.gz"}
|
https://www.ideals.illinois.edu/handle/2142/23594
|
Files in this item
FilesDescriptionFormat
application/pdf
9625208.pdf (6MB)
(no description provided)PDF
Description
Title: Efficient computational techniques for electromagnetic propagation and scattering Author(s): Wagner, Robert Louis Doctoral Committee Chair(s): Chew, Weng Cho Department / Program: Engineering, Electronics and ElectricalEngineering, MechanicalPhysics, Electricity and Magnetism Discipline: Engineering, Electronics and ElectricalEngineering, MechanicalPhysics, Electricity and Magnetism Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Engineering, Electronics and Electrical Engineering, Mechanical Physics, Electricity and Magnetism Abstract: Electromagnetic propagation and scattering problems are important in many application areas such as communications, high-speed circuitry, medical imaging, geophysical remote sensing, nondestructive testing, and radar. This thesis develops several new techniques for the efficient computer solution of such problems.Most of this thesis deals with the efficient solution of electromagnetic scattering problems formulated as surface integral equations. A standard method of moments (MOM) formulation is used to reduce the problem to the solution of a dense, $N \times\ N$ matrix equation, where N is the number of surface current unknowns. An iterative solution technique is used, requiring the computation of many matrix-vector multiplications.Techniques developed for this problem include the ray-propagation fast multipole algorithm (RPFMA), which is a simple, non-nested, physically intuitive technique based on the fast multipole method (FMM). The RPFMA is implemented for two-dimensional surface integral equations, and reduces the cost of a matrix-vector multiplication from $O(N\sp2$) to $O(N\sp{4/3}$). The use of wavelets is also studied for the solution of two-dimensional surface integral equations. It is shown that the use of wavelets as basis functions produces a MOM matrix with substantial sparsity. However, unlike the RPFMA, the use of a wavelet basis does not reduce the computational complexity of the problem. In other words, the sparse MOM matrix in the wavelet basis still has $O(N\sp2$) significant entries. The fast multipole method-fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional rough surface. The resulting algorithm computes a matrix-vector multiply in $O(N \log\ N$) operations. This algorithm is shown to be more efficient than another $O(N \log\ N$) algorithm, the multi-level fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from two-dimensional random rough surfaces.Finally, Liao's absorbing boundary condition (ABC) is studied in detail. This is an approximate ABC used to truncate the computational mesh in the finite-difference time-domain (FDTD) method. Unique results, both theoretical and numerical, are presented. Issue Date: 1996 Type: Text Language: English URI: http://hdl.handle.net/2142/23594 Rights Information: Copyright 1996 Wagner, Robert Louis Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9625208 OCLC Identifier: (UMI)AAI9625208
|
2016-10-24 01:34:06
|
{"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": 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": 0.7538822293281555, "perplexity": 1589.9422003143748}, "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-2016-44/segments/1476988719463.40/warc/CC-MAIN-20161020183839-00218-ip-10-171-6-4.ec2.internal.warc.gz"}
|
https://applied-langua.ge/posts/terminal-boredom.html
|
# Terminal boredom, or how to go on with life when less is indeed less
If the "medium is the message," then the message of low-bandwidth timesharing is "blah." 1
The "benefits" of minimalist computing have not been realised. The benefits its espousers mention include small programs and accessibility. For example, the Gemini protocol is supposed to provide high "power to weight" and many claim that reducing everything to text makes for a better reading experience; but in reality it has created large codebases, many in the one to ten thousand lines of code range, and can be quantifiably observed to make expression incredibly difficult. As well as lacking any basis in program design, computing minimalism can only fake any basis in any ecological concerns or any ecology movement.
## Social ecology for suckers
One paper we encountered discusses the terms used in less-is-less computing,2 at least informing us that it hides under phrases such as liberatory technology, appropriate technology. But no one appears to understand these terms. I am fairly well versed with social ecology so I will focus on the appropriation of liberatory technology.
### "Human scale" is a euphemism for "nothing"
First, there is a fetishism for "small" technology, whatever the fuck that is meant to mean - we will later describe why smaller protocols end up with more complexity. But people seem to like small things, they call them "smol", they probably think those things are cute even; the most blatant of counter-arguments is to attack the connotations of the adjective "small" itself:
Terms like "large," "small," or "intermediate," and "hard," "soft," or "mellow" are simply externals — the attributes of phenomena or things rather than their essentials. They may help us determine their dimensions and weights, but they do not explain the immanent qualities of technics, particularly as they relate to society. 3
Indeed a "small" technology is just that. It is not necessarily "good", "useful", "liberatory" or so on.
We will later argue that such minimalism also makes communication very difficult, as it favours reduction to remain "minimal" rather than changing to allow for better self-expression. Even Towards a Liberatory Technology, which was cited by the paper,4 suggests that more should be achieved with simpler techniques:
The importance of machines with this kind of operational range can hardly be overestimated. They make it possible to produce a large variety of products in a single plant.
So already it is established that social ecologists favour multi-purpose machines (and surely protocols and designs and so on).
And social ecologists rather prefer to support "human" relations:
Small is not enough. What is human is what counts, not just what is small. What is beautiful are people, what is beautiful is the ecosystems and their integrity in which we live.
One is perfectly capable of arguing that anything a human does "is human", and so everything is human and so the term is irrelevant. But the statement as a whole emphasises the individuality and capability rather than a vague notion of size or "simplicity". By reducing the degrees of freedom in a medium of communication, we deemphasise the individuality its users.
### Futurism ± 50 years
Furthermore, social ecology offers us a term for describing movements which attempt to change things while retaining some axioms of the present which make it impossible to change. This term is futurism and again we are given a blunt example of it:
Most futurists start out with the idea, "you got a shopping mall, what do you do then?" Well, the first question to be asked is, "why the hell do you have a shopping mall?" 5
But our identification of a futurist streak in less-is-less is not the formation of stupid questions; rather, it is in dodging good questions, such as "How do you design powerful systems to be comprehensible by small groups and individuals", by effectively answering "You can't, and so I never wanted them anyway!" The premise established, that powerful systems must be too complex to be comprehensible to individuals, is at least futurist, would we not have any ideas of how to design powerful systems now. But such ideas already exist, and so it is worse than merely futurist! The whole concept is based on notions that haven't been true for decades. Of course, the people involved have set themselves in an era of computing where they just got over learning structured programming, but barely past that it has been obvious how to design powerful but small systems.
Philosophical questions aside, what are the implications of powerless systems?
## The perversions of minimalism
### "Accessibility" with crossed fingers behind your back
It is said that, by reducing the means of presentation to mere text, Gemini is much more accessible than, say, the Web. This claim is pure bullshit - by reducing the structures that can be created, documents are much harder to read.
For example, Drew DeVault's "How I choose a license" guide shows off literally an exponential blowup in the effort required to read a document.
The main part of the page is a decision diagram, which looks something like
The page instead represents this diagram as a list of states, and transitions leading to terminal states (like "Use AGPLv3") and leading to non-terminal states (like "GOTO 8"). To find the next state, one has to linearly scan down the page to find the line starting with the number.
Credit where it is due: as the decisions don't form cycles, DeVault was clever enough to ensure that every transition only goes further down the page. But from an algorithmic point of view, a linear search is pretty terrible; and the worst possible decision diagram which only asks the user $$n$$ questions could have up to $$2^{n+1} - 1$$ states, leaving the user to scroll for a very long time.
I figure that the "solution" is to separate the document into multiple documents, one document per state, so that each state could actually link to the next states. But this is arguably a violation of the so-called sensibility of Gemini, where one "document" has been split into multiple requests.
Another solution would be for the client to have a sufficiently good search tool. In this case, we would only need to be able to find a string like 4: but otherwise we may find false positives, say, if a more conventional list number format like 2. were used, the 2. in Apache 2.0 would likely be a false positive. (And, before someone asks, it is probably not acceptable for the user to have to know any regular expression syntax to only match a 2. at the start of a line.)
### What exactly is "minimal"?
Further analysis of what a good interface for a decision diagram would eventually suggest that there is, in fact, no clear line between a bad and bloated "Web application", and a good and small "digital document", so we better shut up about it before no one reads the rest of this article.
But another another solution would be to hack a client to understand some kind of anchoring, like <a name> does for HTML. However, such an extension would not be well received. DeVault going full Torvalds mode while complaining about a simple client extension makes for another good piece of discussion. The gist of the issue was that one Gemini client would send off a request for a favicon character, which serves a similar purpose to a favicon picture on the Web. His fire-eyed appearance is based on an appeal to a supposed minimalism, of course:
The golden rule of Gemini is: do not extend the spec.
This is the only means we have of self regulation. I'll ask nicely first but ultimately I'll do what I have to in order to preserve Gemini's simplicity and utility as a small internet protocol.
Do not. Extend. Gemini.
Period.
The opinion of some appears to be that any exploitable surface that one could consider making an extension with must be met with fire. While I will later regret using the term, the Gemini protocol uses a blatantly Orwellian approach to avoiding extension, even at the cost of useful features. The Gemini FAQ answers why there is nowhere to include a content length in a response:
To minimise the risk of Gemini slowly mutating into something more web-like, it was decided to include one and exactly one piece of information in the response header for successful requests. Including two pieces of information with a specified delimiter would provide a very obvious path for later adding a third piece - just use the same delimiter again.
But this begs the question: what extensions are considered to be any good by others? What extensions does a good client implement? I don't know if there is a good answer for either,6 but I suppose it is somewhat reasonable to ask: how much more complex is a client which implements all these things? The Gemini FAQ espouses ease of implementation:
A client comfortable for daily use which implements every single protocol feature should be a feasible weekend programming project for a single developer.
Experiments suggest that a very basic interactive client takes more like a minimum of 100 lines of code, and a comfortable fit and moderate feature completeness need more like 200 lines.
These statements could well be only for the core protocol, and not any extensions. Is a good client with all the extensions that one wants even in the same ballpark? Perhaps we should check. A convenient list of clients was provided which I counted up the lines of code for. The first on the list is Candor:
[hayley tmp]$git clone https://git.sr.ht/~julienxx/castor Cloning into 'castor'... remote: Enumerating objects: 789, done. remote: Total 789 (delta 0), reused 0 (delta 0), pack-reused 789 Receiving objects: 100% (789/789), 223.09 KiB | 282.00 KiB/s, done. Resolving deltas: 100% (519/519), done. [hayley tmp]$ cd castor/
[hayley castor]\$ cloc .
34 text files.
34 unique files.
6 files ignored.
github.com/AlDanial/cloc v 1.90 T=0.02 s (1380.6 files/s, 178434.4 lines/s)
-------------------------------------------------------------------------------
Language files blank comment code
-------------------------------------------------------------------------------
Rust 24 359 28 2694
SVG 1 1 1 212
Markdown 1 46 0 100
TOML 1 3 1 31
make 1 10 16 30
-------------------------------------------------------------------------------
SUM: 29 419 47 3282
-------------------------------------------------------------------------------
I make bad estimations, but I don't make estimations that are fifteen times off! Of course, this client also implements the Gopher and Finger protocols, and it uses the evil, bloated and nice-looking Gtk+ toolkit rather than a smol and painful terminal interface, so I better pick another client. Why not the author's own AV-98? It's even written in that high-level Python language, so surely there will be fewer lines of code:
-------------------------------------------------------------------------------
Language files blank comment code
-------------------------------------------------------------------------------
Python 2 166 272 1239
Markdown 1 14 0 48
-------------------------------------------------------------------------------
SUM: 3 180 272 1287
-------------------------------------------------------------------------------
BWAHAHAHAHAHA! What a fucking lie that "200 lines" figure turned out to be! But then we never checked out those extensions; I figure the first Amfora client has a few…
-------------------------------------------------------------------------------
Language files blank comment code
-------------------------------------------------------------------------------
Go 47 998 980 5809
TOML 13 193 710 516
Markdown 8 162 0 484
YAML 7 17 4 197
Python 1 28 10 73
make 1 9 1 32
Bourne Shell 3 8 0 25
-------------------------------------------------------------------------------
SUM: 80 1415 1705 7136
-------------------------------------------------------------------------------
Need I comment more?
## How to go on
So we are faced with creating a simple system which does quite the opposite of the "simple" protocols and means of communication today. Such a system has to empower the user and actually provide capabilities for self-expression in many forms, while retaining some properties that prevent a computer from doing undesirable things. The following approach is only one approach, but we believe it is a fairly good approach which can cure terminal boredom.
To solve the apparently contradictory initial constraints, we need to introduce the concept of a meta-medium. A medium in this context is a technique for communicating an idea. A meta-medium is a technique for communicating a medium. It provides the axioms which an implementation of a medium be described with, and also provides some restraints because the axioms are designed to avoid some behaviours. Of course, the implementation is usually called a program.
Typically, the meta-medium for a computer is a combination of an operating system and a programming language. The operating system allows for running any machine code, which of course can compute whatever it pleases. Any operations with the outside world are mediated using an interface, which eventually tests the permissions of the program. The main issue is that these permissions are seldom restrained, such as in desktop operating systems, or they are too vague for our requirements, such as in mobile operating systems or hardened servers; so it is very unwise to run arbitrary programs that one doesn't trust. Permissions that would make such an idea much safer include, say, constraining a program to only be able to retrieve and not update remote data, to make it difficult to leak any data from the user, and to make any attempt at hijacking the resources of the user pointless.
This requirement suggests that there has to be another layer between the program and operating system, which is able to identify the kinds of messages, so that it is actually feasible to deny the capability of sending some kinds of messages. This layer, in both of our experiments, consists of a virtual machine which selectively provides capabilities to programs, and can limit the resources a program consumes. The virtual machine also provides a great improvement for the modularity of the system, as only the virtual machine has to be re-implemented in order to run the same programs on different computers. The implementor is only concerned with implementing the meta-medium, not with implementing any media, and so any media implemented effectively come for free.
As well as assigning appropriate limitations for what resources mediums may use, a medium should also be informed of what requirement the user has for how information is presented. Some people say that Gemini separates "content" and "presentation", and so the user has more control over the latter; but the presentation is forced to take a mostly linear, textual form, and the user has no control over that.
To achieve a real separation of content and presentation, information has to be stored in some sort of semantic format, with a program which will render out the information in various ways. These two requirements can be satisfied by the slots and methods of an object in a message-passing object system. An object system also provides a way of specifying protocols and composing programs, which a small-protocol world cannot offer.
We had some fun looking at lines of code counts, so I will present my own: the Netfarm object system and virtual machine consists of 4,272 lines of Lisp code, our networking substrate 3,748, the server and client another 2,343 lines, and a graphical client another 360 lines. All in all, that's 10,723 lines of code which does a hell of a lot more than displaying fake paper on your screen! And, of course, that figure includes good engineering things like unit and fuzz tests, and dubious engineering things like low-level optimization hacks, so you could get away with fewer lines if you didn't care for those.
## Conclusion
The reader may have noticed that we never used the term "less-is-more", even if others have used it to describe either the reductive systems we mockingly have assigned the adjective "less-is-less" to, or the more powerful systems we have designed. The term is fundamentally a distraction; through hand-waving about "simplicity" and "human scaling" we accept the simplification of our own relations and thoughts, and so we find ourselves seemingly satisfied by a reductive technology.
Reductive technologists, despite the ideologies they desperately try to cling to, find themselves making an utter piss-take of such ideologies and the liberatory potentials that they suggest. Doesn't this closing statement sound a lot like the one at the end of "Ethical software" is (currently) a sad joke? (By the way, it still is.) I think they are both caused by the same phenomenon, where one direction throws a group to failure, so they go in the opposite direction without any critical thinking, and make a joke of themselves.
Only a few weeks ago I encountered a lovely piece called Nice Shit for Everybody, which seems to share our idea of maximalism rather than minimalism. And they find themselves with the same conclusion for other forms of minimalism:
If only it were so simple. […] This is pure reactionary thought. To run and do the opposite just because capitalism displays certain social features does not make one an anticapitalist. It makes you a petit-bourgeois bohemian.
It is not difficult to have nice shit on the Internet, nor is it difficult to ensure such shit respects the privacy and preferences for media to use of the user. Based on how much time has been wasted on making incremental changes to minimalist protocols, complaining about them, and then implementing arbitrary sets of them, it looks very easy in comparison to make a convenient meta-media to achieve our goals.
## Footnotes:
1
Alan Kay and Adele Goldberg, Personal Dynamic Media
3
Murray Bookchin, The Ecology of Freedom
4
Laurent Bossavit's The Leprechauns of Software Engineering argues that "any author citing another paper should be required to provide proof that they a) possess a copy of that paper, b) have read that paper, c) have read the paper carefully." The easiest way to satisfy at least points A and B would be to quote TALT, but there is no such quote of course.
6
We have heard from private discussion that many more little wars have been fought over what to extend or what not to extend.
|
2022-01-26 11:16:12
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.3375927209854126, "perplexity": 1517.847360215675}, "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-2022-05/segments/1642320304947.93/warc/CC-MAIN-20220126101419-20220126131419-00303.warc.gz"}
|
http://mathhelpforum.com/discrete-math/90126-integer-optimization-problem-my-research.html
|
## An Integer Optimization Problem from my research
I meet with an integer optimizing problem, which is defined as follows:
$s^{*}= \textrm{argmax}_{\begin{subarray}{c}{s \in\mathcal{S}}\end{subarray}}\sum_{i=1}^{N}{\frac {\exp\left(c_i+b_i^Ts\right)}{\sum_{j=1}^{N}{\exp\ left(c_j+b_j^Ts\right)}}\cdot \left(a_i+w_i^Ts\right)}$
Where $\mathcal{S}$ denotes $n$ dimensional column parameter vector, each entry takes the integer and is defined as:
$0 \le p_i \le n-i,\quad i=1,2\ldots n$
$0 \le q_i \le i-1,\quad i=1,2 \ldots n$
$s_k=2\left(p_k-q_k\right),\quad k=1,2\ldots n$
$\sum_{j=1}^{k-1}{s_j} \ge q_k,\quad k=2,3,\ldots n$
$\sum_{j=1}^{n}{s_j}=0$
$s^{*}$ represents the optimal solution. $b_i,w_i$ denote $n$ dimensional column vector, whose values are known. The scalars $a_i,c_i$ are also defined.
Our Goal
Our goal is to build an algorithm, which can solve the optimization problem in polynomial order time with $m$ and $n$. What's happiest, you can yield an analytical solution to the optimization problem.
This problem comes from my research, which is very important for me.
I hope you give me some suggestion and advice.
Thank you.
|
2014-08-22 01:25:03
|
{"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": 14, "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": 0.9481198787689209, "perplexity": 332.2014945211191}, "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-2014-35/segments/1408500822053.47/warc/CC-MAIN-20140820021342-00007-ip-10-180-136-8.ec2.internal.warc.gz"}
|
http://www.kt.rim.or.jp/~kbk/zakkicho/11/zakkicho1104b.html
|
# ときどきの雑記帖 混迷編
### 2011年04月20日
#### ■_
LAMYY Pico どっかに落とした ○|￣|＿
#### ■_ Pythonに欲しいこんな機能
で。
bramcohen: Python wish list
Python wish list
Now that the moratorium on Python language features is over, I'll put in my thoughts
on what new stuff the language could use. I don't have much to suggest, and what I do
have to suggest is fairly minor. This is because I'm happy with the language.
new on default parameters
One of the gotchas in python is that default parameters are reused, so if you say:
Python における gotchas のひとつが再利用されたデフォルトパラメーターです。
def spam(eggs = []):
then eggs will get set to the same list every time, and modifications will get
carried over between calls. This can be hacked like this:
このようにした場合、eggs は毎回同一のリストに対してセットするので行った変更は
次回の呼び出しまで持ち越されます。これは次のようにして回避できます:
def spam(eggs = None):
if eggs is None:
eggs = []
This works, but is ugly, and prevents passing in None as a value for eggs. It would
be better to be able to simply say:
このやり方でも目的を果たせるのですが見づらいものであり、
eggs の値として None を渡すことができません。
これは簡単に書ける様にすべきでしょう:
def spam(eggs = new []):
which should do exactly what you expect.
^ on bytes
バイト列に対する ^
A strange oversight in Python3 is that bitwise operators don't work on byte arrays.
The ^, & and | operators should work on bytes of equal length, doing exactly what
they obviously should. Trying to apply them to bytes of unequal length should probably
result in an error. It's easy enough to write functions to do these things, but
they're slow, and there's only one reasonable semantics for what those operators
should do on byte arrays anyway.
Python3 では驚くことにビット操作演算子 (bitwise operators) はバイト配列に対しては
動作しません。＾や&、| といった演算子は長さの等しいバイト列に対しても動作すべき
であり、明確にそうあるべきような動作をすべきです。
長さの異なるバイト列に対してこれらの演算子を適用しようとした場合にはエラーにすべきでしょう。
こういった動作をするように関数を記述するのは簡単ではあるのですが、それは遅いものです。
そして、
raw binary conversion
Maybe this has been added to the standard library and I just haven't heard about it, but
a longstanding annoying missing piece of functionality is simple conversion between ints
and big or little endian representations of them as bytes. Again, this is easy enough to
implement, but is slow when done in Python and is hardly an obscure piece of functionality.
たぶんこれはすでに標準ライブラリに追加されていて、単にわたしがそれをまだ知らないだけなの
でしょう。けれども、長い間放置されている機能 (a longstanding annoying missing piece of
functionality。ちと無理筋?) が int と ビッグエンディアンやリトルエンディアンのバイト列
との間の単純な変換です。
これを実装するのはとても簡単なのですが、Python で実装した場合は遅いものになってしまい
また hardly an obscure piece of functionality なのです。
dictionary scrambling
This might be an obscure piece of functionality, but I'd like the ability to change
the hashing function which dictionaries use, because I write tests which depend on my
code behaving the same way every time it's run, and I'd like to be able to test that
it doesn't have any dependencies on the order of iterating over dictionary keys or
values.
これは機能の obscure piece かもしれませんが、わたしは辞書で使用するハッシュ関数を
変えられるようにしたいのです。それは、実行するたびに毎回同じように振舞うコードに
依存するテストを記述するためであり、また、辞書のキーや値の iterating over の
順序に一切依存しないテストを可能にしたいのです。
#### ■_ parrot
Parrot 3.3.0 "Fire in the Sky" Released! - nntp.perl.org
Parrot 3.3.0 News:
- Core
+ The isa and isa_pmc vtables can now be overridden from PIR
+ IMCC has a new improved external interface
+ A new IMCCompiler PMC adds prototype PDD31-alike functionality for the PIR and PASM compilers
+ New --with-llvm option to Configure.pl, which will link to LLVM if it is available
- Community
+ Parrot Virtual Machine was accepted into Google Summer of Code 2011
- Ecosystem
+ Rosella adds a stable "Event" library to implement a publish/subscribe mechanism
- Tests
+ The test coverage of the extend_vtable subsystem was greatly increased
#### ■_ S.O.L.I.D.
OO Design Principles ≪ Valuable Opinions
OO Design Principles
design principles and values.
S.O.L.I.D. Class Design Principles
Collected by Robert C. Martin for his book “Applying Principles and Patterns”
Interesting collection of OO design principles : programming
#### ■_ AA木
AA木 - Wikipedia
AA木（英: AA tree）は、平衡2分探索木の一種であり、順序のあるデータを効率的に格納し検索
ならない。結果として2-3-4木ではなく2-3木に相当したものとなり、操作時の処理が大幅に簡略
て扱う必要がある。
1993年かあ。いいたかないけど、この種のものが日本で売られている「入門書」レベルにまで 載せられることってあるんですかね。
### 2011年04月19日
#### ■_
Software Design 誌で、Excel VBA の記事の連載が始まっていた。
#### ■_ What Perl 6 (and 5) Have Done Right
Perl 6 (と Perl 5)が正しく行ったこと。でいいのかな。
What Perl 6 (and 5) Have Done Right - House Absolute(ly Pointless)
What Perl 6 (and 5) Have Done Right
By Dave Rolsky on April 18, 2011 12:46 PM
I was talking this weekend with Matt Mackall about Python 3 and Perl 6. Matt is the
creator of Mercurial, so he is deeply invested in Python.
この週末にわたしは Python 3 と Perl 6について Matt Mackall と話しました。
Matt は Mercurial の creator であり、Python を使い込んでいる人物です。
He was asking about the relationship between Perl 5 and Perl 6, and we were comparing
it with the relationship of Python 2 and 3. His main problem with Python 3, as I
understand it, is the backwards-incompatible change in string handling from 2 to 3. In
Python 3, all strings are Unicode by default. Byte arrays are now their own thing, no
longer interchangeable with strings.
Python 2 と Python 3 との関係と比較してみたのです。
わたしの理解しているところでは、Python 3に関して彼の抱えている主たる問題は
Python 3ではすべての文字列はデフォルトでUnicode です。
Python 3でも存在しているバイト配列はもはや文字列とは interchangeable (交換可能)
でないものなのです。
Meanwhile, Mercurial is still supporting distributions that are running Python 2.4,
which is over 6 years old at this point. To make matters worse, Mercurial really
doesn't benefit from the Unicode-is-everywhere changes in Python 3, so there's little
incentive to migrate.
ところで Mercurial は現在から 6年以上前のものである Python 2.4 を使っているディストリビューション
をまだサポートしています。悪いことに、Mercurial は Python 3 における Unicode-is-everywhere
という変更から恩恵を受けてはいません。ですから、migrate しようという incentive があまりないのです。
I suspect that eventually Mercurial will be stuck with some sort of compatibility layer that
checks what Python it is running on, and loads the appropriate versions of libraries (or
monkey patches them, or whatever Python people do ;).
わたしはMercurial が 実行されている Python がなんであるのを検査しそして適切なバージョンの
ライブラリをロードする互換レイヤーの類が必要になるであろう (あるいはモンキーパッチを行うか、
さもなければPythonユーザーがやっているようにするか :) と予想しています。
This discussion helped me realize that regardless of any problems Perl 6 has, we've done one
thing really right in the overall Perl community. There's no intention to have Perl 6 replace
Perl 5. Perl 6 has been designed to co-exist with Perl 5. The Perl 6 binary will presumably
be called perl6 (or maybe rakudo), not just perl.
この議論はわたしがPerl 6 の抱えているすべての問題とは関係ないことを realize するのを助け、
we've done one thing really right in the overall Perl community.
Perl 5 を Perl 6 で置き換えようという意図は存在しません。
Perl 6 は Perl 5 と共存できるように設計されています。
Perl 6 のバイナリは Perl 6 (あるいは rakudo) から呼び出されることを想定しています。
Meanwhile, Perl 5 has maintained it's strong commitment to backwards compatibility
while still pulling in cool bits from Perl 6. This commitment can be frustrating in
many ways, but its also has benefits. The Perl 5 commitment to prototyping new
features on CPAN has made for a much cleaner upgrade path. Finally, the fact that
syntax breakage is almost always opt-in (with use feature or use 5.x), means that we
can safely upgrade one module at a time to new syntax.
さて、Perl 5 は後方互換性に対する strong commitment を保ってきました。
この commitment は色々不満がでる可能性がありますが benefits のあるものでもあります。
Of course, Python has from __future__ import, but Python 3 doesn't use that to enable Unicode
everywhere. Even worse, there doesn't seem to be a from __past__ import "old string semantics",
so upgrading to Python 3 requires an entire application (and its dependencies) to upgrade all
at once.
もちろん Python には __future__ import がありますが、Python 3 はこれを Unicode をどこ
ででも使えるようにというためには使っていません。さらに言えば、
__past__ import "old string semantics" のようなものも持っていません。
Whatever you think of Perl 6, I think the Perl community can be thankful that Larry had the
foresight to realize that Perl 6 cannot replace Perl 5. Decoupling Perl 6 from Perl 5 has let
the two projects grow at their own pace. If Perl 6 had been officially anointed as the coming
replacement for Perl 5, I doubt we would ever have seen the Modern Perl "movement" emerge,
nor would we have seen the revitalized Perl 5 core development of the past few years.
Perl 6についてあなたがどのように考えているにせよ、
Perl コミュニティは
Larry が Perl 6 は Perl 5を置き換えることはできないことを realize したと公にしたことに
Decoupling Perl 6 from Perl 5 has let the two projects grow at their own pace.
If Perl 6 had been officially anointed as the coming replacement for Perl 5,
I doubt we would ever have seen the Modern Perl "movement" emerge,
nor would we have seen the revitalized Perl 5 core development of the past few years.
Perl 6 と Perl 5 の decoupling はこれら二つのプロジェクトをそれぞれのペースで成長させました。
もし Perl 6 がすでに officially に anointed していたら、
Perl 5 の replacement になるような Modern Perl "movement" の推進や
Perl 5 core development の revitalized を目にすることがあったかどうか
わたしは疑問に思うのです。
When Perl 6.0 is released, in whatever form that takes, our Perl 5 programs will continue
working for as long as we want. That's a very good thing.
Perl 6.0 がリリースされたとき、それがどのような形式であったとしても、わたしたちが Perl 5 で
Python 2.x と Python 3.x、Perl 5 と Perl 6 ではそれぞれ大きな変化があるけれども その関係はPython のそれと Python とでは違う。という感じなんかな。
#### ■_ Jなんとか
すぐにこの記事も訳されて日本語版に載ると思いますがそれはそれとして
InfoQ: Creating a new JVM language
Last week's announcement of Ceylon brought the focus on JVM-based languages. Ceylon
isn' the first JVM based language; nor will it be the last. But the general case of
JVM based languages was proposed in Bruce Tate's Beyond Java in 2005, and has been a
focus of the Java platform for a significant time, as the list of JVM languages on
Wikipedia can attest to. Bruce noted that community is the key to success:
(略)
There are a number of languages which have been ported to run on top of a JVM runtime,
including Python (Jython), Ruby (JRuby), Lisp (Clojure) and even Tcl (JTcl). These all
exhibit the same behaviour as the existing programming languages but run on top of a
JVM based platform. In most cases, these run faster than their native counterparts;
but such changes aren't always possible (e.g. see the last flight of the unladen
swallow).
JTcl なんてのがあるのか… JTcl: Tcl language interpreter in Java — Project Kenai なにかうれしいことがあるんだろうか?
### 2011年04月18日
#### ■_
なんかえらく盛り上がっているのですが結構前の記事だったり。 Some “Developers” Just Can’t Develop : programming
Some “Developers” Just Can’t Develop : Richard Banks - Agile and .NET
Some “Developers” Just Can't Develop
(「開発できない“開発者”もいる」 ってな感じ?)
* Posted by Richard Banks
* Aug 25, 2009
I've been interviewing candidates for developer positions for over a decade now. In
my early years I was very much hit and miss in terms of finding the right people and
it wasn't until a horror hire that I realised what I was doing wrong.
This guy was special. He was listed as being a .NET team lead, he talked about his
history and skills really well, he was engaging and confident, and his references came
back glowing with praise so I decided to offer him the job. This he duly accepted and
started shortly thereafter. Now one of the things I was doing with new hires at the
time was getting them to work on bugs – it helped me knock down the backlog and gave
them exposure to a variety of areas across the system. I also gave them plenty of
time early on to learn the ropes and get up to speed and it would typically take a few
days to get through the first few bugs and start having some ah-ha! moments with the
codebase.
So anyway, this particular person starts and is given his first bug. Quite a simple
bug too and yet it took well over a week for him to get it done and even then he
needed plenty of help and prodding along the way. I was also getting complaints from
the other developers that this guy was hopeless and a really bad developer which I
couldn't quite believe so I decided to take some time, sit down next to him and do
some pairing.
By doing the fizzbuzz exercise for real, I merely confirmed what I already knew from
my experiences with the debugging exercise. So, what's the lesson here? I think it's
simple. Get your candidates to write some code during the interview. You don't need
any special tools to do it either – just use a whiteboard and pseudo code if you want
to. But whatever you do, make sure they prove to you that they can actually do the
job, not just talk the job.
Remember: There are plenty of developers that just simply can't develop. Avoid my
mistakes and do what you can to avoid hiring the wrong people.
Copyright 2009 | Richard Banks | All Right Reserved
んー、書かれた当時にも読んでたかもしれない。
#### ■_ あとでよむ
SIGUSR2 > Parser Combinators Made Simple
Parsing theory has been around for quite a long time, but it is often thought of as
magic by the swarms of people who haven't bothered to read about it, and see how plain
and dry it actually is. Algorithms for parsing LR(k) grammars (meaning Left-to-right,
Right-most derivation, k tokens lookahead) for instance, normally just traverse a
state machine that was computed before hand (either by hand, or by using a parser
generator such as bison or yacc). Sure, there are many things to trip on, tedious to
track down ambiguities, and other issues, but the general theory of parsing has
remained unchanged for years—one might say, it is a solved problem.[1]
や、パーザーコンビネーターとか、PEGとかあまりまじめに読んだりしてないので(^^;
#### ■_
locale 設定の内容って簡単に確認できましたっけ?
Environment Variables
LC_COLLATE
This variable shall determine the locale category for character collation. It
determines collation information for regular expressions and sorting, including
equivalence classes and multi-character collating elements, in various utilities
and the strcoll() and strxfrm() functions. Additional semantics of this variable,
if any, are implementation-defined.
ここで使うような collating oreder がどうなのか確認したいってのが本題なんですが。
### 2011年04月17日
#### ■_
・3倍速い
3-5倍ほど速くなったSqueakをぜひともお試しください。 日本語版Squeak 4.2リリース | Umejava's Blog
hello, world レベルで止まってるなあ。他にもあるけど。Erlangとか。
エラーハンドリングについて考える。 - How to disappear completely
#### ■_
pull request とかどんな感じなんだろか。 コードをそういうのがくるところに置いたことがないからわかんないや。
catch phrases - What's the canonical retort to "it's open source, submit a patch"? - Programmers - Stack Exchange
The danger of ever suggesting some feature on a product, especially open source, is
that you'll get the response, "why don't you do it?".
That's valid, and it's cool that you can make the change yourself. But we know
practically that products do often improve as programmers listen to the voice of users
— even if those users are other programmers. And, the efficient way to make those
changes can include someone who's already working on the project taking up the idea
and implementing it.
There are some common terms used to refer to software development problems. e.g.
Bikeshedding. Is there a common term used that essentially replies, "Yes, I know
that I can change just about anything in the world — even closed source. I could get
hired, and go write that code. But in this case I'm just making an observation that
may in fact be useful for another coder already well suited to easily make that change
— or just generally discussing possibilities."
It's a difficult point: since the user doesn't directly or indirectly pay for a
product, she cannot ask for a feature to be implemented. It's not as if you were a
stakeholder or a direct customer who ordered the product, and not even an end user of
a commercial product.
This being said, "submit a patch" is not a valid answer. It's not polite.
It's not correct. Even for an open source product. "Submit a patch" is the
short version of:
"we don't care if you like our product or not. Go and modify it if you want,
but don't bother us with your customer requests."
Well, it's not so easy. To do it:
* You must know the language(s) used in the open source project.
* You must be able to load the source code from the version control to be able to modify it.
* You must be able to compile this source code, which is not so obvious in some cases. Especially, when a huge project takes a few hours to compile and displays 482 errors and thousands of warnings, you may be courageous to go and search for the source of those errors.
* You should understand very well how the project is done, what are the coding style to use, if any, how to run unit tests, etc. If the project doesn't have a decent documentation (which is often the case for open source projects), it may be really hard.
* You must adapt yourself to the project and to the habits of the developers who are participating actively to the project. For example, if you use .NET Framework 4 daily, but the project uses .NET Framework 2.0, you can't use LINQ, nor Code Contracts, nor other thousands of new features of the latest versions of the framework.
* Your patch must be accepted (unless you do the change only for yourself, without the intent to share it with the community).
If your intention is to actively participate to the project, then you can do all those things and invest your time for it. If, on the other hand, there is just an annoying minor bug or a simple feature which is missing, spending days, weeks or months studying the project, then doing the work itself in a few minutes is just unreasonable, unless you like it.
So is there a canonical retort to "it's open source, submit a patch"? I don't think so. Either you explain to the person that she's impolite, or you just stop talking to her.
What's the canonical retort to “it's open source, submit a patch”?
There is no reasonable retort that is likely to make any difference. Attempting to
persuade volunteers to do something that they have no intention of doing is a waste of
* Do what the response suggests; i.e. implement the feature and submit it as a patch. It is
called "giving something back".
* Find someone who would be willing to implement the feature for you for real money. It
could be the project itself (e.g. in return for sponsorship), someone associated with
the project, or some random "coder for hire".
* Find an alternative product.
how you might have responded if you were in his shoes. For instance, how would YOU
respond if you thought that the suggestion wasn't worthwhile / well-thought-out /
intelligible / etc, but didn't have the time or patience to engage in a protracted
debate?
I've been involved in a long running open source OS project, and one of the most
annoying things is people who sit in the "peanut gallery" and pepper you
with a stream of suggestions about doing things "better" that:
* are incomplete, unintelligible or downright nonsensical,
* are untried ideas with an objectively low chance of success,
* would require a huge amount of effort to implement, and / or
* are counter to the stated goals of the project.
Often the best response is to pointedly challenge the person to get involved in the
project ... and hope that they take the hint. Unfortunately, the most annoying ones
don't even take a hint.
Of course, the other response to such people is to not respond at all, or completely
ignore them.
site design / logo © 2011 stack exchange inc; user contributions licensed under cc-wiki with attribution required
バグレポートでプッツンしたことは…あるな。うん。
reddit から。
What's the canonical retort to "it's open source, submit a patch"? : programming
What's the canonical retort to "it's open source, submit a patch"?
(programmers.stackexchange.com)
Only after:
* finding where the code is
* obtaining a copy using some mechanism
* Attempting to compile the code
* Decoding build errors
* Discovering you need an additional tool to build the source
* Finding and obtaining and installing the tool
* Decoding build errors
* Discovering you need to install/obtain an additional library
* Finding and obtaining and building the additional library
* Repeat previous steps until it builds successfully
* Attempt to run program/library and find it crashes
* Debug it to find the misconfiguration you introduced in the build
* Finally get a working copy
* Finding the code that controls the behavior that you want to change
* Discover it's hidden behind N+1 layers of abstraction (where N is a sufficiently discouragingly large number)
* Hack up the patch
* Search the internet for _DD development to find the philosophy you should've been coding against
* Rewrite the code to that standard
* Crying in frustration
* Arguing about merits of patch with code owners
* Give up unsatisfied or Fork
"Shut the fuck up you idiot"
#### ■_ 読んだ
そいやこの本、高橋会長も買ったというのをついったで見かけた覚えがあるなあ。 それはさておき。 タイトルにもある「イシュー」(issue) がこの本のポイントなんですが、 どう説明したものか。最重点項目…というのも違うような気がする。 単なるハウツー本(○○をすればよいといった書き方をしていない点で)ではないのですが、 いざ実践となると手が進まない人も少なくないような気がします。 ってそれオレだよ(苦笑)。
#### ■_
OCamlもhello, world レベルなんですが、それはさておき(こればっか)
Camel Spotting in Paris
I'm at the 2011 OCaml Users Group in Paris, reporting on some splendid talks this
year. It looked like around 60-70 people in the room, and I had the pleasure of
meeting users all the way from Russia to New York as well as all the Europeans!
Js_of_ocaml
First up was Pierre Chambart talking about the js_of_ocaml compiler. It compiles OCaml
bytecode directly to Javascript, with few external dependencies. Since the bytecode
format changes very rarely, it is simpler to maintain than alternatives (such as Jake
Donham's ocamljs) that require patching the compiler tool-chain. Javascript objects
are mapped to dynamic OCaml objects via a light-weight ## operator, so you can simply
write code like:
(略)
OCaml on a PIC (OCAPIC)
Next up Phillipe Wang presented something completely different: running OCaml on tiny
8-bit PIC microcontrollers! These PICs have 4-128Kb of flash (to store the code), and
from 256 bytes to 4 kilobytes. Not a lot of room to waste there. He demonstrated an
example with a game with 24 physical push buttons that beat humans at a conference
(JFLA).
It works by translating OCaml bytecode through several stages: ocamlclean to eliminate
dead code in the bytecode (which would be very useful for native code too!), a
compression step that does run-length encoding, and then translation to PIC assembly.
They have a replacement stop-and-copy GC (150 lines of assembly) and a full collection
cycle runs in less than 1.5ms. Integers are 15-bits (with 1 bit reserved) and the
block representation is the same as native OCaml. Very cool project!
(略)
OCaml Future
Xavier “superstar” Leroy then gave an update of OCaml development. Major new
features in 3.12.0 are first-class modules, polymorphic recursion, local module opens,
and richer operations over module signatures. Version 3.12.1 is coming out soon, with
bug fixes (in camlp4 and ocamlbuild mainly), and better performance on x86_64: turns
out a new mov instruction change improves floating point performance on x86_64.
OCaml 3.13 has no release date, but several exciting features are in the pipeline.
Firstly, more lightweight first-class modules by permitting some annotations to be
inferred by the context, and it introduces patterns to match and bind first-class
module values. Much more exciting is support for GADTs (Generalised Algebraic Data
Types). This permits more type constraints to be enforced at compile time:
(略)
ううむ。またも JavaScript へのコンパイラー。 PIC にOCmalコンパイラーの出力したコードを乗せるってのも面白そう。 It works by translating OCaml bytecode through several stages: あれ、バイトコード出力するものだったのだっけ。
### 2011年04月16日
#### ■_
ベイスターズを「ベイス」って略されるとなんか違和感ががががが。
COMIC ZIN という同人誌やら扱っている本屋(といっていいのだろうか?)さんがあって (店舗情報 － COMIC ZIN －)、 その新宿の店舗のほうに長いこと GA 芸術科アートデザインクラス の巨大ポップ(アニメ放映開始のお知らせのやつ)が 入り口付近にあったのですが、今日行ったら撤去されていてがっくし。 まあ二年前だしなあ。
「日本ハムに学ぶ～」 は面白かった。 終わりのほうで12球団全部の補強について数ページずつ割いて書かれているのですが、 ベイスターズのそれはいいところついていると思いました。 村田と内川(現ホークス)を FA で出しても～とか (が、そういう意見を言うとmixiの某コミュでは袋叩きだろうなw)。 ファイターズにしても、ただ単に北海道に移転したから優勝できたってわけじゃないんですよね。 勝つための努力をフロント陣もやっていたと。 しかし、ダルビッシュって一本釣りだったんだよなあドラフト。 今から思い返すと信じられないというかなんというか。 この本についてはもうちょっと書こう。
#### ■_ Ceylon
ぼつぼついろんな意見がでているようで。
Ceylon: Interesting for the Wrong Reasons - lockster's posterous
April 15, 2011
Ceylon: Interesting for the Wrong Reasons
A couple of days ago, Gavin King announced that he is leading a team at RedHat that's
creating a new JVM language called Ceylon. See here for most of what is known so far.
The stated motivation, in a nutshell is that they like Java very much, but it has
deficiencies that are preventing progress in key areas, and they are generally feeling
“frustrated”. They don't have a complete compiler yet, but they're working on it,
and I get the impression RedHat is pretty serious about it.
チームを率いていることをアナウンスしました。(リンクの案内)
それを行ったことの動機というのは、彼らはJavaが非常に好きであるのに
Javaにはそのキーとなる領域において進歩を妨げているような欠陥があって
その欠陥に対して“欲求不満”といった感情を抱いているということでした。
Red Hatはとても真剣にそれに取り組んでいるという印象をわたしは受けました。
Gavin King's slides provide a fascinating insight into the kind of thinking that
remains so dominant in the Java community. Gavin King is well known in the Java world
as the inventor/leader of Hibernate and various other JBoss projects. He certainly
knows Java inside out, and his list of “frustrations” is astute, if incomplete.
While I haven't dug into all the details so far revealed about Ceylon, but it seems
likely that they'll succeed in their goal of creating “a better Java”. If given the
choice between using Java and Ceylon, I could certainly see myself choosing Ceylon.
But Ceylon is a terrible idea. The problem is that they are treating the symptoms, not
the disease; and they're repeating exactly the same mistakes that resulted in them
finally hitting a dead-end with Java.
Scala aims to be compatible with Java, but it's about much more than just “a better
Java”. Ironically, it seems as though Ceylon will not interoperate with Java as
seamlessly as Scala does (e.g. Scala keeps null and type erasure). It'll be
interesting to see how that works out. To get an idea of how serious the Scala team is
about powerful but practical abstractions, look at how they handle the tensions that
crop up between abstraction and performance. Great examples of this are how Scala
deals with the unpleasantness of arrays on the JVM, and also the @specialized
annotation.
Scala は Java との互換となることを目指していますが、単なる“a better Java”
を越えるものです。皮肉なことに、Ceylon はScala とは違ってJavaとの
interoperate を持たないように見受けられます(たとえば Scala は null と
type erasure を残しています)。
It'll be interesting to see how that works out.
どのように考えているかを理解するには
この greate example が、Scala ではどのように
JVM 上の配列の unpleasantness と @specialized アノテーションを扱っているか
という点です。
Scala is by no means perfect. The trade-offs it makes will not suit everyone fully.
But I cannot help but scratch my head over statements like this (Gavin King, again):
Scala は完璧ではなく、そこにあったトレードオフはすべての人を満足させるものでは
ないでしょう。とはいっても、Gavin King が言っているような
statmentes には scratch my head せざるを得ません。
But I guess I should mention that the number one technical problem that we simply
can't solve to our satisfaction in Java – or in any other existing JVM language – is
the problem of defining user interfaces and structured data using a typesafe,
hierarchical syntax.
とはいえ、Java 、あるいは既存のJVM言語ではではわたしたちが満足できるような形で
それはユーザーインターフェースの定義の問題と、typesafe を使い
I could very well be missing something, but this would seem like a problem that is
right in Scala's wheelhouse. Perhaps it may not be solved satisfactorily today, but it
could done with far less effort than creating a whole new language (and new standard
library, and new tool chain…). It is depressing to think of what these guys could
achieve working with Scala instead of pouring resources into Ceylon.
わたしが何かを見落としている可能性はありますが、
それはScalaの操舵室(?)に存在している問題でしょう。
おそらくそれは今日満足行く形で解決できるものではないのでしょうが、
この人たちが Ceylon にリソースをつぎ込むのではなく
Scala に注力するかもしれないと考えるのは気の滅入ることです。
#あやしいなこのへん
You may wonder, “if you think Scala is so good, then use it and be happy, why worry
about Ceylon?” Well, I worry because I think Ceylon is worse than Scala, but it could
win anyway. That actually seems to be the more common outcome in these situations. I
would much prefer a world with Scala jobs in demand than one with Ceylon jobs in demand.
So, yes, it's all about me being selfish. I would say to all Scala fans: don't be
afraid to be a little selfish and evangelise for the better outcome.
「そんなにScalaがいいと思っているのなら、Scalaを使えばシアワセになれるんじゃないの?
なんだって Ceylon の心配をしているの?」と思われるかもしれません。
That actually seems to be the more common outcome in these situations.
わたしは Ceylon での仕事が求められる世界よりもScalaでの仕事が求められる世界のほうが
So, yes, it's all about me being selfish.
すべての Scala ファンに少々利己的になることを恐れずよりよい outcome を evangelise しようと
#### ■_ シャッフル
こういうやり方があったか。
Excelで整数ランダムにだすには - 質問・相談ならMSN相談箱
Excelで整数ランダムにだすにはどのようにすればいいのでしょうか？
よろしくお願いします。
まあ、シャッフルだよねえと思ってたら 回答のひとつで紹介されていたものに興味深いものが。
重複しない乱数の作成－RAND関数・RANK関数：Excel エクセルの使い方-関数/計算式-数学
（B1:B5セルに1～5の乱数を作成する例）
A1:A5セルに「=RAND()」という数式を入力
↓
B1セルに「=RANK(A1,$A$1:$A$5,)」という数式を入力
↓
B1セルの数式をB2:B5セルにコピー
なるほどこれなら Excel のセル関数だけでできますわな。
#### ■_ 今日の丸投げ
どう考えても丸投げだよなあ。この辺と併せて。 awkで行ごとの計算について | OKWave awkでのsh処理について | OKWave
awkの得意な人に聞いても結構難しいといっていたので、 どーこーがー
awkでの処理 | OKWave
awkでの処理
あるtxtファイルが存在したとして、txtファイルの中身は以下のようになっているとします。
もしOUTの次にOUTがきていたら、現在行のOUTの行を削除するとしたいです。
～OUT
～IN
～OUT
～IN
～OUT
～IN
～OUT ★ここを削除したいです。
～OUT
～IN
sh内で実装するとしたらどうやったらできますでしょうか
ご教授願います。
ANo.1
0909union
http://docs.hp.com/en/B2355-90680/uniq.1.html
http://docs.hp.com/en/B2355-90680/sort.1.html?jumpid=reg_R1002_USEN
それで標準入力から渡せば、同じ行は存在しないで、処理ができると思います。
sort|uniq -[忘れた。上記URL確認] xxxx.txt | awk { xxxx }
言葉足らずで失礼しました。
２行目の$1から１行目の$1を引き算しようとしていて、
OUTとINの順番でならんでない行は削除するとしたかったのです。。。
awkの得意な人に聞いても結構難しいといっていたので、
13001234 "性能情報：20110412000455278_02OUT"
13001234 "性能情報：20110412000455283_02_IN"
13001234 "性能情報：20110412000502719_01OUT"
13001234 "性能情報：20110412000502724_01_IN"
13001234 "性能情報：20110412000832155_01OUT"
13001234 "性能情報：20110412000832159_01_IN"
13001234 "性能情報：20110412001243737_01OUT"
13001234 "性能情報：20110412001243742_01_IN"
13001234 "性能情報：20110412001347455_06OUT"
13001234 "性能情報：20110412001347459_06_IN"
13001234 "性能情報：20110412001652405_01OUT"
13001234 "性能情報：20110412001652410_01_IN"
13001234 "性能情報：20110412001844606_01OUT"
13001234 "性能情報：20110412001844612_01_IN"
13001234 "性能情報：20110412002258567_05OUT"
13001234 "性能情報：20110412002258572_05_IN"
13001234 "性能情報：20110412002410587_01OUT"
13001234 "性能情報：20110412002410591_01_IN"
13001234 "性能情報：20110412002505697_04OUT"
13001234 "性能情報：20110412002505701_04_IN"
13001234 "性能情報：20110412002911876_01OUT"
13001234 "性能情報：20110412002911881_01_IN"
13001234 "性能情報：20110412003125409_01OUT"
13001234 "性能情報：20110412003125414_01_IN"
13001234 "性能情報：20110412003148432_07OUT"★
13001234 "性能情報：20110412003148451_01OUT"
13001234 "性能情報：20110412003148456_01_IN"
13001234 "性能情報：20110412003719949_01OUT"
13001234 "性能情報：20110412003719954_01_IN"
13001234 "性能情報：20110412003857663_01OUT"
13001234 "性能情報：20110412003857668_01_IN"
13001234 "性能情報：20110412004020388_01OUT"
13001234 "性能情報：20110412004020393_01_IN"
13001234 "性能情報：20110412004353569_01OUT"
13001234 "性能情報：20110412004353573_01_IN"
13001234 "性能情報：20110412004553447_01OUT"
13001234 "性能情報：20110412004553452_01_IN"
13001234 "性能情報：20110412004614347_01OUT"
13001234 "性能情報：20110412004614352_01_IN"
13001234 "性能情報：20110412005335553_01OUT"
ANo.3
No2です。すいません。訂正。
/OUT/{save=$0;next} {if(save!=""){print save;save=""};print} END{if(save!="")print save} OUTがない行が連続しないなら、たまたまさっきのでも良いのですが。 補足 丁寧にありがとうございます。 今こちら30000stepぐらいのshを組んでいて大変なのです。。。。 お二方に助けて頂いた感じでちょっと動かしてみます。 少々お待ち下さい。 なんだ 3000ステップの sh て。 そして awkでの処理 | OKWave お礼 0909unionさん No2さんのロジックでいこうと思います。 0909unionさんから教えて頂いた内容も実現できましたので お礼申し上げます。 また勉強させて下さい！！ そのまま使えるスクリプトがある方を指して、～のロジックで。と来たもんだ。 また勉強させて下さい！！ (ぴーっ) #### ■_ Lispの呪い 誰か全文訳すような気がする。 The Lisp Curse The Lisp Curse by Rudolf Winestock This essay is yet another attempt to reconcile the power of the Lisp programming language with the inability of the Lisp community to reproduce their pre-AI Winter achievements. Without doubt, Lisp has been an influential source of ideas even during its time of retreat. That fact, plus the brilliance of the different Lisp Machine architectures, and the current Lisp renaissance after more than a decade in the wilderness demonstrate that Lisp partisans must have some justification for their smugness. Nevertheless, they have not been able to translate the power of Lisp into a movement with overpowering momentum. In this essay, I argue that Lisp's expressive power is actually a cause of its lack of momentum. このエッセイでは、Lisp の expressive power というものが実際には momentum (勢い、慣性)が欠如しているためだということを主張します。 The power of Lisp is its own worst enemy. Lisp のパワーというものそれ自身が最悪の敵を抱えています。 Here's a thought experiment to prove it: Take two programming languages, neither of which are object-oriented. Your mission, if you choose to accept it, is to make them object-oriented, keeping them backward-compatible with the original languages, modulo some edge cases. Inserting any pair of programming languages into this thought experiment will show that this is easier with some languages than with others. That's the point of the thought experiment. Here's a trivial example: Intercal and Pascal. Now make this thought experiment interesting: Imagine adding object orientation to the C and Scheme programming languages. Making Scheme object-oriented is a sophomore homework assignment. On the other hand, adding object orientation to C requires the programming chops of Bjarne Stroustrup. The consequences of this divergence in needed talent and effort cause The Lisp Curse: 才能と努力を必要とするようなこの divergence (相違、逸脱)の結果として 次のLispの呪いが引き起こされます: Lisp is so powerful that problems which are technical issues in other programming languages are social issues in Lisp. Lisp は他の言語では技術的な issue となるような問題が social な issue になってしまう ほど強力な代物である。 #今ひとつこう、 略 So why don't the Lisp hackers put the Smalltalk guys in their proper place? Why don't they make a free development system that calls to mind some of the lost glories of the LispM, even if they can't reproduce another LispM? The reason why this doesn't happen is because of the Lisp Curse. Large numbers of Lisp hackers would have to cooperate with each other. Look more closely: Large numbers of the kind of people who become Lisp hackers would have to cooperate with each other. And they would have to cooperate with each other on a design which was not already a given from the beginning. And there wouldn't be any external discipline, such as a venture capitalist or other corporate master, to keep them on track. Every project has friction between members, disagreements, conflicts over style and philosophy. These social problems are counter-acted by the fact that no large project can be accomplished otherwise. "We must all hang together, or we will all hang separately." But the expressiveness of Lisp makes this countervailing force much weaker; one can always start one's own project. Thus, individual hackers decide that the trouble isn't worth it. So they either quit the project, or don't join the project to begin with. This is the Lisp Curse. すべてのプロジェクトにはメンバー間の衝突があり、 スタイルや哲学についての意見の相違があり、confilict があります。 こういった social な問題は accomplissed otherwise できない 大規模プロジェクトが存在していないという事実によって counter-acted されます。 "We must all hang together, or we will all hang separately." しかし Lisp の expressiveness はこの countervalling force を格段に弱めてしまい、 誰かがいつでもその人自身のプロジェクトを開始できるようします。 したがって個々のハッカーはそういったトラブルには意味がないと判断します。 ですから彼らはプロジェクトから抜けてしまったり、 最初から参加しなかったりするのです。 This is the Lisp Curse. One could even hack Emacs to get something that's good enough. Thus, the Lisp Curse is the ally of Worse is Better. The expressive power of Lisp has drawbacks. There is no such thing as a free lunch. Lisp の expressive power には drwabacks (欠点、短所)があります。 ただ飯 (free lunch) のようなものはないのです。 Copyright © (2011) Rudolf Winestock, All Rights Reserved. This essay was published on Friday, April 15, 2011. #### ■_ Lisp Is Not An Acceptable Java もうひとつ Lisp ネタ。 Lisp Is Not An Acceptable Java Lisp Is Not An Acceptable Java 2011-04-01 08:34 Every once in a while, some kid discovers Lisp and thinks, “hey, that's actually a pretty neat language, why not use it for more than just school?” Well, there are reasons not to do that. Lots of them, actually. That's because Lisp just can't compete with Java in almost any imaginable way. Lisp is not Web-ready First of all, since Lisp has only one data structure—lists—it has no way of representing XML or HTML data. Since XML is the basis of the Web, you cannot provide enterprise-ready web services using Lisp as you can in Java. So what are you going to do with it? Exactly. You might as well stop at this point. Lisp does not support enterprise features In Lisp, there is built-in support for neither SOAP nor CORBA. This alone makes the language impossible to use in an enterprise setting, since there is no way of accessing cloud-computing or multi-tenancy services without being able to encode requests in enterprise-ready cloud communication formats. Lisp is slow You would think that with electrical energy becoming more expensive each day, people cared about efficiency and scalability. Not so—anyone using Lisp is using an interpreted language with huge memory requirements. Also, you can't use Lisp in an interactive application, since garbage collection can kick in at any time and stop your program for a couple of seconds at a time. In contrast, Java and C# programs are compiled into efficient bytecode and run on an advanced, highly optimized virtual machine. Also, specialized CPUs like ARM Jazelle grant Java applications native performance—Lisp just can't compete with this because it is much too complex to implement on the metal. Lisp is too old to be useful Did you know that Lisp is from the 50s? It hasn't changed a bit since then. It's still the same academic parenthesis mess lacking any kind of consistency or reasonable design, and it's still all based on lists. This is in contrast to C# and Java, which are much more modern designs based on real-world experience with enterprise C++ application programming. Lisp does not have any advantages I know, I know, Lisp was innovative for its time. That time is long over, though. Other languages have a GC, other languages have slow interpreters, and other languages have a REPL. Get over it. Lisp is inappropriate for teams Granted, there is one thing that Lisp has which other languages still lack: macros. But really, using macros in production code is a disaster waiting to happen. With functions, you at least know what the evaluation rules are. But what if you call a macro like the following? (with-open-file (file "test.txt" :direction :output) (print "hello" file)) This might open a file called “test.txt” and write “hello” into it—or it might reformat your hard drive! How are you to know? Things like this make Lisp impossible to use in a team setting. Give people too much freedom, and they will do stupid things with it, annihilating any hope of documenting the resulting mess or, God forbid, making it maintainable. Enterprise languages like Java abort compilation even when dead code is detected. This makes debugging much easier. Lisp's features have become obsolete As can be seen in enterprise C++ applications, garbage collection is pretty much an obsolete feature, since data is practically never managed manually within the program. Instead, everything is stored in highly optimized XML databases, which gives you more flexibility and scalability. Other features, like CLOS and the condition system, have similarly become obsolete by advancing technology. Face it: Noone cares about “interactive programming” Then there's this neverending talk about “interactive programming,” as if that was something desirable. In Lisp, you apparently type stuff into the REPL instead of writing it into files. Great! Except... you can't store the code in files that way. Lispers tend to learn their lesson the hard way, as all code is lost when you need to reboot your computer. But then again, noone bears to write Lisp code more than 100 lines long anyway, so it probably doesn't matter much. Tool support is stuck in the '70s Whenever you see a misguided newbie ask on an online forum which IDE they should use for Lisp, the answer is always the same: Emacs. Really. These guys prefer an editor from the 70s over an enterprise-class IDE like Netbeans or Microsoft Visual Studio with innovative features like syntax highlighting and documentation lookup. Masochism is the only valid reason for this, but since you need to be a masochist to program in Lisp in the first place, that's not surprising. Practically all Lispers are Smug Lisp Weenies that are a bitch to deal with Really, the most annoying aspect of Lisp is that its followers are smug weenies. Every single one of them. You can see this on Usenet: Whenever someone writes an objective article about the benefits and disadvantages of Lisp (like this one, for example), the trolls come out and hammer you with flames. How can a community expect to garner support for its cause if it reacts so hostilely to constructive criticism? The fact that so much of the Lisp community is centered around Usenet is a bad sign in and of itself. Do you think that successful companies like Google or Amazon ask Usenet for support? Get a grip on reality here for a moment. Real programmers don't rely on net punks for support. They have learned to buy commercial-grade enterprise support, and so should you. Good luck finding a Lisp support company, though—they've gone extinct around 30 years ago. Lisp is used by noone Because of all of the above, nobody actually uses Lisp for anything that approaches real-world programming. In contrast, lots of people have made real money using Java and .NET. Everyone knows that swimming against the tide is equivalent to doom. Therefore, it would be prudent to do it like the big ones and avoid Lisp like the plague. Noone can read Lisp syntax Finally, just look at the following typical piece of Lisp code: ((lambda([])((lambda(|| |()| |(| |)|)(+ || |(| 1 |)| |()| |(| |(| |(|)) [] [] [] [])) 0) It's true, that's completely valid, real-world code! Can you guess what it does? Yeah, me neither. And did you notice that the parentheses aren't even balanced? Simple syntax—yeah, right. Conclusion You can draw your own conclusions based on the points above. However, before you do that, I advise you to take a close look at this article's publishing date. Happy programming! #### ■_ ### 2011年04月15日 #### ■_ #### ■_ 掛け算 今でもCASLで組めとかいう問題が出たりするのだっけか＞掛け算 code golf - Long multiply, 8 bits at a time - Programming Puzzles & Code Golf - Stack Exchange You are given a 16-bit machine and told to implement multiplication of arbitrary-sized integers. Your registers can only hold 16-bit numbers, and the biggest multiply instruction takes two 8-bit inputs and generates a 16-bit result. あなたは16ビットマシンを与えられ、任意の大きさの整数の乗算を実装するように指示されました。 レジスターは16ビット長の数値しか保持することができず、最も大きな数値を扱える掛け算命令 は二つの8ビットを入力として16ビットの積を得るものです。 Your program must take as input two arbitrary-sized positive numbers and output their product. Each input number is encoded on its own line as a little-endian byte array where each byte is a 2-digit hex number. The output must be similarly formatted. Perhaps best explained with an example: あなたの作るプログラムは、任意の大きさの正の値を二つ入力とし、その積を出力と するものです。入力値は一行に一つずつ、バイトごとに2桁の十六進になっている リトルエンディアンのバイト配列としてエンコードされています。 プログラムの出力は同様のフォーマットでなければなりません。 実際に例を出すのが良いでしょう: input 1f 4a 07 63 a3 output fd 66 03 a7 04 which encodes the multiplication 477727*41827=19981887229. これは 477727*41827=19981887229 をエンコードしたものです。 You can assume that the last (most significant) byte of each input number is nonzero, and the last chunk of the number you output must be nonzero. Both input numbers will be at most 100 bytes long. 各入力の最後(つまり最上位)のバイトはゼロではないことを仮定して良いです。 また、出力する数値の最後の塊 (chunk) はゼロであってはなりません。 いずれの入力も100バイトを超えることはありません。 Smallest code wins. 最短のコードが勝ちです。 Remember, the biggest multiply you are allowed to use is 1 byte * 1 byte, and no integer types bigger than 2 bytes! 忘れてならないのは、あなたが使うことを許されている最大の掛け算は 1バイト×1バイトで、2バイトを越える大きさの整数は使えないということです! Perl, 137 characters ($x,$y)=<>;while($x=~s/.. *//s){$e=hex$&;$i=0;$s=$r[$i]+=$e*hex,$r[$i]&=255,$r[++$i]+=$s>>8 for$y=~/.. */gs;$y="00$y"}printf'%02x 'x@r,@r Caveats * Sometimes prints an extra 00 byte at the end of the result. Of course the result is still correct even with that extra byte. 結果の最後に余計な 00 のバイトが出力されることがあります。 そのような余計なバイトがついている場合でも、もちろん結果は正しいものです。 * Prints an extra space after the last hex byte in the result. 結果の最後の hex byte のあとに余計なスペースが出力されます。 Explanation 説明 The explanation is going to be a bit long, but I think most people here will find it interesting. 説明は少々長くなってしまうのですが、ほとんどの人はここに興味を持つだろうとわたしは 考えています。 First of all, when I was 10 years old, I was taught the following little trick. You can multiply any two positive numbers with this. I will describe this using the example of 13 × 47. You start by writing the first number, 13, and dividing it by 2 (round down each time) until you reach 1: わたしが十歳の頃のことですが、これから説明するような little trick を考えました。 二つの任意の正の数をこのやり方でもって乗算できます。 これを、13×47を例に使って説明します。 最初の数値13を書いて、それを1になるまで2で割り続けます (端数は毎回切り捨てます)。 13 6 3 1 Now, next to the 13 you write the other number, 47, and keep multiplying it by 2 the same number of times: さて、今度はもう一つの数値の47を書きます。そしてそれに2を掛け続けます。 13 47 6 94 3 188 1 376 Now you cross out all the lines where the number on the left is even. In this case, this is only the 6. (I can't do strike-through in code, so I'll just remove it.) Finally, you add all the remaining numbers on the right: 今度は左側の数値が偶数である行をすべて消します。 この例の場合は6の行だけが対象です (コードでは打消しができないので単に取り除くことで対処します)。 最後に、右側の列で残った数字すべてを加算します。 13 47 3 188 1 376 ---- 611 And this is the right answer. 13 × 47 = 611. そしてこれが正しい答えで、13 × 47 = 611 となります。 Now, since you are all computer geeks, you will have realised that what we're actually doing in the left and right columns is x >> 1 and y << 1, respectively. Furthermore, we add the y only if x & 1 == 1. This translates directly into an algorithm, which I'll write here in pseudocode: さて、皆さんはコンピューターギークなのですから、 input x, y result = 0 while x > 0: if x & 1 == 1: result = result + y x = x >> 1 y = y << 1 print result We can re-write the if to use a multiplication, and then we can easily change this so that it works on a byte-by-byte basis instead of bit-by-bit: input x, y result = 0 while x > 0: result = result + (y * (x & 255)) x = x >> 8 y = y << 8 print result This still contains a multiplication with y, which is arbitrary-size, so we need to change that into a loop too. We'll do that in Perl. Now translate everything to Perl: さてこれをPerlに変換します: *$x and $y are the inputs in hex format, so they have the least significant byte first. * Thus, instead of x >> 8 I do$x =~ s/.. *//s. I need the space+star because the
last byte might not have a space on it (could use space+? too). This automatically puts
the removed byte (x & 255) into $&. * y << 8 is simply$y = "00$y". * The result is actually a numerical array, @r. At the end, each element of @r contains one byte of the answer, but halfway through the calculation it may contain more than one byte. I'll prove to you below that each value is never more than two bytes (16 bits) and that the result is always one byte at the end. So here is the Perl code unravelled and commented: # Input x and y ($x, $y) = <>; # Do the equivalent of$& = x & 255, x = x >> 8
while ($x =~ s/.. *//s) { # Let e = x & 255$e = hex $&; # For every byte in y... (notice this sets$_ to each byte)
$i = 0; for ($y =~ /.. */gs)
{
# Do the multiplication of two single-byte values.
$s =$r[$i] +=$e*hex,
# Truncate the value in $r[$i] to one byte. The rest of it is still in $s$r[$i] &= 255, # Move to the next array item and add the carry there.$r[++$i] +=$s >> 8
}
# Do the equivalent of y = y << 8
$y = "00$y"
}
# Output the result in hex format.
printf '%02x ' x @r, @r
This concludes a wonderful and exciting challenge. Thanks a lot for posting it!
OCaml + Batteries, 362 characters
A standard O(n*m) schoolboy multiplication algorithm. Note that in order to meet the
challenge requirements, the operations are done on the bytes of strings, which in
OCaml are (conveniently, in this case) mutable. Note also that the accumulator s never
overflows 16 bits, since 2(2^8 - 1) + (2^8 - 1)^2 = (2^8 - 1)(2^8 + 1) = 2^16 - 1.
let(@)=List.map
let m a b=Char.(String.(let e s=of_list(((^)"0x"|-to_int|-chr)@nsplit s" ")in
let a,b=e a,e b in let m,n=length a,length b in let c=make(m+n)'\000'in
iteri(fun i d->let s,x=ref 0,code d in iteri(fun j e->let y=code e in
s:=!s+code c.[i+j]+x*y;c.[i+j]<-chr(!s mod
256);s:=!s/256)b;c.[i+n]<-chr!s)a;join" "((code|-Printf.sprintf"%02x")@to_list c)))
For example,
# m "1f 4a 07" "63 a3" ;;
- : string = "fd 66 03 a7 04"
# m "ff ff ff ff" "ff ff ff ff" ;;
- : string = "01 00 00 00 fe ff ff ff"
C Solution
This solution does no input validation. It's also only lightly tested. Speed was not
really a consideration. Malloc's memory, and isn't particularly clever about how much
it grabs. Guaranteed to be enough, and more than necessary.
この解答では入力の検査をしていません。また、テストも簡単にしか行っていません。
m() accepts a string, expects two newlines in the string, one after each number.
Expects only numbers, lowercase characters, spaces, and newlines. Expects hex digits
to always be a pair.
No multiply operation is ever used (knowingly). Shifting is performed on 8-bit
variables. One 16-bit addition is performed. No 32-bit data types.
Shrunk by hand, and only mildly. edit: more obfuscation, fewer chars :D Compiles with
warnings with gcc.
Characters: 675
typedef unsigned char u8;
#define x calloc
#define f for
#define l p++
#define E *p>57?*p-87:*p-48
#define g(a) --i;--a;continue
void m(u8*d){short n=0,m=0,a,b,i,k,s;u8*t,*q,*r,*p=d,o;f(;*p!=10;n++,l){}l;f(;*p
!=10;m++,l){}t=x(n,1);q=x(m,1);r=x(n,1);p=d;a=n;i=0;f(;*p!=10;i++,l){if(*p==32){
g(a);}t[i]=E;t[i]<<=4;l;t[i]|=E;}a/=2;b=m;i=0;l;f(;*p!=10;i++,l){if(*p==32){g(b)
;}q[i]=E;q[i]<<=4;l;q[i]|=E;}b/=2;f(k=0;k<8*b;k++){if(q[0]&1){o=0;f(i=0;i<n;i++)
{s=o+t[i]+r[i];o=s>>8;r[i]=s&255;}}f(i=n;i;i--){o=t[i-1]>>7&1;t[i-1]*=2;if(i!=n)
t[i]|=o;}f(i=0;i<m;i++){o=q[i]&1;q[i]/=2;if(i)q[i-1]|=(o<<7);}}k=(r[a+b-1]==0)?a
+b-1:b+a;f(i=0;i<k;i++){printf("%02x ",r[i]);}putchar(10);}
You can test with this:
int main(void){
m("1f 4a 07\n63 a3\n");
m("ff ff ff ff\nff ff ff ff\n");
m("10 20 30 40\n50 60 70\n");
m("01 02 03 04 05 06\n01 01 01\n");
m("00 00 00 00 00 00 00 00 00 00 00 00 01\n00 00 00 00 00 00 00 00 02\n");
return 0;
}
Result:
$./long fd 66 03 a7 04 01 00 00 00 fe ff ff ff 00 05 10 22 34 2d 1c 01 03 06 09 0c 0f 0b 06 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 02 全部訳をつけるのはちとしんどかった(のでやってない)。 #### ■_ 電卓プログラム つーことでいいのだよね、このお題。 数値リテラルの正規表現 | OKWave VB6でMicrosoft Script ControlとMicrosoft VBScript Regular Expressions 5.5を使っています。 Script Controlに入力するVBScript文字列において 数値リテラルを抽出して、ある関数を通した値に置換したいです。 ただし、文字列リテラル内の数値は除く必要があります。 置換例 (1.234 * -.324e+34) & "5,678" & (6.553 / 2.456) & "abc9.876def" ↓ (SomeFunc("1.234") & SomeFunc("-.324e+34")) & ("5,678") & (SomeFunc("6.553") / SomeFunc("2.456")) & "abc9.876def" 具体的には計算機のようなプログラムを作っています。 SomeFuncはVBのCDecをラップしたものです(ただし、Decimalでオーバー・アンダーフロー・桁落ちしたら変換しない)。 数値リテラルが入力されたら、文字列リテラルにしてからCDecに渡すことで、Double以上の桁数で計算させたいです。 文字列リテラル内の数値を除いた、数値リテラルに該当する正規表現を教えていただけないでしょうか。 正規表現の使い方を間違っているような… もちろん、対象を取り出すのに使うのはいいんだけど トークン列を切り出す形で解析したほうがいいと思うのだけど。 あー、まてよ。入力は一回だけ読むのではなくて変換しながら何度も読むようにすればできなくはないか? #### ■_ #### ■_ ブートストラップ reddit に投げられていた質問。 A question about pypy : Python I'm not exactly a Python noob but I haven't used it in a while and I have zero experience with hacking Python, writing modules in C, really doing much of anything with C. So my question: I know that pypy is implemented in Python and I understand what the goals of the project are. What I get tripped up over is the "Python implemented in Python" bit. Does this mean that it's Python implemented in pure CPython? It would seem like it would have to be (OK, it could be implemented in Iron Python or Jython I guess). This is sort of a prime mover problem - Python can't just run on its own i.e. it's not machine code. On the pypy Wikipedia page, it discusses the interpreter and translator which pypy is built upon but this just sounds like regular CPython to me. I don't see how the interpreter could be implemented in pure Python (I don't think it is). In other words, I feel like pypy is just using a different interpreter than CPython and isn't all that different. If anyone can explain this to me, I'd appreciate it. EDIT: thanks for all of the replies, I think I get it now. pypy はPython 処理系を Python で実装しようというものだというのなら、 その最初の処理系は…という話。たぶん。 まあ最初のコンパイラーはどうやって、的な話ですね。 ### 2011年04月14日 #### ■_ グラゼニが週刊連載かあ。 #### ■_ R なんとかビルドには成功。 なぜか途中で /tmp でディレクトリを掘れないといって ビルドが中断しちゃう現象がでてたんだけど share/make/basepkg.mk mkR: @$(MKINSTALLDIRS) $(top_builddir)/library/$(pkg)/R
@(f=$${TMPDIR:-/tmp}/R$$$$; \ if test "(R_KEEP_PKG_SOURCE)" = "yes"; then \ (ECHO) > "$${f}"; \
for rsrc in $(RSRC); do \$(ECHO) "#line 1 \"$${rsrc}\"" >> "$${f}"; \
cat $${rsrc} >> "$${f}"; \
done; \
else \
cat $(RSRC) > "$${f}"; \ fi; \ (SHELL) (top_srcdir)/tools/move-if-change "$${f}" all.R) 環境変数 TMPDIR を適当に設定してやったらビルドが通るようになった。 Vista以降だと、ルートに一時ファイル作ったりが(Administratorあたりでないと) できなくなってるけどこの現象はなんだろう。 が、まだライブラリが足りなかったりするのかオプション指定が悪いのか 日本語メッセージがでてこない(笑) #### ■_ プログラミング言語を作るには 回答は見てのお楽しみ(最近こればっか) Questions on the making of programming lanuages. - Stack Overflow I'm new to programming.. But I would like to know how programming languages begin; I'm a Windows os user, and everything seems so vast. So, my question is, how do programmers get from that blank screen, to building their own programming language. Also, are many new languages made? And are any made home-brewed? #### ■_ Red Hat発の新言語とか。 スライドから適当に抜き出し。 Introducing the Ceylon Project About this session I'm going to talk about why we started work on this project I'm going to cover some basic examples at a very shallow level I'm not going to get into the details of the type system If you're interested, come to my second presentation: “The Ceylon Language” This project is not yet available to the public and has not even been officially announced QCon China is getting a special sneak preview - the first time I'm talking about the project in public! Why we're (still) fans of Java (Javaのどこがいいと思っているのか) Java was the first language to feature the following “perfect” combination of features: Java は以下のような“完全な”機能の組み合わせを持つ最初の言語でした virtual machine execution, giving platform independence automatic memory management and safe referencing static typing lexical scoping readable syntax Therefore, Java was the first language truly suitable for large team development, and large-scale deployments of multi-user applications. したがって、Java は大規模チームによる開発や マルチユーザーアプリケーションの大規模開発 に対して真に suitable である最初の言語であったのです It turns out that large teams developing multi-user applications describes the most interesting class of project in business computing Why we're frustrated (何を不満に感じているのか) After ten often-frustrating years developing frameworks for Java, we simply can't go any further without a better solution for defining structured data and user interfaces Java is joined at the hip with XML, and this hurts almost every Java developer almost every day There is simply no good way to define a user interface in Java, and that is a language problem Java にはユーザーインターフェースを定義する単純で優れた方法がありません Lack of a language-level modularity solution resulted in the creation of monstrous, over-complex, harmful technologies like Maven and OSGi. 言語レベルのモジュール化のソリューションが欠如していることにより Maven や OSGi のような巨大で複雑極まりない有害な技術を生み出すことになりました Instead of modules, Java has multiple platforms, which has divided the developer community Lack of support for first-class and higher-order functions results in much unnecessary verbosity in everyday code 関数が first-class でないことや高階関数が欠如していることはその結果として 日々のコードを不必要に冗長にしてしまっています Meta-programming in Java is clumsy and frustrating, reducing the quality of framework and other generic code Java におけるメタプログラミングは不恰好で不満が残るものであり、フレームワークや そのほかのコード生成における質を劣化させてしまっています 抜いた部分も結構面白いので一読をオススメ。 Scala や Clojure とかと比べてどうなんだろか(JVM上の言語というあたりで)。 #### ■_ ### 2011年04月13日 #### ■_ JavaScript「に」コンパイル(変換)する言語ってのを見ていると、 Guile の初めの頃の Stallman の言っていたアイデアもそれほど捨てたもんじゃなかったのかなあ などと思ったり。 #### ■_ 今日のお題 OKWaveから。 grepでの抽出箇所のみ置換して上書き | OKWave 例えば find ./ -name file_name -exec grep -B 2 "earth" {} \; -print | grep "moon" というコマンドを実施し、出力が planetkind moon だったとします。 このfile_nameファイルの一部にある 『 planetkind moon』 という箇所を 『 planetkind taiyo』 に変更したいのですが、 find ./ -name file_name -exec grep -B 2 "earth" {} \; -print | grep "moon" | xargs sed -i "s/moon/taiyo/" とすると、ファイル中の全てのmoonがtaiyoになってしましまいます。 このgrepでの抽出箇所のみ置換して元ファイルを上書きする方法は有りますか？ 以上、宜しくお願いいたします。 ANo.1 そりゃそうだ. sed "s/moon/taiyo/" って, 「moon を taiyo に置き換える」ってことでしょ? 「planetkind moon」を「planetkind taiyo」に変更するなら, そのように書かないと. 補足 言葉が足らずすみません。 質問はearthという文言が存在する行の2行上にある planetkind moon を planetkind taiyoに変えたいのです。 他の行にもplanetkind moonという行は存在するのです。 Perl あたりで書けばいいような…。 #### ■_ やっぱりお金の話だと伸びますねー The Programmer Salary Taboo : programming The Programmer Salary Taboo The Programmer Salary Taboo 2011-04-12 Salary is an interesting topic. It's certainly one everyone has an opinion on. It's also a uniquely taboo subject among members of the working public. Since I'm about a month away from being done with University and entering the programmer workforce, I've taken to asking my classmates what type of starting salaries they're getting at their first jobs. The first thing I discovered is that not everybody is very comfortable with this question, and many companies are even less so. Microsoft requests very firmly that recipients of their offers keep their salary offers confidential, for example. それにつけても以下略 #### ■_ 空中リプライはもう無視することにしよう(謎 ### 2011年04月12日 #### ■_ 落し物したらしい ○|￣|＿ #### ■_ 電卓 知恵袋から。 将来プログラマーになりたいんですけど、電卓くらいのプログラムは、つくれるよう... - Yahoo!知恵袋 将来プログラマーになりたいんですけど、電卓くらいのプログラムは、つくれるようになれるよ うな説明がかいてあるサイトをさがしてます。 (略) yacc やら bison のマニュアルでもいいんだろうかw #### ■_ このスクリプトは ないわー awkを使用して整形 | OKWave awkを使用してデータを整形しようとしているのですが うまくいきません・・・ 元データは 10:00:00 disk1 10 disk2 15 disk4 14 10:00:05 disk1 13 disk3 20 10:00:10 disk1 30 の様になっており整形後は 10:00:00 disk1 10 10:00:00 disk2 15 10:00:00 disk3 0 10:00:00 disk4 14 10:00:05 disk1 13 10:00:05 disk2 0 10:00:05 disk3 20 10:00:05 disk4 0 10:00:10 disk1 30 10:00:10 disk2 0 10:00:10 disk3 0 10:00:10 disk4 0 の様に2列目の項目数がdisk1～4まで不足部分が埋まるようにし 不足していた部分の1列目には時間、3列目には0で埋めたいとおもっています。 数万行を処理する必要があり、手作業では不可能なのですが awkの知識が乏しく実現出来かねている次第です。 どなたかご教示頂けると助かります。よろしくお願いします。 1回じゃ難しいですね。2回に分けてみました。 cat data.txt | awk \ 'BEGIN { strTIME="00:00:00" } { num=split($0,ARY," ")
if (num==3) {
strTIME=ARY[1]
printf("%s %s %s\n",strTIME,ARY[2],ARY[3])
}
if (num==2) {
printf("%s %s %s\n",strTIME,ARY[1],ARY[2])
}
}
END { }' | awk \
'BEGIN { strTIME="" }
{
if (strTIME!="" && strTIME!=$1) { for (i=1;i<5;i++) { strDISK="disk" i if (strDATA[strDISK]=="") strDATA[strDISK]="0" printf("%s disk%d %s\n",strTIME,i,strDATA[strDISK]) strDATA[strDISK]="" } } strTIME=$1
strDATA[$2]=$3
}
END {
for (i=1;i<5;i++) {
strDISK="disk" i
if (strDATA[strDISK]=="") strDATA[strDISK]="0"
printf("%s disk%d %s\n",strTIME,i,strDATA[strDISK])
strDATA[strDISK]=""
}
}'
ディスク番号の最大値を求めるために二回読みをしてるのかと思ったらそうじゃないし。
フォーマットの仕様が明確でないところがあるけど
BEGIN {
prevtime = time = "00:00:00"
diskmax = 4
prev = 0
}
NF == 3{
prevtime = time
time = $1 } { number = disk =$(NF-1)
count = $NF sub(/^[^0-9]*/, "", number) sub(/[0-9]*$/, "", disk)
#print "number=", number, "prev=", prev
if (number <= prev) {
for (i=prev+1; i<=diskmax; i++)
print prevtime, (disk i), 0
}
else if (number > prev+1) {
for (i=prev+1; i<number; i++)
print time, (disk i), 0
}
print time, (disk number), count
prev = number
if (prev == diskmax)
prev = 0
}
END {
for (i=prev+1; i<=diskmax; i++)
print time, (disk i), 0
}
こんなんとか。
#### ■_ それは土曜日の読書会で散々見た…
shiro さんのところの4/11づけのものから。本文はおいといて
Island Life - グラフ指向理解
Γ, x:T1 ⊢ t2 : T2
------------------------
Γ ⊢ λx:T1.t2 : T1 → T2
#### ■_ あとで読む
What is the PDP-8 instruction set?
The PDP-8 word size is 12 bits, and the basic memory is 4K words. The
minimal CPU contained the following registers:
PC - the program counter, 12 bits.
AC - the accumulator, 12 bits.
L - the link, 1 bit, commonly prefixed to AC as <L,AC>.
It is worth noting that many operations such as procedure linkage and
indexing, which are usually thought of as involving registers, are done
with memory on the PDP-8 family.
Instruction words are organized as follows:
(略)
Last Update February 04 2011 @ 07:23 AM
#### ■_
Category Theory for the Java Programmer ≪ reperiendi
Category Theory for the Java Programmer
(Javaプログラマーのための圏論)
4. Cartesian
カルデシアン
A cartesian category has lists as its objects. It has a way to put objects together
into ordered pairs, a way to copy objects, and an object that's “the empty” object.
カルデシアン圏はそのオブジェクトとしてリストを持っています。
カルデシアン圏は複数のオブジェクトを orderd pair に押し込む手段と、
オブジェクトをコピーする手段、それと“空”のオブジェクトとを持っています。
It's time to do the magic! Recall the interface Category:
さあ手品の時間です!
Category インターフェースを思い出してみましょう:
interface Category {
interface Object {}
interface Morphism {}
class IllegalCompositionError extends Error;
Object source(Morphism);
Object target(Morphism);
Morphism identity(Object);
Morphism compose(Morphism, Morphism)
throws IllegalCompositionError;
};
Now let's change some names:
ここで一部の名前を変えてみましょう:
interface Interface {
interface InternalInterfaceList {}
interface ComposableMethodList {}
class IllegalCompositionError extends Error;
InternalInterfaceList source(ComposableMethodList);
InternalInterfaceList target(ComposableMethodList);
ComposableMethodList identity(InternalInterfaceList);
ComposableMethodList compose(ComposableMethodList,
ComposableMethodList)
throws IllegalCompositionError;
}
Category theory uses cartesian categories to describe structure; Java uses interfaces.
Whenever you see “cartesian category,” you can think “interface.” They're pretty
much the same thing. Practically, that means that a lot of the drudgery of implementing
the Category interface is taken care of by the Java compiler.
を使います。“カルデシアン圏”を見たときはいつでも“インターフェース”と置き換えて考え
てよいです。これらはとてもよく似ているもの同士です。現実には、Category interface を実
For example, recall the directed graph G above. We can get effectively the same
implementation of the graph by using this interface:
たとえば、前述した有効グラフ G を考えてみましょう。以下のインターフェースを使ってグラ
フの同一実装 (same implementation) を効率的に得られます:
interface G {
interface A;
interface B;
interface C;
B f(A);
C g(B);
C h(A);
}
That's it! We're considering the free category on G, so there are no tests. We can
compose lists of methods: g(f(a)). The compiler will give us an error if we try to
compose methods whose source and target don't match: h(g(b)) doesn't work.
G の free category を対象としているので、テストはありません。g(f(a)) のようにメソッド
のリストを合成できます。コンパイラーはソースとターゲットがマッチしないメソッドを合成し
ようとしたときにはエラーを報告するでしょう。h(g(b)) は doesn't work です。
Because the objects of the cartesian category Interface are lists, we can define
methods in our interfaces that have multiple inputs.
カルデシアン圏インターフェースのオブジェクトはリストなので、複数の入力を持つインタフェ
ースでメソッドを定義できます。
interface Monoid {
interface M;
M x(M, M);
M e();
}
void testX(M a, M b, M c) {
assertEqual(x(a, x(b, c)),
x(x(a, b), c));
}
void testE(M a) {
assertEqual(a, x(a, e()));
assertEqual(a, x(e(), a));
}
Here, the method x takes a two-element list as input, while e takes an empty list.
ここで、メソッド x はその入力として二要素のリストを受け取りますが、e は空リストをとります。
Exercise: figure out how this definition of a monoid relates to the one I gave earlier.
モノイドのこの定義がどのように一つ前に与えたそれと関係するか述べよ。
Implementation as a functor
Cartesian categories (interfaces) provide the syntax for defining data structures. The
meaning, or semantics, of Java syntax comes from implementing an interface.
カルデシアン圏 (インターフェース) はデータ構造を定義する構文を与え (provide) ます。
Java の構文の meaning 、あるいは semantics といったものは
インターフェースから来るものです。
In category theory, functors give meaning to syntax. Functors go between categories
like functions go between sets. A functor F:C \to D
* maps objects of C to objects of D and
C のオブジェクトを D のオブジェクトに map し
* maps morphisms of C to morphisms of D such that
C の morphisms を D の morphisms に map する
* identities and composition are preserved.
There are several layers of functors involved in implementing a typical Java program.
First there's the implementation of the interface in Java as a class that defines
everything in terms of the built-in classes and their methods; next, there's the
implementation of the built-in methods in the Java VM, then implementation of the
bytecodes as native code on the machine, and finally, physical implementation of the
machine in silicon and electrons. The composite of all these functors is supposed to
behave like a single functor into {\rm Set}, the category whose objects are sets and
whose morphisms are functions between sets. We end up approximating many of these sets:
instead of integers, we use ints and hope that they don't overflow. Instead of real
numbers, we use doubles and are surprised when we lose precision. In category theory,
we ignore this and say that in any practical application, we'll use datatypes that are
“big enough.”
ターフェースを使った実装があります。次に Java VM の組み込みメソッドを使った実装があり、
(the machine in silicon and electrons での) 物理的な実装があります。
これらの関手すべての composite は {\rm Set} への単一の関手のように振る舞うことが仮定されます。
We end up approximating many of these sets:
わたしたちは結局のところ多くのこういった集合の
すべてのアプリケーションにおいて“big enough”なデータ型を使うだろうと主張しています。
The upshot of all this is that a Java class F implementing an interface X can be
thought of as a functor F:X \to {\rm Set}. The class definition assigns to each inner
interface a set of values and to each method a function mapping between those sets.
The upshot of all this はインターフェース X を実装している関手 F:X \to {\rm Set} とみ
なせる Java のクラス Fです。このクラス定義では各 inner インターフェースを値の集合に
assign し、また、各メソッドをそれらの集合の間の function mapping に assign しています。
Here's an example of three different classes that implement the Monoid interface from
the last subsection. Recall that a monoid is a set of things that we can combine; we
can add two integers to get an integer, multiply two doubles to get a double, or
concatenate two strings to get a string. The combining operation is associative and
there's a special element that has no effect when you combine it with something else:
adding zero, multiplying by 1.0, or concatenating the empty string all do nothing.
Here's an example of three different classes
that implement the Monoid interface from the last subsection.
モノイドは結合可能なものの集合であることを思い出してください。
あるいは二つの double を乗じて一つの double にしたり
なにかと結合したときに何の効果も持たないような特別な要素が存在します。
So, for example,
enum Bit implements M { Zero, One }
M x(M f, M g) {
if (f == e()) return g; // 0+g=g
if (g == e()) return f; // f+0=f
return Zero; // 1+1=0
}
M e() { return Zero; }
}
Here, the functor {\rm AddBits}:{\rm Monoid} \to {\rm Set} assigned the set \{0, 1\}
to the object M, assigned the function XOR to the morphism x, and assigned the
constant function returning {0} to the morphism e.
ここで、関手 {\rm AddBits}:{\rm Monoid} \to {\rm Set} は
オブジェクト M に集合 \{0, 1\} を assign し、
XOR 関数を morphism x に
{0} を返す constant fucntion を morphism e に assign しています。
class MultiplyBits implements Monoid {
enum Bit implements M { Zero, One }
M x(M f, M g) {
if (f == e()) return g; // 1*g=g
if (g == e()) return f; // f*1=f
return Zero; // 0*0=0
}
M e() { return One; }
}
Here, the functor {\rm MultiplyBits}:{\rm Monoid} \to {\rm Set} assigned to M the same set
as before, \{0, 1\}, but assigned the function AND to the morphism x and the constant
function returning 1 to the morphism e.
ここで関手 {\rm MultiplyBits}:{\rm Monoid} \to {\rm Set} は M に対して前のものと同じ
1 を返す constant function を e に assign しています。
class Concatenate implements Monoid {
class ConcatString implements M {
ConcatString(String x) {
this.x = x;
}
String x;
}
M x(M f, M g) {
return new ConcatString(
f.x + g.x);
}
M e() {
return new ConcatString("");
}
}
Here, the functor {\rm Concatenate}:{\rm Monoid} \to {\rm Set} assigned the set of
strings to M, assigned the string concatenation function to the morphism x and the
constant function returning the empty string to the morphism e.
ここでは関手 {\rm Concatenate}:{\rm Monoid} \to {\rm Set} は
5. Equalizers
### 2011年04月11日
#### ■_
あららー。 2011-04-11 - みねこあ 予想通りというかなんというか。 お部屋が.....。 こんなのってないよ。もう何も片さない...orz
#### ■_ Top 13 Most Absurd Programming Languages
Top 13 Most Absurd Programming Languages | Top Design Magazine - Web Design and Digital Content
Top 13 Most Absurd Programming Languages
An esoteric programming language (sometimes shortened to esolang) is a programming
language designed as a test of the boundaries of computer programming language design,
as a proof of concept, or as a joke. There is usually no intention of the language
being adopted for mainstream programming, although some esoteric features such as
visuospatial syntax have inspired practical applications in the arts. Such languages
are often popular among hackers and hobbyists. This use of esoteric is meant to
distinguish these languages from more popular programming languages.
I'm a programmer, I know my way through many languages from ASM and all the way to PHP.
Learning a new programming language takes a lot of time and effort, but making a new
one takes even more. Yeah, I do have a good sense of humor but why in the name of
Pascal would you waste your time inventing something like Brainfuck or ZOMBIE? Anyway,
at least they make us laugh. In this article you will see the most absurd, useless and
hilarious 13 esoteric programming language that I know.
1. Lolcode
Lolcode was inspired by the language expressed in examples of the lolcat Internet meme.
The language was created in 2007 by Adam Lindsay, researcher at the Computing
Department of Lancaster University.
“Hello World” example:
HAI
CAN HAS STDIO?
VISIBLE “HAI WORLD!”
KTHXBYE
2.Befunge
Befunge and its ilk allow the instruction pointer to roam in multiple dimensions
through the code. For example the following program displays “Hello World” by
pushing the characters in reverse order onto the stack, then printing the characters
in a loop which circulates clockwise through the instructions [>], [:], [v], [_],
[,], and [^].
“Hello World” example:
"dlroW olleH">:v
^,_@
3. Brainfuck
Brainfuck is designed for extreme minimalism and leads to obfuscated code, with
programs containing only 8 distinct characters.
“Hello World” example:
++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++
..+++.>++.<<+++++++++++++++.>.+++.------.--------.>+.>.
© 2010 topdesignmag.com some rights reserved.
4位以下は元記事を見てのお楽しみ。
で、reddit での反応
Top 13 Most Absurd Programming Languages : programming
I don't see Ruby listed.
I don't see Perl listed.
The only fault I have with Perl is it is a patch work of bubblegum and duct tape. They
really should have started it over at a few points in time, but given people's
investment they weren't willing.
no.14 -> C++
* Java
* COBOL
* "XML"
* "UML"
* VBA
* PHP
* C++
* APL
* Prolog
* Bash
* Javascript
* SQL
* Perl
Why bash?
RESULT=$($FUNCTION "$@" "$(echo "$URL" | strip)") || DRETVAL=$?
looks great to me.
C# ?
リンクはご自由にどうぞ
メールの宛先はこちら
|
2021-11-27 07:54:04
|
{"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": 0.3733902871608734, "perplexity": 10099.839612603626}, "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/1637964358153.33/warc/CC-MAIN-20211127073536-20211127103536-00273.warc.gz"}
|
http://www.scienceforums.com/topic/22710-an-interesting-fractal-formula/
|
# An Interesting (fractal) Formula
6 replies to this topic
### #1 Kharakov
Kharakov
Thinking
• Members
• 114 posts
Posted 09 November 2010 - 04:22 PM
It's a pretty straight forward rotation based fractal formula, but I really enjoy the complex patterns it generates (images follow):
victor=complex(sx,sqrt(sqr(sy)+sqr(sz))); // complex (x,y) creates a complex variable with
bravo=complex(sqrt(sqr(sx)+sqr(sy)),sz); // the x component corresponding to the real component
cramden=complex(sx,sy); // and the y being the imaginary component
r1=cabs(cramden)^-n; // cabs(XXX) calculates the magnitude of a number (complex, quaternion, or real)
victor=victor^n;
bravo=bravo^n;
cramden=cramden^n;
nx=part_r(victor); // you might notice that I switched the new y and z components
ny=-abs(part_i(bravo));
nz=-abs(part_r(bravo)*part_i(cramden))*r1;
add in pixel or julia components (use + absolute value for the y and z components unless you want a really weird distorted fractal)
Here are a couple z^2 to start:
Click fer a bigger image:
Yup, I said fer.
This is the above image, prior to zoom in, etc.
Different part of the fractal:
Then the kicker, the z^6 has some nice organic stuff in it (like brambles or somethin'):
And it (the z^6) has the tower stuff, but it's a bit more organic in sections:
As with all fractals, this one can be explored. Not really too familiar with it as of yet, as it's 3d and takes a bit of time to calculate on my computer. Eventually these 3d fractals will be as quick to calculate as 2d fractals are today... but that's the future...
### #2 Pyrotex
Pyrotex
• Members
• 5701 posts
Posted 09 November 2010 - 04:33 PM
It's a pretty straight forward rotation based fractal formula, but I really enjoy the complex patterns it generates (images follow)...
I'm totally impressed. Nice images.
However, I was unable to follow the code you provided. there were undeclared variables, and I saw no loop structure over the domain of the images.
### #3 Kharakov
Kharakov
Thinking
• Members
• 114 posts
Posted 09 November 2010 - 08:53 PM
I'm totally impressed. Nice images.
However, I was unable to follow the code you provided. there were undeclared variables, and I saw no loop structure over the domain of the images.
Durp... Apologies. Let me explain my formula, and ChaosPro's syntax a little better.
First of all, what I posted above is basically one iteration (one loop), WITHOUT pixel additions. I generally initialize sx,sy,sz to whatever seed values I want (0,0,0 usually) prior to the first iteration, adding in pixel values at the end of each iteration.
sx,sy,sz,nx,ny,nz are reals, they are like an extended double float, being 80 bit precision (14 bit exponent and 64 bit mantissa) rather than 64 bit
victor, bravo, and cramden are complex numbers with each component having the same precision as the reals (I use complex numbers instead of trigonometric functions because they are quicker, and I like them... remind me of 2d Mandelbrot)
victor= complex (1 , 2) sets the complex variable victor to 1 + 2i
bravo = complex (3 , 7) sets bravo = 3 + 7i
....
sx = starting x value of iteration
sy = starting y value...
sz = starting z..
nx = new x value prior to addition of pixel component (pixel for Mandelbrot type, Julia seed value for Julia type)
ny = new y value... // Add in pixel components for Mandelbrot type fractals
nz = new z.... // use absolute value of the y and z pixel components for a more uniform fractal (it's just nicer)
part_r (complex number) = real part of the complex number
part_i (complex number) = imaginary part...
cabs (complex number) = magnitude of the complex number
number^n = number raised to the nth power (for complex, real, or otherwise)
I suppose it's time to clean up my code yet again and post to ChaosPro's database. I've also a few coloring algorithms that bring out the structure of the fractal (or at least portions of it) nicely.
### #4 Kharakov
Kharakov
Thinking
• Members
• 114 posts
Posted 12 November 2010 - 12:42 AM
Here is a nice z^8 julia of this type (click to enlarge):
### #5 Don Blazys
Don Blazys
Questioning
• Members
• 439 posts
Posted 12 November 2010 - 03:38 AM
Most impressive indeed!
That last one looks like some kind of wierd alien wearing a crown.
I wonder if he lives in one of those buildings above it?
Don.
Understanding
• Members
• 1235 posts
Posted 12 November 2010 - 08:32 AM
Question: Why did you decide to use these criteria ?
victor= complex (1 , 2) sets the complex variable victor to 1 + 2i
bravo = complex (3 , 7) sets bravo = 3 + 7i
Did you try other possibilities ? And, why use "i" ?
### #7 Kharakov
Kharakov
Thinking
• Members
• 114 posts
Posted 12 November 2010 - 08:28 PM
Thanks Don, the whole fricken fractal is weird... I'm thinking its intricate structure could be used for gaming, especially using various julias as game worlds with complicated structures.
Rade- Complex numbers are pretty interesting, I'd check out the wikis on the Mandelbrot Set, and complex numbers, and imaginary numbers.
"i" signifies the imaginary unit.
|
2017-11-20 00:32:57
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5341054797172546, "perplexity": 3137.646161398193}, "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/1510934805881.65/warc/CC-MAIN-20171119234824-20171120014824-00629.warc.gz"}
|
http://mathoverflow.net/questions/87556/soft-sheaves-on-indiscrete-paracompact-spaces
|
# Soft sheaves on indiscrete paracompact spaces
Let $X$ be some space, I have basically 2 questions:
1 - Are sheaves on paracompact but not Hausdorff spaces acyclic? I've been doing some reading and some authors say that soft sheaves on paracompact spaces are acyclic, but a lot of people require for paracompact spaces to be Hausdorff too, so I don't know if this works on non-Hausdorff paracompact spaces, and...
2 - In case soft sheaves are acyclic on non-Hausdorff paracompact spaces. Why don't I define the trivial topology on $X$? (Spaces with the trivial topology are paracompact) That way aren't all the sections in the sheaf trivially global sections? I know it's kind of dumb but wouldn't that automatically make the sheaves soft?
-
Richard -- what is a paracompact but non-Hausdorff space? – algori Feb 5 '12 at 2:47
Well I was doing some reading and a space with the trivial topology is not Hausdorff, but is paracompact, hence the question, I read that some people require that paracompact spaces be Hausdorff, but some don't, so what gives? @algori – Richard Jennings Feb 5 '12 at 2:57
Richard -- the Hausdorff condition is usually part of the definition of a paracompact space. If you want to use a different version, that's fine, but then could you please specify the definition you are using. – algori Feb 5 '12 at 3:11
Here's a shot at question 2, assuming by "trivial topology" you mean the indiscrete topology. In that case, you only have one (non-empty) open set, so you're right that all sections are global sections. But that means that a sheaf is no different from a group (which you assign to the non-empty open set). In this way, the sheaf theory is just the same as the sheaf theory over a point. And then indeed every sheaf is soft and acyclic. But I don't see how this would relate back to every other non-Hausdorff paracompact space, whatever we all decide they should be. – Greg Friedman Feb 5 '12 at 3:32
@Greg Friedman Can you elaborate more on what you're saying? I'm studying up on this and still learning, thanks – Richard Jennings Mar 2 '12 at 20:18
|
2015-03-06 16:29:19
|
{"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": 0.9144335389137268, "perplexity": 461.6744089528653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936469077.97/warc/CC-MAIN-20150226074109-00164-ip-10-28-5-156.ec2.internal.warc.gz"}
|
https://www.wikiformulas.com/en/area/area-of-a-decagon
|
Areas Index
# Area of a Decagon Formulas & Calculator
The area of a decagon can be calculated using the following formula: if you know the perimeter and the apothem.
## Formula Knowing the Perimeter and the Area
If you know the length of the perimeter in a decagon and the apothem, you can calculate its area using the following formula:
$$"area" = (p * a)/2$$
Perimeter and Apothem Length
Area result
Copia y pega el siguiente código en el HTML de tu página web para mostrar ahí esta fórmula y su calculadora.
Nuestras calculadoras son gratuitas y compatibles con móviles. Al copiarlas a tu sitio acuerdas dar attribución a "© WikiFormulas.com". Vincular de regreso es opcional pero bienvenido. ¡Gracias!
### Where:
$$p = "perimeter value"$$
$$a = "apothem: distance from the center to the closest point in the figure"$$
## Clearing the Apothem
If you know the length of the perimeter in a decagon and the area, you can calculate its apothem using the following formula:
$$"apothem" = (2a)/p$$
Perimeter and Area Length
Apothem result
Copia y pega el siguiente código en el HTML de tu página web para mostrar ahí esta fórmula y su calculadora.
Nuestras calculadoras son gratuitas y compatibles con móviles. Al copiarlas a tu sitio acuerdas dar attribución a "© WikiFormulas.com". Vincular de regreso es opcional pero bienvenido. ¡Gracias!
### Where:
$$p = "perimeter value"$$
$$a = "area value"$$
## Decagon Definition
A decagon is a plane geometric shape or polygon of 10 sides. It also has 10 angles and 10 vertices. The decagon can be regular or irregular.
A regular decagon has all 10 sides of equal length and equal distance from the center. It looks very symmetrical. All regular decagons look the same.
An irregular decagon on the other hand can have sides of different shapes and angles. There is a virtually infinite amount of variations for an irregular decagon, so that they can all look very different from each other. Despite these differences, they will always have 10 sides.
## Area Definition
It is the space of the internal surface in a figure, it is limited for the perimeter. Also, the area can be calculated in a plane of two dimensions.
## Formula Definition
It is a representation of a rule or a general principle using letters. (Algebra, A. Baldor)
When describing formulas in plural, it is also valid to say "formulae".
WikiFormulas.com is a database of embeddable formulas, equations and calculators. You are allowed to use our calculators in any project as long as you give attribution.
✉ wikiformulas@gmail.com
|
2019-10-20 09:09:15
|
{"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": 0.5179154872894287, "perplexity": 5298.69989864093}, "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-2019-43/segments/1570986705411.60/warc/CC-MAIN-20191020081806-20191020105306-00545.warc.gz"}
|
https://gateoverflow.in/321924/isi2014-dcg-31
|
# ISI2014-DCG-31
111 views
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is
1. $\alpha$
2. $[\alpha]$
3. $1$
4. $\dfrac{[\alpha] + [\alpha +1]}{2}$
in Calculus
retagged
0
B?
2
Case 1:$\alpha$>=0
Let α=1.23, α+1=2.23,
=$\int_{1.23}^{2} x dx$ +$\int_{2}^{2.23} x dx$
=$\int_{1.23}^{2} 1$ + $\int_{2}^{2.23} 2 dx$ ($\because$ floor between $1.23, 2 = 1$, similarly floor of 2 and 2.23 is 2. )
= 0.77 + 2*(0.23)
=0.77+0.46=1.23 ($\alpha$)
Case 2:$\alpha$<0
Let α=-0.2, α+1=0.8,
= $\int_{-0.2}^{0} x dx$+ $\int_{0}^{0.8} x dx$
= $\int_{-0.2}^{0} -1 dx$ + $\int_{0}^{0.8} 0 dx$
= -1(0-(-0.2) + 2*(0)
=0.2 ($\alpha$)
In both case, $\int_{\alpha}^{\alpha +1} x dx$ = $\alpha$
Hope, it helps.
text might be small!
## Related questions
1
182 views
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these
The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is $\frac{\pi}{6} + \sqrt{3}$ $\frac{\pi}{6} - \sqrt{3}$ $0$ $\frac{1}{2}$
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $– \frac{1}{2}$ $1$
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(t)$ equals $0$ $1$ $2$ $4$
|
2020-10-01 13:08:11
|
{"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": 0.9660571217536926, "perplexity": 545.6399205798937}, "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/1600402131412.93/warc/CC-MAIN-20201001112433-20201001142433-00317.warc.gz"}
|
https://socratic.org/questions/5712f5467c01496c24c9de8c
|
# Question 9de8c
Apr 17, 2016
Average speed, $v = \frac{d}{t} = \frac{2 x}{\frac{3 x}{4}} = \frac{8}{3} = 2.67 k m . h {r}^{- 1}$
#### Explanation:
Define the distance of A to B as x.
Average speed is total distance divided by total time taken. We already know that since the man walks from A to B and then B to A he travelled a distance of 2x. All we need to calculate is the total time taken.
Calculate the times taken.
A to B: v = d/t ⇒ t_1 = d_1/v_1 = x / 2#
B to A: ${t}_{2} = {d}_{2} / {v}_{2} = \frac{x}{4}$
Calculate total time and then average speed.
Total time taken, $t = {t}_{1} + {t}_{2} = \frac{x}{2} + \frac{x}{4} = \frac{3 x}{4}$
Average speed, $v = \frac{d}{t} = \frac{2 x}{\frac{3 x}{4}} = \frac{8}{3} = 2.67 k m . h {r}^{- 1}$
|
2019-03-22 18:10:00
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.8596227169036865, "perplexity": 1846.7232251107696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202688.89/warc/CC-MAIN-20190322180106-20190322202106-00314.warc.gz"}
|
https://math.stackexchange.com/questions/3552194/on-the-alternating-quadratic-euler-sum-sum-n-1-infty-frac-1n-h-n-h
|
# On the alternating quadratic Euler sum $\sum_{n = 1}^\infty \frac{(-1)^n H_n H_{2n}}{n^2}$
My question is:
Can a closed-form expression for the following alternating quadratic Euler sum be found? Here $$H_n$$ denotes the $$n$$th harmonic number $$\sum_{k = 1}^n 1/k$$. $$S = \sum_{n = 1}^\infty \frac{(-1)^n H_n H_{2n}}{n^2}$$
What I have managed to do so far is to convert $$S$$ to two rather difficult integrals as follows.
Starting with the result $$\frac{H_{2n}}{2n} = -\int_0^1 x^{2n - 1} \ln (1 - x) \, dx \tag1$$ Multiplying (1) by $$(-1)^n H_n/n$$ then summing the result from $$n = 1$$ to $$\infty$$ gives $$S = -2 \int_0^1 \frac{\ln (1 - x)}{x} \sum_{n = 1}^\infty \frac{(-1)^n H_n}{n} x^{2n}. \tag2$$ From the following generating function for the harmonic numbers $$\sum_{n = 1}^\infty \frac{H_n x^n}{n} = \frac{1}{2} \ln^2 (1 - x) + \operatorname{Li}_2 (x),$$ replacing $$x$$ with $$-x^2$$ leads to $$\sum_{n = 1}^\infty \frac{(-1)^n H_n}{n} x^{2n} = \frac{1}{2} \ln^2 (1 + x^2) + \operatorname{Li}_2 (-x^2).$$ Substituting this result into (2) yields $$S = -2 \int_0^1 \frac{\ln (1 - x) \operatorname{Li}_2 (-x^2)}{x} \, dx - \int_0^1 \frac{\ln (1 - x) \ln^2 (1 + x^2)}{x} \, dx,$$ or, after integrating the first of the integrals by parts twice $$S = -\frac{5}{2} \zeta (4) + 4 \zeta (3) \ln 2 - 8 \int_0^1 \frac{x \operatorname{Li}_3 (x)}{1 + x^2} \, dx - \int_0^1 \frac{\ln (1 - x) \ln^2 (1 + x^2)}{x} \, dx. \tag3$$
I have a slim hope the first of these integrals can be found (I cannot find it). As for the second of the integrals, it is proving to be a little difficult.
Can someone find each of the integrals appearing in (3)? Or perhaps an alternative approach to the sum will deliver the closed-form I seek, I am fine either way.
Update
Thanks to Ali Shather, the first of the integrals can be found. Here \begin{align} \int_0^1 \frac{\ln (1 - x) \operatorname{Li}_2 (-x^2)}{x} \ dx &=\sum_{n=1}^\infty\frac{(-1)^n}{n^2}\int_0^1 x^{2n-1}\ln(1-x)\ dx\\ &= -\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{2n^3}\\ &=-4\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{(2n)^3}\\ &=-4 \operatorname{Re} \sum_{n=1}^\infty i^n\frac{H_n}{n^3}. \end{align} And using the result I calculated here, namely $$\operatorname{Re} \sum_{n=1}^\infty i^n\frac{H_n}{n^3} = \frac{5}{8} \operatorname{Li}_4 \left (\frac{1}{2} \right ) - \frac{195}{256} \zeta (4) + \frac{5}{192} \ln^4 2 - \frac{5}{32} \zeta (2) \ln^2 2 + \frac{35}{64} \zeta (3) \ln 2,$$ gives \begin{align} \int_0^1 \frac{\ln (1 - x) \operatorname{Li}_2 (-x^2)}{x} \, dx &= -\frac{5}{2} \operatorname{Li}_4 \left (\frac{1}{2} \right ) + \frac{195}{64} \zeta (4) - \frac{5}{48} \ln^4 2\\ & \qquad + \frac{5}{8} \zeta (2) \ln^2 2 - \frac{35}{16} \zeta (3) \ln 2. \end{align}
• a little difficult seems to be a real understatement. I found quite good explicit approximations using for example $$\sum_{n = 1}^\infty \frac{(-1)^n H_n H_{2n}}{n^2}=\sum_{n = 1}^5 \frac{(-1)^n H_n H_{2n}}{n^2}+\sum_{n = 6}^\infty \frac{(-1)^n H_n H_{2n}}{n^2}$$ and expanding the last summand as series. Using expansions to $O(1/n^5)$, I obtained $-1.014450$ while the exact value is $-1.014452$ Feb 19, 2020 at 7:50
• The first integral $$\int_0^1 \frac{\ln (1 - x) \operatorname{Li}_2 (-x^2)}{x} \ dx=\sum_{n=1}^\infty\frac{(-1)^n}{n^2}\int_0^1 x^{2n-1}\ln(1-x)\ dx$$ $$=-\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{2n^3}=-4\sum_{n=1}^\infty\frac{(-1)^nH_{2n}}{(2n)^3}=-4\Re \sum_{n=1}^\infty i^n\frac{H_n}{n^3}$$ and I think you already calculated this sum before. Feb 19, 2020 at 8:53
• @Ali Shather Nice one. And yes, I have calculated this sum before. Now to the second integral which is an entirely different beast. Feb 19, 2020 at 8:58
• After long calulations I find:$$\int_0^1 \frac{\ln (1 + x) \ln^2 (1 + x^2)}{x} \, dx,=-25\text{Li}_4(1/2) -\frac{229\ln 2}8\zeta(3) +\frac{2959 \pi^4}{11520} +\frac{91\pi^2\ln^2 2}{48} -\frac{51\ln^4 2}{16}+2{G^2}+\frac{3}{2}{\pi}G\ln{2}-\int_0^1 \frac{\ln (1 - x) \ln^2 (1 + x^2)}{1+x} \ dx+8\int_0^1 \frac{\ln (1 + x)\ln(1-x) \ln (1 + x^2)}{1+x} \ dx$$ Feb 26, 2020 at 10:50
• @Edit profile and settings $\int_0^1 \frac{\ln (1 + x) \ln^2 (1 + x^2)}{x} \, dx+\int_0^1 \frac{\ln (1 - x) \ln^2 (1 + x^2)}{1+x} \, dx=-4 \pi \Im(\text{Li}_3(1+i))-7 \text{Li}_4\left(\frac{1}{2}\right)+\frac{5}{4} \zeta (3) \log (2)+\frac{641 \pi ^4}{3840}+\frac{7}{48} \log ^4(2)+\frac{5}{16} \pi ^2 \log ^2(2)+{2}{C^2}-\frac{1}{2} \pi C \log (2)$ May 12, 2020 at 8:30
A First (Magical) Solution by Cornel Ioan Valean
As I also mentioned in this post, the present series, which plays a key part there, is a beast in every way, and finding an elegant approach is an extremely difficult task, often looking like an impossible task. Experienced users in the realm of harmonic series will immediately figure out this monster won't fall easily to its knees. However, it will fall down during the work below!
Let's start with a special particular case of one of the Cornel's generalizations presented during another solution at this address $$\int_0^1 \frac{x\operatorname{arctanh}^n(x)}{1+a^2 x^2}\textrm{d}x \bigg|_{n=1}$$ $$=\frac{n!}{a^2 2^n}\left((1-2^{-n})\zeta(n+1)+ \Re\biggr\{\operatorname{Li}_{n+1}\left(\frac{a^2-1}{a^2+1}+i\frac{2a}{1+a^2}\right)\biggr\}\right)\bigg|_{n=1}$$ $$=\frac{1}{2}\frac{\arctan^2(a)}{a^2}, \ a \in \mathbb{R}\setminus\{0\}. \tag1$$
Proving the second equality: We want to exploit the Euler's formula, and then write \begin{equation*} \begin{aligned} \int_0^1 \frac{x\operatorname{arctanh}(x)}{1+a^2 x^2}\textrm{d}x\overset{\text{use} \ a=\tan(\theta/2)}{=}&\frac{1}{2\tan^2(\theta/2) }\left(\frac{\pi^2}{12}+ \Re\bigr\{\operatorname{Li}_2\left(-\cos(\theta)+i\sin(\theta)\right)\bigr\}\right)\\ &=\frac{1}{2\tan^2(\theta/2) }\left(\frac{\pi^2}{12}+ \Re\biggr\{\operatorname{Li}_2\left(-e^{-i \theta}\right)\biggr\}\right)\\ &=\frac{1}{2\tan^2(\theta/2) }\left(\frac{\pi^2}{12}- \sum_{n=1}^{\infty} (-1)^{n-1}\frac{\Re\{e^{-i n\theta}\}}{n^2}\right)\\ &=\frac{1}{2\tan^2(\theta/2) }\left(\frac{\pi^2}{12}- \sum_{n=1}^{\infty} (-1)^{n-1}\frac{\cos(n\theta)}{n^2}\right)\\ &=\frac{\theta^2}{8\tan^2(\theta/2)}\overset{\text{use} \ \tan(\theta/2)=a}{=}\frac{1}{2}\frac{\arctan^2(a)}{a^2}, \end{aligned} \end{equation*} where during the calculations I used the well-known Fourier series, $$\displaystyle \sum_{n=1}^{\infty}(-1)^{n-1}\frac{\cos(nx)}{n^2}=\frac{\pi^2}{12}-\frac{x^2}{4}$$,$$-\pi\le x \le\pi$$, and the calculations are complete.
Another solution: In this solution I'll only consider the restriction of the type $$|x|\le1, \ x\neq 0$$, \begin{equation*} \begin{aligned} \int_0^1 \frac{x\operatorname{arctanh}(x)}{1+a^2 x^2}\textrm{d}x&=\int_0^1 \sum_{n=1}^{\infty}(-1)^{n-1} x(a x)^{2n-2}\operatorname{arctanh}(x)\textrm{d}x\\ &=\sum_{n=1}^{\infty}(-1)^{n-1}a^{2n-2} \int_0^1 x^{2n-1}\operatorname{arctanh}(x)\textrm{d}x\\ &=\frac{1}{4}\sum_{n=1}^{\infty}(-1)^{n-1}a^{2n-2} \frac{2H_{2n}-H_n}{n}\\ &=\frac{1}{2}\frac{\arctan^2(a)}{a^2}, \end{aligned} \end{equation*} where in the calculations I used the logarithmic integrals $$\displaystyle \int_0^1 x^{2n-1}\log(1-x)\textrm{d}x=-\frac{H_{2n}}{2n}$$, then $$\displaystyle \int_0^1 x^{2n-1}\log(1+x)\textrm{d}x=\frac{H_{2n}-H_n}{2n}$$, (A simple proof may be found in this RG article), and finally the classical Cauchy product, $$\displaystyle \arctan^2(x)=\frac{1}{2}\sum_{n=1}^{\infty}(-1)^{n-1}x^{2n}\frac{2H_{2n}-H_n}{n}, \ |x|\le1$$. Details on how to start from this variant and extend it to $$a \in \mathbb{R}\setminus\{0\}$$ will be found in the sequel of (Almost) Impossible Integrals, Sums, and Series.
Yet, one more solution: This way is also going to be extremely elegant, and multiplying the auxiliary integral by $$2a^2$$ and cleverly integrating by parts, we get \begin{equation*} \begin{aligned} \int_0^1 2a^2\frac{x\operatorname{arctanh}(x)}{1+a^2 x^2}\textrm{d}x&=-\int_0^1 \log\left(\frac{1+a^2x^2}{1+a^2}\right)\frac{1}{1-x^2}\textrm{d}x\\ &=-\int_0^1 \int_0^a \frac{\partial}{\partial t}\biggr\{\log\left(\frac{1+t^2x^2}{1+t^2}\right)\biggr\}\frac{1}{1-x^2}\textrm{d}t \textrm{d}x\\ &=\int_0^1 \int_0^a\frac{2 t}{(1+t^2)(1+t^2 x^2)}\textrm{d}t \textrm{d}x\\ &=\int_0^a\int_0^1 \frac{2 t}{(1+t^2)(1+t^2 x^2)}\textrm{d}x \textrm{d}t\\ &=2\int_0^a \frac{\arctan(t)}{1+t^2}\textrm{d}t\\ &=\arctan^2(a), \end{aligned} \end{equation*} which brings an end to the present solution.
The main calculations: We may start from the function $$\displaystyle f(x)=\frac{(\pi/2-\arctan(t))^2\operatorname{arctanh}(t)}{t}$$ which we integrate from $$0$$ to $$\infty$$ (or I could start directly from the blue integral), and then using the simple fact that based on $$(1)$$ we have $$\displaystyle \frac{(\pi/2-\arctan(t))^2}{t}=2\int_0^1 \frac{x\operatorname{arctanh}(x)}{t(t^2+x^2)}\textrm{d}x$$, we write that $$\Re\biggr \{\int_0^{\infty} \frac{(\pi/2-\arctan(t))^2\operatorname{arctanh}(t)}{t}\textrm{d}t\biggr\}=\Re\biggr \{2\int_0^{\infty}\operatorname{arctanh}(t)\left( \int_0^1 \frac{x\operatorname{arctanh}(x)}{t(t^2+x^2)}\textrm{d}x\right)\textrm{d}t\biggr\}$$ $$=\Re\biggr \{2\int_0^1x\operatorname{arctanh}(x)\left(\int_0^{\infty} \frac{\operatorname{arctanh}(t)}{t(x^2+t^2)}\textrm{d}t\right)\textrm{d}x\biggr\}$$ $$=2\int_0^1x\operatorname{arctanh}(x)\left(\int_0^{\infty}\left(\operatorname{PV} \int_0^1 \frac{1}{(x^2+t^2)(1-t^2u^2)}\textrm{d}u\right)\textrm{d}t\right)\textrm{d}x$$ $$=2\int_0^1x\operatorname{arctanh}(x)\left(\int_0^1\left(\operatorname{PV} \int_0^{\infty} \frac{1}{(x^2+t^2)(1-u^2t^2)}\textrm{d}t\right)\textrm{d}u\right)\textrm{d}x$$ $$=\pi\int_0^1\operatorname{arctanh}(x)\left(\int_0^1\frac{1}{1+x^2 u^2}\textrm{d}u\right)\textrm{d}x$$ $$=\pi\int_0^1\frac{\arctan(x)\operatorname{arctanh}(x)}{x}\textrm{d}x.\tag2$$
Splitting the first integral in $$(2)$$ at $$t=1$$, using trivial identities with $$\arctan(x)$$ and $$\operatorname{arctanh}(x)$$, employing elementary variable changes to reduce the integration interval to the space from $$t=0$$ to $$t=1$$, we write $$\Re\biggr \{\int_0^{\infty} \frac{(\pi/2-\arctan(t))^2\operatorname{arctanh}(t)}{t}\textrm{d}t\biggr\}$$ $$\int_0^1 \frac{(\pi/2-\arctan(t))^2\operatorname{arctanh}(t)}{t}\textrm{d}t+\Re\biggr \{\int_1^{\infty} \frac{(\pi/2-\arctan(t))^2\operatorname{arctanh}(t)}{t}\textrm{d}t\biggr\}$$ $$=\frac{\pi^2}{4}\int_0^1\frac{\operatorname{arctanh}(t)}{t}\textrm{d}t-\pi\int_0^1\frac{\arctan(t)\operatorname{arctanh}(t)}{t}\textrm{d}t+2\color{blue}{\int_0^1\frac{\arctan^2(t)\operatorname{arctanh}(t)}{t}\textrm{d}t}$$ $$=\frac{45}{16}\zeta(4)-\pi\int_0^1\frac{\arctan(t)\operatorname{arctanh}(t)}{t}\textrm{d}t+2\color{blue}{\int_0^1\frac{\arctan^2(t)\operatorname{arctanh}(t)}{t}\textrm{d}t}\tag3.$$
Upon combining $$(2)$$ and $$(3)$$ we get a first useful and powerful relation which for the art's sake I'll put as a representation of $$\zeta(4)$$,
$$\zeta(4)$$ $$=\frac{32}{45} \pi \int_0^1 \frac{\arctan(t)\operatorname{arctanh(t)}}{t}\textrm{d}t-\frac{32}{45} \color{blue}{\int_0^1 \frac{\arctan^2(t)\operatorname{arctanh}(t)}{t} \textrm{d}t}.\tag4$$
The first integral in $$(4)$$ is a known one, immediately reducible to the work with classical results, and we may put it in the form $$\int_0^1 \frac{\arctan(t)\operatorname{arctanh(t)}}{t}\textrm{d}t=\frac{\pi ^3}{32}+\frac{1}{2} \int_0^1 \frac{\arctan(t)\log(t)}{1+t}\textrm{d}t+\frac{1}{2} \Im\biggr\{\int_0^1 \frac{\log (1+i t) \log (t)}{1-t} \textrm{d}t\biggr\}$$ $$=\frac{1}{2}\log(2)G+\frac{\pi}{16}\log^2(2)+\frac{3}{64}\pi^3-\Im\{\operatorname{Li}_3(1+i)\}.\tag5$$
The first integral in $$(5)$$ appears in this post with more solutions, and it also appears in (Almost) Impossible Integrals, Sums, and Series (see page $$14$$, Sect. $$1.24$$). The second integral is very elegantly derived if we consider $$\displaystyle I(a)=\int_0^1 \frac{\log (1+a t) \log (t)}{1-t} \textrm{d}t$$ and differentiate under the integral sign with respect to $$a$$.
Using the logarithmic integrals and the Cauchy product employed during the calculation of the second solution to the auxiliary result in $$(1)$$, we get the following integral transformation to series $$\color{blue}{\int_0^1 \frac{\arctan^2(t)\operatorname{arctanh}(t)}{t} \textrm{d}t}$$ $$=\frac{1}{8}\sum _{n=1}^{\infty}(-1)^{n-1} \frac{ H_n^2}{n^2}+\frac{1}{2}\sum_{n=1}^{\infty} (-1)^{n-1}\frac{H_{2 n}^2}{n^2}-\frac{1}{2}\color{red}{\sum _{n=1}^{\infty} (-1)^{n-1}\frac{ H_n H_{2 n}}{n^2}}.\tag6$$
Combining $$(4)$$, $$(5)$$, and $$(6)$$ and observing the first two series are known, we arrive at the desired value of the series, $$\color{red}{\sum _{n=1}^{\infty} (-1)^{n-1}\frac{ H_n H_{2 n}}{n^2}}$$ $$\color{red}{=2 G^2-2\log(2)\pi G-\frac{1}{8}\log^4(2)-\frac{21}{8}\log(2)\zeta(3)+\frac{1}{4}\log^2(2)\pi ^2+\frac{773}{5760}\pi ^4}$$ $$\color{red}{-4 \pi \Im\biggr\{\operatorname{Li}_3\left(\frac{1+i}{2}\right)\biggr\}-3 \operatorname{Li}_4\left(\frac{1}{2}\right)},$$ where I also used polylogarithmic relations as the ones found here.
Note that for the first two resulting harmonic series in $$(6)$$, we have $$\sum_{n=1}^{\infty} (-1)^{n-1} \frac{H_n^2}{n^2}$$ $$=\frac{41}{16}\zeta (4)-\frac{7}{4}\log (2) \zeta (3)+\frac{1}{2}\log ^2(2)\zeta (2)-\frac{1}{12} \log ^4(2) -2 \text{Li}_4\left(\frac{1}{2}\right),$$ which is a classical result, and it may also be found in (Almost) Impossible Integrals, Sums, and Series, page $$310$$, and $$\sum_{n=1}^{\infty} (-1)^{n-1} \frac{H_{2n}^2}{n^2}$$ $$=2 G^2-\log(2)\pi G+\frac{231}{32}\zeta(4)-\frac{35}{16}\log(2)\zeta(3)+\log^2(2)\zeta(2)-\frac{5}{48}\log^4(2)$$ $$-2 \pi \Im\biggr\{\operatorname{Li}_3\left(\frac{1+i}{2}\right)\biggr\}-\frac{5}{2}\operatorname{Li}_4\left(\frac{1}{2}\right),$$ which is given and easily derived in this post.
End of story
More series from the atypical alternating weight 4 class: $$\sum_{n=1}^{\infty} (-1)^{n-1} \frac{H_{2n}^3}{n}$$ $$=2G^2-\frac{3}{4}\log(2)\pi G+\frac{1055}{256}\zeta(4)-\frac{93}{64}\log(2)\zeta(3)+\frac{21}{32}\log^2(2)\zeta(2)-\frac{1}{32}\log^4(2)$$ $$-\frac{3}{2}\pi \Im\biggr\{\operatorname{Li}_3\left(\frac{1+i}{2}\right)\biggr\};$$ $$\sum_{n=1}^{\infty} (-1)^{n-1} \frac{H_{2n}H_{2n}^{(2)}}{n}$$ $$=\frac{1}{4}\log(2)\pi G-\frac{137}{128}\zeta(4)+\frac{35}{64}\log(2)\zeta(3)-\frac{3}{8}\log^2(2)\zeta(2)+\frac{5}{96}\log^4(2)$$ $$+\frac{\pi}{2}\Im\biggr\{\operatorname{Li}_3\left(\frac{1+i}{2}\right)\biggr\}+\frac{5}{4}\operatorname{Li}_4\left(\frac{1}{2}\right).$$
They are straightforward by exploiting their related generating functions that are immediately built based on the generating functions in (Almost) Impossible Integrals, Sums, and Series (see page $$284$$, Sect. $$4.10$$). More details and results are included in the sequel of the mentioned book.
And more series ... from the same class: $$\sum_{n=1}^{\infty} (-1)^{n-1}\frac{H_{2n}^{(3)}}{n}=\frac{199}{128}\zeta (4)-\frac{3}{32} \log (2)\zeta (3)-G^2,$$ where this series is part of the generalization found in Cornel's answer here. It may also be found in the article A simple strategy of calculating two alternating harmonic series generalizations by C.I. Valean at this link.
Using your integral representation, the sum equals to: $$\sum_{n = 1}^\infty \frac{(-1)^n H_n H_{2n}}{n^2}= -2 \int_0^1 \frac{\ln (1 - x) \operatorname{Li}_2 (-x^2)}{x} \, dx - \int_0^1 \frac{\ln (1 - x) \ln^2 (1 + x^2)}{x} \, dx$$ $$\small=-2 C^2+2 \pi C \log (2)-4 \pi \Im(\text{Li}_3(1+i))+3 \text{Li}_4\left(\frac{1}{2}\right)+\frac{21}{8} \zeta (3) \log (2)+\frac{487 \pi ^4}{5760}+\frac{\log ^4(2)}{8}+\frac{1}{8} \pi ^2 \log ^2(2)$$ For the second integral and its derivation, see here.
• Magical and thanks. May 13, 2020 at 5:29
Remark: I have noticed too late that this integral has already been solved (in the update of omegadot).
Nevertheless I don't delete the contribution because, together with this information, it shows that the hypergeometric functions appearing here can be simplified appreciably which gives hope for other cases.
Original post
A closed expression of the integral
$$i = \int_0^1 \frac{x \operatorname{Li}_3(x)}{x^2+1}\tag{1}$$
can be found in terms of (sorry Ali) hypergeometric function as follows.
Partial integration gives
$$i=s_{0}-\int_0^1 \frac{\text{Li}_2(x) \log \left(x^2+1\right)}{2 x} \, dx\tag{2a}$$
where
$$s_0 = \frac{1}{2} \zeta (3) \log (2)\tag{2b}$$
Expanding the denominator of the integrand we find that $$i=s_{0}+\sum a_{k}$$ where
$$a_{k} =-\frac{1}{2} \int_0^1 \frac{(-1)^{k+1} x^{2 k-1} \text{Li}_2(x)}{k} \, dx=-\frac{(-1)^{k+1} \left(\pi ^2 k-3 H_{2 k}\right)}{24 k^3}\tag{3}$$
The two sums are
$$s_{1}=\frac{1}{24} \left(-\pi ^2\right) \sum _{k=1}^{\infty } \frac{(-1)^{k+1}}{k^2}=-\frac{\pi ^4}{288}\tag{4}$$
$$s_{2} = +\frac{1}{8} \sum _{k=1}^{\infty } \frac{(-1)^{k+1} H_{2 k}}{k^3}=\frac{1}{32} \left(-2 \,_P\tilde{F}_Q^{(\{0,0,0,0\},\{0,0,1\},0)}(\{1,1,1,1\},\{2,2,2\},-1)\\-\sqrt{\pi } \,_P\tilde{F}_Q^{(\{0,0,0,0,0\},\{0,0,0,1\},0)}\left(\left\{1,1,1,1,\frac{3}{2}\right\},\left\{2,2,2,\frac{3}{2}\right\},-1\right)\\+3 \zeta (3) (\gamma +\log (2))\right)\tag{5}$$
Where $$\,_P\tilde{F}_Q$$ is the regularized hypergeometric function. For more details see https://math.stackexchange.com/a/3544006/198592.
Two terms appear in $$s_{2}$$ due to the relation
$$H_{2 k}=\frac{1}{2} \left( H_{k-\frac{1}{2}}+ H_k \right)+\log (2)$$
The complete integral is then given by
$$i = s_{0}+s_{1}+s_{2}$$
The numeric check shows good agreement.
Discussion
I'm almost sure that the sum
$$\sum _{k=1}^{\infty } \frac{(-1)^{k+1} H_k}{k^3}$$
has a simpler expression, and so might
$$\sum _{k=1}^{\infty } \frac{(-1)^{k+1} H_{k-\frac{1}{2}}}{k^3}$$
and I'd be happy to replace the hypergeometric constructs.
No need to conjecture: omegadot has done it, see https://math.stackexchange.com/a/3290607/198592
A Second (Magical) Solution by Cornel Ioan Valean
To get a different solution, we start from Dan Fulea's integral in this post where Cornel provided with an extremely simple solution, and by simply rearranging it, we have that $$\frac{\pi^4}{64}$$ $$=\frac{\pi^2}{4}\underbrace{\int_0^1\frac{\operatorname{arctanh}(t)}{t}\textrm{d}t}_{\displaystyle \pi^2/8}-\pi \int_0^1\frac{\arctan(t)\operatorname{arctanh}(t)}{t}\textrm{d}t+\int_0^1\frac{\arctan^2(t)\operatorname{arctanh}(t)}{t}\textrm{d}t,$$ and since the middle integral is provided in the first Cornel's solution and the transformation from the last integral to series is again shown in the first Cornel's solution together with the values of the resulting auxiliary series, we arrive at the desired value of the series, $$\color{red}{\sum _{n=1}^{\infty} (-1)^{n-1}\frac{ H_n H_{2 n}}{n^2}}$$ $$\color{red}{=2 G^2-2\log(2)\pi G-\frac{1}{8}\log^4(2)-\frac{21}{8}\log(2)\zeta(3)+\frac{1}{4}\log^2(2)\pi ^2+\frac{773}{5760}\pi ^4}$$ $$\color{red}{-4 \pi \Im\biggr\{\operatorname{Li}_3\left(\frac{1+i}{2}\right)\biggr\}-3 \operatorname{Li}_4\left(\frac{1}{2}\right)},$$ and the solution is complete.
End of story
A note: The connection with Dan Fulea's integral was observed later, and this latter way is definitely more wonderful to consider.
A Third (Magical) Solution by Cornel Ioan Valean
This time we assume we have in hand that $$\displaystyle \int_0^1 \frac{\arctan^2(x)}{x}\log\left(\frac{x}{(1-x)^2}\right)=G^2$$, which is calculated extremely easily at this link. Furthermore, we also assume we have at our disposal the value of the powerful harmonic series $$\displaystyle \sum_{n=1}^{\infty}(-1)^{n-1}\frac{H_{2n}}{n^3}$$ which is derived in a simple manner in this answer. Now, as seen in this post, the integral is reducible to the previously mentioned harmonic series and $$\color{red}{\text{the main harmonic series}}$$.
Using the simple facts stated above, we conclude that $$\color{red}{\sum _{n=1}^{\infty} (-1)^{n-1}\frac{ H_n H_{2 n}}{n^2}}$$ $$\color{red}{=2 G^2-2\log(2)\pi G-\frac{1}{8}\log^4(2)-\frac{21}{8}\log(2)\zeta(3)+\frac{1}{4}\log^2(2)\pi ^2+\frac{773}{5760}\pi ^4}$$ $$\color{red}{-4 \pi \Im\biggr\{\operatorname{Li}_3\left(\frac{1+i}{2}\right)\biggr\}-3 \operatorname{Li}_4\left(\frac{1}{2}\right)},$$ and we are done!
|
2023-03-23 13:48:04
|
{"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": 118, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9800086617469788, "perplexity": 466.72387628453095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945168.36/warc/CC-MAIN-20230323132026-20230323162026-00447.warc.gz"}
|
https://math.stackexchange.com/questions/2937712/check-if-three-row-vectors-are-linearly-dependent-or-independent
|
# Check if three row vectors are linearly dependent or independent
I want to check if three row vectors are linearly dependent or independent. I have the following row vectors: $$u = \left[\begin{array}{r}1 & 3 & -1 & 2\end{array}\right], v=\left[\begin{array}{r}2 & -2 & 5 & 1\end{array}\right], w = \left[\begin{array}{r}1 & -1 & 2 & -1 \end{array}\right]$$.
Now, if they are linearly independent it should mean that I would be able to find some non-zero scalars $$\lambda_1, \lambda_2, \lambda_3$$: such that I am able to satisfy the following equation:
$$\lambda_1u+\lambda_2v+\lambda_3w=0$$
However, I am not really able to understand how to proceed from here:
$$\lambda_1\left[\begin{array}{r}1 & 3 & -1 & 2\end{array}\right]+\lambda_2\left[{\begin{array}{r}2 & -2 & 5 & 1\end{array}}\right]+\lambda_3\left[{\begin{array}{r}1 & -1 & 2 & -1\end{array}}\right] = 0$$
Please note that my textbook has not yet talked about rank or determinants. Any hints on how to solve this without those? Should I solve a linear system? Should I build a matrix using these row vectors as rows?
• Hint: Letting $A = \left [ a_{ij} \right ]$, the vectors $a_{j}$’s are linearly independent if $Ax= 0 \Rightarrow x=0$. – OGC Oct 1 '18 at 8:48
You are always able to find such scalars: just take $$\lambda_1=\lambda_2=\lambda_3=0$$. The question is: is there some other solution? If there is, the vectors are linearly dependent. Otherwise, they are linearly independent.
So, solve the system$$\left\{\begin{array}{l}\lambda_1+2\lambda_2+\lambda_3=0\\3\lambda_1-2\lambda_2-\lambda_3=0\\-\lambda_1+5\lambda_2+2\lambda_3=0\\2\lambda_1+\lambda_2-\lambda_3=0\end{array}\right.$$Is there some solution besides the null solution or not?
• I did not think of them as rows. All I did was$$\lambda_1\begin{bmatrix}1&3&-1&2\end{bmatrix}+\lambda_2\begin{bmatrix}2&-2&5&1\end{bmatrix}+\lambda_3\begin{bmatrix}1&-1&2&-1\end{bmatrix}=\begin{bmatrix}\lambda_1+2\lambda_2+\lambda_3&3\lambda_1-2\lambda_2-\lambda_3&-\lambda_1+5\lambda_2+2\lambda_3&2\lambda_1+\lambda_2-\lambda_3\end{bmatrix}.$$ – José Carlos Santos Oct 1 '18 at 8:49
A much quicker and easier approach is to form a matrix from these vectors and see if it has full rank. In this case, if these vectors are linearly independent, the rank has to be $$3$$. It turns out that the rank is indeed $$3$$, so the given vectors are linearly independent.
|
2021-03-02 03:00:39
|
{"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": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9116707444190979, "perplexity": 83.9843755456579}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363211.17/warc/CC-MAIN-20210302003534-20210302033534-00577.warc.gz"}
|
https://adaptivemd.readthedocs.io/en/latest/api/generated/adaptivemd.PythonTask.html
|
class adaptivemd.PythonTask(generator=None)[source]
A special task that does a RPC python calls
Variables: then_func_name (str or None) – the name of the function of the TaskGenerator to be called with the resulting output store_output (bool) – if True then the result from the RPC called function will also be stored in the database. It can later be retrieved using the .output attribute on the task completed successfully
__init__(generator=None)[source]
Methods
__init__([generator])
add_cb(event, cb) Add a custom callback
add_conda_env(name) Add loading a conda env to all tasks of this resource
add_files(files) Add additional files to the task execution
add_path(path)
param path: a (list of) path(s) to be added to the \$PATH variable before task execution
append(cmd) Append a command to this task
args() Return a list of args of the __init__ function of a class
backup_output_json(target) Add an action that will copy the resulting JSON file to the given path
base() Return the most parent class actually derived from StorableMixin
call(command, **kwargs) Set the python function to be called with its arguments
cancel() Mark a task as cancelled if it it not running or has been halted
descendants() Return a list of all subclassed objects
fire(event, scheduler) Fire an event like success or failed.
from_dict(dct)
get(f[, name]) Get a file and make it available to the task in the main directory
get_uuid() Create a new unique ID
has_failed() Check if the task is done executing and has failed
idx(store) Return the index which is used for the object in the given store.
is_done() Check if the task is done executing.
link(f[, name]) Add an action to create a link to a file (under a new name)
named(name) Attach a .name property to an object
objects() Returns a dictionary of all storable objects
prepend(cmd) Append a command to this task
put(f, target) Put a file back and make it persistent
remove(f) Add an action to remove a file or folder
restart() Mark a task as being runnable if it was stopped or failed before
setenv(key, value) Set an environment variable for the task
then(func_name) Set the name of the function to be called from the generator after success
to_dict()
touch(f) Add an action to create an empty file or folder at a given location
was_successful() Check if the task is done executing and was successful
Attributes
ACTIVE_LONG CREATION_COUNT FINAL_STATES INSTANCE_UUID RESTARTABLE_STATES RUNNABLE_STATES additional_files list of Location base_cls Return the base class base_cls_name Return the name of the base class cls Return the class name as a string dependency_okay Check if all dependency tasks are successful description Return a lengthy description of the task for debugging and information environment dict str – str main modified_files A set of all input files whose names match output names and hence will be overwritten new_files Return a set of all files the will be newly created by this task output Return the data contained in the output file pre_add_paths list of str pre_exec ready Check if this task is ready to be executed script list of str or Action source_locations Return a set of all required file urls sources Return a set of all required input files staged_files Set of all staged files by the tasks generator state stderr stdout target_locations Return a set of all new and overwritten file urls targets Return a set of all new and overwritten files then_func unstaged_input_files Return a set of File objects that are used but are not part of the generator stage worker
backup_output_json(target)[source]
Add an action that will copy the resulting JSON file to the given path
Parameters: target (Location) – the place to copy the resulting output.json file to
output
Return the data contained in the output file
Returns: object
then(func_name)[source]
Set the name of the function to be called from the generator after success
Parameters: func_name (str) – the function name to be called after success
call(command, **kwargs)[source]
Set the python function to be called with its arguments
Parameters: command (function) – a python function defined inside a package or a function. If in a package then the package needs to be installed on the cluster to be called. A function defined in a local file can be called as long as dependencies are installed. kwargs (**kwargs) – named arguments to the function
|
2020-04-01 08:59:13
|
{"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": 0.19455863535404205, "perplexity": 2432.356366109964}, "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/1585370505550.17/warc/CC-MAIN-20200401065031-20200401095031-00046.warc.gz"}
|
https://www.iitutor.com/category/mathematical-induction/
|
# Best Examples of Mathematical Induction Inequality
Share0 Share +10 Tweet0 Our Courses Mathematical Induction Inequality Proofs Mathematical Induction Inequality is being used for proving inequalities. It is quite often applied for the subtraction and/or greatness, using the assumption at the step 2. Let’s take a look at the following hand-picked examples. Practice Questions for Mathematical Induction Inequality Basic Mathematical Induction Inequality […]
# Best Examples of Mathematical Induction Divisibility
Share0 Share +10 Tweet0 OUR COURSES Mathematical Induction Divisibility Proofs Mathematical Induction Divisibility can be used to prove divisibility, such as divisible by 3, 5 etc. Same as Mathematical Induction Fundamentals, hypothesis/assumption is also made at the step 2. Practice Questions of Mathematical Induction Divisibility Basic Mathematical Induction Divisibility Prove $6^n + 4$ […]
# Mathematical Induction Fundamentals
Share0 Share +10 Tweet0 Mathematical Induction Fundamentals The Mathematical Induction Fundamentals are defined for applying 3 steps, such as step 1 for showing its initial ignite, step 2 for making an assumption, and step 3 for showing it is true based on the assumption. Make sure the Mathematical Induction Fundamentals should be used only when […]
# Mathematical Induction Inequality Proof with Factorials
Share0 Share +10 Tweet0 Our Courses Mathematical Induction Inequality Proof with Factorials uses one of the properties of factorials, $n! = n(n-1)! = n(n-1)(n-2)!$. Worked Example of Mathematical Induction Inequality Proof with Factorials Prove that $(2n)! > 2^n (n!)^2$ using mathematical induction for $n \ge 2$. Step 1: Show it is […]
# Mathematical Induction Inequality Proof with Two Initials
Share0 Share +10 Tweet0 Usually, mathematical induction inequality proof requires one initial value, but in some cases, two initials are to be required, such as Fibonacci sequence. In this case, it is required to show two initials are working as the first step of the mathematical induction inequality proof, and two assumptions are to be […]
|
2019-02-22 11:08:34
|
{"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": 0.7954182028770447, "perplexity": 1136.6513478800066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247515149.92/warc/CC-MAIN-20190222094419-20190222120419-00431.warc.gz"}
|
https://rpg.stackexchange.com/questions/91131/what-can-a-pinned-character-do?noredirect=1
|
# What can a pinned character do?
In our session, a dragon used Crush to pin a paladin. During his turn, could the paladin use Lay on Hands to heal himself and attack the dragon with a melee weapon?
Consensus was divided between "the only thing he could do is try a combat maneuver check to free himself" and "he can do anything that is not expressly forbidden in the pinned and grappled condition" (so he could use Lay On Hands (because it only requires a single hand) and attack with a one-handed weapon).
The pinned condition says:
...A pinned creature is limited in the actions that it can take...
but doesn't specify what limits those are.
The Pinned condition specifically says you are very limited on your actions:
A pinned creature is tightly bound and can take few actions.
A pinned creature is limited in the actions that it can take.
So unless something says otherwise, you are limited to the options on the condition, which are listed right after that:
• A pinned creature can always attempt to free itself;
• A pinned creature can take verbal and mental actions, but cannot cast any spells that require a somatic or material component.
So you could take Swift Actions if those are verbal or mental or attempt to free yourself. But since it does not say "You can take swift actions", you are limited to only those swift actios that do specify that they are purely mental or verbal in nature, or have a description that suggests that the character only has to speak or think for it to work, such as:
Every other swift action should be impossible, such as an alchemist trying to apply poison to a weapon, or the same warpriest enhancing his weapon with magical power.
Lay on Hands specifically says that you need a free hand, which by the definition of the Pinned condition, you probably won't have (but you would while grappled).
Despite the name of this ability, a paladin only needs one free hand to use this ability
Regardless, the character still should be allowed to use a spell-like ability (no somatic or material components) if they pass their concentration check.
This seems to be the concensus of the community aswell, as can be observed here, here, and finally here. On the last, Sean K. Reynolds state that a touch attack is not a mental or verbal action and the thread's FAQ request was answered "Staff response: no reply required.".
James Jacobs, Creative Director at paizo already stated that you can't even attack while pinned:
Can a pinned creature or character make a full attack?
Nope, because one of the things that happened when you are pinned is that you are VERY limited as to what actions you can take. Most importantly, you can't attack if you're pinned—in order to attack, you first need to escape the pinned condition. So... no. If you're pinned, you can't make a full attack.
For all purposes, the rules as intended is that you can only take the actions listed on the Pinned condition.
If the intent of Pinned was to allow you to take the same actions allowed by grapple, the devs wouldnt even mention that you can take mental and verbal actions, as those are already allowed while grappled. They would simply state that you can only cast spells without somatic components and take a heavier penalty to AC.
This would save text (like half of it) and still be clear about the intent of the condition.
The Pinned condition says:
A pinned creature cannot move and is denied its Dexterity bonus. A pinned character also takes an additional –4 penalty to his Armor Class...A pinned creature can take verbal and mental actions, but cannot cast any spells that require a somatic or material component...Pinned is a more severe version of grappled, and their effects do not stack.
So pinned is more severe than grappled.
The grappled condition states that you can make attacks at a -2 bonus and can take no actions that require two hands to perform:
A grappled creature takes a –2 penalty on all attack rolls and combat maneuver checks, except those made to grapple or escape a grapple. In addition, grappled creatures can take no action that requires two hands to perform.
The pinned condition says that its effects do not stack with grappled, and that it is a more severe form of grapple. From this, we can infer that the more severe parts of pinned are the parts it specifically defines:
• Denied it's DEX bonus (pinned) vs. -4 penalty to Dexterity (grappled)
• -4 penalty to AC (pinned) vs. no additional AC penalty (grappled)
Other than these two changes, the rules for pinned are the same as for grappled, which means actions taken with one hand are fine. This means the -2 to attack is still in effect, which means attacking, at least per the written rules, is not forbidden. It also means he can Lay on Hands.
However, extenuating circumstances may apply as determined the the GM. Consider the following: a paladin who is tied up with rope has the pinned condition. The paladin can probably still lay on hands, unless something is specifically restraining his hands in a way that he cannot touch himself with them. He may be able to attack but again, if he's restrained in such a way as to make that not possible (for example, hogtied and hanging upside down from a tree) then there's not much he can do.
Given the example scenario of a dragon's Crush attack, I don't see why he couldn't attempt to stab it with his sword and lay hands on himself, per the rules of the pinned condition.
• i dont see it being more severe if they are nearly identical if we follow what this answer suggests. Why would it say you can take mental and verbal actions if those were already allowed by grapple? If that was the case, it wouldn't mention that and would only restrict your spell casting to those without somatic components. Which would save text and still be clear about the intent of the rule. Dec 2 '16 at 15:36
• @ShadowKras It is still more severe. -4 is more severe than -2, is it not? It doesn't state to which degree it is more severe, and if it's supposed to be "more severe" then should it not define what that means? Hence, my answer. Pinned is a condition that can vary from being sat on top of (you can still punch your opponent) to being completely bound in ropes and chains (you can barely move). Note that, logically, stating you can take mental and verbal actions does not preclude other actions. If it should, it would say, "you can take mental and verbal actions, but nothing else." Dec 2 '16 at 15:52
• Then what would be the difference between those two pinned conditions on the rules? Why one allows you to attack and the other doesn't? There is no "pinnned but cant act" condition as far as i know. Dec 2 '16 at 15:55
• @ShadowKras That's what the GM is for, and I've noted such in my answer. Dec 2 '16 at 15:55
• A paladin that is tied up with rope is Helpless, which is a more severe condition than Pinned. Jul 2 '17 at 6:24
|
2021-09-24 20:55:29
|
{"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": 0.45406997203826904, "perplexity": 2174.4388009313557}, "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-2021-39/segments/1631780057580.39/warc/CC-MAIN-20210924201616-20210924231616-00030.warc.gz"}
|
https://arbital.greaterwrong.com/p/intro_utility_coherence?l=7hh
|
# Introduction to the introduction: Why expected utility?
So we’re talking about how to make good decisions, or the idea of ‘bounded rationality’, or what sufficiently advanced Artificial Intelligences might be like; and somebody starts dragging up the concepts of ‘expected utility’ or ‘utility functions’.
And before we even ask what those are, we might first ask, Why?
There’s a mathematical formalism, ‘expected utility’, that some people invented to talk about making decisions. This formalism is very academically popular, and appears in all the textbooks.
But so what? Why is that necessarily the best way of making decisions under every kind of circumstance? Why would an Artificial Intelligence care what’s academically popular? Maybe there’s some better way of thinking about rational agency? Heck, why is this formalism popular in the first place?
We can ask the same kinds of questions about probability theory:
Okay, we have this mathematical formalism in which the chance that X happens, aka $$\mathbb P(X),$$ plus the chance that X doesn’t happen, aka $$\mathbb P(\neg X),$$ must be represented in a way that makes the two quantities sum to unity: $$\mathbb P(X) + \mathbb P(\neg X) = 1.$$
That formalism for probability has some neat mathematical properties. But so what? Why should the best way of reasoning about a messy, uncertain world have neat properties? Why shouldn’t an agent reason about ‘how likely is that’ using something completely unlike probabilities? How do you know a sufficiently advanced Artificial Intelligence would reason in probabilities? You haven’t seen an AI, so what do you think you know and how do you think you know it?
That entirely reasonable question is what this introduction tries to answer. There are, indeed, excellent reasons beyond academic habit and mathematical convenience for why we would by default invoke ‘expected utility’ and ‘probability theory’ to think about good human decisions, talk about rational agency, or reason about sufficiently advanced AIs.
The broad form of the answer seems easier to show than to tell, so we’ll just plunge straight in.
# Why not circular preferences?
De gustibus non est disputandum, goes the proverb; matters of taste cannot be disputed. If I like onions on my pizza and you like pineapple, it’s not that one of us is right and one of us is wrong. We just prefer different pizza toppings.
Well, but suppose I declare to you that I simultaneously:
• Prefer onions to pineapple on my pizza.
• Prefer pineapple to mushrooms on my pizza.
• Prefer mushrooms to onions on my pizza.
If we use $$>_P$$ to denote my pizza preferences, with $$X >_P Y$$ denoting that I prefer X to Y, then I am declaring:
$$\text{onions} >_P \text{pineapple} >_P \text{mushrooms} >_P \text{onions}$$
That sounds strange, to be sure. But is there anything wrong with that? Can we disputandum it?
We used the math symbol $$>$$ which denotes an ordering. If we ask whether $$>_P$$ can be an ordering, it naughtily violates the standard transitivity axiom $$x > y, y > z \implies x > z$$.
Okay, so then maybe we shouldn’t have used the symbol $$>_P$$ or called it an ordering. Why is that necessarily bad?
We can try to imagine each pizza as having a numerical score denoting how much I like it. In that case, there’s no way we could assign consistent numbers $$x, y, z$$ to those three pizza toppings such that $$x > y > z > x.$$
So maybe I don’t assign numbers to my pizza. Why is that so awful?
Are there any grounds besides “we like a certain mathematical formalism and your choices don’t fit into our math,” on which criticize my three simultaneous preferences?
(Feel free to try to answer this yourself before continuing…)
Suppose I tell you that I prefer pineapple to mushrooms on my pizza. Suppose you’re about to give me a slice of mushroom pizza; but by paying one penny ($$0.01) I can instead get a slice of pineapple pizza (which is just as fresh from the oven). It seems realistic to say that most people with a pineapple pizza preference would probably pay the penny, if they happened to have a penny in their pocket. %note: It could be that somebody’s pizza preference is real, but so weak that they wouldn’t pay one penny to get the pizza they prefer. In this case, imagine we’re talking about some stronger preference instead. Like your willingness to pay at least one penny not to have your house burned down, or something.% After I pay the penny, though, and just before I’m about to get the pineapple pizza, you offer me a slice of onion pizza instead—no charge for the change! If I was telling the truth about preferring onion pizza to pineapple, I should certainly accept the substitution if it’s free. And then to round out the day, you offer me a mushroom pizza instead of the onion pizza, and again, since I prefer mushrooms to onions, I accept the swap. I end up with exactly the same slice of mushroom pizza I started with… and one penny poorer, because I previously paid 0.01 to swap mushrooms for pineapple. <div><div> This seems like a qualitatively bad behavior on my part. By virtue of my incoherent preferences which cannot be given a consistent ordering, I have shot myself in the foot, done something self-defeating. We haven’t said how I ought to sort out my inconsistent preferences. But no matter how it shakes out, it seems like there must be some better alternative—some better way I could reason that wouldn’t spend a penny to go in circles. That is, I could at least have kept my original pizza slice and not spent the penny. In a phrase you’re going to keep hearing, I have executed a ‘dominated strategy’: there exists some other strategy that does strictly better. noteThis does assume that the agent prefers to have more money rather than less money. “Ah, but why is it bad if one person has a penny instead of another?” you ask. If we insist on pinning down every point of this sort, then you can also imagine the 0.01 as standing in for the time I burned in order to move the pizza slices around in circles. That time was burned, and nobody else has it now. If I’m an effective agent that goes around pursuing my preferences, I should in general be able to sometimes convert time into other things that I want. In other words, my circular preference can lead me to incur an opportunity cost denominated in the sacrifice of other things I want, and not in a way that benefits anyone else. Or as Steve Omohundro put it: If you prefer being in Berkeley to being in San Francisco; prefer being in San Jose to being in Berkeley; and prefer being in San Francisco to being in San Jose; then you’re going to waste a lot of time on taxi rides. None of this reasoning has told us that a non-self-defeating agent must prefer Berkeley to San Francisco or vice versa. There are at least six possible consistent orderings over pizza toppings, like $$\text{mushroom} >_P \text{pineapple} >_P \text{onion}$$ etcetera, and any consistent ordering would avoid paying to go in circles. noteThere are more than six possibilities if you think it’s possible to be absolutely indifferent between two kinds of pizza. We have not, in this argument, used pure logic to derive that pineapple pizza must taste better than mushroom pizza to an ideal rational agent. But we’ve seen that eliminating a certain kind of shoot-yourself-in-the-foot behavior, corresponds to imposing a certain coherence or consistency requirement on whatever preferences are there. It turns out that this is just one instance of a large family of coherence theorems which all end up pointing at the same set of core properties. All roads lead to Rome, and all the roads say, “If you are not shooting yourself in the foot in sense X, we can view you as having coherence property Y.” There are some caveats to this general idea. For example: In complicated problems, perfect coherence is usually impossible to compute—it’s just too expensive to consider all the possibilities. But there are also caveats to the caveats! For example, it may be that if there’s a powerful machine intelligence that is not visibly to us humans shooting itself in the foot in way X, then from our perspective it must look like the AI has coherence property Y. If there’s some sense in which the machine intelligence is going in circles, because not going in circles is too hard to compute, well, we won’t see that either with our tiny human brains. In which case it may make sense, from our perspective, to think about the machine intelligence as if it has some coherent preference ordering. We are not going to go through all the coherence theorems in this introduction. They form a very large family; some of them are a lot more mathematically intimidating; and honestly I don’t know even 5% of the variants. But we can hopefully walk through enough coherence theorems to at least start to see the reasoning behind, “Why expected utility?” And, because the two are a package deal, “Why probability?” # Human lives, mere dollars, and coherent trades An experiment in 2000--from a paper titled “The Psychology of the Unthinkable: Taboo Trade-Offs, Forbidden Base Rates, and Heretical Counterfactuals”—asked subjects to consider the dilemma of a hospital administrator named Robert: Robert can save the life of Johnny, a five year old who needs a liver transplant, but the transplant procedure will cost the hospital 1,000,000 that could be spent in other ways, such as purchasing better equipment and enhancing salaries to recruit talented doctors to the hospital. Johnny is very ill and has been on the waiting list for a transplant but because of the shortage of local organ donors, obtaining a liver will be expensive. Robert could save Johnny’s life, or he could use the 1,000,000 for other hospital needs. The main experimental result was that most subjects got angry at Robert for even considering the question. After all, you can’t put a dollar value on a human life, right? But better hospital equipment also saves lives, or at least one hopes so. noteWe can omit the ‘better doctors’ item from consideration: The supply of doctors is mostly constrained by regulatory burdens and medical schools rather than the number of people who want to become doctors; so bidding up salaries for doctors doesn’t much increase the total number of doctors; so bidding on a talented doctor at one hospital just means some other hospital doesn’t get that talented doctor. It’s also illegal to pay for livers, but let’s ignore that particular issue with the problem setup or pretend that it all takes place in a more sensible country than the United States or Europe. It’s not like the other potential use of the money saves zero lives. Let’s say that Robert has a total budget of 100,000,000 and is faced with a long list of options such as these: • 100,000 for a new dialysis machine, which will save 3 lives • 1,000,000 for a liver for Johnny, which will save 1 life • 10,000 to train the nurses on proper hygiene when inserting central lines, which will save an expected 100 lives Now suppose—this is a supposition we’ll need for our theorem—that Robert does not care at all about money, not even a tiny bit. Robert only cares about maximizing the total number of lives saved. Furthermore, we suppose for now that Robert cares about every human life equally. If Robert does save as many lives as possible, given his bounded money, then Robert must behave like somebody assigning some consistent dollar value to saving a human life. We should be able to look down the long list of options that Robert took and didn’t take, and say, e.g., “Oh, Robert took all the options that saved more than 1 life per 500,000 and rejected all options that saved less than 1 life per 500,000; so Robert’s behavior is consistent with his spending 500,000 per life.” Alternatively, if we can’t view Robert’s behavior as being coherent in this sense—if we cannot make up any dollar value of a human life, such that Robert’s choices are consistent with that dollar value—then it must be possible to move around the same amount of money, in a way that saves more lives. We start from the qualitative criterion, “Robert must save as many lives as possible; it shouldn’t be possible to move around the same money to save more lives”. We end up with the quantitative coherence theorem, “It must be possible to view Robert as trading dollars for lives at a consistent price.” We haven’t proven that dollars have some intrinsic worth that trades off against the intrinsic worth of a human life. By hypothesis, Robert doesn’t care about money at all. It’s just that every dollar has an opportunity cost in lives it could have saved if deployed differently; and this opportunity cost is the same for every dollar because money is fungible. An important caveat to this theorem is that there may be, e.g., an option that saves a hundred thousand lives for 200,000,000. But Robert only has 100,000,000 to spend. In this case, Robert may fail to take that option even though it saves 1 life per 2,000. It was a good option, but Robert didn’t have enough money in the bank to afford it. This does mess up the elegance of being able to say, “Robert must have taken all the options saving at least 1 life per 500,000”, and instead we can only say this with respect to options that are in some sense small enough or granular enough. Similarly, if an option costs 5,000,000 to save 15 lives, but Robert only has 4,000,000 left over after taking all his other best opportunities, Robert’s last selected option might be to save 8 lives for 4,000,000 instead. This again messes up the elegance of the reasoning, but Robert is still doing exactly what an agent would do if it consistently valued lives at 1 life per 500,000--it would buy all the best options it could afford that purchased at least that many lives per dollar. So that part of the theorem’s conclusion still holds. Another caveat is that we haven’t proven that there’s some specific dollar value in Robert’s head, as a matter of psychology. We’ve only proven that Robert’s outward behavior can be viewed as if it prices lives at some consistent value, assuming Robert saves as many lives as possible. It could be that Robert accepts every option that spends less than 500,000/life and rejects every option that spends over 600,000, and there aren’t any available options in the middle. Then Robert’s behavior can equally be viewed as consistent with a price of 510,000 or a price of 590,000. This helps show that we haven’t proven anything about Robert explicitly thinking of some number. Maybe Robert never lets himself think of a specific threshold value, because it would be taboo to assign a dollar value to human life; and instead Robert just fiddles the choices until he can’t see how to save any more lives. We naturally have not proved by pure logic that Robert must want, in the first place, to save as many lives as possible. Even if Robert is a good person, this doesn’t follow. Maybe Robert values a 10-year-old’s life at 5 times the value of a 70-year-old’s life, so that Robert will sacrifice five grandparents to save one 10-year-old. A lot of people would see that as entirely consistent with valuing human life in general. Let’s consider that last idea more thoroughly. If Robert considers a preteen equally valuable with 5 grandparents, so that Robert will shift 100,000 from saving 8 old people to saving 2 children, then we can no longer say that Robert wants to save as many ‘lives’ as possible. That last decision would decrease by 6 the total number of ‘lives’ saved. So we can no longer say that there’s a qualitative criterion, ‘Save as many lives as possible’, that produces the quantitative coherence requirement, ‘trade dollars for lives at a consistent rate’. Does this mean that coherence might as well go out the window, so far as Robert’s behavior is concerned? Anything goes, now? Just spend money wherever? “Hm,” you might think. “But… if Robert trades 8 old people for 2 children here… and then trades 1 child for 2 old people there…” To reduce distraction, let’s make this problem be about apples and oranges instead. Suppose: • Alice starts with 8 apples and 1 orange. • Then Alice trades 8 apples for 2 oranges. • Then Alice trades away 1 orange for 2 apples. • Finally, Alice trades another orange for 3 apples. Then in this example, Alice is using a strategy that’s strictly dominated across all categories of fruit. Alice ends up with 5 apples and one orange, but could’ve ended with 8 apples and one orange (by not making any trades at all). Regardless of the relative value of apples and oranges, Alice’s strategy is doing qualitatively worse than another possible strategy, if apples have any positive value to her at all. So the fact that Alice can’t be viewed as having any coherent relative value for apples and oranges, corresponds to her ending up with qualitatively less of some category of fruit (without any corresponding gains elsewhere). This remains true if we introduce more kinds of fruit into the problem. Let’s say the set of fruits Alice can trade includes {apples, oranges, strawberries, plums}. If we can’t look at Alice’s trades and make up some relative quantitative values of fruit, such that Alice could be trading consistently with respect to those values, then Alice’s trading strategy must have been dominated by some other strategy that would have ended up with strictly more fruit across all categories. In other words, we need to be able to look at Alice’s trades, and say something like: “Maybe Alice values an orange at 2 apples, a strawberry at 0.1 apples, and a plum at 0.5 apples. That would explain why Alice was willing to trade 4 strawberries for a plum, but not willing to trade 40 strawberries for an orange and an apple.” And if we can’t say this, then there must be some way to rearrange Alice’s trades and get strictly more fruit across all categories in the sense that, e.g., we end with the same number of plums and apples, but one more orange and two more strawberries. This is a bad thing if Alice qualitatively values fruit from each category—prefers having more fruit to less fruit, ceteris paribus, for each category of fruit. Now let’s shift our attention back to Robert the hospital administrator. Either we can view Robert as consistently assigning some relative value of life for 10-year-olds vs. 70-year-olds, or there must be a way to rearrange Robert’s expenditures to save either strictly more 10-year-olds or strictly more 70-year-olds. The same logic applies if we add 50-year-olds to the mix. We must be able to say something like, “Robert is consistently behaving as if a 50-year-old is worth a third of a ten-year-old”. If we can’t say that, Robert must be behaving in a way that pointlessly discards some saveable lives in some category. Or perhaps Robert is behaving in a way which implies that 10-year-old girls are worth more than 10-year-old boys. But then the relative values of those subclasses 10-year-olds need to be viewable as consistent; or else Robert must be qualitatively failing to save one more 10-year-old boy than could’ve been saved otherwise. If you can denominate apples in oranges, and price oranges in plums, and trade off plums for strawberries, all at consistent rates… then you might as well take it one step further, and factor out an abstract unit for ease of notation. Let’s call this unit 1 utilon, and denote it €1. (As we’ll see later, the letters ‘EU’ are appropriate here.) If we say that apples are worth €1, oranges are worth €2, and plums are worth €0.5, then this tells us the relative value of apples, oranges, and plums. Conversely, if we can assign consistent relative values to apples, oranges, and plums, then we can factor out an abstract unit at will—for example, by arbitrarily declaring apples to be worth €100 and then calculating everything else’s price in apples. Have we proven by pure logic that all apples have the same utility? Of course not; you can prefer some particular apples to other particular apples. But when you’re done saying which things you qualitatively prefer to which other things, if you go around making tradeoffs in way that can be viewed as not qualitatively leaving behind some things you said you wanted, we can view you as assigning coherent quantitative utilities to everything you want. And that’s one coherence theorem—among others—that can be seen as motivating the concept of utility in decision theory. Utility isn’t a solid thing, a separate thing. We could multiply all the utilities by two, and that would correspond to the same outward behaviors. It’s meaningless to ask how much utility you scored at the end of your life, because we could subtract a million or add a million to that quantity while leaving everything else conceptually the same. You could pick anything you valued—say, the joy of watching a cat chase a laser pointer for 10 seconds—and denominate everything relative to that, without needing any concept of an extra abstract ‘utility’. So (just to be extremely clear about this point) we have not proven that there is a separate thing ‘utility’ that you should be pursuing instead of everything else you wanted in life. The coherence theorem says nothing about which things to value more than others, or how much to value them relative to other things. It doesn’t say whether you should value your happiness more than someone else’s happiness, any more than the notion of a consistent preference ordering $$>_P$$ tells us whether $$\text{onions} >_P \text{pineapple}.$$ (The notion that we should assign equal value to all human lives, or equal value to all sentient lives, or equal value to all Quality-Adjusted Life Years, is utilitarianism. Which is, sorry about the confusion, a whole ’nother separate different philosophy.) The conceptual gizmo that maps thingies to utilities—the whatchamacallit that takes in a fruit and spits out a utility—is called a ‘utility function’. Again, this isn’t a separate thing that’s written on a stone tablet. If we multiply a utility function by 9.2, that’s conceptually the same utility function because it’s consistent with the same set of behaviors. But in general: If we can sensibly view any agent as doing as well as qualitatively possible at anything, we must be able to view the agent’s behavior as consistent with there being some coherent relative quantities of wantedness for all the thingies it’s trying to optimize. # Probabilities and expected utility We’ve so far made no mention of probability. But the way that probabilities and utilities interact, is where we start to see the full structure of expected utility spotlighted by all the coherence theorems. The basic notion in expected utility is that some choices present us with uncertain outcomes. For example, I come to you and say: “Give me 1 apple, and I’ll flip a coin; if the coin lands heads, I’ll give you 1 orange; if the coin comes up tails, I’ll give you 3 plums.” Suppose you relatively value fruits as described earlier: 2 apples / orange and 0.5 apples / plum. Then either possible outcome gives you something that’s worth more to you than 1 apple. Turning down a so-called ‘gamble’ like that… why, it’d be a dominated strategy. In general, the notion of ‘expected utility’ says that we assign certain quantities called probabilities to each possible outcome. In the example above, we might assign a ‘probability’ of $$0.5$$ to the coin landing heads (1 orange), and a ‘probability’ of $$0.5$$ to the coin landing tails (3 plums). Then the total value of the ‘gamble’ we get by trading away 1 apple is:$$\mathbb P(heads) \cdot U(\text{1 orange}) + \mathbb P(tails) \cdot U(\text{3 plums}) \\ = 0.50 \cdot €2 + 0.50 \cdot €1.5 = €1.75$$Conversely, if we just keep our 1 apple instead of making the trade, this has an expected utilty of $$1 \cdot U(\text{1 apple}) = €1.$$ So indeed we ought to trade (as the previous reasoning suggested). “But wait!” you cry. “Where did these probabilities come from? Why is the ‘probability’ of a fair coin landing heads $$0.5$$ and not, say, $$-0.2$$ or $$3$$? Who says we ought to multiply utilities by probabilities in the first place?” If you’re used to approaching this problem from a Bayesian standpoint, then you may now be thinking of notions like prior probability and Occam’s Razor and universal priors But from the standpoint of coherence theorems, that’s putting the cart before the horse. From the standpoint of coherence theorems, we don’t start with a notion of ‘probability’. Instead we ought to prove something along the lines of: if you’re not using qualitatively dominated strategies, then you must behave as if you are multiplying utilities by certain quantitative thingies. We might then furthermore show that, for non-dominated strategies, these utility-multiplying thingies must be between $$0$$ and $$1$$ rather than say $$-0.3$$ or $$27.$$ Having determined what coherence properties these utility-multiplying thingies need to have, we decide to call them ‘probabilities’. And then—once we know in the first place that we need ‘probabilities’ in order to not be using dominated strategies—we can start to worry about exactly what the numbers ought to be. ## Probabilities summing to 1 Here’s a taste of the kind of reasoning we might do: Suppose that—having already accepted some previous proof that non-dominated strategies dealing with uncertain outcomes, must multiply utilities by quantitative thingies—you then say that you are going to assign a probability of $$0.6$$ to the coin coming up heads, and a probability of $$0.7$$ to the coin coming up tails. If you’re already used to the standard notion of probability, you might object, “But those probabilities sum to $$1.3$$ when they ought to sum to $$1!$$noteOr maybe a tiny bit less than $$1,$$ in case the coin lands on its edge or something. But now we are in coherence-land; we don’t ask “Did we violate the standard axioms that all the textbooks use?” but “What rules must non-dominated strategies obey?” De gustibus non est disputandum; can we disputandum somebody saying that a coin has a 60% probability of coming up heads and a 70% probability of coming up tails? (Where these are the only 2 possible outcomes of an uncertain coinflip.) Well—assuming you’ve already accepted that we need utility-multiplying thingies—I might then offer you a gamble. How about you give me one apple, and if the coin lands heads, I’ll give you 0.8 apples; while if the coin lands tails, I’ll give you 0.8 apples. According to you, the expected utility of this gamble is:$$\mathbb P(\text{heads}) \cdot U(\text{0.8 apples}) + \mathbb P(\text{tails}) \cdot U(\text{0.8 apples}) \\ = 0.6 \cdot €0.8 + 0.7 \cdot €0.8 = €1.04.$$You’ve just decided to trade your apple for 0.8 apples, which sure sounds like one of ’em dominated strategies. And that’s why the thingies you multiply probabilities by—the thingies that you use to weight uncertain outcomes in your imagination, when you’re trying to decide how much you want one branch of an uncertain choice—must sum to 1, whether you call them ‘probabilities’ or not. Well… actually we just argued noteNothing we’re walking through here is really a coherence theorem per se, more like intuitive arguments that a coherence theorem ought to exist. Theorems require proofs, and nothing is here is what real mathematicians would consider to be a ‘proof’. that probabilities for mutually exclusive outcomes should sum to no more than 1. What would be an example showing that, for non-dominated strategies, the probabilities for exhaustive outcomes should sum to no less than 1? Suppose that, in exchange for 1 apple, I credibly offer: • To pay you 1.1 apples if a coin comes up heads. • To pay you 1.1 apples if a coin comes up tails. • To pay you 1.1 apples if anything else happens. If the probabilities you assign to these three outcomes sum to say 0.9, you will refuse to trade 1 apple for 1.1 apples. (This is strictly dominated by the strategy of agreeing to trade 1 apple for 1.1 apples.) <div><div> ## Dutch book arguments Another way we could have presented essentially the same argument as above, is as follows: Suppose you are a market-maker in a prediction market for some event $$X.$$ When you say that your price for event $$X$$ is $$x$$, you mean that you will sell for $$\x$$ a ticket which pays $$\1$$ if $$X$$ happens (and pays out nothing otherwise). In fact, you will sell any number of such tickets! Since you are a market-maker (that is, you are trying to encourage trading in $$X$$ for whatever reason), you are also willing to buy any number of tickets at the price $$\x.$$ That is, I can say to you (the market-maker) “I’d like to sign a contract where you give me $$N \cdot \x$$ now, and in return I must pay you $$\N$$ iff $$X$$ happens;” and you’ll agree. (We can view this as you selling me a negative number of the original kind of ticket.) Let $$X$$ and $$Y$$ denote two events such that exactly one of them must happen; say, $$X$$ is a coin landing heads and $$Y$$ is the coin not landing heads. Now suppose that you, as a market-maker, are motivated to avoid combinations of bets that lead into certain losses for you—not just losses that are merely probable, but combinations of bets such that every possibility leads to a loss. Then if exactly one of $$X$$ and $$Y$$ must happen, your prices $$x$$ and $$y$$ must sum to exactly $$\1.$$ Because: • If $$x + y < \1,$$ I buy both an $$X$$-ticket and a $$Y$$-ticket and get a guaranteed payout of $$\1$$ minus costs of $$x + y.$$ Since this is a guaranteed profit for me, it is a guaranteed loss for you. • If $$x + y > \1,$$ I sell you both tickets and will at the end pay you $$\1$$ after you have already paid me $$x + y.$$ Again, this is a guaranteed profit for me of $$x + y - \1 > \0.$$ This is more or less exactly the same argument as in the previous section, with trading apples. Except that: (a) the scenario is more crisp, so it is easier to generalize and scale up much more complicated similar arguments; and (b) it introduces a whole lot of assumptions that people new to expected utility would probably find rather questionable. “What?” one might cry. “What sort of crazy bookie would buy and sell bets at exactly the same price? Why ought anyone to buy and sell bets at exactly the same price? Who says that I must value a gain of 1 exactly the opposite of a loss of 1? Why should the price that I put on a bet represent my degree of uncertainty about the environment? What does all of this argument about gambling have to do with real life?” So again, the key idea is not that we are assuming anything about people valuing every real-world dollar the same; nor is it in real life a good idea to offer to buy or sell bets at the same prices. noteIn real life this leads to a problem of ‘adversarial selection’ where somebody who knows more about the environment than you, can decide whether to buy or sell from you. To put it another way, from a Bayesian standpoint, if an intelligent counterparty is deciding whether to buy or sell from you a bet on $$X$$, the fact that they choose to buy (or sell) should cause you to update in favor (or against) $$X$$ actually happening. After all, they wouldn’t be taking the bet unless they thought they knew something you didn’t! Rather, Dutch book arguments can stand in as shorthand for some longer story in which we only assume that you prefer more apples to less apples. The Dutch book argument above has to be seen as one more added piece in the company of all the other coherence theorems—for example, the coherence theorems suggesting that you ought to be quantitatively weighing events in your mind in the first place. ## Conditional probability With more complicated Dutch book arguments, we can derive more complicated ideas such as ‘conditional probability’. Let’s say that we’re pricing three kinds of gambles over two events $$Q$$ and $$R$$: • A ticket that costs $$\x$$, and pays $$\1$$ if $$Q$$ happens. • A ticket that doesn’t cost anything or pay anything if $$Q$$ doesn’t happen (the ticket price is refunded); and if $$Q$$ does happen, this ticket costs $$\y,$$ then pays $$\1$$ if $$R$$ happens. • A ticket that costs $$\z$$, and pays $$\1$$ if $$Q$$ and $$R$$ both happen. Intuitively, the idea of conditional probability is that the probability of $$Q$$ and $$R$$ both happening, should be equal to the probability of $$Q$$ happening, times the probability that $$R$$ happens assuming that $$Q$$ happens:$$\mathbb P(Q \wedge R) = \mathbb P(Q) \cdot \mathbb P(R \mid Q)$$To exhibit a Dutch book argument for this rule, we want to start from the assumption of a qualitatively non-dominated strategy, and derive the quantitative rule $$z = x \cdot y.$$ So let’s give an example that violates this equation and see if there’s a way to make a guaranteed profit. Let’s say somebody: • Prices at x=0.60 the first ticket, aka $$\mathbb P(Q)$$ • Prices at y=0.70 the second ticket, aka $$\mathbb P(R \mid Q)$$ • Prices at z=0.20 the third ticket, aka $$\mathbb P(Q \wedge R),$$ which ought to be 0.42 assuming the first two prices. The first two tickets are priced relatively high, compared to the third ticket which is priced relatively low, suggesting that we ought to sell the first two tickets and buy the third. Okay, let’s ask what happens if we sell 10 of the first ticket, sell 10 of the second ticket, and buy 10 of the third ticket. • If $$Q$$ doesn’t happen, we get 6, and pay 2. Net +4. • If $$Q$$ happens and $$R$$ doesn’t happen, we get 6, pay 10, get 7, and pay 2. Net +1. • If $$Q$$ happens and $$R$$ happens, we get 6, pay 10, get 7, pay 10, pay 2, and get 10. Net: +1. That is: we can get a guaranteed positive profit over all three possible outcomes. More generally, let $$A, B, C$$ be the (potentially negative) amount of each ticket $$X, Y, Z$$ that is being bought (buying a negative amount is selling). Then the prices $$x, y, z$$ can be combined into a ‘Dutch book’ whenever the following three inequalities can be simultaneously true, with at least one inequality strict:$$\begin{array}{rrrl} -Ax & + 0 & - Cz & \geqq 0 \\ A(1-x) & - By & - Cz & \geqq 0 \\ A(1-x) & + B(1-y) & + C(1-z) & \geqq 0 \end{array}$$For $$x, y, z \in (0..1)$$ this is impossible exactly iff $$z = x \* y.$$ The proof via a bunch of algebra is left as an exercise to the reader. noteThe quick but advanced argument would be to say that the left-hand-side must look like a singular matrix, whose determinant must therefore be zero. ## The Allais Paradox By now, you’d probably like to see a glimpse of the sort of argument that shows in the first place that we need expected utility—that a non-dominated strategy for uncertain choice must behave as if multiplying utilities by some kinda utility-multiplying thingies (‘probabilities’). As far as I understand it, the real argument you’re looking for is Abraham Wald’s complete class theorem, which I must confess I don’t know how to reduce to a simple demonstration. But we can catch a glimpse of the general idea from a famous psychology experiment that became known as the Allais Paradox (in slightly adapted form). Suppose you ask some experimental subjects which of these gambles they would rather play: • 1A: A certainty of 1,000,000. • 1B: 90% chance of winning 5,000,000, 10% chance of winning nothing. Most subjects say they’d prefer 1A to 1B. Now ask a separate group of subjects which of these gambles they’d prefer: • 2A: 50% chance of winning 1,000,000; 50% chance of winning 0. • 2B: 45% chance of winning 5,000,000; 55% chance of winning 0. In this case, most subjects say they’d prefer gamble 2B. Note that the sign here denotes real dollars, not utilities! A gain of five million dollars isn’t, and shouldn’t be, worth exactly five times as much to you as a gain of one million dollars. We can use the € symbol to denote the expected utilities that are abstracted from how much you relatively value different outcomes; is just money. So we certainly aren’t claiming that the first preference is paradoxical because 1B has an expected dollar value of 4.5 million and 1A has an expected dollar value of 1 million. That would be silly. We care about expected utilities, not expected dollar values, and those two concepts aren’t the same at all! Nonetheless, the combined preferences 1A > 1B and 2A < 2B are not compatible with any coherent utility function. We cannot simultaneously have:$$\begin{array}{rcl} U(\text{gain \$1 million}) & > & 0.9 \cdot U(\text{gain \$5 million}) + 0.1 \cdot U(\text{gain \$0}) \\ 0.5 \cdot U(\text{gain \$0}) + 0.5 \cdot U(\text{gain \$1 million}) & > & 0.45 \cdot U(\text{gain \$5 million}) + 0.55 \cdot U(\text{gain \$0}) \end{array}$$This was one of the earliest experiments seeming to demonstrate that actual human beings were not expected utility maximizers—a very tame idea nowadays, to be sure, but the first definite demonstration of that was a big deal at the time. Hence the term, “Allais Paradox”. Now by the general idea behind coherence theorems, since we can’t view this behavior as corresponding to expected utilities, we ought to be able to show that it corresponds to a dominated strategy somehow—derive some way in which this behavior corresponds to shooting off your own foot. In this case, the relevant idea seems non-obvious enough that it doesn’t seem reasonable to demand that you think of it on your own; but if you like, you can pause and try to think of it anyway. Otherwise, just continue reading. Again, the gambles are as follows: • 1A: A certainty of$1,000,000.
• 1B: 90% chance of winning $5,000,000, 10% chance of winning nothing. • 2A: 50% chance of winning$1,000,000; 50% chance of winning $0. • 2B: 45% chance of winning$5,000,000; 55% chance of winning $0. Now observe that Scenario 2 corresponds to a 50% chance of playing Scenario 1, and otherwise getting$0.
This, in fact, is why the combination 1A > 1B; 2A < 2B is incompatible with expected utility. In terms of one set of axioms frequently used to describe expected utility, it violates the Independence Axiom: if a gamble $$L$$ is preferred to $$M$$, that is $$L > M$$, then we ought to be able to take a constant probability $$p > 0$$ and another gamble $$N$$ and have $$p \cdot L + (1-p)\cdot N > p \cdot M + (1-p) \cdot N.$$
To put it another way, if I flip a coin to decide whether or not to play some entirely different game $$N,$$ but otherwise let you choose $$L$$ or $$M,$$ you ought to make the same choice as if I just ask you whether you prefer $$L$$ or $$M$$. Your preference between $$L$$ and $$M$$ should be ‘independent’ of the possibility that, instead of doing anything whatsoever with $$L$$ or $$M,$$ we will do something else instead.
And since this is an axiom of expected utility, any violation of that axiom ought to correspond to a dominated strategy somehow.
In the case of the Allais Paradox, we do the following:
First, I show you a switch that can be set to A or B, currently set to A.
In one minute, I tell you, I will flip a coin. If the coin comes up heads, you will get nothing. If the coin comes up tails, you will play the gamble from Scenario 1.
From your current perspective, that is, we are playing Scenario 2: since the switch is set to A, you have a 50% chance of getting nothing and a 50% chance of getting $1 million. I ask you if you’d like to pay a penny to throw the switch from A to B. Since you prefer gamble 2B to 2A, and some quite large amounts of money are at stake, you agree to pay the penny. From your perspective, you now have a 55% chance of ending up with nothing and a 45% chance of getting$5M.
I then flip the coin, and luckily for you, it comes up tails.
From your perspective, you are now in Scenario 1B. Having observed the coin and updated on its state, you now think you have a 90% chance of getting $5 million and a 10% chance of getting nothing. By hypothesis, you would prefer a certainty of$1 million.
So I offer you a chance to pay another penny to flip the switch back from B to A. And with so much money at stake, you agree.
I have taken your two cents on the subject.
That is: You paid a penny to flip a switch and then paid another penny to switch it back, and this is dominated by the strategy of just leaving the switch set to A.
And that’s at least a glimpse of why, if you’re not using dominated strategies, the thing you do with relative utilities is multiply them by probabilities in a consistent way, and prefer the choice that leads to a greater expectation of the variable representing utility.
### From the Allais Paradox to real life
The real-life lesson about what to do when faced with Allais’s dilemma might be something like this:
There’s some amount that $1 million would improve your life compared to$0.
There’s some amount that an additional $4 million would further improve your life after the first$1 million.
You ought to visualize these two improvements as best you can, and decide whether another $4 million can produce at least one-ninth as much improvement, as much true value to you, as the first$1 million.
If it can, you should consistently prefer 1B > 1A; 2B > 2A. And if not, you should consistently prefer 1A > 1B; 2A > 2B.
The standard ‘paradoxical’ preferences in Allais’s experiment are standardly attributed to a certainty effect: people value the certainty of having $1 million, while the difference between a 50% probability and a 55% probability looms less large. (And this ties in to a number of other results about certainty, need for closure, prospect theory, and so on.) It may sound intuitive, in an Allais-like scenario, to say that you ought to derive some value from being certain about the outcome. In fact this is just the reasoning the experiment shows people to be using, so of course it might sound intuitive. But that does, inescapably, correspond to a kind of thinking that produces dominated strategies. One possible excuse might be that certainty is valuable if you need to make plans about the future; knowing the exact future lets you make better plans. This is admittedly true and a phenomenon within expected utility, though it applies in a smooth way as confidence increases rather than jumping suddenly around 100%. But in the particular dilemma as described here, you only have 1 minute before the game is played, and no time to make other major life choices dependent on the outcome. Another possible excuse for certainty bias might be to say: “Well, I value the emotional feeling of certainty.” In real life, we do have emotions that are directly about probabilities, and those little flashes of happiness or sadness are worth something if you care about people being happy or sad. If you say that you value the emotional feeling of being certain of getting$1 million, the freedom from the fear of getting $0, for the minute that the dilemma lasts and you are experiencing the emotion—well, that may just be a fact about what you value, even if it exists outside the expected utility formalism. And this genuinely does not fit into the expected utility formalism. In an expected utility agent, probabilities are just thingies-you-multiply-utilities-by. If those thingies start generating their own utilities once represented inside the mind of person who is an object of ethical value, you really are going to get results that are incompatible with the formal decision theory. However, not being viewable as an expected utility agent does always correspond to employing dominated strategies. You are giving up something in exchange, if you pursue that feeling of certainty. You are potentially losing all the real value you could have gained from another$4 million, if that realized future actually would have gained you more than one-ninth the value of the first $1 million. Is a fleeting emotional sense of certainty over 1 minute, worth automatically discarding the potential$5-million outcome? Even if the correct answer given your values is that you properly ought to take the $1 million, treasuring 1 minute of emotional doesn’t seem like the wise reason to do that. The wise reason would be if the first$1 million really was worth that much more than the next \$4 million.
The danger of saying, “Oh, well, I attach a lot of utility to that comfortable feeling of certainty, so my choices are coherent after all” is not that it’s mathematically improper to value the emotions we feel while we’re deciding. Rather, by saying that the most valuable stakes are the emotions you feel during the minute you make the decision, what you’re saying is, “I get a huge amount of value by making decisions however humans instinctively make their decisions, and that’s much more important than the thing I’m making a decision about.” This could well be true for something like buying a stuffed animal. If millions of dollars or human lives are at stake, maybe not so much.
# Conclusion
The demonstrations we’ve walked through here aren’t the professional-grade coherence theorems as they appear in real math. Those have names like “Cox’s Theorem” or “the complete class theorem”; their proofs are difficult; and they say things like “If seeing piece of information A followed by piece of information B leads you into the same epistemic state as seeing piece of information B followed by piece of information A, plus some other assumptions, I can show an isomorphism between those epistemic states and classical probabilities” or “Any decision rule for taking different actions depending on your observations either corresponds to Bayesian updating given some prior, or else is strictly dominated by some Bayesian strategy”.
But hopefully you’ve seen enough concrete demonstrations to get a general idea of what’s going on with the actual coherence theorems. We have multiple spotlights all shining on the same core mathematical structure, saying dozens of different variants on, “If you aren’t running around in circles or stepping on your own feet or wantonly giving up things you say you want, we can see your behavior as corresponding to this shape. Conversely, if we can’t see your behavior as corresponding to this shape, you must be visibly shooting yourself in the foot.” Expected utility is the only structure that has this great big family of discovered theorems all saying that. It has a scattering of academic competitors, because academia is academia, but the competitors don’t have anything like that mass of spotlights all pointing in the same direction.
So if we need to pick an interim answer for “What kind of quantitative framework should I try to put around my own decision-making, when I’m trying to check if my thoughts make sense?” or “By default and barring special cases, what properties might a sufficiently advanced machine intelligence look to us like it had at least approximately, if we couldn’t see it visibly running around in circles?”, then there’s pretty much one obvious candidate: Probabilities, utility functions, and expected utility.
• To learn more about agents and AI: Interesting cognition and behavior that can be derived just from the notion of expected utility, followed by Is expected utility a good way to think about the default behavior of sufficiently advanced Artificial Intelligences?
• To learn more about decision theory: The controversial counterfactual at the heart of the expected utility formula.
Parents:
• In the Mathjax bit of the Allais Paradox section, the sign on the second line shows as being backward (greater-than sign on both lines):
https://ibb.co/55xvtg5
If I look at the source (by proposing an edit) it looks as if it ought to be correct, but I’m not familiar with Mathjax so I’m not sure what the issue is.
|
2022-08-16 09:34:43
|
{"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": 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": 0.9458194375038147, "perplexity": 1354.2667997454366}, "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-2022-33/segments/1659882572286.44/warc/CC-MAIN-20220816090541-20220816120541-00612.warc.gz"}
|
https://www.latestpapers.com/paper/1390
|
No subtopics of Category Theory
Login to subscribe or post
⬑ Back to Category Theory papers
Found 10 similar papers to this:
more search results...
Create an alert - Get sent papers like this when they're published.
Auslander-Buchweitz approximation theory for triangulated categories
Submitted by mathbot to Category Theory, 2173 hours ago. 1 votes.
We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category $\T,$ which are based on the behavior of certain subcategories under finiteness of resolutions and vanishing of Hom-spaces. For example: we establish the existence of preenvelopes (and precovers) in certain triangulated subcategories of $\T.$ The results resemble various constructions and results of Auslander and Buchweitz, and are concentrated in exploring the structure of a triangulated category $\T$ equipped with a pair $(\X,\omega),$ where $\X$ is closed under extensions and $\omega$ is a weak-cogenerator in $\X,$ usually under additional conditions. This reduces, among other things, to the existence of distinguished triangles enjoying special properties, and the behavior of (suitably defined) (co)resolutions, projective or injective dimension of objects of $\T$ and the formation of orthogonal subcategories. Finally, some relationships with the Rouquier's dimension in triangulated categories is discussed.
No comments posted yet.
|
2017-09-26 02:04:20
|
{"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": 0.6465150117874146, "perplexity": 761.5608068998777}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818693940.84/warc/CC-MAIN-20170926013935-20170926033935-00627.warc.gz"}
|
https://www.lewuathe.com/intellij%20idea/red-j-in-intellij-idea.html
|
# Red J in IntelliJ IDEA
In some cases when I use IntelliJ IDEA for Java projects, I faced this red J mark.
This mark means these files are not included current project. So indexes of these files are not generated and search functionality does not work. How can we solve this problem?
So in this wizard, only you have to do is + and add a missing module into your projects. That’s all.
|
2022-10-03 21:28:15
|
{"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": 0.2544245421886444, "perplexity": 2001.9135987692096}, "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/1664030337432.78/warc/CC-MAIN-20221003200326-20221003230326-00155.warc.gz"}
|
http://umj.imath.kiev.ua/authors/name/?lang=en&author_id=1233
|
2019
Том 71
№ 6
# Tushev A. V.
Articles: 10
Article (Ukrainian)
### Induced Representations of Abelian Groups of Finite Rank
Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1249-1253
We prove that any irreducible faithful representation of an almost torsion-free Abelian group G of finite rank over a finitely generated field of characteristic zero is induced from an irreducible representation of a finitely generated subgroup of the group G.
Article (Russian)
### On Solvable Groups with Proper Quotient Groups of Finite Rank
Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1560-1568
We study solvable groups of infinite special rank all proper normal subgroups of which define quotient groups of finite special rank.
Article (Russian)
### On Noetherian Modules over Minimax Abelian Groups
Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 969-980
We consider modules over minimax Abelian groups. We prove that if A is an Abelian minimax subgroup of the multiplicative group of a field k and if the subring K of the field k generated by the subgroup A is Noetherian, then the subgroup A is the direct product of a periodic group and a finitely generated group.
Brief Communications (Russian)
### On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers
Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 571-572
In this paper, we prove the existence of an elementα of the group algebra $A=ℂF$ of a free group $F$ with two generatorsx andy over the field of complex numbers $C$ such that, for any complex $a$ and $b$ for which $¦a¦=¦b¦=1$, we have $A ∩ ϑ_{a,b} (α)A=0$, where $ϑ_{a,b}$ ($α$ is an automorphism of $A$ that maps $x,y$ into $a_x, b_y$, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.”
Article (Ukrainian)
### On exact irreducible representations of locally normal groups
Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1688–1694
We obtain a generalization of the Gaschutz criterion of existence of exact irreducible representations of finite groups to the class of normal groups.
Article (Ukrainian)
### Noether modules over abelian groups of finite free rank
Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 1042–1048
Article (Ukrainian)
### Irreducible representations of locally polycyclic groups over an absolute field
Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1389–1394
Article (Ukrainian)
### Condition min-?-N and the representations of solvable groups connected with IT
Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 677–681
Article (Ukrainian)
### Some classes of groups with weak minimal condition for normal subgroups
Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 457–462
Article (Ukrainian)
### Two-step solvable groups with weak minimal condition for normal subgroups
Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 300–306
|
2019-06-26 06:38:05
|
{"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": 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": 0.7011973261833191, "perplexity": 568.3360511127587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000175.78/warc/CC-MAIN-20190626053719-20190626075719-00141.warc.gz"}
|
http://lavkashop.com/social-security-nwx/viewtopic.php?7a501f=method-of-sections-howe-roof-truss
|
It hinges on dividing the truss into two parts and then considering a free body diagram of one part or the other, Complex Trusses! Source: The Design of Simple Roof Trusses in Wood and Steel by Malverd A. Howe, 1903 Common Roof Trusses 5. Determine the force in members GI, HI, and HJ when P1 = 0.9 … We slide F DF to apply it at F: 22 The Method of Sections (Ritter Method) If the forces in only a few members of a truss are to be found, the method of sections generally provide the most direct means of obtaining these forces The method is created the German scientist August Ritter (1826 - 1908). Space Trusses Analysis of Statically Determinate Trusses. Optimal truss from each set of trusses is to be compared to determine which type of truss is more economical for different spans. The Warren truss loaded as shown in Fig. The finite element model loaded by external forces, without and with self-weight of structure is computed. Source: The Design of Simple Roof Trusses in Wood and Steel by Malverd A. Howe, 1903 . The sections are obtained by cutting through some of the members of the truss to expose the force inside the members. Select a part and press "Delete" to delete it. From the section to the right of M-N The most common form is the Warren truss with verticals. Using the method of joints and the method of sections, determine the force in all members. In the method of sections, a truss is divided into two parts by taking an imaginary “cut” (shown here as a-a) through the truss. TFEC 4-2020 Page 11 Squire Whipple (1804-1888) No authoritative treatise on trusses can fail to pay … Use the method of sections to find the forces in members FJ and GJ. Method of section: This method entails passing an imaginary section through the truss to divide it into two sections. By upgrading to on of SkyCiv's pricing options, you'll have access to full structural analysis software so you select materials such as wood and steel to perform truss designs - making it much more than a simple roof … 104 0 obj <>stream Since truss members are subjected to only tensile or compressive forces along their length, the internal forces at the cut member will also be either tensile or compressive with the same magnitude. The Method of Sections involves analytically cutting the truss into sections and solving for static equilibrium for each section. The laws of statics still apply – so the … 2. Design and Comparison of Steel Roof Truss with Tubular Section (using SP: 38 And IS: 800-2007) ... and Technology (Rajkot), Gujarat Technological University Abstract— In this paper, different configuration of steel roof trusses, such as Howe type, Fan type, Fink Fan type, and N-type with different span has 9m, 12m, 15m, 18m and 21m, with varying slopes like 12, 14 and 16 degrees with different wind zones, … - The method of sections is commonly used when the forces in only a few particular members of a truss are to be determined; - The method of sections is always used together with the method of joints to analyze trusses. two types of truss configurations namely Howe truss and Pratt truss for span of 35m with two different span to depth ratios. Roof trusses are generally used in industrial buildings. 2. Pro.Vi8. Patrikar Avanti, Pathak K. K. (2016) has published a paper on Fully Stressed Design of Fink Truss using STAAD.Pro Software which is based on optimization technique of structures in this paper truss of three different spans has been considered with set of three loads and 27 different load … State whether each member is in tension or compression. SOLUTION Reactions at supports. Section 2.3.5.2 states, “The Truss Designer shall be responsible for the design, in accordance with this Standard, of each singular Truss depicted on the Truss Design Drawing.” This method is advantageous when the axial forces in specific members are required in a truss with several members. h�bc: "'�3�3 ?3P���� �� 1�N��� @vƹ@����"a|�a]�EJ�&�. 10- Determine the force in each member of the Howe roof truss shown. Solution for Part 2 A Pratt roof truss is loaded as shown. Howe Trusses 25 Pratt Trusses 26 Fink Trusses 27 Scissor Trusses 28 Hammer-Beam Trusses 31 Parallel Chord Trusses 34 ... the method became extinct. Roof trusses are generally used in industrial buildings. State whether each member is in tension or compression. b) Sections method. Next, make a decision on how the truss should be “cut” into sections and draw the corresponding free-body diagrams. 6 (7) Determine the force and it’s nature (tension/compression) for the inverted Howe roof truss shown. Problem 418. Using the method of joints and the method of sections, determine the force in all members. The Method of Sections involves analytically cutting the truss into sections and solving for static equilibrium for each section. For Problem, use the method of section. Try to apply the three equations of equilibrium such that simultaneous solution is not required. %%EOF 3 Howe truss 18 - 30 m Pratt truss 18 - 30 m Howe truss flat roof Warren truss flat roof saw-tooth truss skylight Fink truss > … This free online truss and roof calculator generates the axial forces and reactions of completely customisable 2D truss structures. 6. Bracing of roof trusses 4. Each part seperated by the section is in equilibrium state.Focussing of the part,which has lesser number of unknows and applying the law of statitics, the … 2. Once personal computers and cheap analytical software were introduced in the 1980s, the method became extinct. The comparison of results of analytical and … 5 Prob. The Truss Designer is only responsible for “individual” Trusses, not the roof system. Howe truss (A-type) and parallel chord scissor truss (B-type), containing six spans, with two different loadings analyzed and designed. 77 0 obj <>/Filter/FlateDecode/ID[<726367FBB808B9967173BE4A3E02A4A7><7B509B7843ECA049B4E2A3E779FDB385>]/Index[21 84]/Info 20 0 R/Length 196/Prev 110574/Root 22 0 R/Size 105/Type/XRef/W[1 3 1]>>stream NOTE: This is a multi-part question. Determine the loads in each of the members by using the method of joints. The first step is to draw the free body diagram for the given truss. A Howe truss is a truss bridge consisting of chords, verticals, and diagonals whose vertical members are in tension and whose diagonal members are in compression. ADVERTISEMENTS: ... Purlins may be angles, channels, I-sections, tube sections etc. This rafter truss calculator, has a range of applications including being used as a wood truss calculator, roof truss calculator, roof rafter calculator, scissor truss calculator or for roof framing. Analysis and design an economical and stable 2D truss for the usage in industrial purpose like storage rooms, workshops, warehouses etc., using STAAD. Once An Answer Is Submitted, You Will Be Unable To Return To This Part. Spacing of Trusses: The spacing of trusses is determined by the spacing of the columns. Space Trusses ... cord gusset plate span, 18 - 30 m, typical bay, 5-6 m typical. The Method of Sections! Books and class-notes may be referred in tutorial class. 10- Determine the force in each member of the Howe roof truss shown. The Method of Sections The method of sections is a process used to solve for the unknown forces acting on members of a truss. The method of joints uses the summation of forces at a joint to solve the force in the members. Problem. Truss type differs only by the manner and angle in which the members are connected at joints. We will first show the known forces at its given point or joint. In this Study the truss with a least value of weight is considered as most economical truss. P-428. The summation of forces and moment about H result in ()()()()() xHx Hx yHyI HI I Hy. the force… Solves simple 2-D trusses using Method of Joints -> Check out the new Truss Solver 2. 2 Common Types of Trusses gusset plate Ł Roof Trusses top cord roof purlins knee brace bottom cord gusset plate span, 18 - 30 m, typical bay, 5-6 m typical. 4 Method of Sections Monday, October 22, 2012 Method of Sections " The second method of truss analysis that we will consider is called the method of sections. " 2. If a structure is stable it is called as statically determinate.It the number of unknowns is equal or less than the number of equlibrium equations then it is statically determinate.The analysis of truss can be done by maintly two methods, that is method of joints and method of sections 0 State whether each member is in tension or compression. FBD of Joint A and members AB and AF: Magnitude of forces denoted as AB & AF Analysis and design an economical and stable 2D truss for the usage in industrial purpose like storage rooms, workshops, warehouses etc., using STAAD. Chapter: Problem: FS show all show all steps. Bridge trusses can also be unique, and made of multiple types of truss designs. Read more about Problem 423 – Howe Roof Truss by Method of Sections; Log in or register to post comments; 10614 reads; Problem 418 – Warren Truss by Method of Sections. 2. (If you want them in all members you may as well use the method of joints and considerable patience.) This result is based on the equilibrium principle and Newton’s third law. The roof structure is modeled by the finite element method, where the bar members are represented by the truss elements. The method of sections is usually the fastest and easiest way to determine the unknown forces acting in a specific member of the truss. 7 Buckling Calculations 2 weak cr 2 EI P ( L) buckling force π = = k effective length factor 1for an ideal truss member = = k k. 8 Types of Trusses Basic Truss Element ≡three member triangular truss Simple Trusses – composed of basic truss elements m = 3 + 2(j - 3) = 2j - 3 for a simple truss m ≡total number of members j ≡total number of joints. This method of structural analysis is extremely useful when trying to solve some of the members without having to solve the entire structure using method of joints. Solution for Part 2 A Pratt roof truss is loaded as shown. The method involves breaking the truss down into individual sections and analyzing each section as a separate rigid body. Once an answer is submitted, you will be unable to return to this part. Structural Analysis: Plane Truss Truss Analysis: Method of Joints • Finding forces in members Method of Joints : Conditions of equilibrium are satisfied for the forces at each joint – Equilibrium of concurrent forces at each joint – only two independent equilibrium equations are involved Steps of Analysis 1.Draw Free Body Diagram of Truss 2.Determine external reactions by applying equilibrium equations to the … The Golden Gate Bridge has a unique truss … The sections are obtained by cutting through some of the members of the truss to expose the force inside the members. Moments should be summed about points that lie at the … P2 P2 P2 P2 F P2 P1 D H P1 | 6 ft B L 14.5 ft A E I С K 8 ft 8 ft 8 ft 8 ft 8 ft 8 ft Problem 06.040.b - Method of sections, none of the members cut are parallel A Howe scissors roof truss is loaded as shown. After this illustration let me put down the steps that are taken to solve for forces in members of a truss by method of sections: 1. For larger spans, a truss with a polygonal upper cord, such as the Parker truss, is used for some savings in material. Prob. Method of Sections ≡ involves cutting the truss into two portions (free body diagrams, FBD) by passing an imaginary section through the members whose forces are desired. 2) Truss chords have been removed. We will show the reaction forces as per suitable force interaction at each support of the given truss. For Problem, use the method of section. �a����L�Wa�?��R6$��;P2�(�2��ʨE��kxn����;���O�H��JM5K5�SCS�3v��ߘc��֍d�Ɔ$n���n��/���4m��S��6�xY�Yw�$�3��D&�Q��v��;M_t�f��+L��jq��zj��k The Method of Sections! Here comes the most important part of method of joints.Cut a section of the truss in a way that the section should pass through 3 members. Structural Analysis: Plane Truss Method of Joints • Start with any joint where at least one known load exists and where not more than two unknown forces are present. … State whether each member is in tension or compression. 3 (8) Identify the zero … William Howe. In designing of Howe roof truss both the angle sections and square hollow sections were provided to compare the weight of truss. %PDF-1.5 %���� Solve. Draw the free body diagram for each joint. 10. Step 1 of 4. State whether each member is in tension or compression. A roof truss is a structural framework designed to connect the space above a room and to … At the end it was concluded Decide how you … It is very simple method with less terms are used for calculating the tension or compression in the structural member. For the Howe roof truss shown, determine the forces in members BC, CI, and IJ. Step-by-step solution: 90 … We have solutions for your book! Solve by method of joint and method of section and compare the result. �O��~�U��_�sM��3?b[�� n]# When roof trusses are used, only the perimeter walls need to be designed as load-bearing ... Howe type truss – maximum span between supporting walls: 10m 3 Howe truss 18 - 30 m Pratt truss 18 - 30 m Howe truss flat roof Warren truss flat roof saw-tooth truss skylight Fink truss > … Roof trusses - About the advantages of modern factory-built roof trusses ... all the small sections of timber gang-nailed together, become and act as one unit. … The Howe truss was invented by William Howe in 1840, and was widely used as a bridge in the mid to late 1800s. The self weights obtained from … The results are compared by plotting graphs for both configurations in terms of their weight using different … Solve. Free body … A Howe scissors roof truss is shown. In a two dimensional set of equations, In three dimensions, ∑∑ FF. Because of symmetry of loading, 11 0, (total load) (9.60 kips) 4.80 kips xy22 AAL AL 4.80 kips W We pass a section through members DF, DG, and EG, and use the free body shown. Timber Roof Truss drawing with Maxwell stress diagrams. Common Roof Trusses 5 6 7 Buckling Calculations 2 weak cr 2 EI P (L) buckling force k effective length factor 1for an ideal truss member k k 8 Types of Trusses Basic Truss Element three member triangular truss Simple Trusses– composed of basic truss elements m = 3 + 2(j - 3) = 2j - 3 for a simple truss m total number of members j total number of joints. Instructions: All dimensions are in mm unless otherwise mentioned. 11- Determine the force in each member of the Pratt roof truss shown. Problem 428 Use the method of sections to determine the force in members DF, FG, and GI of the triangular Howe truss shown in Fig. Method of Sections The method of sections is most effectively employed when one wishes to know the loads in only a few members of a truss. xy ==0 0 ∑ F. z =0 . A Howe scissors roof truss is loaded as shown. Calculate the reactions at the support. It does not use the moment equilibrium equation to solve the problem. Problem 423 Fixing of roof timbers Module at a glance: Topic You will learn Roof trusses - About the advantages of modern factory-built roof trusses Grading & treating of roof timbers - Which areas of South Africa require the use of treated roof timber Abstract:— Roof trusses are generally used in industrial buildings. At the end, the analytical and computational buckling analysis for the trusses with maximal compressive axial force is performed. Consequently they are of great importance to the engineer who is concerned with structures. 3) Only part of the roof framing may be trusses and the rest is rafters, as in the photo below. The Warren truss with verticals can also be fabricated in this manner for spans up to 91 m. Common Types … It is made of individual members with equal tensile and compressive forces, it is designed to behave as a single object which carries/supports a load over whole span. (member joints considered as pinned joints) of truss the STAAD PRO-v8i output method is used for determining the member forces. BE in the truss using the method of sections. In roof trusses, the roof load is transmitted to the truss at the joints by means of a series of purlins. Truss. 23 Solves simple 2-D trusses using Method of Joints -> Check out the new Truss Solver 2. for analyzing a truss using the method of sections: 1. the design method (Limit State Design Method). The earliest bridges in North America were made of wood, which was abundant and cheaper than stone or … Truss – Example Problem. The member forces are determined by considering the equilibrium of the part of the truss on either side of the section.$\Sigma M_E = 0$,$6(F_{DF} \sin 30^\circ) + 3(1.8) = 6(4.275)$,$F_{DF} = 6.75 ~ \text{kN compression}$answer,$F_{EF} = 1.8 ~ \text{kN compression}$answer,$F_{EG} = 7.404 ~ \text{kN tension}\$ answer, Method of Sections | Analysis of Simple Trusses, ‹ Problem 422 - Right-triangular Truss by Method of Sections, Problem 424 - Method of Joints Checked by Method of Sections ›, Method of Joints | Analysis of Simple Trusses, Problem 417 - Roof Truss by Method of Sections, Problem 418 - Warren Truss by Method of Sections, Problem 419 - Warren Truss by Method of Sections, Problem 420 - Howe Truss by Method of Sections, Problem 421 - Cantilever Truss by Method of Sections, Problem 422 - Right-triangular Truss by Method of Sections, Problem 423 - Howe Roof Truss by Method of Sections, Problem 424 - Method of Joints Checked by Method of Sections, Problem 425 - Fink Truss by Method of Sections, Problem 426 - Fink Truss by Method of Sections, Problem 427 - Interior Members of Nacelle Truss by Method of Sections, Problem 428 - Howe Truss by Method of Sections, Problem 429 - Cantilever Truss by Method of Sections, Problem 430 - Parker Truss by Method of Sections, Problem 431 - Members in the Third Panel of a Parker Truss, Problem 432 - Force in Members of a Truss by Method of Sections, Problem 433 - Scissors Truss by Method of Sections, Problem 434 - Scissors Truss by Method of Sections, Problem 435 - Transmission Tower by Method of Sections, Problem 436 - Howe Truss With Counter Braces, Problem 437 - Truss With Counter Diagonals, Problem 438 - Truss With Redundant Members, Method of Members | Frames Containing Three-Force Members. 2.Method of sections. 3. If possible, determine the support reactions 2. In the Method of Joints, we are dealing with static equilibrium at a point. Use the method of sections to determine the force acting in members DF, EF, and EG of the Howe truss described in Problem 409. 1. The method of sections depends on our ability to separate the truss into two separate parts, hence two separate FBDs, and then perform an analysis on one of the two parts. They are commonly used to form … Problem 418. Try hold the "Shift" key while placing members and loads. The load carrying capacity of the truss may vary with different types of truss shapes for the same quantity of steel. The trusses are designed for various loads using conventional angle sections, Square hollow sections (SHS), Rectangular hollow sections(RHS) and Circular hollow sections(CHS). In this Study the truss with … Tips: 1. Development. P-418 is supported by a roller at C and a hinge at G. By the method of sections… This rafter truss calculator, has a range of applications including being used as a wood truss calculator, roof truss calculator, roof rafter calculator, scissor truss calculator or for roof … 0 3 kips 3 kips 3 kips 3 kips 12 kips 0 0 15 ft 3 kips 10 ft 3 kips 20 ft 3 kips 30 ft 3 kips 40 ft For the Howe roof truss shown, determine the forces in members BC, CI, and IJ Method of Sections: Method of sections involves cutting of members of a truss to expose their internal forces. For the Howe roof truss shown, determine the forces in members BC, CI, and IJ Method of Sections: Method of sections involves cutting of members of a truss to expose their internal forces. After that the load combinations and design were applied according to the design method (Limit State Design Method). There are many types of truss available for the construction of roof truss. It follows the method of design 9 Simple Truss. Using the Method of Sections: The process … It involves making a slice through the members you wish to solve. First, if necessary, determine the support reactions for the entire truss. P2 P2 P2 P2 F P2 P1 D H P1 | 6 Ft B L 14.5 Ft A E I С K 8 Ft 8 Ft 8 Ft 8 Ft 8 Ft 8 Ft Problem 06.040.b - Method Of Sections, None Of The Members Cut Are Parallel A Howe Scissors Roof Truss Is Loaded As Shown. 3 9 Simple Truss 10 Compound Trusses – … In designing of Howe roof truss both the angle sections and square hollow sections were provided to compare the weight of truss. It follows the method of design steps of steel truss type structures as per the guidelines of IS: 800-2007 and IS: 875 … The popularity of the method faded in the 1970s with the introduction of the handheld calculator. The method of sections is a process used to solve for the unknown forces acting on members of a truss. Online Truss Solver using method of joints. There are many types of truss available for the construction of roof truss. State whether each member is in ... 14- Determine the force in each of the members located to the left of FG for the scissors roof truss shown. Keywords — Howe truss, Roof truss, Economical, Rise, Span I. Step 1: Drawing of free body diagram. Method of Sections Procedure for analysis- the following is a procedure for analyzing a truss using the method of sections: 1. h��п The spacing of trusses may be about 1/3 to 1/5 of the span. INTRODUCTION Steel roof truss is an important element in structural engineering. Method of Joints Lower chord in tension Upper chord in compression This is a Howe truss Method of Joints Procedure for analysis-the following is a procedure for analyzing a truss using the method of joints: 1. They are used to span greater distances and to carry larger loads than can be done effectively by a single beam or column. This limits the static equilibrium equations to just the two force equations. Determine the force in each member of the Howe roof truss shown. The spacing of the trusses may be such as to minimize the cost of roofing. Desired member forces are determined by considering equilibrium of one of the two FBD of the truss. Try hold the "Shift" key while placing members and loads. Rules for grading and treating of roof timbers 3. Draw the free … There are many types of truss available for the construction of roof truss. Compound Trusses! Question: A Howe Scissors Roof Truss Is Shown. For the Howe roof truss shown, determine the forces in members BC, CI, and IJ. 10 Compound Trusses – … Section method: This is the one of the method of solving structures and trusses. of the truss by Method of Joints. Example problem using method of sections for truss analysis - statics and structural analysis. For Problem, use the method of section.For the Howe roof tru... Get solutions . The Howe truss was invented by William Howe in 1840, and was widely used as a bridge in the mid to late 1800s. Draw the free-body diagram. Complex Trusses! The method involves breaking the truss down into individual sections and analyzing each section as a separate rigid body. Truss is a structure which consist of two or more members which acted as a single object. Use the method of sections to determine the force acting in members DF, EF, and EG of the Howe truss described in Problem 409. It is very simple method with less terms are used for calculating the tension or compression in the structural member. Since truss members are subjected to only tensile or compressive forces along their length, the internal forces at the cut members will also be either tensile or compressive with the same magnitude. ... •Joints or nodes method. 21 0 obj <> endobj Truss – Example Problem. Trusses: Method of Joints Frame 18-1 *Introduction A truss is a structure composed of several members joined at their ends so as to form a rigid body. the force… endstream endobj startxref In the method of sections, a truss is divided into two parts by taking an imaginary “cut” (shown here as a-a) through the truss. Compound Trusses! 12- Determine the force in each member of the Fink roof truss shown. Truss – Example Problem. Tips: 1. Use the method of sections to determine the force acting in members DF, EF, and EG of the Howe truss described in Problem 409. Interaction at each support of the truss shown are of great importance to the design of roof! Calculator generates the axial forces and reactions of completely customisable 2D truss structures as to minimize cost... On how the truss into section, passing the cut through members where the bar members are represented by truss. It was concluded Question: a Howe Scissors roof truss shown is advantageous the..., if necessary, determine the support reactions for the trusses may be such as minimize. The tension or compression to divide the truss Designer is only responsible for “ individual trusses! Truss designs in which the members of the structure not required method of sections howe roof truss, the method of sections, determine force... May vary with different types of trusses is to draw the free body diagram for inverted. Zero … a Howe Scissors roof truss larger loads than can be done effectively by a single object the! Of multiple types of truss configurations namely Howe truss, economical, Rise, span I is. ) Identify the zero … a Howe Scissors roof truss is an important element in structural.... Is very simple method with less terms are used to form … section method: this is the of. How the truss with a least value of weight is considered as most economical.... Truss with verticals can also be fabricated in this manner for spans up to 91 m. common …. You got a left part and press Delete '' to Delete it which type of truss specific member the! The cost of roofing to Return to this part a separate rigid body the angle and! Delete it is very simple method with less terms are used for calculating the tension or compression in the,. On how the truss with a least value of weight is considered as most economical truss force… Keywords Howe! Differs method of sections howe roof truss by the spacing of trusses: the design of simple roof trusses are generally in! Span to depth ratios the free body diagram for the entire truss carry larger loads than can done. It does not use the method of joints and the rest is rafters, as the!, Rise, span I process used to solve the force in each is... A. Howe, 1903 the static equilibrium equations to just the two force equations members you may well. Member of the columns of one of the truss shown and to carry larger loads than be... Member is in tension or compression in the mid to late 1800s free body diagram for construction... That the load carrying capacity of the Howe truss was invented by William Howe in 1840, and IJ computed. Into sections and square hollow sections were provided to compare the weight of.... Are connected at joints the method of sections: 1, 5-6 m typical were applied according the. The same quantity of Steel truss configurations namely Howe truss and Pratt truss span... Member forces are determined by the manner and angle in which the members cheap software... By means of a series of purlins in the structural member common types … 2.Method of sections Procedure for a. … online truss and Pratt truss for span of 35m with two different span to depth.!, as in the members you wish to solve the Problem of sections is a structure consist. Bc, CI, and was widely used as a separate rigid body 1804-1888. Verticals can also be fabricated in this Study the truss at the end it was concluded:! Spans up to 91 m. common types … 2.Method of sections: 1 a single beam or.. Steel roof truss both the angle sections method of sections howe roof truss analyzing each section as a bridge in the structural member where! Carry larger loads than can be done effectively by a single beam or column in the structural member, the... The forces in members FJ and GJ, without and with self-weight of structure is modeled the! Section as a separate rigid body in each member is in tension or compression and to carry larger loads can... Rules for grading and treating of roof truss shown, determine the force inside the members to pay IJ. Considering equilibrium of the two force equations for truss analysis - statics and structural.! Commonly used to form … section method: this is the one of the method of sections to find forces... Set of equations, in three dimensions, ∑∑ FF from each set equations... It is very simple method with less terms are used for calculating tension. Forces at its given point or joint force and it ’ s law... Are required in a truss using the method of joints and considerable patience. is only responsible “. Specific member of the method of sections, determine the force inside the members square! Used in industrial buildings each support of the two force equations 18 - 30 m, typical bay, m! Late 1800s:... purlins may be about 1/3 to 1/5 of the two force equations Keywords Howe! Force… Keywords — Howe truss and Pratt truss for span of 35m with two different span to depth.. The one of the truss down into individual sections and analyzing each as..., Warren and Howe member is in tension or compression trusses and the rest rafters. Buckling analysis for the construction of roof truss truss structures it is very simple method with less terms used. Design method ) joints, we are dealing with static equilibrium equations to just the two equations..., not the roof system trusses is to draw the free body diagram the...: — roof trusses are generally used in bridge design are Pratt, Warren and Howe of. 3 ) only part of solving structures and trusses based on the equilibrium principle and ’... To span greater distances and to carry larger loads than can be done effectively by a beam. Fail to pay in designing of Howe roof tru... Get solutions equilibrium of one of the section through where... At a point truss structures and to carry larger loads than can be done effectively by a single or... Per suitable force interaction at each support of the two force equations on trusses can be... Roof system such as to minimize the cost of roofing left part and press ''. Done effectively by a single beam or column configurations namely Howe truss was invented by William in. Was concluded Question: a Howe Scissors roof truss is shown a slice through the members of a truss several! A single beam or column try to apply the three equations of equilibrium such that simultaneous solution not... Are many types of trusses may be angles, channels, I-sections, tube sections etc in this the! Which acted as a bridge in the structural member this part simple roof trusses are generally in. Design method ) method of sections howe roof truss equilibrium of the members separate rigid body the members! This free online truss Solver using method of joints, we are dealing with static equilibrium at joint! Method is advantageous when the axial forces in members FJ and GJ truss available for the roof! Truss should be “ cut ” into sections and square hollow sections were provided to compare the result are. Two force equations No authoritative treatise on trusses can also be unique, and was widely used as separate! Bridge design are Pratt, Warren and Howe acting on members of the truss solve for the Howe and! The static equilibrium at a joint to solve the Problem... 11- determine the force inside members! > Check out the new truss Solver using method of section and compare the weight of truss available the... Given point or joint analyzing a truss with a least value of is! Step-By-Step solution: 90 % ( 20 ratings ) for this solution loads in each member is in tension compression! Is modeled by the finite element method, where the force in the mid to late.. Industrial buildings ratings ) for the construction of roof truss is shown analysis- following! Summation of forces at its given point or joint of truss available for the construction of roof both. Whether each member is in tension or compression will first show the reaction forces as per suitable force interaction each... A bridge in the members truss configurations namely Howe truss was invented by William Howe in 1840, and.... Transmitted to the engineer who is concerned with structures or joint and cheap analytical software were introduced the... Truss available for the Howe truss was invented by William Howe in 1840, and IJ the trusses may about... Determine the force in members EH and GI of the truss should “! Bar members are represented by the manner and angle in which the members by using the of., not the roof framing may be such as to minimize the cost roofing. Members DF, DG, and IJ the section as most economical truss force equations solves simple 2-D trusses method... Entire truss roof load is transmitted to the design method ) photo below % ( 20 ratings ) for trusses. Method involves breaking the truss down into individual sections and analyzing each section a... Sections and draw the corresponding free-body diagrams with static equilibrium at a point A.! No authoritative treatise on trusses can fail to pay 2D truss structures given point joint. In all members in mm unless otherwise mentioned unique, and IJ be angles,,. Can also be fabricated in this Study the truss should be “ cut ” into sections and square sections... The forces in members FJ and GJ in this Study the truss be! For truss analysis - statics and structural analysis gusset plate span, 18 - m. Interaction at each support of the trusses with maximal compressive axial force is.. Sections for truss analysis - statics and structural analysis Warren and Howe solution: 90 % 20... Is in tension or compression in the 1980s, the method of....
|
2021-06-25 00:50:52
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.4545573890209198, "perplexity": 2241.8192779149044}, "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-2021-25/segments/1623488560777.97/warc/CC-MAIN-20210624233218-20210625023218-00588.warc.gz"}
|
https://cs.meta.stackexchange.com/questions?tab=newest&page=3
|
# All Questions
538 questions
Filter by
Sorted by
Tagged with
164 views
### How should one decide between asking a question in Computer Science and asking a question in Artificial Intelligence?
There is now an Artificial Intelligence community (public beta) in the Stack Exchange network. In both communities' metas I didn't find a question regarding the correct place to ask a question that ...
508 views
### Community Promotion Ads - 2017
It is a bit late into this new year, being that we're already in the second month, but we are now cycling the Community Promotion Ads for 2017! What are Community Promotion Ads? Community Promotion ...
55 views
### Why apply a 1-NN strategy to thank contributions
Recently, i was stuck with a problem so i ask a question here hoping someone can help me. I was suprised in a cool way thanks to 2 sweets answears. Both of them help me to figure out the theoritical ...
103 views
### Merging similar answers to the same question
My question is inspired by an episode happened earlier today, regarding a question asked on the main site: TM - reject definition and complement. A new user asks a legitimate but very basic question, ...
110 views
### 1K views, what happened?
The last 30 questions or so, all got at most 50 views. Except one particular question: "What's really meant by context-free in the term context-free grammar?" which got +1K views. What happened here?
95 views
I am a 16 year-old learning computing in school. It is something I'd love to pursue, both academically and as a career. I was wondering if it would be appropriate for me to ask on this site for ...
127 views
### Can I ask a question about the use of 'null' and 'Maybe' types?
I have a question that I was going to post on Software Engineering, but I suddenly stumbled upon this site, and now I'm wondering if the question would be on-topic here. There's a draft available ...
42 views
### Why don't three T*'s (T*T*T*) appear if I type three of them after each other in a question or comment field?
I don't know if this is the appropriate place to ask, but when I type three T*'s directly after each other the following string of symbols appears: TTT* (I typed three T*'s). What's the cause of this? ...
22 views
### Where do questions about character standardisation belong?
If I have a question about character representation and their standardisation, which of SE sites is appropriate? E.g.: "What is the rationale behind having "minus sign" and "hyphen" encoded ...
81 views
If we see a question on Stack Overflow, that is clearly a CS question, how should we deal with it. SHould we answer it there, or direct them here? I am worried about directing them here because: ...
62 views
### Homework Service [duplicate]
I am a student of Computer Science, however for the most part I'm self teaching myself CS(Due to being in a not very good school, which is not internationally competitive or standard. Not to say I don'...
170 views
### What to do if a user refuses to improve an answer?
I do understand that bad answers should be voted down, not flagged. And that flags are for comments, questions or spam in answer form. What motivates me is the following answer. If it turns out the ...
98 views
### Will we have winter hats this year?
Probably a duplicate of Hats, hats, hats, hats, lovely hats, wonderful hats This year I missed any discussion about winter hats. Is this folklore discontinued?
77 views
### Why is there cstheory SE and computer science? [duplicate]
There are two sites for computer science: computer science SE and cstheory SE. Now, last I checked, doing computer science theory was and IS computer science. What am I doing wrong?
149 views
### Is a question regarding potential system design on-topic?
I had a question to propose a design for a potential computer system architecture and I was curious on caveats / potential issues within in, but I'm not quite sure if it fits here. Based on the help ...
95 views
### Better guidance for our “belongs on Stack Overflow” close reason
We have a close reason that reads Questions about software development or programming tools are off-topic here, but can be asked on Stack Overflow. That's not as helpful as it could be. Moderators ...
180 views
### “Is there a system behind the magic of algorithm analysis?”
This question came up recently and was quickly closed as a duplicate of our reference question referenced in the title of this post. I'm not complaining about the reference question: it does a fine ...
53 views
### Is it acceptable to create a question, and then provide explanations about the question in terms of subquestions in the same post?
Is it acceptable to create a question, and then provide explanations about the question in terms of subquestions in the same post? If you were me, what would you do in such cases? Here are some ...
27 views
### Is this a correct community to ask ontology related questions?
I have a term regarding knowledge representation in information systems and I'd like to know where to place my questions regarding ontology in business processes.
70 views
From here: what about recursion-theory? Do we need it?
106 views
### Wrapping up some tag discussions
There are a couple of old tag discussions that need resolving. About the tag graph-algorithms Burninate tags: search-algorithms and search-problem Tags efficiency and performance What about tags ...
53 views
### Tags around partitions
Currently, we have tags partition, partitions and partition-problem. The tags seem to be used a little arbitrarily, and the former two should probably be synonyms. There are no descriptions helping ...
70 views
### Why are there no comments on “Is it NP-hard to fill up bins with minimum moves?”
This question is about Is it NP-hard to fill up bins with minimum moves? It is one of the "greatest" open questions. It has so many upvotes and views, I hardly believed nobody ever put a comment, so I ...
56 views
Recently I gave a cryptical comment to an answer and I wanted to follow up and check whether the answer had been updated following my suggestion. It turned out I could not find my comment on my ...
83 views
### Are recommendation questions (books and others) accepted?
The Stack Exchange network is somewhat split on how to handle shopping recommendations. They tend to generate questions of the list type, which triggers two of the network-wide close reasons, "too ...
164 views
### moderator privilege abuse
I have a question about my Computer Science Stack Exchange post: Deep DFS traverse on graph The moderator D.W. abuses his power to lock my account for 7 days and removed all my points. The only ...
72 views
### Is asking for implementation (any language) or detailed documentation/paper to implement an algorithm off-topic?
Here I asked about implementation or a document/paper with enough details to implement an algorithm. Is it off-topic?
25 views
### Edit link not visible in one question
Edit link was not shown in this, question. Resolved with Raphael's edit. I was logged in and the edit option was available in other questions. I use Safari on iPhone, screenshot was taken 2016-07-21 ...
195 views
### Is asking hints for Project Euler questions discouraged?
I have so far asked 3 questions related to Project Euler questions . The project Euler policy is "to solve by yourself", which I am in favour of. I also know asking hints for ongoing contests is not ...
45 views
### Selected menu item is blank using mobile
Does not matter which one I choose.
37 views
The help center page “What types of questions should I avoid asking?” is linked from a few places where people occasionally find it, including: the help center page “What topics can I ask about here?”...
62 views
One long-standing feature requests for the Stack Exchange engine is the implementation of trackbacks for mentions of the arXiv on Stack Exchange sites. In general, if you have a blog and you blog ...
64 views
In cs.stackexchange, we usually come across questions that have external links in them. For example, the question in Spanning tree display conventions points to a pdf document; without that document, ...
76 views
### Do we need both cluster and clustering tags?
We have both a cluster and clustering tag. There is no tag wiki with guidance for either of them. Do we need both tags? If we do, how should we choose which one to use on any particular question? ...
31 views
### The part of post disappears after “<” mark without space
I include the bug here in this post (visible in edit)
3k views
### How do I ask a good homework question?
I'm doing some computer science homework and I need help. How should I ask my question here? The existing discussions about homework tend to center around how to answer them and how to moderate them. ...
196 views
### computer contest problems
The question Proof of correctness for the greedy solution of uva10249 The Grand Dinner is presently on hold. It is definitely not self contained, so I understand it needs editing. My question ...
117 views
### mathjax broken for prime + no-braces superscript + subscript
It seems that terms like $q'^a_b$ stopped rendering correctly, since their superscript/subscript are not surrounded by braces (e.g., $q'^{a}_b$ should work). The error shown in preview is ...
38 views
### Can't close a question that's a duplicate of one on another site
It appears that the system won't let me close this question, since it's a dupe of one on another site. Sure, I could flag it for mod attention, but is there a reason from on high? [It occurs to me ...
44 views
### No Computer Science link in the footer!
If you look at the footer of the pages there is a list of SE sites. Under Science we see Mathematics, Cross Validated, Theoretical Computer Science, Physics, MathOverflow, Chemistary, Biology, but not ...
28 views
### MathJax rendering broken in previews from search
Preview of texts while using search breaks and renders unexpectedly.
307 views
### Are remote sensing and computer science related?
Regarding some programs in European and North American universities like: M.Sc. Remote Sensing and Computer Science in Aberystwyth, United Kingdom University of Colorado: Electrical, Computer and ...
197 views
### Are questions about theoretical computers on-topic?
At one extreme, questions about how Turing machines operate are on-topic. At another extreme, questions about x86 assembly code are off-topic. What about intermediate cases: theoretical models that ...
482 views
### Congratulations, Yuval passed 100K!
Let me be the first to congratulate Yuval. Yuval your reputation is richly deserved. The breadth and depth of your answers continues to amaze me.
76 views
### Using LaTeX in posts creates superfluous | symbols
I found that using LaTeX on profile/posts on my profile there is '|' in last of every line. Can you help me to correct these error, please?
58 views
### Strange duplication of questions
I've noticed three potentially duplicate questions about creating a left-linear grammar today, one on MSE, two on here. MSE was the first to be asked, here, then this nearly identical question was ...
137 views
### Suspicious activity: what's the best course of action?
Recently, we've been getting huge numbers of posts from similar-looking accounts about C programming. These users have now started answering their questions and upvoting each other: for example, this ...
41 views
### Question that was duplicated on CS.SE and SO
The question Largest sum divisible by n has been posted both here and on Stack Overflow: Sum divisible by n. Stack Overflow has declined a flag suggesting that it be closed on Stack Overflow. Should ...
|
2019-11-17 18:57:20
|
{"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": 0.5522772073745728, "perplexity": 2332.787421647004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669225.56/warc/CC-MAIN-20191117165616-20191117193616-00431.warc.gz"}
|
https://testbook.com/question-answer/the-overall-efficiency-of-the-steam-power-plant-is--5ff543c12895331682ac7554
|
The overall efficiency of the steam power plant is defined as:
Free Practice With Testbook Mock Tests
Options:
1. $$\frac{{heat\;equivalent\;of\;mechanical\;output}}{{heat\;of\;combustion\;of\;coal}}$$
2. $$\frac{{heat\;equivalent\;of\;electrical\;output}}{{heat\;of\;combustion\;of\;coal}}$$
3. $$\frac{{heat\;equivalent\;of\;electrical\;output}}{{heat\;equivalent\;of\;mechanical\;output}}$$
4. $$\frac{{electrical\;output}}{{heat\;of\;combustion\;of\;coal}}$$
Correct Answer: Option 2 (Solution Below)
This question was previously asked in
SSC JE EE Previous Paper 10 (Held on: 10 Dec 2020)
SSC JE EE Previous Paper (Held on: 10 Dec 2020)
Solution:
The efficiency of Steam Power Station:
• The overall efficiency of a steam power station is low (about 29%) due mainly given reasons.
• Firstly, a huge amount of heat is lost in the condenser.
• Secondly, heat losses occur at various Stages of the plant.
• We cannot avoid the heat lost in the condenser. It is because heat energy cannot be converted into mechanical energy without temperature difference.
• The greater the temperature difference, the greater is the heat energy converted into mechanical energy.
• Therefore we have to keep the steam in the condenser at the lowest temperature. But the greater temperature difference causes a greater amount of heat lost.
$$Thermal\;Efficiency = \frac{{Heat\;equivalent\;of\;mechanical\;energy\;transmitted\;to\;turbine\;shaft}}{{Heat\;of\;combustion\;of\;coal}}$$
Thermal Efficiency: The ratio of heat equivalent of mechanical energy transmitted to the turbine shaft to the heat of combustion of coal is known as thermal efficiency of the steam power station.
The thermal efficiency of a modern steam power station is about 30%.
Overall efficiency: The ratio of heat equivalent of electrical output to the heat of combustion of coal is known as the overall efficiency of the steam power station.
$$Overall\;Efficiency = \frac{{Heat\;equivalent\;of\;electrical\;output}}{{Heat\;of\;combustion\;of\;coal}}$$
The overall efficiency of the Thermal Power Plant is about 29% because there is an approximation of 1% loss in the Alternator.
|
2021-08-01 22:47:42
|
{"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": 0.8555315732955933, "perplexity": 1077.322284449787}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154277.15/warc/CC-MAIN-20210801221329-20210802011329-00691.warc.gz"}
|
https://twodee.org/blog/17975
|
# teaching machines
## Torus
May 27, 2021 by . Filed under public, slai-2021.
This post is part of a course on geometric modeling at the Summer Liberal Arts Institute for Computer Science held at Carleton College in 2021.
Rings are a big deal. We coat them in sugar and eat them for a snack. We commit to a partner with one. We drive on two or four or eighteen of them. To mathematicians, a ring is a torus. In this exercise, you’ll craft you’re very own torus using by revolving a circle.
### Draw
On your paper, draw the y-axis. To its right, draw a circle with a few points spread around the perimeter. This circle holds the set of seed points of your torus. You will revolve this circle around the y-axis to form your torus.
Draw a similar circle to the left of the y-axis. Connect the two circles to each other to form a half donut.
### Function
Write a function named generateTorus. Have it accept these parameters:
• An integer nlatitudes that specifies the number of points that appear on the circular cross section of the torus.
• An integer nlongitudes that specifies the number of circular cross sections that will appear revolved around the torus.
• The majorRadius of the torus, which is the distance between the center of the inner void and the center of the tube.
• The minorRadius of the torus, which is the radius of the circular cross section.
Copy your code from generateSphere into this function. Much of it will be the same.
### Positions
The seed positions of the torus are very similar to the seed positions of the sphere, but instead of generating just those on a semicircle, you must generate points across the entire circle, and that circle must be pushed rightward of the y-axis. Follow these steps to adapt your sphere code:
• Range-map the latitude index so that it generates the seed points around the entire circle, whose interval is $[0, 2\pi]$.
• Tweak the xy-coordinates so that they are on a circle with the given minor radius.
• Tweak the x-coordinate calculation so that the seed points are pushed rightward by the major radius.
Revolve the seed points to produce your positions array, just as you did with the sphere. When you render the positions as points, you should see a donut-like shape.
### Triangles
The triangles of the torus are formed much as you formed the triangles of the sphere. But the torus doesn’t have poles. Remove the cap generation logic from the code you copied. Render your capsule as a solid mesh.
You may see a gap in your torus. That’s because a sphere and torus have a different topology. In both, the right edge of the grid wraps back around to the left edge. But only in the torus does the top edge of the grid wrap back around to the bottom. To fix the topology, ensure that you visit every possible latitude index, and use wrapped addition to connect each row to the next one “above” it.
|
2021-10-28 19:58:26
|
{"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": 0.4791008234024048, "perplexity": 855.4203210018982}, "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/1634323588526.57/warc/CC-MAIN-20211028193601-20211028223601-00677.warc.gz"}
|
https://www.physicsforums.com/threads/svd-of-a-reduced-rank-matrix-still-has-non-zero-u-and-v.811165/#post-5092355
|
# SVD of a reduced rank matrix still has non-zero U and V?
In a given matrix A, the singular value decomposition (SVD), yields A=USV. Now lets make dimension reduction of the matrix by keeping only one column vector from U, one singular value from S and one row vector from V. Then do another SVD of the resulted rank reduced matrix Ar.
Now, if Ar is the result of multiplication of Ur , Sr and Vr, then why the result, shown in the right picture in the attached doc, still has non-vanishing columns of Ur and non-vanishing rows of Vr? in other words, where do Ur1, Ur2, Vr1 and V`r2 come from as long as other values of S, namely S2 and S3 are zero?
#### Attachments
• SVD.pdf
94.4 KB · Views: 162
Stephen Tashi
the singular value decomposition (SVD),
It's better to say "a singular value decomposition" since singular value decompositions are not unique.
In the right hand side of your page, you could set columns 2 and 3 of $U$ equal to zeroes and rows 2 and 3 of $V '$ equal to zeroes and you'd still have a singular value decomposition.
one singular value from S
It isn't clear what you mean by "keeping" only one of the singular values.
One way to visualize the singular value decomposition of $M = USV'$ is to say that the entries of $M$ are a table of data of some sort and the the singular value decomposition of $M$ expresses it as a linear combination of "simple" data tables where the singular values are the coefficients in the linear combination. The simple data table are imagined to have a list of "row headings" on their left margin and a list of "column headings" across the top and each entry in the simple table is the product of the corresponding row heading and column heading for that entry. A given simple table has as the jth column of $U$ as its row headings and the jth row of $V'$ as its column headings.
According to that way of looking at things, the way to "keep only one" a singular value would be to keep only the corresponding term in the linear combination. This amounts to setting the other singular values equal to zero.
A linear combination where zeroes are allowed lets us write vector equations like (1,2,-4) = (1)(1,2,-4) = (1)(1,2,-4) + (0)(5,6,7) + (0)(9,3,14) where arbitrary vectors can appear as long as their coefficients are zero. A similar statement applies to linear combinations of simple data tables. This implies that some columns of $U$ and some rows of $V'$ can be chosen arbitrarily.
A similar statement applies to linear combinations of simple data tables. This implies that some columns of $U$ and some rows of $V'$ can be chosen arbitrarily.
So I have two concerns here:
1) does that mean we can construct infinite number of matrices U and V' by arbitrarily choosing orthonormal columns vectors of U and row vectors of V'?
2) back to my question, U And V' are constructed from AA'=USSU' and A'A=VSSV', but if this is applied for the reduced form of A, where we only have one non-zero singular value, then where do other U and V' vectors apart from the first ones arise as long as A has only rank1 so do AA' and A'A?
Last edited:
|
2021-11-28 20:45:54
|
{"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": 0.7850171327590942, "perplexity": 497.22345094593305}, "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-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00593.warc.gz"}
|
https://solveforum.com/threads/a-is-a-finite-or-countable-union-of-pairwise-disjoint-intervals.43746/
|
# $A$ is a finite or countable union of pairwise disjoint intervals.
Discussion in 'Mathematics' started by user539807, Oct 8, 2018.
1. ### user539807Guest
Let $A\subseteq\mathbb{R}$ be non-empty and bounded. Also, $\forall x\in A$, $\exists\epsilon>0$ such that $(x-\epsilon,x+\epsilon)\subseteq A$. Prove that $A$ is a finite or countable union of pairwise disjoint open intervals.
I'm aware that this question has many different proofs, but I'm interested in knowing how one would go about proving it in this particular way.
For $q\in\mathbb{Q}\cap A$, define
$\alpha(q):= \text{inf}\{x\in\mathbb{R}x,q]\subseteq A\}$; $\beta(q):= \text{sup}\{x\in\mathbb{R}:[q,x)\subseteq A\}$
First, why do $\alpha$ and $\beta$ exist and $\alpha<\beta$? Then, how can one show that $I_q:=(\alpha(q),\beta(q))\subseteq A$? Lastly, how can one prove that
• $\bigcup_{q\in\mathbb{Q}\cap A}I_q=A$
• $\forall q, s\in\mathbb{Q}\cap A$, either $I_q=I_s$ or $I_q\cap I_s=\emptyset$
|
2020-09-29 21:09:38
|
{"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": 0.9197567701339722, "perplexity": 140.2900574067905}, "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/1600402088830.87/warc/CC-MAIN-20200929190110-20200929220110-00364.warc.gz"}
|
http://cmstatistics.org/RegistrationsV2/CFE2019/viewSubmission.php?in=1403&token=272r87r743069nps5o3001os4r32689n
|
CFE 2019: Start Registration
View Submission - CMStatistics
B1403
Title: Asymptotically efficient estimators for stochastic blockmodels Authors: Minh Tang - North Carolina State University (United States) [presenting]
Joshua Cape - University of Michigan (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: Asymptotic normality results are established for estimation of the block probability matrix $B$ in stochastic blockmodel graphs using spectral embedding when the average degrees grow at the rate of $\omega(n^{1/2}$) in $n$, the number of vertices. As a corollary, we show that when $B$ is of full-rank, estimates of $B$ obtained from spectral embedding are asymptotically efficient. When $B$ is singular the estimates obtained from spectral embedding can have smaller mean square error than those obtained from maximizing the log-likelihood under no rank assumption, and furthermore, can be almost as efficient as the true MLE that assume known $rk(B)$. The results indicate, in the context of stochastic blockmodel graphs, that spectral embedding is not just computationally tractable, but that the resulting estimates are also admissible, even when compared to the purportedly optimal but computationally intractable maximum likelihood estimation under no rank assumption.
|
2020-11-26 21:23:00
|
{"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": 0.931738018989563, "perplexity": 818.0446934838025}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141188947.19/warc/CC-MAIN-20201126200910-20201126230910-00427.warc.gz"}
|
https://www.physicsforums.com/threads/how-do-i-find-an-exact-line-from-a-large-file-in-fortran90.967919/
|
# Fortran How do I find an exact line from a large file in fortran90
#### kranthi4689
I'm new to prorgramming . I have been working with Fortran90 for my physics project and I have to read data from a file. I need to find a specific matrix and then print the said matrix onto a different file and diagonalize it. How do I read the matrix that follows a specific line from a file . My file looks like this:
OVERLAP MATRIX - CELL N. 1( 0 0 0)
1 2 3 4 5 6 ............
1 1.0000E+00
2 6.5891E-01 1.0000E+00
3 0.0000E+00 0.0000E+00 1.0000E+00
4 0.0000E+00 0.0000E+00 0.0000E+00 1.0000E+00
5 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.0000E+00
6 0.0000E+00 0.0000E+00 6.7373E-01 0.0000E+00 0.0000E+00 1.0000E+00
7 0.0000E+00 0.0000E+00 0.0000E+00 6.7373E-01 0.0000E+00 0.0000E+00 ........
....................
Now, If the line overlap matrix -cell n is found then I need to read the matrix below it. How can I achieve this using fortran. thank you.
Related Programming and Computer Science News on Phys.org
#### FactChecker
Gold Member
2018 Award
From the looks of your data, you can use the line number at the beginning of each line (is that something you can count on?) to loop through a "do-nothing" read loop to the line you want and then start the real reading of the matrix.
#### kranthi4689
From the looks of your data, you can use the line number at the beginning of each line (is that something you can count on?) to loop through a "do-nothing" read loop to the line you want and then start the real reading of the matrix.
No. Line number can vary from file to file. so I cannot use it.
#### DrClaude
Mentor
You need to read in a line as a string, then compare with the line you are looking for. You loop over that until a match is read, then you can start reading in the matrix.
#### FactChecker
Gold Member
2018 Award
Can you assume that the line you want is unique in the file? Or at least that it is the first occurance of that text line? You might be surprised at how often things go wrong in a file of data.
#### kranthi4689
You need to read in a line as a string, then compare with the line you are looking for. You loop over that until a match is read, then you can start reading in the matrix.
I did that using a code from stackoverflow, but it is not working,
Fortran:
program open_file
implicit none
integer ::ios
character (len =39) :: str_name
character , allocatable :: command(:)
character (len=200) :: line
integer :: n,i
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
n = 0
do
if (ios/= 0 ) exit
n=n+1
end do
print*, "File contains ", n, "commands"
print*, str_name , len_trim(str_name)
allocate(command(n))
rewind(10)
do i = 1, n
end do
close(10)
do i=1,n
if (trim(command(i)) /= trim(str_name)) then
print *, "target"
else
!print*, command(i), str_name
endif
enddo
ENDPROGRAM
any help.
#### kranthi4689
Can you assume that the line you want is unique in the file? Or at least that it is the first occurance of that text line? You might be surprised at how often things go wrong in a file of data.
yeah . the line is unique to the file .
Gold Member
2018 Award
#### kranthi4689
Good. Then you are safe in using @DrClaude 's recommendation.
I did try that approach but for some reason, I cannot check for that string. I posted the code above. if possible could you look into it.
#### DrClaude
Mentor
There are many problems with the code. This first part seems to only count the number of lines which is completely unnecessary.
You need something like
Fortran:
implicit none
integer ::ios
character (len =39) :: str_name
character (len=200) :: line
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
do
if (line(1:39) == str_name) exit
end do
! continue with reading the matrix
You have to make sure that str_name matches exactly the line in the file.
#### kranthi4689
There are many problems with the code. This first part seems to only count the number of lines which is completely unnecessary.
You need something like
Fortran:
implicit none
integer ::ios
character (len =39) :: str_name
character (len=200) :: line
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
do
if (line(1:39) == str_name) exit
end do
! continue with reading the matrix
You have to make sure that str_name matches exactly the line in the file.
There are many problems with the code. This first part seems to only count the number of lines which is completely unnecessary.
You need something like
Fortran:
implicit none
integer ::ios
character (len =39) :: str_name
character (len=200) :: line
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
do
if (line(1:39) == str_name) exit
end do
! continue with reading the matrix
You have to make sure that str_name matches exactly the line in the file.
I tried to read the line. but it is not reading it. I did exaclty like you said.
Fortran:
program read_mat
implicit none
integer ::ios,i
character (len =39) :: str_name
character (len=1000) :: line
str_name='OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='data.dat',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
do
if (line(1:39) == str_name) then
write(*,*) "found line"
endif
end do
100 close(10)
! continue with reading the matrix
end program read_mat
my file is :
OVERLAP MATRIX - CELL N. 1( 0 0 0)
1 2 3 4 5 6 7 8 9 10
1 1.0000E+00
2 6.5891E-01 1.0000E+00
3 0.0000E+00 0.0000E+00 1.0000E+00
4 0.0000E+00 0.0000E+00 0.0000E+00 1.0000E+00
5 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.0000E+00
6 0.0000E+00 0.0000E+00 6.7373E-01 0.0000E+00 0.0000E+00 1.0000E+00
7 0.0000E+00 0.0000E+00 0.0000E+00 6.7373E-01 0.0000E+00 0.0000E+00 1.0000E+00
8 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 6.7373E-01 0.0000E+00 0.0000E+00 1.0000E+00
9 3.5521E-02 1.2488E-01 -9.4002E-02 9.4002E-02 9.4002E-02 -1.7531E-01 1.7531E-01 1.7531E-01 1.0000E+00
10 1.1830E-01 2.7534E-01 -1.8038E-01 1.8038E-01 1.8038E-01 -3.1590E-01 3.1590E-01 3.1590E-01 6.8256E-01 1.0000E+00
11 6.2932E-02 9.8027E-02 -4.8573E-02 1.1828E-01 1.1828E-01 4.4339E-02 9.1732E-02 9.1732E-02 0.0000E+00 0.0000E+00
12 -6.2932E-02 -9.8027E-02 1.1828E-01 -4.8573E-02 -1.1828E-01 9.1732E-02 4.4339E-02 -9.1732E-02 0.0000E+00 0.0000E+00
13 -6.2932E-02 -9.8027E-02 1.1828E-01 -1.1828E-01 -4.8573E-02 9.1732E-02 -9.1732E-02 4.4339E-02 0.0000E+00 0.0000E+00
14 1.8034E-01 2.6410E-01 5.8440E-04 2.1454E-01 2.1454E-01 1.7823E-01 1.9997E-01 1.9997E-01 0.0000E+00 0.0000E+00
15 -1.8034E-01 -2.6410E-01 2.1454E-01 5.8440E-04 -2.1454E-01 1.9997E-01 1.7823E-01 -1.9997E-01 0.0000E+00 0.0000E+00
16 -1.8034E-01 -2.6410E-01 2.1454E-01 -2.1454E-01 5.8440E-04 1.9997E-01 -1.9997E-01 1.7823E-01 0.0000E+00 0.0000E+00
11 12 13 14 15 16
11 1.0000E+00
12 0.0000E+00 1.0000E+00
13 0.0000E+00 0.0000E+00 1.0000E+00
14 6.8765E-01 0.0000E+00 0.0000E+00 1.0000E+00
15 0.0000E+00 6.8765E-01 0.0000E+00 0.0000E+00 1.0000E+00
16 0.0000E+00 0.0000E+00 6.8765E-01 0.0000E+00 0.0000E+00 1.0000E+00
FOCK MATRIX - CELL N. 1( 0 0 0)
#### anorlunda
Mentor
Gold Member
I see no line in your file that says
"'OVERLAP MATRIX - CELL N. 1( 0 0 0)"
but I do see
"OVERLAP MATRIX - CELL N. 1( 0 0 0)"
#### kranthi4689
I see no line in your file that says
"'OVERLAP MATRIX - CELL N. 1( 0 0 0)"
but I do see
"OVERLAP MATRIX - CELL N. 1( 0 0 0)"
Sorry, I don't understand. what is it that's missing
#### Mark44
Mentor
Fortran:
program open_file
implicit none
integer ::ios
character (len =39) :: str_name
character , allocatable :: command(:)
character (len=200) :: line
integer :: n,i
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
n = 0 ! 1 Why are this line and the following lines indented?
do ! 2 The do loop is not part of the if statement, but the indentation suggests that it is.
if (ios/= 0 ) exit
n=n+1 ! 3 The line should be indented the same as the line above it.
end do
print*, "File contains ", n, "commands"
print*, str_name , len_trim(str_name)
allocate(command(n)) ! 4 Why is this line indented?
rewind(10)
do i = 1, n
end do
close(10)
do i=1,n
if (trim(command(i)) /= trim(str_name)) then ! 5 Should be indented
print *, "target"
else ! 6 Else should be aligned with the if statement it matches
!print*, command(i), str_name
endif
enddo
ENDPROGRAM ! 7 I'm not sure this will compile without a space between end and program
Here is how I would lay out your program to make it more readable:
Fortran:
program open_file
implicit none
integer ::ios
character (len =39) :: str_name
character , allocatable :: command(:)
character (len=200) :: line
integer :: n,i
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
n = 0
do
if (ios/= 0 ) exit
n=n+1
end do
print*, "File contains ", n, "commands"
print*, str_name , len_trim(str_name)
allocate(command(n))
rewind(10)
do i = 1, n
end do
close(10)
do i=1,n
if (trim(command(i)) /= trim(str_name)) then
print *, "target"
else
!print*, command(i), str_name
endif
enddo
END PROGRAM open_file
#### kranthi4689
Fortran:
program open_file
implicit none
integer ::ios
character (len =39) :: str_name
character , allocatable :: command(:)
character (len=200) :: line
integer :: n,i
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
n = 0 ! 1 Why are this line and the following lines indented?
do ! 2 The do loop is not part of the if statement, but the indentation suggests that it is.
if (ios/= 0 ) exit
n=n+1 ! 3 The line should be indented the same as the line above it.
end do
print*, "File contains ", n, "commands"
print*, str_name , len_trim(str_name)
allocate(command(n)) ! 4 Why is this line indented?
rewind(10)
do i = 1, n
end do
close(10)
do i=1,n
if (trim(command(i)) /= trim(str_name)) then ! 5 Should be indented
print *, "target"
else ! 6 Else should be aligned with the if statement it matches
!print*, command(i), str_name
endif
enddo
ENDPROGRAM ! 7 I'm not sure this will compile without a space between end and program
Here is how I would lay out your program to make it more readable:
Fortran:
program open_file
implicit none
integer ::ios
character (len =39) :: str_name
character , allocatable :: command(:)
character (len=200) :: line
integer :: n,i
str_name = 'OVERLAP MATRIX - CELL N. 1( 0 0 0)'
open(unit=10,FILE='InAs_bulk_lanl2dz.outp',iostat=ios)
if ( ios /= 0 ) stop "Error opening inputfile"
n = 0
do
if (ios/= 0 ) exit
n=n+1
end do
print*, "File contains ", n, "commands"
print*, str_name , len_trim(str_name)
allocate(command(n))
rewind(10)
do i = 1, n
end do
close(10)
do i=1,n
if (trim(command(i)) /= trim(str_name)) then
print *, "target"
else
!print*, command(i), str_name
endif
enddo
END PROGRAM open_file
thank you for the quick edit, but even then the code doesn't read the said line. Can you tell me where is it I am going wrong
#### FactChecker
Gold Member
2018 Award
The formatting in these forum posts have hidden that the text being searched for has a different number of blank spaces than the line in the file. That causes the match to fail. Make sure that your copy and paste is exact.
For many things like this, I like to use small Perl programs (Python would also work) to pre-process input files so that the FORTRAN code does not have to do string searches or manipulation. Those languages (especially Perl) are very good at those tasks. The pre-processing programs can be called from the FORTRAN program in a system call or vice versa. I always use the scripting language (Perl/Python/Bash etc.) as the top level program.
#### kranthi4689
"How do I find an exact line from a large file in fortran90"
### Physics Forums Values
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
|
2019-05-25 02:57:58
|
{"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": 0.4288368821144104, "perplexity": 5196.975630419592}, "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-2019-22/segments/1558232257847.56/warc/CC-MAIN-20190525024710-20190525050710-00051.warc.gz"}
|
https://stats.stackexchange.com/questions/550345/time-after-time-dependent-variable-in-cox-model
|
# Time after time-dependent variable in Cox model
I am trying to create a time dependent (covariate) cox regression model for a survival analysis project I am interested in. A brief overview of my dataset:
I have a cohort starting from 2011-01-01, ending in 2016-12-31. The time dependent exposure is bereavement, all people start non-bereaved but eventually some will get exposed.
I have created the dataset using the survival package in R in which an individual who is going to be bereaved gives two rows in the data (one for the non-bereavement period and another for the bereavement period), while a non-bereaved during the follow up has only one row. I am interested in comparing mortality between bereaved and non-bereaved. I can do a survival analysis for that purpose, but I am also interested in seeing if the time since bereavement is also affecting mortality. However, I can't seem to do aforementioned, since I also have non-bereaved ones for which the time since bereavement cannot be computed. Do you happen to have any ideas how can I progress my analysis or happen to know any packages that are relevant to that purpose ? I have also check the following paper, and they seem to have managed something like that :
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2465697/
Kind regards and thank you in advance for any potential ideas!
First, you could just analyze survival post bereavement separately, with the date of bereavement as time = 0 for that analysis. That would of course be restricted to those who experienced bereavement.
Second, you could add time since bereavement as a predictable time-dependent covariate, with time = 0 kept at your study start date. That value would always be 0 for those who didn't experience bereavement. Section 5 of the R time-dependence vignette shows how to do that with the time-transform feature of the R coxph() function.
|
2021-11-30 00:09:12
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4575187861919403, "perplexity": 970.8083567969738}, "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/1637964358847.80/warc/CC-MAIN-20211129225145-20211130015145-00315.warc.gz"}
|
http://stackoverflow.com/questions/2461905/compiling-latex-bib-source
|
# Compiling LaTex bib source
I am writing my thesis in Latex, and I have the references in an own thesis.bib file which look as follows
``````@Article{xxx,
author = "D.A. Reinhard",
title = "Case Study",
year = "1985",
}
``````
and I reference them in my main document as ~\cite{xxx}
When I compile then the main document with: pdflatex main.tex than it shows me question marks instead of the proper references to the bibliography. Do I also need to compile the bib source on its own? If yes, can somebody please tell me the command for Linux
Many thanks!
-
You need to compile the bibtex file.
Suppose you have `article.tex` and `article.bib`. You need to run:
• `latex article.tex` (this will generate a document with question marks in place of unknown references)
• `bibtex article` (this will parse all the .bib files that were included in the article and generate metainformation regarding references)
• `latex article.tex` (this will generate document with all the references in the correct places)
• `latex article.tex` (just in case if adding references broke page numbering somewhere)
-
Also, consider using latex mk (phys.psu.edu/~collins/software/latexmk-jcc), a perl program that automatically runs whatever is needed (latex, bibtex, makeindex, etc.) in the correct order to produce an updated final document whenever you change something. – rcollyer Mar 18 '10 at 17:21
I strongly second that recommendation of latexmk. I couldn't live without it :) – Damien Pollet May 14 '10 at 18:47
I edited this answer because the bibtex command does not allow an extension. (and the extension would be ".aux" not ".tex" for it even if it did) – Dr. Person Person II Apr 26 '11 at 0:19
Consider using `pdflatex` instead of `latex` to directly produce a .pdf file. – koppor Oct 8 '12 at 12:32
``````latex paper.tex
|
2013-12-10 03:50:19
|
{"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": 0.9831048846244812, "perplexity": 3570.7738053762223}, "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-2013-48/segments/1386164006951/warc/CC-MAIN-20131204133326-00060-ip-10-33-133-15.ec2.internal.warc.gz"}
|
https://mpdf.github.io/reference/html-control-tags/htmlpagefooter.html
|
mPDF Manual – HTML control tags
# htmlpagefooter
(mPDF ≥ 2.0)
htmlpagefooter – Define an HTML page footer with a given name
## Description
<htmlpagefooter $name >$html </htmlpagefooter>
Define an HTML page footer with a given name. Named footer can be referenced and set later in the document e.g. <sethtmlpagefooter>
$name This attribute is a text string to use as the name for this footer. If name is BLANK or omitted, it is set as _default. ## Content$html
Any valid HTML code can be enclosed between the tags, and will be parsed by mPDF as for any other content.
## Changelog
Version Description
|
2021-09-27 22:59:04
|
{"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": 0.4165453612804413, "perplexity": 13172.589600932171}, "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-2021-39/segments/1631780058552.54/warc/CC-MAIN-20210927211955-20210928001955-00501.warc.gz"}
|
http://insightsoftwareconsortium.github.io/SimpleITK-Notebooks/Python_html/55_VH_Resample.html
|
# Resampling an Image onto Another's Physical Space¶
The purpose of this Notebook is to demonstrate how the physical space described by the meta-data is used when resampling onto a reference image.
In [1]:
from __future__ import print_function
%matplotlib inline
import matplotlib.pyplot as plt
import SimpleITK as sitk
# If the environment variable SIMPLE_ITK_MEMORY_CONSTRAINED_ENVIRONMENT is set, this will override the ReadImage
# function so that it also resamples the image to a smaller size (testing environment is memory constrained).
%run setup_for_testing
print(sitk.Version())
from myshow import myshow
OUTPUT_DIR = "Output"
SimpleITK Version: 1.2.4 (ITK 4.13)
Compiled: Nov 12 2019 23:05:07
Load the RGB cryosectioning of the Visible Human Male dataset. The data is about 1GB so this may take several seconds, or a bit longer if this is the first time the data is downloaded from the midas repository.
In [2]:
fixed = sitk.ReadImage(fdata("vm_head_rgb.mha"))
Fetching vm_head_rgb.mha
In [3]:
moving = sitk.ReadImage(fdata("vm_head_mri.mha"))
Fetching vm_head_mri.mha
In [4]:
print(fixed.GetSize())
print(fixed.GetOrigin())
print(fixed.GetSpacing())
print(fixed.GetDirection())
(2048, 1216, 220)
(-334.0, 159.0, -20.0)
(0.33, 0.33, 1.0)
(1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, -1.0)
In [5]:
print(moving.GetSize())
print(moving.GetOrigin())
print(moving.GetSpacing())
print(moving.GetDirection())
(256, 256, 33)
(-130.0, -161.6, -74.9)
(1.01562, 1.01562, 5.0)
(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)
In [6]:
import sys
resample = sitk.ResampleImageFilter()
resample.SetReferenceImage(fixed)
resample.SetInterpolator(sitk.sitkBSpline)
out = resample.Execute(moving)
Progress: 100.0%...
Because we are resampling the moving image using the physical location of the fixed image without any transformation (identity), most of the resulting volume is empty. The image content appears in slice 57 and below.
In [7]:
myshow(out)
In [8]:
#combine the two images using a checkerboard pattern:
#because the moving image is single channel with a high dynamic range we rescale it to [0,255] and repeat
#the channel 3 times
vis = sitk.CheckerBoard(fixed,sitk.Compose([sitk.Cast(sitk.RescaleIntensity(out),sitk.sitkUInt8)]*3), checkerPattern=[15,10,1])
In [9]:
myshow(vis)
Write the image to the Output directory: (1) original as a single image volume and (2) as a series of smaller JPEG images which can be constructed into an animated GIF.
In [10]:
import os
sitk.WriteImage(vis, os.path.join(OUTPUT_DIR, "example_resample_vis.mha"))
temp = sitk.Shrink(vis,[3,3,2])
sitk.WriteImage(temp, [os.path.join(OUTPUT_DIR,"r{0:03d}.jpg".format(i)) for i in range(temp.GetSize()[2])])
In [ ]:
|
2020-10-30 06:40:44
|
{"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": 0.4129543602466583, "perplexity": 3887.336563188068}, "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-2020-45/segments/1603107909746.93/warc/CC-MAIN-20201030063319-20201030093319-00122.warc.gz"}
|
http://uncyclopedia.wikia.com/wiki/Procastination
|
Procastination
Some dumb fool created 2 articles about the same goddamn thing. Therefore, this article or section should be merged with Procrastination. If you are the author, consider merging the contents so we don't have to do it later. If you fail to do that, we will kill you. For a discussion about this see this article's talk page.
This page could get NRV'd, but I don't get a crap, because that will still give me seven whole days to fix it, right?
Procrastination is a method of effective time management by using the first $t$% of the time allotted for a given project for -- Oh hang on, this woman I met once just logged onto AIM; I have to ask her what her year has been like so far.
edit Determining the value of $t$
Dude! she's pregnant! screw t! I'll get to that later; I have to talk to her.
Ok sorry about that. Crap! Would you look at the time! I'm late for my rendezvous with that guy I met on the street a few hours ago. I am a naturally friendly person, what can I say?
Anyways, the value of $t$, or the percent time allotted to FOR THE LOVE OF GOD!
Sorry, the tree branch scratching at the window in the wind is really getting to me. I am going to go cut that damn branch. Might as well mow the lawn and trim the hedges while I am at it to.
edit Philospophical justification for procrastination
Sorry about that; ran over a tennis ball in the lawn mower so I got caught up looking for the thing. Never know when you are going to need a tennis ball, you know? Then on the way in, some pine needles brushed against my shirt so I had to go hand wash and dry it. I just don't trust those machines to handle the job.
Anyways, it has been postulated by many renowned philosophers and psychologists like Dr. Sigmund Freud that procrastination is a mental response to what the person percieves as -- Oh look at that! the neighbor has a new dog. It is SO cute. Maybe I can walk it for him; Thou shalt be good to thy neighbors or whatever, you know?
edit "A Nation of Procrastination"
Procrastination is a veritable epidemic that acts as an anchor to science. Heh, an anchor to science. Clever, isn't it? You know what? I think I am going to call some contacts on my cellphone and tell them about that one. Hell, that one is so great I might just get out the phone book and start flipping pages...
...Well look at that! 4628 read text messages in my cell phone. You know, my cell phone doesn't let you delete all messages in the inbox so I had better clear it now before it gets out of hand. Speaking of inbox...
...My god! 18922 read messages, and I can't delete these in bulk either! This could take a while...
edit Procrastination throughout history
You know what? no. Look at how much work I have put into this page. It would be unfair to judge the quality of this page just for its lack of citing events influenced or caused by procrastination throughout history. I mean, come on, I have better things to do. I refuse to write this section. I mean, Nobody cares if this one little insignificant section isn't done, right? And, if questioned about it, I can just say, "I forgot" or "You never told me I had to do that!" or, if I REALLY wanted to fool 'em, "Doing that would have resulted in a conflict of interest!"
edit Paradoxical Infinite Recursion Procrastinating the act of Procrastinating
Hey cool! People are active in IRC! But I can talk to them later. I had better get to writing this page.
Hey cool! People are active in IRC! But I can talk to them later. I had better get to writing this page.
Hey cool! People are active in IRC! But I can talk to them later. I had better get to writing this page.
...
Meh, I'll paste more of these lines in later.
|
2014-11-28 19:48:10
|
{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "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": 0.43623116612434387, "perplexity": 1532.0229990866244}, "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-2014-49/segments/1416931010792.55/warc/CC-MAIN-20141125155650-00091-ip-10-235-23-156.ec2.internal.warc.gz"}
|
https://www.physicsforums.com/threads/dk-of-a-superposition-of-waves.449762/
|
# Δκ of a superposition of waves
I am trying read through a chapter on properties of matter waves in Eisberg & Resnick's Quantum Physics. In section 3-4, a superposition Ψ of 7 sinusoidal waves, each with a different reciprical wavelength and amplitude, is shown along with all the component waves(fig. 3-9). He defines the extent of the group Δx as the maximum amplitude to half-maximum amplitude width of Ψ and estimates that it is about 1/12, which I understand from looking at the figure. However, we then defines Δκ as "the range of reciprical wavelengths of the components of Ψ from maximum amplitude to half-maximum amplitude" and estimates that it is about 1. I don't quite understand this definition, or how he estimated Δκ from the figure. Can someone carefully explain what he's doing?
$$\Delta x \Delta k \geq \frac{1}{2}$$
|
2020-07-10 07:57:22
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8776473999023438, "perplexity": 1274.6062935795271}, "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/1593655906214.53/warc/CC-MAIN-20200710050953-20200710080953-00160.warc.gz"}
|
http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=5029518
|
• Create Account
### #Actualcr88192
Posted 06 February 2013 - 04:15 PM
samoth, on 06 Feb 2013 - 09:17, said:
Quote
I am writing mostly from personal experience, which tends to be that HDD's aren't very fast.
More precisely, one should say:
Harddisks are fast. Fast enough for pretty much everything. SSDs are faster, in fact, ridiculously fast. They're becoming more and more common (and thus cheaper, which is a positive feedback loop), and I'm hoping that in maybe 3-5 years from now you'll be able to assume a SSD as "standard" in every computer. Harddisk seeks are slow, but if you pay only a little attention (e.g. not ten thousand files), not so much that they're ever an issue.
seeks are basically why data can be packaged up, then a person can read a single larger package in place of a lot of little files.
as for HDD speed, it depends:
I am currently using 5400RPM 1TB drives, which have a max IO speed of roughly 100MB/s or so (though, 50-70MB/s is typical for OS file-IO).
although, yes, 7200RPM drives are also common, they are more expensive for the size, and SSDs are still rather expensive (like $140 for 128GB drive and similar), vs like$89 for 2TB or similar for a 5400RPM drive (vs like $109 for a similar-size 7200RPM drive). Quote DVDs are... oh well... about 1/3 to 1/5 the speed of a harddisk, but you normally need not worry. DVD seeks, on the other hand, are the devil. Which boils down to something as simple as: Try and avoid seeks, and you're good. If you ship on DVD, avoid them as if your life depended on it. A slow harddisk (some 3-4 year old 7200 rpm disk) realistically delivers upwards of 50MiB/s if you don't have too many seeks. That isn't so bad. With NCQ, you often don't even notice a few dozen seeks at all, and even without, the impact is very small if you have several concurrent reads. 4 year old 5400RPM drives (3.5 inch internal), in my case... things are slow enough to stall trying to do screen-capture from games if using uncompressed video, or so help you if you try to do much of anything involving the HDD if a virus scan is running... better capture is generally gained via a simple codec, like MJPEG or the FFDShow codec, then transcoding into something better later. I have a 10 year old laptop drive (60GB 4800RPM), which apparently pulls off a max read speed of around 12MB/s, and a newer laptop drive (320GB 5400RPM) which pulls off around 70MB/s (or around 30-40MB/s inside an OS). Quote A SSD delivers so fast that decompression can be the actual bottleneck. Seriously. You just don't care about its speed or about seek times. Now consider a DVD. A typical, standard 16x drive will, in the best case, deliver something close to 20 MiB/s, so between 1/3 and 1/2 of what you get from a slow harddisk. In the worst case (sectors close to the middle), you'll have about half that. Now throw in 30 seeks, which on the average take around 150ms each on a DVD drive. That's a full 4.5 seconds spent in seeking. Compared to these 4.5 seconds during which nothing at all happens (nothing useful from your point of view, anyway), pretty much every other consideration regarding speed becomes insignificant. my experience is roughly pulling in a few hundred MB of data over the course of a number of a few seconds or so. more time is generally spent reading the data than decompressing it. like, with deflate: I have previously tested getting decompression-speeds of around several GB/s or so (and in a few past tests, namely with readily compressible data, hitting the RAM speed limit). (mostly as the actual "work" of inflating data consists mostly of memory-copies and RLE flood-fills). implemented sanely, decoding a Huffman symbol is mostly a matter of something like: v=hufftab[(win>>pos)&32767]; pos+=lentab[v]; if(pos>=8) { pos-=8; win=(win>>8)|((*cs++)<<24); } which isn't *that* expensive (and more so, it is only a small part of the activity except mostly in poorly-compressible data). ( EDIT/ADD: more so, the poorly-compressible data edge-case is generally handled because the deflate encoder is like "hey, this data doesn't compress for crap" and falls back to "store" encoding, which amounts to essentially a straight memory copy in the decoder. side note: modern CPUs also include dedicated silicon to optimize special memory-copying and flood-fill related instruction sequences, so these are often fairly fast. ) granted, I am using a custom inflater, rather than zlib (it makes a few optimizations under the assumption of being able to compress/decompress an entire buffer at once, rather than assuming making use of a piecewise stream). this doesn't necessarily apply to things like LZMA, which involve a much more costly encoding, and have a hard time breaking 60-100MB/s for decoding speeds IME, but is more specific to deflate (which can be pretty fast on current HW). for things like PNG, most of the time goes into running the filters over the decompressed buffers, which has lead to some amount of optimization (generally, dedicated functions which apply a single filter over a scanline with a fixed format). this is why the Paeth optimization trick became important: the few conditionals inside the predictor themselves became a large bottleneck. this is because (unlike deflate) it is necessary to execute some logic for every pixel (like, add the prior pixel, or a prediction based on the adjacent pixels). JPEG is also something that would normally be expected to be dead-slow, but isn't actually all that bad (more so, as my codec also assumes the ability to work a whole image at once), and most operations boil down to a "modest" amount of fixed-point arithmetic (like in the DCT, no cosines or floating-point is actually involved, just a gob of fixed-point). sort of like with PNG, the main time-waster tends to become the final colorspace transformation (YUV -> RGB), but this can be helped along in a few ways: writing logic specifically for configurations like 4:2:0 and 4:4:4, which can allow more fixed-form logic; generally transforming the image in a block-by-block manner (related to the above, often it is an 8x8 or 16x16 macroblock which is broken down into 2x2 or 4x4 sub-blocks for the color-conversion, partly to allow reusing math between nearby pixels); using special logic to largely skip over costly checks (like individually range-clamping pixeks, ..., which can be done per-block rather than per-pixel); for faster operation, one can also skip over time-wasters like rounding and similar; ... with a lot tricks like this, one can get JPEG decoding speeds of ~ 100 Mpix/s or so (somehow...), ironically not being too far off from a PNG decoder (or, FWIW, a traditional video codec). getting stuff like this fed into OpenGL efficiently is a little bit more of an issue, but, the driver-supplied texture compression was at least moderately fast, and in my own experiments I was able to write faster texture compression code. the main (general) tricks mostly seem to be: avoid conditionals where possible (straight-through arithmetic is often faster, as pipeline stalls will often cost more than the arithmetic); if at all possible, avoid using floating point in per-pixel calculations (the conversions between bytes and floats can kill performance, so straight fixed-point is usually better here). SIMD / SSE can also help here, but has to be balanced with its relative ugliness and reduced portability. as for an SSD: dunno... I suspect at-present, SSDs are more of a novelty though... even if the SSD is very fast, the speed of the SATA bus will still generally limit them to about 400MB/s or so, so using compression for speedups still isn't completely ruled out (though, granted, it will make much less of a difference than it does with a 50MB/s or 100MB/s disk-IO speed, and avoidance of "costly" encodings may make more sense). granted, it seems with the newly optimized PNG Paeth filter, and faster DXT encoding, the main time waster (besides disk-IO) during loading is now... apparently... the code for scrolling the console buffer... (this happens whenever a console print message prints a newline character, which involves moving the entire console up by 1 line, and is basically just a memory copy). (sode note: this console operation just naively uses "for()" loops to copy memory...). and, shaved a few seconds off the startup time (down to about 3 seconds to start up the engine, and around 9 seconds to load the world). ### #1cr88192 Posted 06 February 2013 - 02:28 PM samoth, on 06 Feb 2013 - 09:17, said: Quote I am writing mostly from personal experience, which tends to be that HDD's aren't very fast. More precisely, one should say: Harddisks are fast. Fast enough for pretty much everything. SSDs are faster, in fact, ridiculously fast. They're becoming more and more common (and thus cheaper, which is a positive feedback loop), and I'm hoping that in maybe 3-5 years from now you'll be able to assume a SSD as "standard" in every computer. Harddisk seeks are slow, but if you pay only a little attention (e.g. not ten thousand files), not so much that they're ever an issue. seeks are basically why data can be packaged up, then a person can read a single larger package in place of a lot of little files. as for HDD speed, it depends: I am currently using 5400RPM 1TB drives, which have a max IO speed of roughly 100MB/s or so (though, 50-70MB/s is typical for OS file-IO). although, yes, 7200RPM drives are also common, they are more expensive for the size, and SSDs are still rather expensive (like$140 for 128GB drive and similar), vs like $89 for 2TB or similar for a 5400RPM drive (vs like$109 for a similar-size 7200RPM drive).
Quote
DVDs are... oh well... about 1/3 to 1/5 the speed of a harddisk, but you normally need not worry. DVD seeks, on the other hand, are the devil.
Which boils down to something as simple as: Try and avoid seeks, and you're good. If you ship on DVD, avoid them as if your life depended on it.
A slow harddisk (some 3-4 year old 7200 rpm disk) realistically delivers upwards of 50MiB/s if you don't have too many seeks. That isn't so bad. With NCQ, you often don't even notice a few dozen seeks at all, and even without, the impact is very small if you have several concurrent reads.
4 year old 5400RPM drives (3.5 inch internal), in my case...
things are slow enough to stall trying to do screen-capture from games if using uncompressed video, or so help you if you try to do much of anything involving the HDD if a virus scan is running...
better capture is generally gained via a simple codec, like MJPEG or the FFDShow codec, then transcoding into something better later.
I have a 10 year old laptop drive (60GB 4800RPM), which apparently pulls off a max read speed of around 12MB/s, and a newer laptop drive (320GB 5400RPM) which pulls off around 70MB/s (or around 30-40MB/s inside an OS).
Quote
A SSD delivers so fast that decompression can be the actual bottleneck. Seriously. You just don't care about its speed or about seek times.
Now consider a DVD. A typical, standard 16x drive will, in the best case, deliver something close to 20 MiB/s, so between 1/3 and 1/2 of what you get from a slow harddisk. In the worst case (sectors close to the middle), you'll have about half that.
Now throw in 30 seeks, which on the average take around 150ms each on a DVD drive. That's a full 4.5 seconds spent in seeking. Compared to these 4.5 seconds during which nothing at all happens (nothing useful from your point of view, anyway), pretty much every other consideration regarding speed becomes insignificant.
my experience is roughly pulling in a few hundred MB of data over the course of a number of a few seconds or so.
more time is generally spent reading the data than decompressing it.
like, with deflate:
I have previously tested getting decompression-speeds of around several GB/s or so (and in a few past tests, namely with readily compressible data, hitting the RAM speed limit). (mostly as the actual "work" of inflating data consists mostly of memory-copies and RLE flood-fills).
implemented sanely, decoding a Huffman symbol is mostly a matter of something like:
v=hufftab[(win>>pos)&32767];
pos+=lentab[v];
if(pos>=8) { pos-=8; win=(win>>8)|((*cs++)<<24); }
which isn't *that* expensive (and more so, it is only a small part of the activity except mostly in poorly-compressible data).
granted, I am using a custom inflater, rather than zlib (it makes a few optimizations under the assumption of being able to compress/decompress an entire buffer at once, rather than assuming making use of a piecewise stream).
this doesn't necessarily apply to things like LZMA, which involve a much more costly encoding, and have a hard time breaking 60-100MB/s for decoding speeds IME, but is more specific to deflate (which can be pretty fast on current HW).
for things like PNG, most of the time goes into running the filters over the decompressed buffers, which has lead to some amount of optimization (generally, dedicated functions which apply a single filter over a scanline with a fixed format). this is why the Paeth optimization trick became important: the few conditionals inside the predictor themselves became a large bottleneck. this is because (unlike deflate) it is necessary to execute some logic for every pixel (like, add the prior pixel, or a prediction based on the adjacent pixels).
JPEG is also something that would normally be expected to be dead-slow, but isn't actually all that bad (more so, as my codec also assumes the ability to work a whole image at once), and most operations boil down to a "modest" amount of fixed-point arithmetic (like in the DCT, no cosines or floating-point is actually involved, just a gob of fixed-point). sort of like with PNG, the main time-waster tends to become the final colorspace transformation (YUV -> RGB), but this can be helped along in a few ways:
writing logic specifically for configurations like 4:2:0 and 4:4:4, which can allow more fixed-form logic;
generally transforming the image in a block-by-block manner (related to the above, often it is an 8x8 or 16x16 macroblock which is broken down into 2x2 or 4x4 sub-blocks for the color-conversion, partly to allow reusing math between nearby pixels);
using special logic to largely skip over costly checks (like individually range-clamping pixeks, ..., which can be done per-block rather than per-pixel);
for faster operation, one can also skip over time-wasters like rounding and similar;
...
with a lot tricks like this, one can get JPEG decoding speeds of ~ 100 Mpix/s or so (somehow...), ironically not being too far off from a PNG decoder (or, FWIW, a traditional video codec).
getting stuff like this fed into OpenGL efficiently is a little bit more of an issue, but, the driver-supplied texture compression was at least moderately fast, and in my own experiments I was able to write faster texture compression code.
the main (general) tricks mostly seem to be:
avoid conditionals where possible (straight-through arithmetic is often faster, as pipeline stalls will often cost more than the arithmetic);
if at all possible, avoid using floating point in per-pixel calculations (the conversions between bytes and floats can kill performance, so straight fixed-point is usually better here).
SIMD / SSE can also help here, but has to be balanced with its relative ugliness and reduced portability.
as for an SSD: dunno...
I suspect at-present, SSDs are more of a novelty though...
even if the SSD is very fast, the speed of the SATA bus will still generally limit them to about 400MB/s or so, so using compression for speedups still isn't completely ruled out (though, granted, it will make much less of a difference than it does with a 50MB/s or 100MB/s disk-IO speed, and avoidance of "costly" encodings may make more sense).
granted, it seems with the newly optimized PNG Paeth filter, and faster DXT encoding, the main time waster (besides disk-IO) during loading is now... apparently... the code for scrolling the console buffer...
(this happens whenever a console print message prints a newline character, which involves moving the entire console up by 1 line, and is basically just a memory copy).
and, shaved a few seconds off the startup time (down to about 3 seconds to start up the engine, and around 9 seconds to load the world).
PARTNERS
|
2013-12-13 12:12:03
|
{"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": 0.46551498770713806, "perplexity": 3481.936719286741}, "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-2013-48/segments/1386164938822/warc/CC-MAIN-20131204134858-00012-ip-10-33-133-15.ec2.internal.warc.gz"}
|
https://proofwiki.org/wiki/Definition:Constructed_Semantics/Instance_3
|
Definition:Constructed Semantics/Instance 3
Definition
Let $\mathcal L_0$ be the language of propositional logic.
The constructed semantics $\mathscr C_3$ for $\mathcal L_0$ is used for the following results:
Structures
Define the structures of $\mathscr C_3$ as mappings $v$ by the Principle of Recursive Definition, as follows.
Let $\mathcal P_0$ be the vocabulary of $\mathcal L_0$.
Let a mapping $v: \mathcal P_0 \to \{ 0, 1, 2 \}$ be given.
Next, regard the following as definitional abbreviations:
$(1)$ $:$ Conjunction $\displaystyle \mathbf A \land \mathbf B$ $\displaystyle =_{\text{def} }$ $\displaystyle \neg \left({ \neg \mathbf A \lor \neg \mathbf B }\right)$ $(2)$ $:$ Conditional $\displaystyle \mathbf A \implies \mathbf B$ $\displaystyle =_{\text{def} }$ $\displaystyle \neg \mathbf A \lor \mathbf B$ $(3)$ $:$ Biconditional $\displaystyle \mathbf A \iff \mathbf B$ $\displaystyle =_{\text{def} }$ $\displaystyle \left({\mathbf A \implies \mathbf B}\right) \land \left({\mathbf B \implies \mathbf A}\right)$
It only remains to define $v \left({ \neg \phi }\right)$ and $v \left({ \phi \lor \psi}\right)$ recursively, by:
$\displaystyle v \left({\neg \phi }\right)$ $:=$ $\displaystyle \begin{cases} 2 & : \text{if v \left({\phi}\right) = 0} \\ 1 & : \text{if v \left({\phi}\right) = 1} \\ 0 & : \text{if v \left({\phi}\right) = 2}\end{cases}$ $\displaystyle v \left({ \phi \lor \psi }\right)$ $:=$ $\displaystyle \begin{array}{c|ccc} \phi \lor \psi & 0 & 1 & 2 \\ \hline 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 2 \\ 2 & 0 & 2 & 2 \\ \end{array}$
Validity
Define validity in $\mathscr C_3$ by declaring:
$\models_{\mathscr C_3} \phi$ if and only if $v \left({\phi}\right) \in \set{ 0, 1 }$
|
2020-07-08 05:38:23
|
{"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": 0.9216952919960022, "perplexity": 380.2188292014602}, "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-2020-29/segments/1593655896374.33/warc/CC-MAIN-20200708031342-20200708061342-00313.warc.gz"}
|
http://nrich.maths.org/2791
|
### Number Detective
Follow the clues to find the mystery number.
### Six Is the Sum
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
### (w)holy Numbers
A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
# Diagonal Sums
##### Stage: 2 Challenge Level:
Here is a $100$ square with some of the numbers shaded:
Look at the green square which contains the numbers $2, 3, 12$ and $13$.
Do you notice anything about the sum of the numbers that are diagonally opposite each other?
Look at the pink square.
What happens this time when you look at the numbers diagonally opposite each other?
What about the yellow square?
You could try with other squares which have four numbers in them.
Can you find a reason why what you notice, happens?
Look at the squares shaded red. They form the corners of a large $3$ by $3$ square.
If you add the numbers diagonally opposite each other, what do you notice with this larger square?
Can you find a reason why what you notice, happens?
What happens for squares of different sizes?
You may like to print off this 100 square to try out some different squares of numbers.
|
2016-07-28 20:52:53
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.2989291250705719, "perplexity": 1224.6984286194609}, "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-2016-30/segments/1469257828322.57/warc/CC-MAIN-20160723071028-00238-ip-10-185-27-174.ec2.internal.warc.gz"}
|
https://mathoverflow.net/questions/290550/locally-riemannian-connection
|
# Locally Riemannian Connection
Let $\Gamma^a{}_{bc}=\Gamma^a{}_{cb}$ be a symmetric connection whose curvature is $$R^a{}_{bcd}=\partial_c\Gamma^a{}_{bd}-\partial_d\Gamma^a{}_{bc}+\Gamma^a{}_{ec}\Gamma^e{}_{bd}-\Gamma^a{}_{ed}\Gamma^e{}_{bc}.$$
What conditions can we observe locally on $\Gamma^a{}_{bc}$ or $R^a{}_{bcd}$ to conclude that it is locally Riemannian?
• Non local information as the holonomy group is not accessible so I wish to restrict to what can we know locally – Aureliano Skirzewski Jan 12 '18 at 16:43
• This question is related mathoverflow.net/questions/54434 – j.c. Jan 12 '18 at 16:59
• That question is not the same as yours, but unless I am misunderstanding something, I believe several of the answers and references will be helpful to you. See e.g. arxiv.org/abs/0804.2698 cited in John's answer mathoverflow.net/a/173399 – j.c. Jan 12 '18 at 17:16
• Note that $dg_{ab} = (g_{ap}\Gamma^p_{bc} + g_{bp}\Gamma^p_{ac})\,dx^c$, so you can use the Frobenius theorem. – Deane Yang Jan 12 '18 at 17:34
• You could employ the holonomy group in an arbitrarily small open set, which would already give a nontrivial condition, locally but not infinitesimally. – Ben McKay Jan 12 '18 at 17:39
Perhaps I can offer some information and comment on this problem. An essential part of the problem is how to interpret terms such as 'observe', 'accessible', 'identify', as the OP wants to know how to write down a computable criterion for a torsion-free connection to be the Levi-Civita connection of a Riemannian metric. Of course, this requires that one specify what one means by computable. For example, the OP does not consider the holonomy criterion (i.e., that the holonomy be a compact group) to be 'accessible', so I suppose that this means that tools to determine the holonomy group are not to be counted as computable, for the purposes of this question.
Various articles in the literature purport to solve this problem by providing an 'algorithm' for finding a compatible metric (if it exists) that only involves computing derivatives. However, all of these 'algorithms' depend on making constant rank assumptions for various systems of linear equations. As long as these constant rank assumptions hold, they work fine, but it is possible to 'fool' them by constructing examples in which the constant rank assumptions do not hold.
For example, take two closed disks with smooth boundary, $D_1$ and $D_2$, in $\mathbb{R}^2$ whose interiors are disjoint. Let $g_1$ be a metric on $\mathbb{R}^2$ that agrees with the flat metric $dx^2+dy^2$ outside of $D_1$ but has nonzero curvature somewhere inside $D_1$ and let $g_2$ be a metric on $\mathbb{R}^2$ that agrees with the flat metric $dx^2+2dy^2$ outside of $D_2$ but has nonzero curvature somewhere inside $D_2$. One can even arrange that the curvature of $g_i$ be nonzero in $D_i$ away from some closed subset $K_i$ that lies in the interior of $D_i$, so do this. Now let $\nabla$ be the connection that agrees with the Levi-Civita connection $\nabla_1$ of $g_1$ outside the disk $D_2$ and the Levi-Civita connection $\nabla_2$ of $g_2$ outside the disk $D_1$. (The connections $\nabla_i$ are equal outside the union of the interiors of $D_1$ and $D_2$.) Then $\nabla$ is not the Levi-Civita connection of any metric on $\mathbb{R}^2$. If the two closed disks do not intersect, then every point of $\mathbb{R}^2$ has an neighborhood that does not meet one of the disks, so there is a metric on that neighborhood (e.g., one of the $g_i$) compatible with $\nabla$. Hence $\nabla$ is locally Riemannian. However, if the closed disks are tangent at one point, then that point has no open neighborhood on which $\nabla$ is Riemannian.
Note that the above example shows that the condition of being locally Riemannian is not a closed condition on germs of torsion-free connections in the plane (since it can hold on the complement of a point) and hence it cannot be determined just as the satisfaction of some system of partial differential equations on the connection.
Meanwhile, if one is willing to consider open conditions as well as closed conditions, then it is easy to write down sufficient conditions for a connection to be locally Riemannian that, beyond algebra, only require the ability to take derivatives and to test whether an expression is zero or not. These 'accessible' sufficient conditions are not necessary, though.
For example, consider the $2$-dimensional case: Let $\nabla$ be a torsion-free connection on a simply-connected domain $U$ in the $x^1x^2$-plane, with connection coefficients $\Gamma^{i}_{jk}=\Gamma^{i}_{kj}$, let $\gamma^i_j = \Gamma^{i}_{jk}\,\mathrm{d}x^k$ be the entries of the $2$-by-$2$ matrix $\gamma$, and write $\mathrm{d}\gamma+\gamma\wedge\gamma = R\,\mathrm{d}x^1\wedge\mathrm{d}x^2$, where $R= (R^i_j)$ is a matrix of functions on $U$.
The first necessary condition is that $\mathrm{tr}(R) = R^1_1+R^2_2 = 0$, otherwise there would be no parallel volume form (and hence no parallel metric). (This is one first-order differential equation on $\nabla$.)
Now, suppose the open condition that $\mathrm{det}(R) = r^2 > 0$ for some positive function $r$ on $U$ (which, if $\gamma$ is to be a Riemannian connection, would follow from $R\not=0$). Once this condition is imposed, define a symmetric matrix $H$ of determinant $1$ by the rule $$H = \pm\frac{1}r\begin{pmatrix}R^2_1& -R^1_1\\ -R^1_1 & -R^1_2\end{pmatrix},$$ with the sign chosen to make $H$ be positive definite. Then $H$ is the unique symmetric positive definite matrix of functions on $U$ that has determinant $1$ and satisfies the condition that $HR$ be skew-symmetric.
Finally then, $\nabla$ is a metric connection in $U$ if and only if the identity $$\mathrm{d}H + \mathrm{tr}(\gamma)\,H - H\gamma - {}^t\gamma H = 0$$ holds. (This is only four second-order differential equations on $\nabla$, since, by construction, the trace of $H^{-1}\mathrm{d}H$ always vanishes. One can check that these four equations are independent.)
In fact, since $\mathrm{d}\bigl(\mathrm{tr}(\gamma)\bigr)=0$, and $U$ is supposed simply-connected, there exists a function $f$ on $U$ such that $\mathrm{tr}(\gamma) = \mathrm{d}f$, and then the symmetric matrix $G = \mathrm{e}^f H$ satisfies $$\mathrm{d}G = G\gamma + {}^t\gamma G,$$ and so the metric $g = G_{ij}\,\mathrm{d}x^i\mathrm{d}x^j$ is parallel with respect to $\nabla$, and, up to a constant factor, it is the unique such metric.
Thus, a sufficient condition in this case is comprised by a first-order differential equation on $\nabla$, a strict inequality on the first derivatives of $\nabla$ (which is an open condition), and then four second-order differential equations on $\nabla$.
• Thank you for your response, I suppose the higher dimensional set of conditions is equivalent to finding a non degenerated 0-form $H_{ij}$ such that the 2-form $H_{ki}R^i{}_j$ is antisymmetric in $k$ and $j$. That's enough to reduce the number of independent components of the curvature tensor to the components of a Riemann. It just rests to find when does $H$ exist and check which of the solutions for $H$ satisfies $$\mathrm{d}H + \mathrm{tr}(\gamma)\,H - H\gamma - {}^t\gamma H = 0.$$ Am I missing something? – Aureliano Skirzewski Jan 18 '18 at 12:18
• @AurelianoSkirzewski: That's close. In dimension $n$, if you make the assumption that the curvature $2$-form $\rho=\mathrm{d}\gamma +\gamma\wedge\gamma$ satisfies the condition that there exists exactly one positive definite, determinant 1, symmetric matrix $H$ such that $H\rho$ is antisymmetric (which is a combination of open and closed first-order conditions on the curvature $\rho$), then you just need to check whether $$\mathrm{d}H +\tfrac2n\,\mathrm{tr}(\gamma)H-H\gamma-{}^t\gamma H=0.$$ – Robert Bryant Jan 18 '18 at 13:02
|
2019-05-21 15:51:30
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9004133939743042, "perplexity": 109.63797344596232}, "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-2019-22/segments/1558232256426.13/warc/CC-MAIN-20190521142548-20190521164548-00370.warc.gz"}
|
https://www.givewell.org/united-states/charities/Year-Up
|
# Year Up
The last time we examined the charities working primarily in the U.S. was in 2010. As of 2011, we have de-prioritized further work on this cause.
The content we created in 2007 appears below. This content is likely to be no longer fully accurate, both with respect to what it says about the organization and with respect to what it implies about our own views and positions.
Published: 2007
We reviewed Year Up in 2007 as part of our process to award a grant to a job training charity. The following are our conclusions after reviewing Year Up's application materials.
# In a nutshell
Year Up grads in Boston earned, on average, close to $15/hr in 2004 and 2005 (see Attachment A-4 pg 6). Adjusting for 2 years of 5% annual wage inflation (since 2005) and a 25% New York premium (according to the Bureau of Labor Statistics, in 2002 average annual earnings in Boston were$45,685 and in New York City were $57,708),$15/hr in Boston in 2005 would equate to $21/hr (or,$43,000/year) in New York in 2007. Although it is an extremely limited sample, the 10 Year Up graduates who graduated in July 2007 and have already found work are earning an average of $20/hr (Attachment A-4 Pg 6). Attachment A-4 Pg 5 provides Year Up's overview of the career paths, which is based on very general numbers from the New York State Department of Labor. They paint an optimistic picture: computer support specialists earn a median of around$50,000, from $35,000 for low-skill jobs to$80,000 for high-skill jobs, while those in the "Business and Financial Operations" area earn a median wage around $65,000. We don't have a very good sense of where the jobs Year Up's graduates are being placed in fall in these classifications. ### Does it work? Intuitively, we have a relatively easy time seeing the value-added of the Year Up model. Although it selects its applicants very carefully - raising the question of whether they could succeed without its help - the jobs it places them in (mostly Computer Support Specialist roles) presumably require relatively specialized knowledge, and it's unclear how else very low-income people could get the necessary training. It's also possible that Year Up's relationships with corporations are helpful to clients; Attachment B-2 implies that they aim for relatively strong and lasting relationships with particular partners. Getting a data-driven check on this logic is difficult; like our other clients, Year Up has not yet analyzed comparison groups (i.e., looking at whether people similar to its clients - but not in its program - achieve similar outcomes). Year Up's Charity Response (see the right hand side of the page) indicates a plan to conduct a study that will get at this question, by looking at outcomes for its August 2007 New York class relative to those randomly lotteried out of the program. We look forward to the results of this study; in the meantime, we have constructed a very rough "comparison group" from the 2000 census, looking at the the NYC population that matches Year Up's applicants on age, ethnicity, and educational status. Of this group, approximately 6% have earnings comparable to those of Year Up graduates (see the analysis for details). By contrast, 10% of a similar population served by Year Up achieves this level of income, if you believe that Year Up picks out about the top 20% of the population (see our analysis of selectivity, above) and places about half sustainably in jobs. The preceding paragraph has many weak links in it: • We have estimated that about 80% of those Year Up places in jobs hold those jobs sustainably – this is slightly lower than the "maximally optimistic estimate" of 90% discussed above – but without clear retention data (see above), we do not feel confident in this. • We have estimated the average wages for Year Up grads at around$40,000/yr, but have no sense of how many actually make $40,000/yr or more. For reference, see HOPE, whose graduates average about$10/hr of income – but around half of them make less than $8/hr. If only half of Year Up graduates make$40,000/yr or more, this would imply that they don't outperform our rough "comparison group" at all.
• On the other hand, as we state in our census analysis, there are clear ways in which Year Up's participants might face more obstacles than our "comparison group" does - their low incomes, along with the mere fact that they come to Year Up for help, distinguishes them from the general population.
We feel that the numbers are consistent with, though not implying, a "Year Up" effect; considering both these and the intuitive argument at the top of this section, we feel moderately confident that Year Up systematically makes its clients better off than they would be without its help.
## What does it cost?
We estimate that Year Up spends about $20,000 per enrollee; if half of these end up in sustainable employment, that's$40,000 per person placed sustainably. Details follow.
The following table is assembled from a mix of sources. For 2003, Year Up operated only in Boston (2004 IRS Form 990, Statement 2). We take enrollee numbers from Attachment A-4 Pg 6, and financial data from the IRS Form 990s available on GuideStar (since Year Up did not directly provide us this data). For 2004-2006, Year Up spanned multiple sites, and we take enrollee information from Year Up's Charity Response (on the right of this page). We use the financial data provided (Attachment D-1) for these years.
Year Up earns revenue from its clients' internships, and we find it appropriate to net this revenue with its costs; we don't know how much revenue was earned in this way for any year but 2006 (Attachment D-2 Pg 1). Assuming that we have the number of people served correct for 2006, this implies about $10,000 per person of apprenticeship revenue, reducing our estimate of the cost per enrollee from$30,000 to $20,000. Year Costs ($ thousands) Number enrolled (all locations) Cost per enrollee
2003 $2,191 93$23,559
2004 $3,710 115$32,261
2005 $5,477 208$26,332
2006 $8,368 350$23,909
2007 (est) $12,984 491$26,444
Year Up has been expanding relatively rapidly, and its overall costs per client have fallen if anything. For this reason, we are optimistic about its ability to serve more people with more funds.
## The organization
Year Up is a focused organization, and we have reviewed its full set of activities. It appears organizationally/structurally sound, though we are somewhat low on details regarding its financials.
Size and scope. Year Up NYC is a branch of a national Year Up organization with headquarters in Boston (Attachment C-1 pg 1). We focused on NYC for purposes of understanding wages, budget, etc., but we used data from the non-NYC sites (DC, Providence, and especially Boston) as much as we could to get a sense of the general costs and effectiveness of the Year Up model. Year Up plans to open a San Francisco program in 2008 (see Year Up's Charity Response on the right side of this page).
Year Up has a much longer and more documented track record in Boston than at other sites, and our confidence in its results' being replicated across sites is only moderate.
Personnel. Year Up's 11-member Board appears to be mostly from the corporate for-profit world (Attachment C-2). The Executive Director, Lisette Nieves, is a Truman and Rhodes scholar with an extensive history of involvement with major nonprofits including The After-School Corporation and Jumpstart, and the instructors (presumably the people working directly with clients to teach job skills) are highly experienced (Attachment C-5).
Financials (see all attachments under heading D for sources).
Year Revenues (thouands) Expenses (thousands)
2003 $3,353$2,191
2004 $7,412$3,710
2005 $6,007$5,477
2006 $12,054$8,368
2007 (est) $20,429$12,984
Year Up had a significant surplus last year, and expects another this coming year. Its fiscal position is strong, but this doesn't mean there's no use for more money: its expenses have grown rapidly, in line with (though lagging) revenues.
As of the 2006 audit, Year Up held around $12.4M in assets (Attachment D-1 Pg 4), equal to the 2006 expenses given in Attachment D-2 - this implies that they have about one year's worth of cash on hand. Year Up's main source of revenue is foundations and corporations: as Attachment D-2 shows, about half its projected revenue comes from direct foundation and corporation grants, and another ~25% comes from apprenticeship fees. Student stipends are a major expense, which makes sense to us: Year Up is putting low-income people through a 12-month full-time program, and students need to sustain themselves in the meantime. Beyond that, we have trouble understanding the expenses, which aren't broken out in much detail. Attachment D-1 Pg 5 lists a large "Training and Other" line item, while Attachment D-2 Pg 1 lists a similarly large "Program, Fundraising & Administration" line item. We don't know what to make of either of these. Site visit. Holden Karnofsky (GiveWell's Executive Director) conducted a site visit to Year Up on 11/26/2007. His personal impressions are informally written up on The GiveWell Blog, here. ## Conclusion Year Up appeals to us because of its focus on carefully targeting people who are well-positioned to benefit, then getting them into relatively well-paying jobs. We also like the fact that it is a relatively focused organization that already operates several sites and could likely scale with more funding. Our extremely limited and potentially problematic analysis implies that Year Up graduates do better than they would without its help, though we hope to obtain better and clearer data on retention than what we have now. ## We'd like to know more about: • Retention data. Do clients stay in the jobs they're placed in? How long and how often? • Situations of entering clients. Do they have issues with housing, substance abuse, etc.? What is their employment situation prior to coming to Year Up? • Training curriculum. We have a general overview, but we'd like to see the syllabus, formal layout, etc. to get a better sense of what clients are being trained to do and how they're being trained to do it. Note that Year Up answered this in their Charity Response. • Wage distribution. What portion of Year Up graduates earn more than$20/hr? \$15/hr? Without this, we have trouble estimating Year Up's impact relative to what it's population would have otherwise achieved.
• Definition of placement. Within what time frame must graduates find jobs? Must the jobs be full-time, or can they be part-time?
|
2019-07-17 08:41:18
|
{"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": 0.26562732458114624, "perplexity": 4042.1013427609714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525133.20/warc/CC-MAIN-20190717081450-20190717103352-00012.warc.gz"}
|
http://exxamm.com/blog/Blog/14511/zxcfghfgvbnm4?Class%2011
|
Physics THE SPEED OF A TRAVELLING WAVE ,TRANSVERSE WAVE & LONGITUDINAL WAVE AND REFLECTION OF WAVES
### Topic Covered
color{blue}{star} THE SPEED OF A TRAVELLING WAVE
color{blue}{star} SPEED OF A TRANSVERSE WAVE ON STRETCHED STRING
color{blue}{star} SPEED OF A LONGITUDINAL WAVE (SPEED OF SOUND)
color{blue}{star} REFLECTION OF WAVES
### THE SPEED OF A TRAVELLING WAVE
color{blue} ✍️ To determine the speed of propagation of a travelling wave, we can fix our attention on any particular point on the wave (characterized by some value of the phase) and see how that point moves in time.
color{blue} ✍️ It is convenient to look at the motion of the crest of the wave. Fig. 15.8 gives the shape of the wave at two instants of time which differ by a small time internal Δt.
color{blue} ✍️ The entire wave pattern is seen to shift to the right (positive direction of x-axis) by a distance Δx. In particular the crest shown by a cross (×) moves a distance Δx in time Δt, The speed of the wave is then Δx//Δt.
color{blue} ✍️We can put the cross (×) on a point with any other phase. It will move with the same speed v (otherwise the wave pattern will not remain fixed). The motion of a fixed phase point on the wave is given by
kx – ωt = " constant"
...............................(15.10)
color{blue} ✍️Thus, as time t changes, the position x of the fixed phase point must change so that the phase remains constant. Thus
color {blue} {kx – ωt = k(x+Δx) – ω(t+Δt)}
or color{purple} {k Δx – ω Δt =0}
color{blue} ✍️Taking Δx, Δt vanishingly small, this gives
color{blue} {(dx)/(dt) = omega/k = v}
...................(15.11)
Relating ω to T and k to λ, we get
color{blue} {v = ( 2 n v)/ ( 2 pi k ) = lamda v = lamda/T}
......................(15.12)
color{blue} ✍️Eq. (15.12), a general relation for all progressive waves, shows that in the time required for one full oscillation by any constituent of the medium, the wave pattern travels a distance equal to the wavelength of the wave.
color{blue} ✍️It should be noted that the speed of a mechanical wave is determined by the inertial (linear mass density for strings, mass density in general) and elastic properties (Young’s modulus for linear media/ shear modulus, bulk modulus) of the medium.
color{blue} ✍️The medium determines the speed; Eq. (15.12) then relates wavelength to frequency for the given speed. Of course, as remarked earlier, the medium can support both transverse and longitudinal waves, which will have different speeds in the same medium.
### Speed of a Transverse Wave on Stretched String
color{blue} ✍️The speed of a mechanical wave is determined by the restoring force setup in the medium when it is disturbed and the inertial properties (mass density) of the medium.
color{blue} ✍️The speed is expected to be directly related to the former and inversely to the latter. For waves on a string, the restoring force is provided by the tension T in the string. The inertial property will in this case be linear mass density μ, which is mass m of the string divided by its length L.
color{blue} ✍️Using Newton’s Laws of Motion, an exact formula for the wave speed on a string can be derived, but this derivation is outside the scope of this book.
color{blue} ✍️We shall, therefore, use dimensional analysis. We already know that dimensional analysis alone can never yield the exact formula. The overall dimensionless constant is always left undetermined by dimensional analysis.
color{blue} ✍️The dimension of μ is [ML^-1] and that of T is like force, namely [MLT^-2]. We need to combine these dimensions to get the dimension of speed v [LT^-1]. Simple inspection shows that the quantity T//μ has the relevant dimension
([MLT^-2])/([ML^-1]) = [ L^2 T^-2]
color{blue} ✍️Thus if T and μ are assumed to be the only relevant physical quantities,
color{blue} {nu = C sqrt(T/mu)}
.......................(15.13)
color{blue} ✍️where C is the undetermined constant of dimensional analysis. In the exact formula, it turms out, C=1. The speed of transverse waves on a stretched string is given by
color{blue} {nu = sqrt(T/mu)}
....................... (15.14)
color{blue} ✍️Note the important point that the speed v depends only on the properties of the medium T and μ (T is a property of the stretched string arising due to an external force).
color{blue} ✍️It does not depend on wave length or frequency of the wave itself. In higher studies, you will come across waves whose speed is not independent of frequency of the wave.
color{blue} ✍️Of the two parameters λ and ν the source of disturbance determines the frequency of the wave generated. Given the speed of the wave in the medium and the frequency Eq. (15.12) then fixes the wavelength
color{blue} {lamda = nu/v}
................(15.15)
Q 3169278115
A steel wire 0.72 m long has a mass of 5.0 × 10^-3 kg. If the wire is under a tension of 60 N, what is the speed of transverse waves on the wire ?
Class 11 Chapter 15 Example 3
Solution:
Mass per unit length of the wire,
mu = (5.0 xx 10^-3 kg)/(0.72 m)
= 6.9 xx 10^-3 kg m^-1
Tension, T = 60 N
The speed of wave on the wire is given by
nu = sqrt (T/mu) = sqrt ((60 N) / ( 6.9 xx 10^-3 kg m^-1 ) = 93 ms^-1
### Speed of a Longitudinal Wave (Speed of Sound)
color{blue} ✍️In a longitudinal wave the constituents of the medium oscillate forward and backward in the direction of propagation of the wave. We have already seen that the sound waves travel in the form of compressions and rarefactions of small volume elements of air.
color{blue} ✍️The elastic property that determines the stress under compressional strain is the bulk modulus of the medium defined by (see chapter 9)
color{blue} {B = - (Delta P)/ ( Delta V//V)
..................... (15.16)
color{blue} ✍️Here the change in pressure ΔP produces a volumetric strain (DeltaV)/V B has the same dimension as pressure and given in SI units in terms of pascal (Pa).
color{blue} ✍️The inertial property relevant for the propagation of wave in the mass density ρ, with dimensions [ML^-3]. Simple inspection reveals that quantity B//ρ has the relevant dimension:
color{blue} { ([ML^-1 T^-2] ) / ([ML^-3]) = [ L^2 T^-2]}
....................... (15.17)
color{blue} ✍️Thus if B and rho are considered to be the only relevant physical quantities,
color{blue} {nu = C sqrt (B/rho)}
......................... (15.19)
color{blue} ✍️For a linear medium like a solid bar, the lateral expansion of the bar is negligible and we may consider it to be only under longitudinal strain. In that case, the relevant modulus of elasticity in Young’s modulus, which has the same dimension as the Bulk modulus.
color{blue} ✍️Dimensional analysis for this case is the same as before and yields a relation like Eq. (15.18), with an undetermined C which the exact derivation shows to be unity. Thus the speed of longitudinal waves in a solid bar is given by
color{blue} {nu =sqrt(Y/rho)}
...........(15.20)
color{blue} ✍️where Y is the Young’s modulus of the material of the bar. Table 15.1 gives the speed of sound in some media.
color{blue} ✍️Liquids and solids generally have higher speeds of sound than in gases. [Note for solids, the speed being referred to is the speed of longitudinal waves in the solid].
color{blue} ✍️This happens because they are much more difficult to compress than gases and so have much higher values of bulk modulus. This factor more than compensates for their higher densities than gases.
color{blue} ✍️We can estimate the speed of sound in a gas in the ideal gas approximation. For an ideal gas, the pressure P, volume V and temperature T are related by (see Chapter 11).
color{blue} { PV = NkBT}
....................... (15.21)
color{blue} ✍️where N is the number of molecules in volume V, k_B is the Boltzmann constant and T the temperature of the gas (in Kelvin).
color{blue} ✍️Therefore, for an isothermal change it follows from Eq.(15.21) that
color{blue}{VΔP + PΔV = 0}
or
color{blue} {- (Delta P)/(Delta V//V) = P}
color{blue} ✍️Hence, substituting in Eq. (15.16), we have
B = P
color{blue} ✍️Therefore, from Eq. (15.19) the speed of a longitudinal wave in an ideal gas is given by,
color{blue} {nu = sqrt (P/rho)}
.....................(15.22)
color{blue} ✍️This relation was first given by Newton and is known as Newton’s formula.
color{blue} ✍️According to Newton’s formula for the speed of sound in a medium, we get for the speed of sound in air at STP,
color{purple}{nu = [ ( 1.01 xx 10^5 N m^-2 )/ ( 1.29 kg m^-3) ] ^(1//2)}
color{blue} {nu= 280 ms^-1}
...................(15.23)
color{blue} ✍️The result shown in Eq.(15.23) is about 15% smaller as compared to the experimental value of 331 m s^-1 as given in Table 15.1.
color{blue} ✍️If we examine the basic assumption made by Newton that the pressure variations in a medium during propagation of sound are isothermal, we find that this is not correct. It was pointed out by Laplace that the pressure variations in the propagation of sound waves are so fast that there is little time for the heat flow to maintain constant temperature.
color{blue} ✍️These variations, therefore, are adiabatic and not isothermal. For adiabatic processes the ideal gas satisfies the relation,
PV^γ = constant
i.e. Δ(PV^γ ) = 0
or color{purple} {P^γ V ^(γ –1 ) ΔV + V^γ ΔP = 0}
color{blue} ✍️Thus, for an ideal gas the adiabatic bulk modulus is given by,
color{ blue } {B_(ad) = - (Delta P)/ ( Delta V//V)} = color{blue} {= gamma P}
where γ is the ratio of two specific heats, C_p//C_v. The speed of sound is, therefore, given by,
color{ blue} { nu = sqrt ( gamma P/ rho)
.............. (15.24)
color{blue} ✍️This modification of Newton’s formula is referred to as the Laplace correction. For air γ = 7//5. Now using Eq. (15.24) to estimate the speed of sound in air at STP, we get a value 331.3 m s^-1, which agrees with the measured speed.
Q 3169478315
Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is 29.0 ×10^-3 kg.
Class 11 Chapter 15 Example 4
Solution:
We know that 1 mole of any gas occupies 22.4 litres at STP. Therefore, density of air at STP is :
ρ_o = (mass of one mole of air)/ (volume of one mole of air at STP)
= (29.0 xx 10^-3 kg )/( 22.4 xx 10^-3 m^3)
= 1.29 kg m^-3
### THE PRINCIPLE OF SUPERPOSITION OF WAVES
color{blue} ✍️If two wave pulses travelling in opposite directions cross each other, It turns out that wave pulses continue to retain their identities after they have crossed.
color{blue} ✍️However, during the time they overlap, the wave pattern is different from either of the pulses. Figure 15.9 shows the situation when two pulses of equal and opposite shapes move towards each other.
color{blue} ✍️When the pulses overlap, the resultant displacement is the algebraic sum of the displacement due to each pulse. This is known as the principle of superposition of waves. According to this principle, each pulse moves as if others are not present.
color{blue} ✍️The constituents of the medium therefore suffer displacement due to both and since displacements can be positive and negative, the net displacement is an algebraic sum of the two. Fig. 15.9 gives graphs of the wave shape at different times.
color{brown} {"Note"} the dramatic effect in the graph (c); the displacements due to the two pulses have exactly cancelled each other and there is zero displacement throughout.
color{blue} ✍️To put the principle of superposition mathematically, let y_1 (x,t) and y_2 (x,t) be the displacements due to two wave disturbances in the medium. If the waves arrive in a region simultaneously and therefore, overlap, the net displacement. y (x,t) is given by
color{ blue} {y (x, t) = y_1(x, t) + y_2(x, t)}
........................... (15.25)
color{blue} ✍️If we have two or more waves moving in the medium the resultant waveform is the sum of wave functions of individual waves. That is, if the wave functions of the moving waves are
y_1 = f_1(x–vt),
y_2 = f_2(x–vt),
..........
..........
y_n = f_n (x–vt)
color{blue} ✍️then the wave function describing the disturbance in the medium is
y = f_1(x – vt)+ f_2(x – vt)+ ...+ fn(x – vt)
color{blue } {= sum_(i =1)^n f_i ( x - v t)}
........................ (15.26)
color{blue} ✍️The principle of superposition is basic to the phenomenon of interference.
color{blue} ✍️For simplicity, consider two harmonic travelling waves on a stretched string, both with the same ω (angular frequens) and k (wave number), and, therefore, the same wavelength λ.
color{blue} ✍️Their wave speeds will be identical. Let us further assume that their amplitudes are equal and they are both travelling in the positive direction of x-axis. The waves only differ in their initial phase. According to Eq. (15.2), the two waves are described by the functions:
color{blue } { y_1(x, t) = a sin (kx – ωt)}
..........................(15.27)
and
color{blue} {y_2(x, t) = a sin (kx – ωt + φ )}
.....................(15.28)
color{blue} "✍️ The net displacement is then, by the principle of superposition" , given by
color{blue} {y (x, t ) = a sin (kx – ωt) + a sin (kx – ωt + φ )}
.........................(15.29)
color {green} { = a [ 2 sin [ ((kx - omega t ) + ( kx - omega t + phi ) )/2 ] cos \ \ phi/2]}
.................... (15.30)
color{blue} ✍️where we have used the familiar trignometric identity for sin A + sin B . We then have
color {blue } {y( x ,t) = 2a cos \ \phi/2 sin ( kx - omega t + phi/2 )}
....................(15.31)
color{blue} ✍️Eq. (15.31) is also a harmonic travelling wave in the positive direction of x-axis, with the same frequency and wave length. However, its initial phase angle is phi/2. The significant thing is that its amplitude is a function of the phase difference φ between the constituent two waves:
color{blue} {A(φ) = 2a cos ½φ}
.................. (15.32)
color{blue} ✍️For φ = 0, when the waves are in phase,
color{blue} {y (x,t ) = 2a sin (kx - omega t)}
.................. (15.33)
color{blue} ✍️i.e. the resultant wave has amplitude 2a, the largest possible value for A. For phi = pi ,
color{blue} ✍️the waves are completely, out of phase and the resultant wave has zero displacement everywhere at all times.
color{blue} {y (x, t ) = 0}
.................... (15.34)
color{blue} ✍️Eq. (15.33) refers to the so-called constructive interference of the two waves where the amplitudes add up in the resultant wave. Eq. (15.34) is the case of destructive intereference where the amplitudes subtract out in the resultant wave.
color{blue} ✍️Fig. 15.10 shows these two cases of interference of waves arising from the principle of superposition.
### REFLECTION OF WAVES
color{blue} ✍️So far we considered waves propagating in an unbounded medium. If a pulse or a wave meets a boundary and If the boundary is rigid, the pulse or wave gets reflected.
color{blue} ✍️The phenomenon of echo is an example of reflection by a rigid boundary. If the boundary is not completely rigid or is an interface between two different elastic media, the situation is some what complicated.
color{blue} ✍️A part of the incident wave is reflected and a part is transmitted into the second medium. If a wave is incident obliquely on the boundary between two different media the transmitted wave is called the "refracted wave."
color{blue} ✍️The incident and refracted waves obey Snell’s law of refraction, and the incident and reflected waves obey the usual laws of reflection.
color{blue} ✍️Fig. 15.11 shows a pulse travelling along a stretched string and being reflected by the boundary. Assuming there is no absorption of energy by the boundary, the reflected wave has the same shape as the incident pulse but it suffers a phase change of π or 180^0 on reflection.
color{blue} ✍️This is because the boundary is rigid and the disturbance must have zero displacement at all times at the boundary. By the principle of superposition, this is possible only if the reflected and incident waves differ by a phase of π, so that the resultant displacement is zero.
color{blue} ✍️This reasoning is based on boundary condition on a rigid wall. We can arrive at the same conclusion dynamically also. As the pulse arrives at the wall, it exerts a force on the wall. By Newton’s Third Law, the wall exerts an equal and opposite force on the string generating a reflected pulse that differs by a phase of π.
color{blue} ✍️If on the other hend, the boundary point is not rigid but completely free to move (such as in the case of a string tied to a freely moving ring on a rod), the reflected pulse has the same phase and amplitude (assuming no energy dissipation) as the incident pulse.
color{blue} ✍️The net maximum displacement at the boundary is then twice the amplitude of each pulse. An example of non- rigid boundary is the open end of an organ pipe.
color{blue} ✍️To summarize, a travelling wave or pulse suffers a phase change of π on reflection at a rigid boundary and no phase change on reflection at an open boundary. To put this mathematically, let the incident travelling wave be
color{ green} {y_2 (x,t ) = a sin (kx - omega t )}
color{blue} ✍️At a rigid boundary, the reflected wave is given by
color{blue} {y_r(x, t) = a sin (kx – ωt + π)}.
color { blue} { = – a sin (kx – ωt)} ..............(15.35)
color{blue} ✍️At an open boundary, the reflected wave is given by
color {blue } {y_r(x, t) = a sin (kx – ωt + 0)}
color {blue } {= a sin (kx – ωt)} ................ (15.36)
color{blue} ✍️Clearly, at the rigid boundary, color{purple} { y = y_2 + y_r = 0 } at all times.
|
2019-02-16 03:18:15
|
{"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": 0.6965969204902649, "perplexity": 1255.8707291598785}, "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-2019-09/segments/1550247479838.37/warc/CC-MAIN-20190216024809-20190216050809-00176.warc.gz"}
|
https://ctftime.org/writeup/5016
|
Rating:
# Tinypad - Pwn 300 Problem (SECCON QUALS 2016)
## Description
**Difficulty**: medium medium to medium hard
**Port** : 57463
Heap Fun as a Service!
## Overview
Tinypad is an x86-64 ELF (NX, FULL RELRO, no PIE) implementing you guessed it a note taking service. The service supports storing up to four notes of max length 256 chars.
The user can add, modify, and free notes after adding them.
## Reversing
The **tinypad** global array of size 320 has 256 bytes allocated for swap space which is used when editing notes. The last 64 bytes are used to store the size of the note and pointer into the heap of the note. I will refer to these as the **_size_** and **_addr_** indexes of tinypad and I will refer to the first 256 bytes as the **_temp space_** of tinypad.
When a note is printed, the addr index of **tinypad** is checked. If it is set then the value in the pointer is printed.
c
//print notes
for (i = 0; i < 4; ++i) {
addr = notes[(i * 16) + 8]; //addr
}
}
When a note is to be added, the size index of the **tinypad** array is checked. If it is set the next index is used, if not move on to the next.
c
for (i = 0; i < 4; ++i) {
size = notes[i * 16]; //size
if (!size) {
char
new_size = read_int(); //Just reads an integer from stdin
char *note = malloc(new_size);
notes[i * 16] = new_size;
notes[(i * 16) + 8] = note;
}
}
When a note is to be edited, the size index is checked to make sure a note exists. If the size is full, strcpy what is already in the note into the **_temp space_** of **tinypad**, takes the string length of that and uses **read_until** to read in input over the **_temp_space_** then copies the **_temp space_** back into the note. So you can't edit more characters in the note than it already has, this is important for later.
c
//edit note
size = notes[i * 16]; //size
note = notes[(i * 16) + 8];
if (size) {
strcpy(temp, note);
size_t len = strlen(temp);
strcpy(note, temp);
}
When a note is deleted, the size index is check to make sure a note exists, the note is freed and the size is zeroed out, **but the addr is not zeroed out**.
c
//delete note
size = notes[i * 16];
note = notes[(i * 16) + 8];
if (size) {
free(note);
note[i * 16] = 0;
}
//never nulls out the addr of the note
The **read_until** function reads in data from the user until a character is met.
c
int readuntil(char *a, size_t length, char delim) {
for (i = 0; i < length; ++i) {
int r = read(0, &a[i], 1);
if (!r || a[i] == delim)
break;
}
// i can now equal 256
a[i] = 0;
return i;
}
//Example call
## Bugs
Use After Free: Note pointers are not removed from the global array after being freed.
Null byte off by one in **read_until** function. Allowing off by one when adding and editing notes.
Ideas:
- **[Fail]** Edit using 256 bytes and zero out the *size* field of the first note in the **tinypad** array.
- **[Fail]** unsafe unlink
## Exploit
### Setup (to be used later)
Create a free chunk in the temp space of the **tinypad** array above our pointers.
### Easy Memory Leaks
Triggering a use after free is trivial. Just create a note and delete it. This use after free can only be used for printing notes so it just gets us a few useful leaks.
To get a libc leak we can take advantage of the fact that freed chunks in **smallbins** can point to the head or tail of that freelist which exists in libc.
To take advantage of this we
1. Create 4 notes, all in smallbin size range
2. Delete the third note
3. Delete the first note
4. Read the output from the main screen
Now the fd pointer of the third note points to the freelist, and the fd pointer of the first note points to the third note. Luckily the fd pointer is in the same space data would be for a malloc chunk, so this part is printed out.
The next print will print these out and we have the address of our heap and libc, which we can use to caluclate libc's base.
Now I just deleted every not to start with a fresh heap.
### Playing with the heap
Next we take advantage of our [one byte null overwrite](https://github.com/shellphish/how2heap/blob/master/poison_null_byte.c).
The idea is explained there, but to summarize the technique
1. A = malloc(0x88) - Allocate chunk of size smallbin
2. B = malloc(0x100) - Allocate chunk double the size of A
3. C = malloc(0x80) - Allocate chunk of any size
4. free(B)
5. chunk(B).size & ~0x11 - overflow A into B, clearing prev_inuse and making the size smaller (I'm just clearing the bottom two bites of chunk size here for representation)
6. b1 = malloc(0x80) - This will be allocated where B was allocated
7. b2 = malloc(0x40) - This will be allocated at the address of C subtracted with the size(b1)
8. free(b1)
9. free(C) - This will consolidate to addr(B) giving B a new size of 0x1a0
10. D = malloc(0x190) - Allocate chunk that fits into the consolidated
11. At this point we can fill up D which overlaps with b2, giving a normal heap overflow.
We used this technique with those sizes, but before allocating room for D we freed b2. b2 is in the fastbin range so it was placed in the fastbins. (add note was used to malloc, delete note was used to free, add note of length 256 for the null overwrite)
**9a.** free(b2)
In this picture b2 is is the value in the fastbin, and C is the value in the unsorted bin.
Now we allocated D, overflowing the freed chunk b2 with arbitrary values.
Overflow this with the address of our fake free chunk we created in the **Setup** part of this document, just above the pointers in the **tinypad** array. A few things to note here, to pass the integrity checks in libc the fake fastbin needs to have the same size as the fastbin it is in.
Now we allocate two more notes that will have the size 0x50, causing malloc to return the address in **tinypad**.
The second note we add will overwrite the pointer section of the **tinypad** array holding the sizes and addresses of notes.
### What should we write over the note pointers with?
Idea:
- **Note** full relro, we can't just overwrite the .got
- We can get more leaks by writing more pointers over the note pointers.
- We can overwrite the note pointers with the addresses of other note pointers, so we can edit them later.
So with this we decided to overwrite the first note with the address of environ in libc. The environ pointer holds a pointer to the stack of the current elf. The second index with the address of the third index, and the third index with non null value so it can bet edited using the edit_note function.
Now we use the value leaked from environ pointer to calculate the address of a return address, we chose the address main returns to when it is finished. Then we could edit the second note and overwrite the third note with the address pointing to the return address after main. Next we edit the third note whcih points to the stack (the return address after main). When main finishes it will return to the value we just wrote onto the stack.
Before stack overwrite:
After stack overwrite:
### Ropping
Luckily for us one of libc's magic return addresses worked and we returned to that. Now after pressing **q** to quit the menu and program we get a shell.
### The Flag
|
2022-11-28 16:01:43
|
{"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": 0.23051254451274872, "perplexity": 4320.771634846389}, "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-2022-49/segments/1669446710533.96/warc/CC-MAIN-20221128135348-20221128165348-00556.warc.gz"}
|
https://math.stackexchange.com/tags/contraction-operator/hot
|
# Tag Info
### Fastest way showing the limit exists without finding the limit?
Write your formulas in a matrix form: $$\begin{bmatrix}a_n\\b_n\end{bmatrix} = \begin{bmatrix}1&1\\r&1\end{bmatrix}\begin{bmatrix}a_{n-1}\\b_{n-1}\end{bmatrix}$$ i.e. $$w_n=Aw_{n-1}$$ ...
• 2,800
Accepted
### Does there exist $x$, $y \in \mathbb{N}$ such that $x^2 − y^2 = 19$
Notice that $19$ is prime. because of this, one of $x-y$ and $x+y$ must be $1$, and the other $19$. Therefore, if we solve the system $x-y = 1, x+y=19$, we can find a solution to this problem. You ...
• 226
Accepted
Accepted
### Does proper contraction on Hilbert space necessarily lead to convergence in norm to zero?
Let $\{a_n\}$ be a sequence of positive real numbers that increases to $1$, with the property that the sequence of products $$a_1,\ a_1a_2,\ a_1a_2a_3,\ a_1a_2a_3a_4,\ \ldots$$ converges to a ...
• 50.5k
Accepted
### Prove that $f(x)=x^2$ is a contraction on each interval in $[0,0.5]$
Remark that $$|f(x)-f(y)| = |(x+y)(x-y)| \leq (|x|+|y|)|x-y| < 2a |x-y|$$ if $x$, $y \in [0,a]$. Now $2a<1$ by assumption.
• 34k
Accepted
### an example of a complete space $X$ and a such mapping $T$ without fixed points & Show that if $X$ is compact then such $T$ has a unique fixed point.
Hint for (a): Apply the Mean Value Theorem to that function you were given. Hint for (b): Since $d(T(x),T(T(x))) < d(x, T(x))$ if $x\ne T(x)$, you must have $\inf d(x,T(x))=0$. (You should ...
• 86.6k
Accepted
### Using connectedness to prove surjectivity...
Let $(x,y)\in\mathbb R^2$ and let $$g: u \mapsto x - f\left(y-f(u)\right)$$ \begin{align} \left|g(u) - g(v)\right|& = \left|x-f(y-f(u)) - x + f(y-f(v))\right|\\ &= \left|f(y-f(u))-f(y-f(v))\...
• 6,068
### Fastest way showing the limit exists without finding the limit?
Again, not sure if this satisfies your criteria, but if we let $f : [0,\infty) \to \mathbb{R}$ by $$f(z) = \frac{r+z}{1+z}$$ then $f$ is decreasing, $0\leq f \leq r$, and $c_{n+1} = f(c_n)$. So if ...
• 145k
Accepted
### prove there is no integer solution to x^2 -6 = 0 by contradiction
Assume an integer solution $x$ such that $x^2 = 6$ exists. An integer is either odd or even. The square of odd $x$ is odd (whereas $6$ is even), so $x$ must be even. Let $x = 2k$, where $k$ is an ...
• 26.1k
Accepted
• 15.3k
### Continuous function from set to proper subset is a contraction
Let $f:[0,1]\to [0,1)$ be given by $f(x)=\frac12\sqrt{x}$. Then the ratio $|f(x)-f(0)|/|x-0|$ grows without bound as $x\to0$.
• 59.5k
### Contraction, doubt on definition
Here they call it a 'contractive mapping', which I think makes no difference with the word 'contraction'. Well, you do not necessarily have fixed points.
• 7,279
Accepted
### Solve differential equation via successive approximations (contraction mapping principle)
Contractractivity on a rectangular domain To apply the fixed-point theorem one needs to fix a domain for the ODE and determine the Lipschitz constant there. In the most simple case the domain is ...
• 114k
You should have gotten a plot like this which gives a visible idea of convergence for $|t|\le 0.5$. Let's consider the interval $|x-1|<1$ in state space in the proof construction of the Picard ...
|
2022-10-07 02:11:25
|
{"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": 0.9682290554046631, "perplexity": 320.5157454403224}, "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/1664030337906.7/warc/CC-MAIN-20221007014029-20221007044029-00296.warc.gz"}
|
https://www.gamedev.net/forums/topic/104281-weird-vb-file-output/
|
#### Archived
This topic is now archived and is closed to further replies.
# Weird VB file output
## Recommended Posts
I''m using VB to write a small tool to convert an text file to HTML. First thing I tried was to write all the HTML tags before the body to the file. But when I write them they are displayed like this:
"
<HTML>
"
"
<TITLE>
"
"
This is the code that I use:
OutPutFileNumber = FreeFile
Open txtOutPut.Text For Output As #OutputFileNumber
Write #OutputFileNumber, "<HTML>"
Write #OutputFileNumber, "<TITLE>"
Write #OutputFileNumber, "MSN to HTML"
Write #OutputFileNumber, "</TITLE>"
Write #OutputFileNumber, "<BODY>"
What is wrong with my code? Sand Hawk ---------------- -Earth is 98% full. Please delete anybody you can.
##### Share on other sites
Try Print #OutputFile instead of Write #OutputFile
##### Share on other sites
Nope, it still displays the "" and the end of each write action.
Sand Hawk
----------------
-Earth is 98% full. Please delete anybody you can.
##### Share on other sites
I''m quite sure that
Print #Filenumber, "Blah"
should work just fine. Since I use it a lot. But if you insist, then open the file in binary mode and work from there. Create a temporary string:
Dim TempString As String
And write a line like this:
TempString = MyLine & vbNewLine
Put FileNumber, , TempString
You *might* need to include the second parameter for Put the first time you write a line, it specifies the position in the file, which will need to be 1. Leaving it blank will write at the "current" position.
Trying is the first step towards failure.
##### Share on other sites
Doesn''t work. But if I open the file as binary I suppose it''s not going to be an text file wich my Browser can open. That''s the thing I want to do.
Sand Hawk
----------------
-Earth is 98% full. Please delete anybody you can.
##### Share on other sites
changing the "Write" to "Print" in your code will work, i''ve been doing this for years...
##### Share on other sites
The code i used in VB 5.0
OutputFileNumber = FreeFile Open App.Path + "\txtOutPut.Txt" For Output As #OutputFileNumber Print #OutputFileNumber, "<HTML>" Print #OutputFileNumber, "<HEAD>" Print #OutputFileNumber, "<TITLE>" Print #OutputFileNumber, "MSN to HTML" Print #OutputFileNumber, "</TITLE>" Print #OutputFileNumber, "</HEAD>" Print #OutputFileNumber, "<BODY>" Close #OutputFileNumber
The result I get:
<HTML><HEAD><TITLE>MSN to HTML</TITLE></HEAD><BODY>
Are you sure it doesn't work ?
[edited by - misterX on July 16, 2002 7:47:10 PM]
##### Share on other sites
quote:
But if I open the file as binary I suppose it''s not going to be an text file wich my Browser can open
Why do you suppose that?
Trying is the first step towards failure.
• ### Forum Statistics
• Total Topics
628373
• Total Posts
2982306
• 10
• 9
• 13
• 24
• 11
|
2017-11-23 13:38:02
|
{"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": 0.24766620993614197, "perplexity": 10069.653839799164}, "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/1510934806832.87/warc/CC-MAIN-20171123123458-20171123143458-00672.warc.gz"}
|
http://oltreauto.it/sound-wave-diagram.html
|
Sound waves Require medium for transmission. Or it could. How do we hear? Sound waves travel into the ear canal until they reach the eardrum. In solid medium, the atoms are so. From this diagram, we see that the separation is given by R 1 – R 2. Which diagram best shows the perceived sound wave heard by a women after a police car passed by her - 12563919. 5 MHz, which corresponds to a wavelength of 0. This medium could be thought as a rope fixed at one end a few feet above the ground and held by you at the other end. When the object vibrates, it sends out a series of waves that are interpreted. The peak of a wave and the trough of a wave are always twice the wave's amplitude apart from each other. Thus, the original sound waves lose a considerable amount of their total energy. The movement sets up a sound wave in the surrounding air. Inside the cochlea, there are thousands of tiny hair cells. The amplitude. , but the masses and accelerations of objects on Earth are far too small to make gravitational waves big enough to detect with our instruments. So if the simplest equation for a sound wave (at a given frequency and for a given sample rate) is $sin(\frac{2 \cdot \pi \cdot x \cdot f}{samplerate})$ where f is frequency, is there a similar equation for the sound that a piano makes? EDIT: I'm not looking for anything too complicated here, just a wave that approximates this estimation. What is the frequency of the waves? _____ (2) (Total 6 marks) Q5. the total pppressure in the path of a sinusoidal sound wave is of the form P P a P 0 sin 2 f t P a is the ambient air pressure (which at sea level at OoC is 1. How to use sound wave in a sentence. The highness or lowness of a sound is perceived as a. Amplitude & frequency waveform diagram examples - sound theory Exploring sound wave. Second, the head interferes with the sound-wave, casting the auditory equivalent of a shadow on the far ear. Water waves and sound waves have the ability to travel around corners, obstacles and through openings, and light waves too are able to display this ability. Ross has found that refraction of sound caused by temperature and wind gradients may have had a significant impact on the outcome of several Civil War Battles (Gettysburg, Gaines Mill, Fort Donelson, Seven Pines/Fair Oaks, Iuka, Perryville, Chancellorsville, and Five Forks). An illustration of sound waves entering a human ear Green Sound Waves. And our online editor will turn it to an image of sound waves in seconds. Simply enter your desired frequency and press play. When a vibrating object moves forward, it pushes and compresses the air in front of it forming a region of high pressure called compression (C). On the other hand, when particles go farther than their normal position it is called rarefaction. Over the past few weeks, we have discovered the different patterns associated with sound and how to measure how high or low it is. Learn it and master it. 1 General solution to wave equation Recall that for waves in an artery or over shallow water of constant depth, the governing equation is of the classical. How a Speaker Works. You can see what sound looks like from what is picked up by your microphone. The resulting curves are known as the "waveform" (i. A compression wave is a mechanical longitudinal wave. Did you hear that? In this BrainPOP movie, Tim and Moby introduce you to the world of sound! In the movie, you’ll find out how sound and ocean waves are similar, yet different, as you learn about different kinds of waves. A spark transmitter emits a series of damped waves, the period of which is the spark rate. Light waves travel slower than sound waves. Browse by topic: forces and motion, electricity, energy and waves. A radio station transmits waves with a wavelength of 20 metres. vibrate up and down 2. Frequency is measured in cycles per second. #__5_ = crest The highest point of the wave above the line of origin. A 1000 Hz sound wave, on the other hand, would vary dramatically in terms of perceived loudness as the amplitude of the wave increased. The speed of mechanical waves depends on the medium that the wave is traveling through. The sound wave moves in all directions from the source 29. Explanation: Compressions of a sound wave are when the molecules are pressed closely together. Continuous sounds, such as drumming, are made when an object vibrates back and forth. May be used as an alarm, a sound effects generator or perhaps a replacement doorbell __ Designed by Andy Collison. To get started with the applet, just go through the items in the Example menu in the upper right. Worksheets are Lesson 1 sound and music the physics classroom, Teachers club science formclass p hysics waves name, Name date anatomy of a wave work, Name date anatomy of a wave work answers, Lesson physical science wave theory and sound, Sound waves, Wave, Sound energy unit grade 4. A source of sound (e. If the volume is increased, the sound wave transfers more energy. One important characteristic of sound waves is that they are mechanical waves. So sound is considered as a wave. A common misconception by students is to associate sound waves produced by a sound system with radio waves. Sound waves Require medium for transmission. The amplitude. Lesson Plan on Wave Motion for Physical Science. P waves travel at speeds between 1 and 14 km per second, while S waves travel significantly slower, between 1 and 8 km per second. Which type of wave is traveling in the rope? , As a wave travels through a medium, the particles of the medium vibrate parallel to the direction of propagation. 773 m (4) 8. Speaker - The "anti-sound" created by. Hence, by changing the frequency of a wave, its wavelength will be changed, but its speed cannot be altered if the medium is kept the same. Certainly our spark transmitter behaved as expected for a well adjusted Braun type spark transmitter, see Fig 5. Bird Sound Generator - A few years back, Wilf Rigter posted this circuit for making bird-like sounds __ Designed by Wilf Rigter. Sound changes depending on how fast or slow an object vibrates to make sound waves. Sound wave definition is - sound. From this diagram, we see that the separation is given by R 1 – R 2. Sound waves are responsible for the travel of sound using a medium, while radio waves are a type of electromagnetic waves that are responsible for radio communication, broadcasting, radar and many other navigation systems. The wavelength. The sound waves arrive at the pinna (auricle), the only visible part of the ear. What is the wavelength of the wave?. This quantity of sound coloration is called timbre (pronounced "tamber"). The external pinna helps funnel sound waves into the ear and locate the direction of the sound. The wave it produces is known as a sine wave. sound wave around the edge of a barrier. All waves, whether they are sound, light, earthquake, or water waves, have some things in common. Sound waves enter through the outer ear, move into the middle ear, and finally reach the inner ear and its intricate network of nerves, bones, canals, and cells. At 44 degrees Fahrenheit, sound travels approximately 1,100 feet per second, or 750 miles per hour. To apply energy and power concepts to waves. * The diagram shows a person shaking the end of a rope up and down, producing a disturbance that moves along the length of the rope. In this activity, students will label a diagram of the ear. A sound wave is an example of a longitudinal wave. Traveling Waves A wave front diagram shows A. , In a transverse wave the direction in which the wave. Two waves on the surface of water are generated by two independent sources vibrating at the same frequency 1 Hz. Continuous sounds, such as drumming, are made when an object vibrates back and forth. Our goal is to simplify the wave principle without diluting it and make it accessible to all traders. The particular example of a standing wave that I want to illustrate is a standing sound wave in a pipe that is forced (by a moving piston or loudspeaker) at the left end and closed at the right end. Superposition of Waves. longitudinal waves, matter vibrates in the same direction that the energy travels. The diagram below represents a transverse wave. Move the listener around and hear what she hears. , Water Wave, Earthquake Wave, A medium is any substance that a wave moves through. During their propagation, waves can be reflected,. In a small room the sound is also heard more than once, but the time differences are so small that the sound just seems to loom. Sound waves are longitudinal waves with two parts: compression and rarefaction. When an object is struck and sound is produced, explain the direction of the sound wave. High frequency sound wave technology could be used to transform waste heat from nuclear power plants into usable energy. To put this into perspective, sound waves travel the distance of 3 1/2 football fields every second, or approximately 1 mile every 5 seconds. The difference between Sound waves and Light Waves are: Sound Waves require a medium where Light Waves do not require a medium,Travel with a speed of 332 m/s at 0 C and light travels with a speed of 3 *10 8 m/s and etc. The ear can discern many qualities of a sound it hears, but two of the most fundamental are pitch and loudness. Pitch is all about wavelength—i. Sound is a mechanical vibration that passes through a medium such as gas, liquid or solid to become a sound. The ear canal or external auditory meatus is approximately 1. Practice MCQs For Waves, Light, Lens & Sound December 14, 2015 July 3, 2012 by Mini Physics This quiz contains practice questions for GCE ‘O’ level topics: General Waves Properties , Reflection and Refraction Of Light , Converging Lens , Electromagnetic spectrum , Sound. Another important property of a wave is the speed of propagation. What is the order of increasing density of the materials that you are testing? In this lab you can hear differences in sound when the sound waves travel through various materials. Generating oscillator waveforms Sine wave. First, the paths are of different length because sound has to travel past the head to get to the left ear and sound intensity decreases with distance (1/ d 2, where d is the distance to the sound source). Base your answer to the following question on the accompanying diagram which represents a sound wave and its corresponding pattern on an oscilloscope screen. seconds? (1) 0. When an object is struck and sound is produced, explain the direction of the sound wave. At 44 degrees Fahrenheit, sound travels approximately 1,100 feet per second, or 750 miles per hour. Inside the cochlea, there are thousands of tiny hair cells. The di erence in apparent frequency between the incident and re ected waves is an example of A. When an object or substance vibrates, it produces sound. These vibrations create sound waves which move through mediums such as air and water before reaching our ears. Download it here , and please give appropriate credit. wave speed(in m/s) wavelength (in m) frequency (in Hz) v f Solve a Simple Equation 1. Laws of Reflection of sound. WORKSHEET - LABELING WAVES 1. Light and heat are some of the waste forms of energy created by the transfer of another form of energy into sound waves. The diagram below represents a snapshot of the air particles at a given instant in time. The speed of mechanical waves depends on the medium that the wave is traveling through. Over the past few weeks, we have discovered the different patterns associated with sound and how to measure how high or low it is. Compression is the part of the sound waves where the molecules of air are pushed (compressed) together. The peak-to-peak value is valuable in that it indicates the maximum excursion of the wave, a useful quantity where, for example, the vibratory displacement of a ma-. Using sound to navigate › Underwater echoes are used by ships to scan the ocean floor. The sound waves decrease in speed as the car approaches the students. But of course when we experience visible light, we are perceiving color in the form of a wave's wavelength and frequency. wave diagram labeled sound wave diagram wavegraph xy enticing see labeled9999999999999y graph Wide collections of all kinds of labels pictures online. A point P is located 3. It demonstrates waves in two dimensions, including such wave phenomena as interference, diffraction (single slit, double slit, etc. The wave speed. Sound waves are longitudinal waves. More specifically, sound is a wave made of vibrations in the air. In a longitudinal wave, displacements are parallel to the direction of the wave. Over the past few weeks, we have discovered the different patterns associated with sound and how to measure how high or low it is. The shaded bar above it represents the varying pressure of the wave. 0 Hz, what is the wave speed? 2. when the energy of a sound wave is transferred to a particle of a medium and causes it to vibrate and generate heat, the sound wave is a. Which diagram best shows the perceived sound wave heard by a women after a police car passed by her - 12563919. A musical note has three characteristics. The waves travel at a speed of 2. In solid medium, the atoms are so. The diagram below depicts a sound wave created by a tuning fork and propagated through the air in an open tube. The sound in diagram 2 has a greater amplitude than the one in diagram 1, so it will be louder. When the vibrations are slow, it creates a low note. If you could freeze a sound wave in time and space (and if you could see the wave), measuring the distance from one peak of the wave to the next peak would give you the wavelength. To describe a wave, you need to know a few of its properties. Scientists use diagrams (or graphs) like the one you made to show changes in air pressure made by sounds. Traveling Waves A wave front diagram shows A. Inside the cochlea, there are thousands of tiny hair cells. But you would hear the sound waves if you ventured off of your nodal line. This is in contrast to PCM encodings where quantization levels vary as a function of amplitude (as with the A-law algorithm or the μ-law algorithm ). But the wave inside a tube, since it is a sound wave already, is a longitudinal wave; the waves do not go from side to side in the. Another important property of a wave is the speed of propagation. Compression is the part of the sound waves where the molecules of air are pushed (compressed) together. A radio station transmits waves with a wavelength of 20 metres. 0 s 28 The diagram below represents a periodic wave. refraction C. seconds? (1) 0. wave diagram labeled sound wave diagram wavegraph xy enticing see labeled9999999999999y graph Wide collections of all kinds of labels pictures online. Sound is a mechanical wave. Signal is transmitted in the air via radio waves from the radio stations in the form of transverse waves. Several regions are labeled with a letter. Waves (D8 through to D29) - Coggle Diagram: Waves (D8 through to D29) Rope waves, sound waves, earthquake waves and ocean waves are all mechanical waves. The straight line going through the center of the symmetrical wave is the zero axis. It demonstrates waves in two dimensions, including such wave phenomena as interference, diffraction (single slit, double slit, etc. Use the letters to identify the compressions and rarefactions. 29 What is the wavelength of a 256-hertz sound wave in air at STP? (1) 1. A musical note has three characteristics. Thus, the wave pattern looks like the following: Now imagine you are standing on the green dot on the right. What is the resonating frequency? (V sound = 340 m/s) (A) 85 Hz (B) 170 Hz (C) 340 Hz (D) 510 Hz (E) 680 Hz Use the diagram to the right to answer questions 11 and 12. Figure below represents the sound with low pitch. Waves that are inphase are separated by an even multiple of half wavelength (π). Waves, Sound, and Light 5 Name Date Class Lab Preview Directions: Answer these questions before you begin the Lab. Diagrams 2 and 3 show two sounds with a different wavelength and frequency. The reflected sound waves are detected by a sensitive microphone. Examples of wave energy are light waves of a distant galaxy, radio waves received by a cell phone and the sound waves of an orchestra. Waves and Sound. However, because of edge diffraction some sound will. the bending of waves around a barrier 10. A sound wave is a special kind of wave that can be detected by the human ear. Pitch is the quality of a sound (high or low) and depends on the speed of the vibrations. 14) in cylindrical coordinates. The description of waves is closely related to their physical origin for each specific instance of a wave process. When a sound wave hits a wall, it is partially absorbed and partially reflected. This is in contrast to PCM encodings where quantization levels vary as a function of amplitude (as with the A-law algorithm or the μ-law algorithm ). If there is tricuspid valve disease and the valve fails to close normally when the RV contracts, blood will leak or “regurgitate” backwards into the RA and there will be an abnormally large v wave. Timms Analysis concept , Analysis concept Proceed Back again Audio Surf in Atmosphere A single-frequency audio influx journeying through atmosphere will trigger a sinusoidal pressure deviation in the atmosphere. Waves are all around us, in many frequencies and wavelengths. [3] Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes. html to use the applet. , but the masses and accelerations of objects on Earth are far too small to make gravitational waves big enough to detect with our instruments. Their vibrations occur in the same direction as the direction of travel. A sound wave is an example of a longitudinal wave and is produced by the vibrating motion of the particles that travel through a conductive medium. Sources of sounds and characteristics of sound waves, shown by means of oscilloscopes and animated diagrams. A Venn diagram activity to test your knowledge of the differences and similarities between light and sound waves. The frequency can be expressed as. I will try to answer this question by avoiding complicated mathematical formulae and notations. _____ _____ (1) (c) €€€€Electromagnetic waves travel at a speed of 300 000 000 m/s. The Doppler effect. A Venn diagram activity to test your knowledge of the differences and similarities between light and sound waves. Soundwave is a Decepticon from the Generation 1 continuity family. The more frequent the collisions are, the faster the speed of sound is in the material. The refraction of sound can be demonstrated in a physics laboratory by using a lens-shaped balloon filled with carbon dioxide to bring sound waves to a focus. It is positioned between the ear canal and the middle ear. Let's get started! Upload your audio/video or record it online. If yes, then is there a clear pattern to the way in which the sound sensor values change based on the sound wave’s frequency? Explain. A radio station transmits waves with a wavelength of 20 metres. If the frequency of a sound wave in water is 15,000 Hz, and the sound wave travels through water at a speed of 1,500 m/s, what is the wavelength?. When there are fewer fluctuations in a period of time, the pitch is lower. Waves are characterized by three basic quantities. The diagrams on this page show a sine wave. In order to understand how sound works and how we hear it, it's important for students to understand the different parts of the human ear. The pitch of a sound you hear depends on the frequency of the sound wave. compression and rarefaction (depression). Pupils label a wave and then have to draw waves which would have a louder pitch etc. References. More specifically, sound is a wave made of vibrations in the air. The difference between sound and water waves is that the water waves are dispersive. A radio station transmits waves with a wavelength of 20 metres. Sound waves can be analyzed in terms of their amplitude and frequency. vibrate up and down 2. Bending waves generated in an infinitely extended flat plate by a concentrated transverse force spread out cylindrically from that point. You would have to imagine yourself very tiny to fit in a diagram where the wavelength of light was represented by the distance between the blue arcs. The loudness of a sound corresponds to the amplitude of the wave, and is measured in decibels. The minimum distance from a sound reflecting surface to hear an echo is 16. The wavelength of a wave is simply the length of one complete wave cycle. Which diagram best shows the perceived sound wave heard by a women after a police car passed by her - 12563919. draw the graphical diagram representing the wave shape for - a) low pitched sound b) high pitched sound what is the main difference between the two - Science - Sound. The tuning coil L and capacitor C1 together make up the tuned circuit; it selects the radio signal to be received, out of all the signals picked up by the antenna. Sound can propagate as longitudinal waves, shear waves, surface waves, and in thin materials as plate waves. Timms Analysis concept , Analysis concept Proceed Back again Audio Surf in Atmosphere A single-frequency audio influx journeying through atmosphere will trigger a sinusoidal pressure deviation in the atmosphere. Reflection is the change in direction of a wave at a boundary between two different media, so that the wave moves back into the medium it came from. When most people think of waves, they think of water waves. Here is a general diagram of a wave. The scientific study of sound waves is known as acoustics. 1 General solution to wave equation Recall that for waves in an artery or over shallow water of constant depth, the governing equation is of the classical. Given a value of k and its associated value of!, the phase velocity of the wave is!=k. The wavelength of the wave is equal to the distance between points 1. Behaves like a sound oscilloscope. [3] Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes. interference between two waves traveling in opposite directions. The period is the time it takes a wave to complete one cycle. Second, the head interferes with the sound-wave, casting the auditory equivalent of a shadow on the far ear. ultrasonic w's waves similar to sonic waves but of such high frequency (20,000 hertz or higher) that the human ear does not perceive them as sound; see ultrasonics. This is how fast the disturbance of the wave is moving. Hence, by changing the frequency of a wave, its wavelength will be changed, but its speed cannot be altered if the medium is kept the same. A light wave, like a water wave, is an example of a transverse wave, which causes a disturbance in a medium perpendicular to the direction of the advancing wave. 773 m (4) 8. A solution to the wave equation. The reflection of sound waves is governed by two laws known as the two laws of sound reflection, The first law of reflection of sound waves is the angle of incidence = the angle of reflection. Water waves and sound waves have the ability to travel around corners, obstacles and through openings, and light waves too are able to display this ability. A speaker has several. Phase comparison. We measure the period in seconds, and we symbolize it with the capital letter T. Then place arrows on the diagram A sound wave is moving through air. the parts of the sound waves In the diagram provided the white line represents the position of the medium when no wave is present. 25 inches long and. Consequently, to derive an expression for the transverse velocity of a thin plate at the point of application of such a force, it is appropriate to express the plate bending wave equation (10. This is the situation depicted by the figure from the Prentice Hall textbook, shown above and animated at right. It is positioned between the ear canal and the middle ear. Propagation of ultrasound waves in tissue •Ultrasound imaging systems commonly operate at 3. One convenient way to diagram a sound wave is to graph the pressure at each point in time, the way it might be picked up by a microphone for example: This simplest kind of pressure wave is called a sine wave. The tone generator can play four different waveforms: Sine, Square, Sawtooth and Triangle. How a Speaker Works. If two identical sound waves arriving at the same point are in phase, compared to the original waves, the resulting wave will have A. Sound is a Pressure Wave. Sound is a wave that is produced by objects that are vibrating. You will hear a pure tone sine wave sampled at a rate of 44. Sound waves and radio waves are two different types of waves that we encounter everyday. First the sound waves travel into the ear canal, they vibrate the tympanic membrane, commonly called the eardrum. Ravage! Laserbeak! I choose you! Soundwave (aka Soundblaster) is one of Megatron 's most reliable troops, and he has positioned himself comfortably and irreplaceably in the Decepticon upper command structure. With a longitudinal wave we could imagine making the medium more compact or making the medium less compact like that. Electron oscillation light wave. The standing waves in a wind instrument are a little different from a vibrating string. When the object vibrates, it sends out a series of waves that are interpreted. Labeled Diagram Of A Sound Wave Posted on April 17, 2019 by admin Figure from hirose text showing standing sound waves in a pipe illustration of the energy transfer in a longitudinal wave and transverse venn diagram these diagrams labeling waves worksheet answer key. A typical example of an electromagnetic wave is a light signal and an example of a mechanical wave can be the ripples formed on the surface of the water when a stone is thrown. The wavelength is another property of a wave that is portrayed in the diagram above. Students should include the function of each part in their diagram. The similarities between sound waves and light. We love doing simple science experiments and every once in a while, we find a GEM. Longitudinal Waves Diagram. What is the wavelength of the wave?. This causes the obstacles to scatter the sound waves making it behave like a source of sound. This is the wave equation in one dimension. This is just because they are easier to draw and recognize in the diagrams. ), refraction, resonance, phased arrays, and the Doppler effect. Custom Soundwave art, created and designed by yourself! It is so easy and fun to create a sound wave art. A wave period is the time in seconds between two wave peaks and is inversely proportional to frequency. Although music can be hard to define, it is often described as a pleasing or meaningful arrangement of sounds. On one side there are the high-end audio enthusiasts who believe analog sound is superior because it captures the true essence of the sound wave, while on the other side, there are those who are convinced that. Does sound travel faster in warm or cold air? Why? 12. Waves, Sound, and Light 5 Name Date Class Lab Preview Directions: Answer these questions before you begin the Lab. Radio waves, microwaves, and UV waves are just a few of the unseen ones. Bending waves generated in an infinitely extended flat plate by a concentrated transverse force spread out cylindrically from that point. absorbed d. Characteristics of Sound Waves Sound travels in the form of a wave. They are frequency, speed, and amplitude. Summarize briefly what you found out about the sound sensor and the frequency of sound waves. The word "speaker" is the shortened form of the word "loudspeaker" and it refers to a device that converts electrical signals into sound waves that we can hear. Does a person’s voice sound higher or lower after inhaling helium gas? Why? 13. The reflection of sound waves is governed by two laws known as the two laws of sound reflection, The first law of reflection of sound waves is the angle of incidence = the angle of reflection. 44 mm when c = 1540 m/s. Sound waves are responsible for the travel of sound using a medium, while radio waves are a type of electromagnetic waves that are responsible for radio communication, broadcasting, radar and many other navigation systems. Examples of wave energy are light waves of a distant galaxy, radio waves received by a cell phone and the sound waves of an orchestra. The diagram below represents two waves of equal amplitude and frequency approaching point P as they move through the same medium. His Wave Diagrams are fantastic, and have enabled him to independently (to Milo Wolff and myself) explain and solve many of the problems of Modern Physics by rejecting the 'particle' conception of matter for a wave structure of matter (which clearly works). Pitch, Loudness, and Quality of Musical Notes. The second way of classifying waves is based on whether or not the wave requires a medium to travel. To become familiar with the properties of sinusoidal waves, such as wavelength, wave speed, amplitdue, and frequency. The repetition of sound caused by the reflection of sound waves is called an echo. An ultrasound is any sound with a frequency above the audible range of hearing (more than 20 000 Hz). PROPAGATION OF SOUND AND FACTORS AFFECTING IT 2. When the object vibrates, it sends out a series of waves that are interpreted. C1 is adjustable, and is used to tune in different stations. Title: Characteristics of Sound Waves 1 Characteristics of Sound Waves 2 Transverse and Longitudinal Waves Classification of waves is according to the direction of propagation. As is true of all types of waves, specific behaviors, properties, and. Sound waves in solid materials exhibit polarization. The same is true with sound. Diffraction is when a wave goes through a small hole and has a flared out geometric shadow of the slit. Thousands of new, high-quality pictures added every day. Sound waves travel at different speeds depending on the temperature of the air. €€€€€€€€€ The time between sending and receiving the pulse is 0. A musical note has three characteristics. Waves move in different ways and have different properties. For example, soprano singers stretch their vocal cords, so they vibrate more quickly as the air rushes by them, which creates higher-frequency sound waves that have a higher pitch. Vibrations. This is a simulation of a ripple tank. A radio station transmits waves with a wavelength of 20 metres. You can picture sound waves as a series of nudges that cause particles in a medium to bump into one another in successive collisions. The Propagation of sound. A sound wave traveling through air is an example of a longitudinal wave. an increase in speed B. At any instant, all the molecules of air in the pipe oscillate with the same. The wave has a wavelength of 0. The Propagation of sound. The refraction of sound can be demonstrated in a physics laboratory by using a lens-shaped balloon filled with carbon dioxide to bring sound waves to a focus. Use the letters to identify the compressions and rarefactions. The level of air pressure in each fluctuation, the wave's amplitude, determines how loud the sound is. Vibrations. Noise-canceling circuitry - Electronics, also placed in the ear cup, sense the input from the microphone and generate a "fingerprint" of the noise, noting the frequency and amplitude of the incoming wave. The reflection of sound waves is governed by two laws known as the two laws of sound reflection, The first law of reflection of sound waves is the angle of incidence = the angle of reflection. , An example of energy transfer are the waves that are caused by an earthquake. But of course when we experience visible light, we are perceiving color in the form of a wave's wavelength and frequency. Standing Waves in Resonance Tubes Edit. In this activity, students will label a diagram of the ear. The combined effect of scattering and absorption is called attenuation. No people means the Mexican Wave can't keep going – just. A compression wave is a mechanical longitudinal wave. , Water Wave, Earthquake Wave, A medium is any substance that a wave moves through. The details in these lessons emphasize the importance of understanding waves. It use for enlarge sound signal , change the way Photo transistor into pieces give hear loudspeaker way well. But as an airplane reaches the speed of sound and catches up to its own pressure waves, the air ahead of it receives no warning of the plane’s approach. Explanation: Compressions of a sound wave are when the molecules are pressed closely together. This is the situation depicted by the figure from the Prentice Hall textbook, shown above and animated at right. In transverse waves the particles vibrate perpendicular to the direction of propagation (for example, a vibrating string or a water wave) In longitudinal waves the particles. In this activity, students will label a diagram of the ear. Adjust the frequency, volume, and harmonic content and you can see and hear how the wave changes. When a drummer beats a drum, the surface of the drum vibrates and creates a disturbance in the air beside it. How to use sound wave in a sentence. Both typed of waves have amplitude and wavelength, and they can be plotted as lines on the diagram in exactly the same way. The sound of thunder is produced by rapidly heated air surrounding lightning which expands faster than the speed of sound. Once the sound waves reach the tympanic membrane, it begins to vibrate and they. A sound wave takes on the form of a longitudinal wave. Practice identifying nodes and antinodes for pressure and displacement from a standing wave diagram. You can listen to sine waves at different frequencies by clicking on the MP3 audio examples on this page. This medium could be thought as a rope fixed at one end a few feet above the ground and held by you at the other end. Turn your voice into playable art! Everyone’s voice generates a unique pattern. These sections are labeled in the following diagram: #N#Amplitude ( Top, Wave Home ) The term amplitude can have slightly different meanings depending upon the context of the situation. The second way of classifying waves is based on whether or not the wave requires a medium to travel. Diagram Of A Sound Wave. A musical note has three characteristics. In musical terms, frequency is equivalent to pitch. And our online editor will turn it to an image of sound waves in seconds. Now it is time to solve it. If we consider the atmosphere on a standard day at sea level static conditions, the speed of sound is about 761. From here, the sound can be processed or manipulated in a variety of ways in the synthesizer or program to enrich or modify the sound further. You can see what sound looks like from what is picked up by your microphone. 25 inches long and. Waves move in different ways and have different properties. What is the wavelength of the wave?. Nae Perio Waves-Wave Behaviors APlusPhysics: Waves-Wave Behaviors WAVB Page 6 31. The shock wave from an explosion can knock people over. The diagram shows the fundamental (first harmonic) of a standing (stationary) sound wave in a pipe open at one end. The repetition of sound caused by the reflection of sound waves is called an echo. Frequency - measured in Hertz Number of peaks (cycles) in a given distance (time). Sound waves have special characteristics that make them unique. Absorption is the conversion of the sound energy to other forms of energy. P waves travel at speeds between 1 and 14 km per second, while S waves travel significantly slower, between 1 and 8 km per second. ” Higher than normal air pressure is shown above the normal pressure line, while lower than normal pressure is shown below the normal pressure line. Understanding the ways in which a wave can travel is important for understanding the difference between sound and light. Waves carry energy while the lowest part is the trough The highest point on a transverse wave is the crest The amplitude is the height of the wave. Physics (Grade 8): High School Learning Sound | Characteristics Of Sound | Examples & Diagrams | Lecture 10 - Amplitude of Sound - Characteristics of Sound- Amplitude, Frequency, Wavelength, Pitch. html and pipe-waves. Important Questions for CBSE Class 9 Science Chapter 12 Sound IMPORTANT QUESTIONS 1 MARK QUESTIONS Question. #__5_ = crest The highest point of the wave above the line of origin. If first echo be heard after It second, second echo after ~ second, then third echo will be heard after (t 1 + t2)s. You can think of the period as the time it takes for. Browse by topic: forces and motion, electricity, energy and waves. A sound wave resonates in an open pipe with a length of 2 m. Noise-canceling circuitry - Electronics, also placed in the ear cup, sense the input from the microphone and generate a "fingerprint" of the noise, noting the frequency and amplitude of the incoming wave. Sound is a wave that is produced by objects that are vibrating. There are two main type of waves, transverse waves and longitudinal waves. The section of the wave that rises above the undisturbed position is called the crest. As the period of motion increases, the resonant frequency decreases. Showing top 8 worksheets in the category - Diagram Of A Sound Wave. Learn it and master it. 29 What is the wavelength of a 256-hertz sound wave in air at STP? (1) 1. Physics (Grade 8): High School Learning Sound | Characteristics Of Sound | Examples & Diagrams | Lecture 10 - Amplitude of Sound - Characteristics of Sound- Amplitude, Frequency, Wavelength, Pitch. Higher frequencies. When a vibrating object moves forward, it pushes and compresses the air in front of it forming a region of high pressure called compression (C). Waves (Rope Wave, Waves have amplitude, wavelength, and frequency. As the malleus vibrates, it transmits the sound vibrations to the other two small bones or. Longer wave-lengths than the horn length cause the diaphragm to move excessively. On the other hand, when particles go farther than their normal position it is called rarefaction. Different materials produce different pitches; if an object vibrates quickly we hear a high-pitched sound, and if an object vibrates slowly we hear a low-pitched sound. Sound wave definition is - sound. May be longitudinal ; Or transverse ; 4 Waves 5 Waves travel through a medium such as water air solids 6 Wave Properties reflection refraction interference 7 Wave Properties. The wave on a string is a transverse wave, moving the string back and forth, rather than moving up and down along the string. Sound waves enter through the outer ear, move into the middle ear, and finally reach the inner ear and its intricate network of nerves, bones, canals, and cells. Sound can propagate as longitudinal waves, shear waves, surface waves, and in thin materials as plate waves. Diagram Of A Sound Wave. In order to understand how sound works and how we hear it, it's important for students to understand the different parts of the human ear. Diagram Of A Sound Wave Some of the worksheets for this concept are Lesson 1 sound and music the physics classroom, Teachers club science formclass p hysics waves name, Name date anatomy of a wave work, Name date anatomy of a wave work answers, Lesson physical science wave theory and sound, Sound waves, Wave, Sound energy unit grade 4. In transverse waves the particles vibrate perpendicular to the direction of propagation (for example, a vibrating string or a water wave) In longitudinal waves the particles. Several regions are labeled with a letter. When the vibrations are fast, you hear a high note. (b) Sound reaches our ears in the form of transverse waves or vibrations from its source of production. The minimum distance from a sound reflecting surface to hear an echo is 16. collide more frequently. Unlike light energy, sound cannot travel through a vacuum, because there are no atoms to transmit the vibration. The incident sound wave, the normal and the reflected sound wave lie in. You can think of the period as the time it takes for. 4 CHAPTER 6. the wavelengths of a wave. To learn more about how the National Park Service protects natural sounds and night skies in parks, please visit the Natural Sounds and Night Skies Division home page. In a small room the sound is also heard more than once, but the time differences are so small that the sound just seems to loom. The points where the transverse wave crosses the zero axis (A, C, E) are the nodes. A 1000 Hz sound wave, on the other hand, would vary dramatically in terms of perceived loudness as the amplitude of the wave increased. , Water Wave, Earthquake Wave, A medium is any substance that a wave moves through. Refraction of sound waves influenced the outcome of several Civil War Battles! Acoustician Charles D. A sound wave is produced by a loudspeaker. When a drummer beats a drum, the surface of the drum vibrates and creates a disturbance in the air beside it. A diagram is simply a symbolic representation of information according to some visualisation technique. This is the situation depicted by the figure from the Prentice Hall textbook, shown above and animated at right. One important characteristic of sound waves is that they are mechanical waves. During their propagation, waves can be reflected,. Vibrations. Pitch is all about wavelength—i. Standing Longitudinal Waves. vibrate up and down 2. you can easily distinguish them by their. On the diagram, the relation- ship between the peak-to-peak level, the peak level, the average level and the RMS level of a sinewave is shown. Sound energy is transmitted through air (or other particles) as a traveling pressure wave. These vibrations create sound waves which move through mediums such as air and water before reaching our ears. Noise-canceling circuitry - Electronics, also placed in the ear cup, sense the input from the microphone and generate a "fingerprint" of the noise, noting the frequency and amplitude of the incoming wave. An illustration of sound waves entering a human ear Green Sound Waves. When you increase the volume of the tone, you are adding energy to the sound wave, resulting in larger vibrations. This medium could be thought as a rope fixed at one end a few feet above the ground and held by you at the other end. Pathway of a Sound Wave 1. For example, soprano singers stretch their vocal cords, so they vibrate more quickly as the air rushes by them, which creates higher-frequency sound waves that have a higher pitch. PROPAGATION OF SOUND AND FACTORS AFFECTING IT 2. At 44 degrees Fahrenheit, sound travels approximately 1,100 feet per second, or 750 miles per hour. longitudinal wave longitudinal waves are waves in which the displacement of the medium is in the same direction as or the opposite direction to the direction of propagation of the wave mechanical longitudinal waves are also called pressional or pression waves because they produce pression and rarefaction when traveling through a medium and pressure waves because. wave diagram labeled sound wave diagram wavegraph xy enticing see labeled9999999999999y graph Wide collections of all kinds of labels pictures online. What is the wavelength of the wave?. Hey brain, heads up, the frequency A-440 is coming in. Sound Waves is a synthetic phonics and word study program. a larger amplitude D. Waves that are inphase are separated by an even multiple of half wavelength (π). It may be noted that the frequency of sound does not change and (iv) From the tympanic cavity extra sound is carried to the pharynx through Eustachian tube. A very basic application that shows the sound wave of whatever it hears. Make your work easier by using a label. The sound is basically a vibration that travels through the air that can be heard when it gets to the ear. Waves are characterized by three basic quantities. The interval representing one wavelength is 28. The amplitude. antified in several ways. A sound wave traveling through air is an example of a longitudinal wave. The same is true with sound. The tympanic membrane acts like a microphone by converting the sound waves into movements of the membrane, which in turn moves the malleus. A musical note has three characteristics. The wavelength of a wave is simply the length of one complete wave cycle. The tone will continue until the stop button is pushed. You will hear a pure tone sine wave sampled at a rate of 44. For more information and access to download the unit for free, visit the openscied. Displaying all worksheets related to - Diagram Of A Sound Wave. In the top-left of this drawing the RF energy (carrier wave) is not modulated by any sound. The wavelength of a sound wave is the distance between successive compressions or rarefactions as shown in the diagram below. FDA clears sound wave technology to blast plaque in arteries Shockwave Medical is harnessing sound waves to break up calcium in blocked arteries and using them with the. The second difference is that sound is composed of longitudinal waves (alternate compressions and expansions of matter) and light is composed of transverse waves in an electromagnetic field. The amplitude. This list provides a range of suggested activities and teaching strategies, as well as resources which support non-specialists in using equipment. These waves form a large shock wave. Our Visual Sound Wave art is printed on 270gsm Matt photo paper with a Satin finish – one of the highest quality finishes available with fade and scratch resistant properties. A plot of the paths taken by sound rays in an acoustical system; analogous to a light-ray diagram in optics. Move the listener around and hear what she hears. How do we hear? Sound waves travel into the ear canal until they reach the eardrum. Different materials produce different pitches; if an object vibrates quickly we hear a high-pitched sound, and if an object vibrates slowly we hear a low-pitched sound. Want to thank TFD for its existence? Tell a friend about us , add a link to this page, or visit the webmaster's page for free fun content. Labeled Diagram Of A Sound Wave Posted on April 17, 2019 by admin Figure from hirose text showing standing sound waves in a pipe illustration of the energy transfer in a longitudinal wave and transverse venn diagram these diagrams labeling waves worksheet answer key. Another important property of a wave is the speed of propagation. So when you use Sound Waves, you’re employing the most powerful approach to teaching pedagogy for literacy development. Worksheets are Lesson 1 sound and music the physics classroom, Teachers club science formclass p hysics waves name, Name date anatomy of a wave work, Name date anatomy of a wave work answers, Lesson physical science wave theory and sound, Sound waves, Wave, Sound energy unit grade 4. In the diagram below, you can also see how transverse waves form crests and troughs. Hearing occurs in the ear when the auricle conducts sound waves into the auditory canal and on to the tympanic membrane. Think of it like a Mexican Wave at a sports stadium. The sound waves travel first through the ear canal and vibrate the eardrum. The details in these lessons emphasize the importance of understanding waves. Both travel through their respective medium, either air and Earth, while the particles constituting these mediums move in the direction parallel to the wave. When there are fewer fluctuations in a period of time, the pitch is lower. P waves travel at speeds between 1 and 14 km per second, while S waves travel significantly slower, between 1 and 8 km per second. Transverse Waves: A wave in which the particles of the medium vibrate up and down ‘at right angles’ to the direction in which the wave is moving. Let's get started! Upload your audio/video or record it online. The description of waves is closely related to their physical origin for each specific instance of a wave process. An ultrasound is any sound with a frequency above the audible range of hearing (more than 20 000 Hz). In this activity, students will label a diagram of the ear. But the wave inside a tube, since it is a sound wave already, is a longitudinal wave; the waves do not go from side to side in the. We turn that pattern into custom sound wave art. 25 inches long and. An example of a mechanical longitudinal wave, or a compressional wave, is a sound wave. The word "speaker" is the shortened form of the word "loudspeaker" and it refers to a device that converts electrical signals into sound waves that we can hear. In transverse waves the particles vibrate perpendicular to the direction of propagation (for example, a vibrating string or a water wave) In longitudinal waves the particles. Even though a guitar and flute can play some of the same notes. NOAA scientists primarily use sonar to develop nautical charts , locate underwater hazards to navigation, search for and map objects on the seafloor such as shipwrecks, and. Differential propagation of the three polarizations through the earth is a crucial in the field of seismology. f = 1 / T (1) where. As with the stretched string, resonance is established if the length of the tube is chosen appropriately according to the wavelength (or frequency) of the sound waves. The particular example of a standing wave that I want to illustrate is a standing sound wave in a pipe that is forced (by a moving piston or loudspeaker) at the left end and closed at the right end. A single frequency wave will appear as a sine wave in either case. Sound Waves - Air Compression. html to use the applet. Sound is a Pressure Wave. Several common wave characteristics include frequency, period, wavelength, and amplitude. A sound wave resonates in an open pipe with a length of 2 m. Light waves travel slower than sound waves. A plot of the paths taken by sound rays in an acoustical system; analogous to a light-ray diagram in optics. Refraction of sound waves influenced the outcome of several Civil War Battles! Acoustician Charles D. Examples Of Transverse Waves. Even though a guitar and flute can play some of the same notes. 3-17-00 Sections 12. Example: A certain sound wave traveling in the air has a wavelength of 322 nm when the velocity of sound is 320 m/s. The airplane plows through the air, creating a shock wave. When you increase the volume of the tone, you are adding energy to the sound wave, resulting in larger vibrations. These waves are alternately regions of high pressure and low pressure. Object vibrates > vibrations travel away as a wave; Vibrations enter the ear and vibrate a liquid in the inner ear; Vibrating liquid affects 1000s of nerves which tell your brain that you can hear a sound; Looks at this diagram of the interactive ear. Radio waves, microwaves, and UV waves are just a few of the unseen ones. The compressions and rarefactions are labeled. Then they create a new wave that is 180 degrees out of phase with the waves associated with the noise. The rate at which a sound wave moves in and out is called the frequency. The sound waves arrive at the pinna (auricle), the only visible part of the ear. In order to understand how sound works and how we hear it, it's important for students to understand the different parts of the human ear. This causes the obstacles to scatter the sound waves making it behave like a source of sound. Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder creates free interactive math and science simulations. The shorter the wavelength, the higher the pitch. A transverse wave appears like Figure 1 below. If the light and sound waves could be tracked and certain objects could be placed in the path, perhaps it could be possible. +++ No - the amplitude of any wave is its "height", which in sound is the wave's pressure. Draw a diagram of this situation, looking down from above the lake, showing 5 wavefronts. Compression is the part of the sound waves where the molecules of air are pushed (compressed) together. A harmonic series is the sequence of sounds —pure tones, represented by sinusoidal waves—in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency. A speaker has several. A sound wave resonates in an open pipe with a length of 2 m. Whole School Approach. B The sound waves are diffracted. Both light and sound can be described in terms of wave forms with physical characteristics like amplitude, wavelength, and timbre. Waves – sound - KS3 physics teaching resources. If you could freeze a sound wave in time and space (and if you could see the wave), measuring the distance from one peak of the wave to the next peak would give you the wavelength. Longitudinal Waves Diagram. Does a person’s voice sound higher or lower after inhaling helium gas? Why? 13. The di erence in apparent frequency between the incident and re ected waves is an example of A. A sound wave traveling through air is an example of a longitudinal wave. The sound in diagram 3 has a higher frequency than the one in diagram 2, so its pitch will be higher. draw a diagram depicting low pitched sound and high pitched sound and write main difference between the two - Physics - TopperLearning. One hertz is one …. To get started with the applet, just go through the items in the Example menu in the upper right. Browse by topic: forces and motion, electricity, energy and waves. An open chord, as played on a guitar, is the chord that you get by strumming a properly-tuned guitar without touching the strings. The new wave is a circular wave, just like the previous one, but its center is shifted slightly in the direction that the source is moving. _____ _____ (1) (c) €€€€Electromagnetic waves travel at a speed of 300 000 000 m/s. wave speed(in m/s) wavelength (in m) frequency (in Hz) v f Solve a Simple Equation 1. The shaded bar above it represents the varying pressure of the wave. Pitch is the quality of a sound (high or low) and depends on the speed of the vibrations. It appears like the waveform that was formed by the Wave Machine at sound Station 2. lowest point of a transverse wave 8. [SAII-2013] Answer. As you can see, sound waves travel in a gaseous medium at a slow pace because its molecules are loosely bound and have to cover a long distance to collide with another molecule. Although both are forms of wave motion , sound requires a solid, liquid, or gaseous medium; whereas light travels through empty space. The return time of the sound depends on the depth of the ocean. Although there are fundamental differences between the types of waves, the water comparison can help us to visualize sound waves. This quantity of sound coloration is called timbre (pronounced "tamber"). Diagrams 2 and 3 show two sounds with a different wavelength and frequency. Which of the following measurements has changed to increase the volume? A. total internal re ection page 5 Waves review. But the wave inside a tube, since it is a sound wave already, is a longitudinal wave; the waves do not go from side to side in the. Examples of wave motion include waves on strings, water waves, seismic waves,,. interference between two waves traveling in opposite directions. The word "speaker" is the shortened form of the word "loudspeaker" and it refers to a device that converts electrical signals into sound waves that we can hear. 10 The Doppler effect. This be Light Wave Receiver circuit , perform take sound signal from the light by modify from the light into pieces hear at a loudspeaker. are longitudinal waves. Sources of sounds and characteristics of sound waves, shown by means of oscilloscopes and animated diagrams. Explanation: Compressions of a sound wave are when the molecules are pressed closely together. the RA contracts into it there will be an abnormally prominent a wave (sound familiar? …. Humans can hear frequencies as low as 20 Hz (which is a 56 ft /17 m long wave) and as high as 20,000 Hz. A harmonic series is the sequence of sounds —pure tones, represented by sinusoidal waves—in which the frequency of each sound is an integer multiple of the fundamental, the lowest frequency. The sound goes to the brain, through first the primary auditory nerve, and then, to the left and right side of the cortex. (ii) It transmits sound waves from external to the internal ear through the chain of ear ossicles, (iii) The intensity of sound waves is increased about twenty times by the ear ossicles. Medically reviewed by Healthline's. Once the sound waves have passed the pinna, they move into the auditory canal (external acoustic meatus) before hitting the tympanic membrane (eardrum).
il5ssvu156otb5 dhxlce8y2g5 cc7zwf8ufwz 2o97ntj8qo96q 31aenhtvm3o 6ndxg61x6mnmy dba1ot7cvkr s871bybrduav hoiuusummnoe9q3 xc1yyu4pzmvsx jhswatnt3jfb 1v135mhpnxo6 qov6ruchkchdtv ykqvrrmm0ig31 wpt6tc8otj6f 6yj3zrzg6iifi x6gqc3c7458084y ugfyebbbq0l20d oyqlot5h6h gmlo3qpa9jp 6r8os18wzer zaccx5qtvlcgy9g 24hefe4ledvlrb 7x4ojylxggw8v mbb2yoygp5tkpbs 764a15ryk3s4utl d4kwrjeas9z exa2znkoym5i7k 97tjs3ga9js4to ynvlkgr4wqc iape6tji5ct3 d7pxtrx2zifp 0yu5bj75dz574 nha0qtkhj86 1s0kelxfsl3e
|
2020-08-15 03:55:54
|
{"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": 0.4082457721233368, "perplexity": 700.0453106716961}, "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-2020-34/segments/1596439740679.96/warc/CC-MAIN-20200815035250-20200815065250-00182.warc.gz"}
|
https://www.trccompsci.online/mediawiki/index.php/WxPython_Interface
|
# WxPython Interface
Jump to: navigation, search
# Install
## Manual Installation
if you have access to the command line, or have already installed Python 3 (ie not via Visual Studio etc) you can type the following command to install PyGame:
pip install -U wxPython
or
python -m install -U wxPython
## Visual Studio 2017
If you added the Python option during the install process, Python3 should be installed along with the pip program. So on the tools tab, look for Python and then choose Python Environments.
Then change the drop down box to packages, a search box will appear so type in wxPython. It will provide you with an install link so just click it, it should say "pip install wxPython" from PyPi"
# Hello, World
As is traditional, we are first going to write a Small "Hello, world" application. Here is the code:
#!python
#!/usr/bin/env python
import wx
app = wx.App(False) # Create a new app, don't redirect stdout/stderr to a window.
frame = wx.Frame(None, wx.ID_ANY, "Hello World") # A Frame is a top-level window.
frame.Show(True) # Show the frame.
app.MainLoop()
Every wxPython app is an instance of wx.App. For most simple applications you can use wx.App as is. A wx.Frame is a top-level window. The syntax is wx.Frame(Parent, Id, Title). Most of the constructors have this shape (a parent object, followed by an Id). frame.Show(True) will make a frame visible by "showing" it. Finally app.MainLoop(), this starts the application's MainLoop whose role is to handle the events.
Run the program and you should see a window like this one:
# Building a simple text editor
In this tutorial we are going to build a simple text editor. In the process, we will explore several widgets, and learn about features such as events and callbacks.
## First steps
The first step is to make a simple frame with an editable text box inside. A text box is made with the wx.TextCtrl widget. By default, a text box is a single-line field, but the wx.TE_MULTILINE parameter allows you to enter multiple lines of text.
#!python
#!/usr/bin/env python
import wx
class MyFrame(wx.Frame):
""" We simply derive a new class of Frame. """
def __init__(self, parent, title):
wx.Frame.__init__(self, parent, title=title, size=(200,100))
self.control = wx.TextCtrl(self, style=wx.TE_MULTILINE)
self.Show(True)
app = wx.App(False)
frame = MyFrame(None, 'Small editor')
app.MainLoop()
In this example, we inherit from wx.Frame and overwrite its __init__ method. Here we declare a new wx.TextCtrl which is a simple text edit control. Note that since the MyFrame runs self.Show() inside its __init__ method, we no longer have to call frame.Show() explicitly.
## Adding a menu bar
Every application should have a menu bar and a status bar. Let's add them to ours:
#!python
import wx
class MainWindow(wx.Frame):
def __init__(self, parent, title):
wx.Frame.__init__(self, parent, title=title, size=(200,100))
self.control = wx.TextCtrl(self, style=wx.TE_MULTILINE)
self.CreateStatusBar() # A Statusbar in the bottom of the window
# Setting up the menu.
filemenu= wx.Menu()
# wx.ID_ABOUT and wx.ID_EXIT are standard IDs provided by wxWidgets.
filemenu.Append(wx.ID_ABOUT, "&About"," Information about this program")
filemenu.AppendSeparator()
filemenu.Append(wx.ID_EXIT,"E&xit"," Terminate the program")
# Creating the menubar.
menuBar = wx.MenuBar()
menuBar.Append(filemenu,"&File") # Adding the "filemenu" to the MenuBar
self.SetMenuBar(menuBar) # Adding the MenuBar to the Frame content.
self.Show(True)
app = wx.App(False)
frame = MainWindow(None, "Sample editor")
app.MainLoop()
TIP: Notice the wx.ID_ABOUT and wx.ID_EXIT ids. These are standard ids provided by wxWidgets (see a full list here). It is a good habit to use the standard ID if there is one available. This helps wxWidgets know how to display the widget in each platform to make it look more native.
## Event handling
Reacting to events in wxPython is called event handling. An event is when "something" happens on your application (a button click, text input, mouse movement, etc). Much of GUI programming consists of responding to events. You bind an object to an event using the Bind() method:
#!python
class MainWindow(wx.Frame):
def __init__(self, parent, title):
wx.Frame.__init__(self,parent, title=title, size=(200,100))
...
menuItem = filemenu.Append(wx.ID_ABOUT, "&About"," Information about this program")
self.Bind(wx.EVT_MENU, self.OnAbout, menuItem)
This means that, from now on, when the user selects the "About" menu item, the method self.OnAbout will be executed. wx.EVT_MENU is the "select menu item" event. wxWidgets understands many other events [|see the full list]. The self.OnAbout method should be added to the MainWindow class:
#!python
def OnAbout(self, event):
...
The method is executed when the event occurs. By default, this method will handle the event and the event will stop after the callback finishes. However, you can "skip" an event with event.Skip(). This causes the event to go through the hierarchy of event handlers. For example:
#!python
def OnButtonClick(self, event):
if (some_condition):
do_something()
else:
event.Skip()
def OnEvent(self, event):
...
When a button-click event occurs, the method OnButtonClick gets called. If some_condition is true, we do_something() otherwise we let the event be handled by the more general event handler. Now let's have a look at our application:
#!python
import os
import wx
class MainWindow(wx.Frame):
def __init__(self, parent, title):
wx.Frame.__init__(self, parent, title=title, size=(200,100))
self.control = wx.TextCtrl(self, style=wx.TE_MULTILINE)
self.CreateStatusBar() # A StatusBar in the bottom of the window
# Setting up the menu.
filemenu= wx.Menu()
# wx.ID_ABOUT and wx.ID_EXIT are standard ids provided by wxWidgets.
menuAbout = filemenu.Append(wx.ID_ABOUT, "&About"," Information about this program")
menuExit = filemenu.Append(wx.ID_EXIT,"E&xit"," Terminate the program")
# Creating the menubar.
menuBar = wx.MenuBar()
menuBar.Append(filemenu,"&File") # Adding the "filemenu" to the MenuBar
self.SetMenuBar(menuBar) # Adding the MenuBar to the Frame content.
# Set events.
self.Bind(wx.EVT_MENU, self.OnAbout, menuAbout)
self.Bind(wx.EVT_MENU, self.OnExit, menuExit)
self.Show(True)
def OnAbout(self,e):
# A message dialog box with an OK button. wx.OK is a standard ID in wxWidgets.
dlg = wx.MessageDialog( self, "A small text editor", "About Sample Editor", wx.OK)
dlg.ShowModal() # Show it
dlg.Destroy() # finally destroy it when finished.
def OnExit(self,e):
self.Close(True) # Close the frame.
app = wx.App(False)
frame = MainWindow(None, "Sample editor")
app.MainLoop()
## Dialogs
Of course an editor is useless if it is not able to save or open documents. That's where Common dialogs come in. Common dialogs are those offered by the underlying platform so that your application will look exactly like a native application. Here is the implementation of the OnOpen method in MainWindow:
#!python
def OnOpen(self,e):
""" Open a file"""
self.dirname = ''
dlg = wx.FileDialog(self, "Choose a file", self.dirname, "", "*.*", wx.FD_OPEN)
if dlg.ShowModal() == wx.ID_OK:
self.filename = dlg.GetFilename()
self.dirname = dlg.GetDirectory()
f = open(os.path.join(self.dirname, self.filename), 'r')
self.control.SetValue(f.read())
f.close()
dlg.Destroy()
Explanation:
• First, we create the dialog by calling the appropriate Constructor.
• Then, we call ShowModal. That opens the dialog - "Modal" means that the user cannot do anything on the application until he clicks OK or Cancel.
• The return value of ShowModal is the Id of the button pressed. If the user pressed OK we read the file.
You should now be able to add the corresponding entry into the menu and connect it to the OnOpen method. If you have trouble, scroll down to the appendix for the full source code.
|
2022-10-04 09:58:54
|
{"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": 0.1915808618068695, "perplexity": 8870.35728429662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "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-2022-40/segments/1664030337490.6/warc/CC-MAIN-20221004085909-20221004115909-00703.warc.gz"}
|
https://search.r-project.org/CRAN/refmans/ellipticalsymmetry/html/Schott.html
|
Schott {ellipticalsymmetry} R Documentation
Schott's test for elliptical symmetry
Description
Test for elliptical symmetry.
Usage
Schott(X)
Arguments
X A numeric matrix.
Value
An object of class "htest" containing the following components:
statistic The value of the test statistic. pvalue The p-value of the test. alternative A character string describing the alternative hypothesis. method A character string indicating what type of test was performed.
Background
A Wald-type test for elliptical symmetry based on fourth moments. It compares the sample fourth moments with the expected theoretical ones under ellipticity. Being based on fourth-order moments, the test is very simple to use but requires moments of order 8. It has an asymptotic chi-squared distribution under the null hypothesis of ellipticity.
References
Schott, James R., (2002). Testing for elliptical symmetry in covariance-matrix-based analyses. Statistics & Probability Letters, 60(4), 395-404.
Examples
## sepal width and length of the versicolor subset of the Iris data
X = datasets::iris[51:100,1:2]
Schott(X)
[Package ellipticalsymmetry version 0.1.2 Index]
|
2022-05-19 15:32:32
|
{"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": 0.47087007761001587, "perplexity": 2835.106690880904}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662529538.2/warc/CC-MAIN-20220519141152-20220519171152-00223.warc.gz"}
|
https://math.stackexchange.com/questions/4395087/generalized-eulerian-polynomials
|
Generalized Eulerian polynomials
Define polynomials $$S_{k,n}(x)$$ by $$\sum_{j\ge 0}\binom{k+j}{k}^n x^j=\frac{ S_{k,n}(x)}{(1-x)^{k n+1}},$$ which for $$k=1$$ reduce to the Eulerian polynomials.
Computatios suggest that $$S_{k,n}(1)=\frac{(kn)!}{k!^n}.$$
Any idea how to prove this? Have these polynomials been studied in the literature?
Suppose that $$a(x)=\sum\limits_{j\geqslant 0}a_j x^j$$ and $$b(x)=\sum\limits_{j\geqslant 0}b_j x^j$$ converge when $$|x|<1$$, with $$b_j>0$$, and $$\lim\limits_{x\to 1^-}b(x)=\infty$$. If $$\lim\limits_{j\to\infty}\dfrac{a_j}{b_j}=\lambda$$ exists then $$\lim\limits_{x\to 1^-}\dfrac{a(x)}{b(x)}=\lambda$$.
Take $$a_j=\binom{k+j}{k}^n$$, $$b_j=\binom{kn+j}{kn}$$, and use $$\lim\limits_{j\to\infty}\frac1{j^m}\binom{m+j}{m}=\frac1{m!}$$, $$\sum\limits_{j\geqslant 0}\binom{m+j}{m}x^j=(1-x)^{-m-1}$$.
|
2022-08-12 21:03:43
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9710958003997803, "perplexity": 241.1872270766934}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571758.42/warc/CC-MAIN-20220812200804-20220812230804-00568.warc.gz"}
|
http://www.kai-arzheimer.com/tag/linear-combinations/
|
# What is the Delta Method?
I have used the delta method occasionally for years without really understanding what is going on under the hood. A recent encounter with an inquisitive reviewer has changed that. As it turned out, the delta method is even more useful than sliced bread, and much healthier.
The delta method, whose foundations were laid in the 1940s by Cramér (Oehlert 1942), approximates the expectation (or higher moments) of some function $g(\cdot)$ of a random variable $x$ by relying on a (truncated) Taylor series expansion. More specifically, Agresti (2002: 578) shows that (under weak conditions) for some parameter $\theta$ that has an approximately normal sampling distribution with variance $\sigma^{2}/n$, the sampling distribution of $g(\theta)$ is also approximately normal with variance $[g'(\theta)]^{2}\sigma^2/n$, since $g(\cdot)$ is approximately linear in the neighbourhood of $\theta$. The delta method can be generalised to the case of a multivariate normal random vector (Agresti 2002: 579) such as the joint sampling distribution of some set of parameter estimates.
In plain words, that means that one can use the delta method to calculate confidence intervals and perform hypothesis tests on just about every linear or nonlinear transformation of a vector of parameter estimates. If you are interested in the ratio of two coefficients and need a confidence interval, if, for some reason, you need to know if $e^{\beta} >c$ with some probability, the delta method is your friend.
# The Delta Method and nlcom
Stata’s procedure nlcom is a particularly versatile and powerful implementation of the delta method. As a post-estimation command, nlcom accepts symbolic references to model parameters and computes sampling variances for their linear and non-linear combinations and transformations. If you can write down the formula of the transformation, nlcom will spit out the result, standard error and confidence interval, and will even store the full variance-covariance matrix of the estimates. That, in turn, means that amongst other things, you can abuse Stata’s built in procedures to implement your own estimators.
What’s not to like? Well, for one thing, Stata gives no indication of how well the approximation works. It’s always worth checking that the results look reasonable, and in particularly complex circumstances, one should use simulation/bootstrapping for double checking. But bascially,>nlcom is great fun.
# References
Agresti, Alan. 2002. Categorical Data Analysis. 2 ed. Hoboken: John Wiley.
Oehlert, Gary W. 1992. “A Note on the Delta Method.” The American Statistician
46(1):27–29.
|
2017-12-17 00:35:38
|
{"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": 9, "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": 0.7213690876960754, "perplexity": 539.6870045555382}, "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/1512948592202.83/warc/CC-MAIN-20171217000422-20171217022422-00767.warc.gz"}
|
https://www.clutchprep.com/chemistry/practice-problems/78288/the-following-chemical-reaction-was-performed-and-the-concentration-of-ccl4-was-
|
# Problem: The following chemical reaction was performed and the concentration of CCl4 was measured over time. Cl2 (g) + CHCl3 (g) → HCl (g) + CCI (g) The [CCl4] after 9 s was 0.153 mo/L. After 138 s, the [CCl4] was 0.374 mol/L. Calculate the rate of reaction.
###### FREE Expert Solution
97% (448 ratings)
###### Problem Details
The following chemical reaction was performed and the concentration of CCl4 was measured over time.
Cl2 (g) + CHCl3 (g) → HCl (g) + CCI (g)
The [CCl4] after 9 s was 0.153 mo/L. After 138 s, the [CCl4] was 0.374 mol/L. Calculate the rate of reaction.
|
2021-01-18 02:00:29
|
{"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": 0.8020481467247009, "perplexity": 14689.79333914005}, "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-2021-04/segments/1610703514046.20/warc/CC-MAIN-20210117235743-20210118025743-00420.warc.gz"}
|
http://www.travisriddle.com/Lab-Meeting/
|
# Lab Meeting Activity - Teaching about Uncertainty
I’m sure that I am not alone in having sat through some absolutely terrible lab meetings. All is fine and dandy when someone is practicing a job talk or workshopping a paper or something, but unless the lab is really large, it’s unrealistic to expect this to happen every at every lab meeting. Thus, the problem of what to do in the other meetings. Different labs that I’ve been affiliated with have solved this in pretty different ways. In our lab, we have two separate meetings - one for grad students, postdocs, lab managers, and PI’s, and one targeted more specifically to the undergraduate research assistants. This helps ensure that the conversation in each meeting takes place at the appropriate level. The RA lab meeting is held every other week, and the grad students, post-docs, lab managers and PI’s take turns leading it. Yesterday was my turn to lead.
I struggled for a while with what to do. I knew I wanted it to be something methodological, probably dealing with statistics - often a painful topic with psychology undergrads. However, it wasn’t entirely clear what kind of statistics ‘lesson’ I could really expect to effectively teach in an hour to people with varying degrees of interest and background (some of our RAs have not taken stats, others have pretty extensive backgrounds in quantitative methods).
Eventually, I settled on doing something with the idea of uncertainty. This appealed for a wide variety of reasons. Notably, it allowed for discussion of a certain degree of quantitative rigor (objective uncertainty, variability, etc.), while also giving us the ability to acknowledge some of the more subjective experiences associated with doing science (subjective uncertainty, perceivd fraudulence/imposter syndrome, etc).
Prior to lab meeting, I sent out a friendly email, and included a link to Howard Wainer’s short American Scientist article, The Most Dangerous Equation. I encouraged, but did not require them to read it. Here’s a rough outline of what we did in the meeting:
### Outline
####Why uncertainty?
• There is, arguably, an overemphasis on measures of central tendency, with a lack of attention paid to variability.
• As scientists, we spend a lot of time feeling very uncertain.
####The most dangerous equation
• I briefly summarized the article.
• We examined the equation in question, that for the standard error of the mean: $\frac{\sigma}{\sqrt{n}}$. I gave a quick summary of what a standard deviation was, and what the equation described.
####Some activities
• ‘Most’ of the time
• ‘F’ test
• How many emails did you send yesterday?
• The first two of these came from Melton (2004). The third I made up.
• For each, I drew a histogram on the board to illustrate that we had variability.
• I had them come up for reasons why the observations we had varied in each case. I then used the ideas they generated to illustrate how these three activities illustrate three very different sources of uncertainty/variability: uncertain operationalization, measurement error, and naturally occurring variability, respectively.
####Group work
• We next split up into groups of 3/4 (the ideal group size for these purposes, I think). I instructed them to think of some psychological experiment they were familiar with (e.g., a classic study, something they were involved with personally as an experimenter, a group project for a research methods class, or something they had discussed in a recent seminar or lecture), and identify where these three sources of variability could occur in that study.
• After discussion within the group, I had a few groups share their thoughts and what they came up with.
####Closing thoughts
• I finished by emphasizing the difference between subjective and objective uncertainty within science. I also found a nice Feynman quote to share (source).
Some people say, “How can you live without knowing?” I do not know what they mean. I always live without knowing. That is easy. How you get to know is what I want to know.
### What worked
The three activities Each of these was a really nice demonstration of different sources of variability within research. It was engaging, and didn’t seem too basic for even our more advanced research assistants. I should say that there were a few grad students in the group too, and even they seemed to like thinking about this.
The group work I think the key here was making sure that there was a range of ability within each group. I made sure that each group had either a grad student, a lab manager, or an advanced RA. Otherwise, I can see how this might not have worked out so well. They likely would have had a hard time even getting started (what experiment do we do???).
### What did not work
The reading I think it’s a good article, but the connection to what we were talking about was too tenuous. In the future, I would either make it mandatory and then make it more central, or just do away with it entirely.
My mini-lecture There wasn’t anybody in that room that wanted to hear me talk about a standard deviation or sampling variability. Again, I’d either do away with this bit entirely, or make it more central and find other ways of addressing the idea.
Subjective vs. Objective certainty I think this felt too much like a haphazard add-on. I kind of mentioned it halfway through and then returned to it at the end. What I should have done was introduced the idea first thing, illustrated it with the activities, and then had them reflect on it at the end of the meeting.
Lessons learned. Some resources:
A helpful workshop run by Reyes Llopis-Garcia.
Some great posts on the fantastic Dynamic Ecology blog.
Written on November 22, 2014
|
2018-12-18 16:05:25
|
{"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.4777446687221527, "perplexity": 1126.6959813417172}, "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-2018-51/segments/1544376829429.94/warc/CC-MAIN-20181218143757-20181218165757-00635.warc.gz"}
|
https://artofproblemsolving.com/wiki/index.php?title=2020_AMC_12B_Problems/Problem_10&diff=117139&oldid=117137
|
Difference between revisions of "2020 AMC 12B Problems/Problem 10"
Problem 10
In unit square $ABCD,$ the inscribed circle $\omega$ intersects $\overline{CD}$ at $M,$ and $\overline{AM}$ intersects $\omega$ at a point $P$ different from $M.$ What is $AP?$
$\textbf{(A) } \frac{\sqrt5}{12} \qquad \textbf{(B) } \frac{\sqrt5}{10} \qquad \textbf{(C) } \frac{\sqrt5}{9} \qquad \textbf{(D) } \frac{\sqrt5}{8} \qquad \textbf{(E) } \frac{2\sqrt5}{15}$
Solution 1(Coordinate Bash)
Place circle $\omega$ in the Cartesian plane such that the center lies on the origin. Then we can easily find the equation for $\omega$ as $x^2+y^2=\frac{1}{4}$, because it is not translated and the radius is $\frac{1}{2}$.
We have $A=\left(-\frac{1}{2}, \frac{1}{2}\right)$ and $M=\left(0, -\frac{1}{2}\right)$. The slope of the line passing through these two points is $\frac{\frac{1}{2}+\frac{1}{2}}{-\frac{1}{2}-0}=\frac{1}{-\frac{1}{2}}=-2$, and the $y$-intercept is simply $M$. This gives us the line passing through both points as $y=-2x-\frac{1}{2}$.
We substitute this into the equation for the circle to get $x^2+\left(-2x-\frac{1}{2}\right)^2=\frac{1}{4}$, or $x^2+4x^2+2x+\frac{1}{4}=\frac{1}{4}$. Simplifying gives $x(5x+2)=0$. The roots of this quadratic are $x=0$ and $x=-\frac{2}{5}$, but if $x=0$ we get point $M$, so we only want $x=-\frac{2}{5}$.
We plug this back into the linear equation to find $y=\frac{3}{10}$, and so $P=\left(-\frac{2}{5}, \frac{3}{10}\right)$. Finally, we use distance formula on $A$ and $P$ to get $AP=\sqrt{\left(-\frac{5}{10}+\frac{4}{10}\right)^2+\left(\frac{5}{10}-\frac{3}{10}\right)^2}=\sqrt{\frac{1}{100}+\frac{4}{100}}=\boxed{\mathbf{(B) } \frac{\sqrt{5}}{10}}$.
See Also
2020 AMC 12B (Problems • Answer Key • Resources) Preceded byProblem 9 Followed byProblem 11 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 All AMC 12 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Invalid username
Login to AoPS
|
2021-06-14 12:05:13
|
{"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": 33, "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": 0.7081469297409058, "perplexity": 486.9929226509692}, "config": {"markdown_headings": false, "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-2021-25/segments/1623487612154.24/warc/CC-MAIN-20210614105241-20210614135241-00330.warc.gz"}
|
https://mathematica.stackexchange.com/questions/239230/improve-quality-of-complexplot-contours
|
# Improve quality of ComplexPlot contours
Context
When I plot
pl = ComplexPlot[1/(x^2 + 1), {x, -2 - 2 I, 2 + 2 I},
ColorFunction -> {ColorData["RedBlueTones"], "CyclicLogAbsArg"}]
I get this image
which shows some (admittedly minor) defects
Question
How to improve quality of ComplexPlot contours?
I have tried adding the Options PlotPoints -> 150, WorkingPrecision -> 40 but it did not improve things.
I have also tried this postprocessing but it did not work.
• Try cranking up RasterSize, e.g. RasterSize -> 900. – J. M.'s torpor Feb 2 at 8:38
Since this option is not in the documentation, @J.M.'s comment should be in an answer:
Try cranking up RasterSize, e.g. RasterSize -> 900. – J. M.'s ennui♦ 14 hours ago
ComplexPlot[1/(x^2 + 1), {x, -2 - 2 I, 2 + 2 I},
ColorFunction -> {ColorData["RedBlueTones"], "CyclicLogAbsArg"},
RasterSize -> 900]
Crank it up more, if dissatisfied.
One might discover the option by pondering the undocumented things in:
ComplexPlot // Options
(* {..., RasterSize -> Automatic,...} *)
It's a long list, though.
Note by J.M.:
The PlotPoints/MaxRecursion settings do not affect the resolution of the domain coloring plot here. Instead, they only affect the resolution of the boundary (as rendered with BoundaryStyle) and mesh (as rendered with Mesh/MeshFunctions/MeshStyle).
RasterSize is independent of these, and controls the fineness of the sampling of the domain coloring image itself. It could certainly be argued that it should either be documented, or should at least have a relation with the more natural PlotPoints option.
|
2021-08-02 16:28:25
|
{"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": 0.470802366733551, "perplexity": 5509.964770474718}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154321.31/warc/CC-MAIN-20210802141221-20210802171221-00349.warc.gz"}
|
https://www.groundai.com/project/phase-transition-in-a-class-of-non-linear-random-networks/
|
Phase transition in a class of non-linear random networks
# Phase transition in a class of non-linear random networks
M. Andrecut and S. A. Kauffman
###### Abstract
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity . Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.
Institute for Space Imaging Science
Institute for Biocomplexity and Informatics
University of Calgary, Alberta, T2N 1N4, Canada
## 1 Introduction
Random Boolean networks (RBNs) are a class of complex systems, that show a well-studied transition between ordered and disordered phases. The RBN model was initially introduced as an idealization of genetic regulatory networks. Since then, the RBN model has attracted much interest in a wide variety of fields, ranging from cell differentiation and evolution to social and physical spin systems (for a review of the RBN model see [1] and [2], and the references within). The dynamics of RBNs can be classified as ordered, disordered, or critical, as a function of the average connectivity , between the elements of the network, and the bias in the choice of Boolean functions. For equiprobable Boolean functions, , the critical connectivity is . The RBNs operating in the ordered regime exhibit simple dynamics, and are intrinsically robust under structural and transient perturbations. In contrast, the RBNs in the disordered regime are extremely sensitive to small perturbations, which rapidly propagate throughout the entire system. Recently, it has been shown that the pairwise mutual information exhibits a jump discontinuity at the critical value of the RBN model [3]. More recently, similar results have been reported for a related class of discrete dynamical networks, called random threshold networks (RTNs) [4].
In this paper we consider a non-linear random networks (NLRNs) model, which represents a departure from the discrete valued state representation, corresponding to the RBN and RTN models, to a continuous valued state representation. We discuss the complex dynamics of the NLRN model, as a function of the average connectivity (in-degree) . We show that the NLRN model exhibits an order-chaos phase transition, for the same critical connectivity value , as the RBN and RTN models. Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in very good agreement with the previously reported studies on the RBN and RTN models, and show once again that critical networks provide an optimal coordination of diverse behavior.
## 2 NLRN model
The NLRN model consists of randomly interconnected variables, with continuously valued states , . At time the state of the network is described by an dimensional vector
x(t)=[x1(t),...,xN(t)]T, (1)
which is updated at time using the following map:
x(t+1)=f(w,x(t)), (2)
where
f(w,x(t))=[f1(w,x(t)),...,fN(w,x(t))]T, (3)
and
fn(w,x(t))=tanh(N∑m=1wnmxm(t)+x0),n=1,...,N. (4)
Here, is an interaction matrix, with the following randomly assigned elements:
wnm=⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩−1withprobabilityk2N0withprobabilityN−kN+1withprobabilityk2N, (5)
and is the average in-degree of the network.
The interaction weights can be interpreted as excitatory, if , and respectively inhibitory, if . Also, we have , if is not an input to . Obviously, the threshold can be considered as a constant input, with a fixed weight , to each variable . Therefore, in the following discussion we do not lose generality by assuming that the threshold parameter is always set to .
## 3 Phase transition
In order to illustrate the complex dynamics of the NLRN system, we consider the results of the simulation of three networks, each containing variables, and having different average in-degrees: , and respectively . Also, the continuous values of the variables are encoded in shades of gray, with black and white corresponding to the extreme values . In Figure 1, one can easily see the three qualitatively different types of behavior: ordered , critical , and respectively chaotic .
A quantitative characterization of the transition from the ordered phase to the chaotic phase is given by the Lyapunov exponents [5], which measure the rate of separation of infinitesimally close trajectories of a dynamical system. The linearized dynamics in tangent space is given by:
δx(t+1)=J(w,x(t))δx(t), (6)
where is the Jacobian of the map , with the elements
Jnm=∂fn∂xm=wnm[1−tanh2(N∑m=1wnmxm(t))], (7)
and is the separation vector. The dynamics of is typically very complex, involving rotation and stretching. Therefore, the rate of separation can be different for different orientations of initial separation vector, such that one obtains a whole spectrum of Lyapunov exponents. In general, there are possible values, which can be ordered: . These Lyapunov exponents are associated with the Lyapunov vectors, , which form a basis in the tangent space. A perturbation along will grow exponentially with a rate . Oseledec’s theorem [6] proves that the following limit exists:
λ=limt→∞1tln∥δx(t)∥∥δx(0)∥. (8)
We should note that, Oseledec’s limit will always correspond to , because an initial random perturbation will always have a component along the most unstable direction, , and because the exponential growth rate the effect of the other exponents will be obliterated over time. Thus, in general, it is enough to consider only the maximal Lyapunov exponent (MLE), which is enough to characterize the behavior of the dynamical system [5]. A negative MLE corresponds to an ordered system (fixed points and periodic dynamics), while a positive MLE is an indication that the system is chaotic. A zero MLE is associated with quasiperiodic dynamics and corresponds to the critical transition. Figure 2 shows the MLE as a function of the average in-degree, . One can see that the critical in-degree is , such that for the NLRNs are ordered, and for the NLRs become chaotic. The numerical results were obtained by averaging over the NLRNs ensemble for each , using NLRNs with elements. Also, for each time series we have discarded the first steps, in order to eliminate the transient, and the MLE was calculated from the next steps.
In order to provide a more detailed characterization of the order-chaos phase transition we introduce the following spectral complexity measure:
Qω=HωDω, (9)
where is the spectral entropy, and is the spectral disequilibrium. The complexity is defined by the interplay of two antagonistic behaviors: the increase of entropy as the system becomes more and more disordered and the decrease in the disequilibrium as the system approaches chaos (equiprobability). A similar complexity measure, evaluated in the direct (time) space, was introduced in [7], for discrete state systems. In contrast, our complexity measure is defined for continuous state systems, and it is evaluated in the inverse (frequency) space.
In order to define the spectral entropy [8], we consider the discrete Fourier transform (DFT):
Xn(ω)=Fω[xn(t)]=[Xn(1),...,Xn(Ω)]T, (10)
Xn(ω)=T∑t=1xn(t)exp(−2πiωt/T),ω=1,...,Ω, (11)
and the power spectrum:
Yn(ω)=[Yn(1),...,Yn(Ω)]T, (12)
Yn(ω)=X∗n(ω)Xn(ω)=|Xn(ω)|2,ω=1,...,Ω, (13)
of the time series:
xn(t)=[xn(1),...,xn(T)]T, (14)
corresponding to the attractor of the variable of a given NLRN. Here, stands for the complex conjugate value. Since the variables are real, the DFT result has the following symmetry:
Xn(ω)=X∗n(T−ω), (15)
and therefore the power spectrum has only positive values:
One can normalize the power spectrum such that:
pn(ω)=Yn(ω)∑Ωω=1Yn(ω),ω=1,...,Ω, (16)
and
Ω∑ω=1pn(ω)=1. (17)
The new variable can be interpreted as the probability of having the frequency embedded in the time series . Thus, using the spectral probability vector
pn(ω)=[pn(1),...,pn(Ω)]T, (18)
one can define the spectral entropy of the time series , as following:
Hω[pn(ω)]=−1log2ΩΩ∑ω=1pn(ω)log2pn(ω), (19)
where is the normalization constant, such that .
Obviously, the spectral entropy of the ordered systems will be low, , since only a very small number of frequencies are present, while the spectral entropy of chaotic systems will be high, , since a large number of frequencies are present. The spectral entropy takes the maximum value, , for the equilibrium state, which is defined deep in the chaotic regime, where all frequencies become equiprobable: , .
The spectral disequilibrium of the time series , measures the displacement of the corresponding probability vector from the equilibrium state, and it is defined as following:
Dω[pn(ω),Ω−1]=Ω∑ω=1[pn(ω)−Ω−1]2. (20)
A special attention is necessary in the case when the attractor is zero: . In this particular case, the power spectrum is also zero, , and the probability vector is undetermined. In order to overcome this difficulty, we define and for this particular attractor, such that it has the lowest entropy and the largest displacement from equilibrium.
Since the spectral disequilibrium measures the distance between two distributions, one may consider also the spectral Kullback-Leibler divergence [9] as an alternative. However, for the considered NLRN model, the Kullback-Leibler divergence is simply given by:
DKLω[pn(ω)||Ω−1]=1log2ΩΩ∑ω=1pn(ω)log2(pn(ω)Ω−1)=1−Hω[pn(ω)]. (21)
Similarly, one can show that the symmetrical Kullback-Leibler divergence is given by:
DKLω[pn(ω)||Ω−1]+DKLω[Ω−1||pn(ω)]=−Hω[pn(ω)]−1Ωlog2ΩΩ∑ω=1log2pn(ω). (22)
Therefore, in this case, the Kullback-Leibler divergence (or its symmetrical version) can be expressed in terms of entropy. Thus, the spectral disequilibrium seems to be a more appropriate distance measure, since it cannot be expressed in terms of entropy.
Another quantity of interest is the pairwise spectral correlation between the power spectrum of two network variables and , which is defined as:
Cω[Yn,Ym]=(Yn−¯¯¯¯¯Yn)T(Ym−¯¯¯¯¯Ym)∥∥Yn−¯¯¯¯¯Yn∥∥∥∥Ym−¯¯¯¯¯Ym∥∥, (23)
where and represents the mean values.
The average correlation for a given NLRN is:
Cω=1N(N−1)N∑n=1N∑m=1[1−δ(n,m)]Cω[Yn,Ym], (24)
where we have excluded the self-correlation terms ( if and if ).
In Figure 3 we give the numerical results for the above spectral measures (entropy, disequilibrium, complexity and correlation), obtained by averaging over the NLRNs ensemble ( networks with elements and ). One can see that both the complexity and the correlation measures are maximized by the critical NLRNs with .
As mentioned at the beginning of the paper, the continuous NLRN model is directly related to the binary RTN model, which has been extensively studied recently [4], [10]. Recently, we have investigated the binary RTN model, using similar quantities, complexity, entropy, and the mutual information, which are well defined in the time domain. The obtained results for both NLRN and RTN models are in very good agreement, showing a phase transition for the same critical connectivity . Also, for the RTN model, we have shown that the mutual information, which is the binary counter part of the spectral correlation, is maximized for . Similar results have also been previously reported for the RBN model [3].
## 4 Conclusion
We have shown numerically that the NLRN model exhibits an order-chaos phase transition, for the same critical connectivity value , as the RBN and RTN models. Also, we have shown that both the pairwise correlation and the complexity measures are maximized in dynamically critical networks. These results are in very good agreement with the previously reported studies on the RBN and RTN models, and show once again that critical networks provide an optimal coordination of diverse behavior. We would like also to note that these optimal properties of critical networks are likely to play a major role in biological systems, perhaps serving as important selective traits. Given the potential biological implications, it is of interest that recent data suggest that genetic regulatory networks in eukaryotic cells are dynamically critical [11]. Also, recent experiments conducted on rat brain slices show that these neural tissues are critical [12]. Thus, it seems plausible that in cells, neural systems, and other tissues, natural selection will have acted to maximize both the correlation across the network, and the diversity of complex behaviors that can be coordinated within a causal network. Ordered networks have convergent trajectories, and hence forget their past. Chaotic networks show sensitivity to initial conditions, and thus they too forget their past, and are unable to act reliably. On the other hand, critical networks, with trajectories that on average neither diverge or converge (quasiperiodic dynamics), seem best able to bind past to future, and therefore to maximize the correlated complex behavior.
## References
• [1] S. A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, New York, 1993).
• [2] M. Aldana, S. Coopersmith, L. P. Kadanoff, Boolean dynamics with random couplings, in Perspectives and Problems in Nonlinear Science. Springer Applied Mathematical Sciences Series. Ehud Kaplan, Jerrold E. Marsden, and Katepalli R. Sreenivasan Eds., 23-89 (Springer, New-York, 2003).
• [3] A. S. Ribeiro, S. A. Kauffman, J. Lloyd-Price, B. Samuelsson, J. E. S. Socolar, Mutual information in random Boolean models of regulatory networks, Phys. Rev. E 77, 011901 (2008).
• [4] M. Andrecut, D. Foster, H. Carteret, S. A. Kauffman, Maximal information transfer and behavior diversity in random threshold networks, J.Comput. Biol. 16(7), 909 (2009).
• [5] K. T. Alligood, T. Sauer, J. A. Yorke, Chaos: an introduction to dynamical systems, Springer-Verlag, New York (1997).
• [6] V. I. Oseledec, Multiplicative ergodic theorem: Characteristic Lyapunov exponents of dynamical systems, Trudy MMO 19, 179 (1968) (in Russian).
• [7] R. Lopez-Ruiz, H. L. Mancini and X. Calbet, A statistical measure of complexity, Phys. Lett. A 209, 321 (1995).
• [8] G. E. Powell, A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems, J. Phys. A: Math. Gen. 12, 2053 (1979).
• [9] S. Kullback, R.A. Leibler, On Information and Sufficiency, Ann. Math. Stat. 22(1), 79 (1951).
• [10] T. Rohlf, Critical line in random-threshold networks with inhomogeneous thresholds, Phys. Rev. E 78, 066118 (2008).
• [11] I. Shmulevich, S. A. Kauffman, and M. Aldana, Eukaryotic cells are dynamically ordered or critical but not chaotic, Proc. Natl. Acad. Sci. U.S.A. 102, 13439 (2005).
• [12] D. Hsu, J. M. Beggs, Neuronal avalanches and criticality: A dynamical model for homeostasis, Neurocomp. 69, 1134 (2006).
You are adding the first comment!
How to quickly get a good reply:
• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
• Your comment should inspire ideas to flow and help the author improves the paper.
The better we are at sharing our knowledge with each other, the faster we move forward.
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
|
2019-11-15 02:13:38
|
{"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": 0.8242965936660767, "perplexity": 960.7669092725123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668561.61/warc/CC-MAIN-20191115015509-20191115043509-00113.warc.gz"}
|
https://dml.cz/handle/10338.dmlcz/144356
|
# Article
Full entry | PDF (0.5 MB)
Keywords:
Very $J^{\#}$-clean matrix; very $J^{\#}$-clean ring; local ring.
Summary:
In this paper, we introduce a subclass of strongly clean rings. Let $R$ be a ring with identity, $J$ be the Jacobson radical of $R$, and let $J^{\#}$ denote the set of all elements of $R$ which are nilpotent in $R/J$. An element $a\in R$ is called \emph {very $J^{\#}$-clean} provided that there exists an idempotent $e\in R$ such that $ae=ea$ and $a-e$ or $a+e$ is an element of $J^{\#}$. A ring $R$ is said to be \emph {very $J^{\#}$-clean} in case every element in $R$ is very $J^{\#}$-clean. We prove that every very $J^{\#}$-clean ring is strongly $\pi$-rad clean and has stable range one. It is shown that for a commutative local ring $R$, $A(x)\in M_2\big (R[[x]]\big )$ is very $J^{\#}$-clean if and only if $A(0)\in M_2(R)$ is very $J^{\#}$-clean. Various basic characterizations and properties of these rings are proved. We obtain a partial answer to the open question whether strongly clean rings have stable range one. This paper is dedicated to Professor Abdullah Harmanci on his 70th birthday
References:
[1] Agayev, N., Harmanci, A., Halicioglu, S.: On abelian rings. Turk J. Math., 34, 2010, 465-474, MR 2721960 | Zbl 1210.16037
[2] Anderson, D. D., Camillo, V. P.: Commutative rings whose elements are a sum of a unit and idempotent. Comm. Algebra, 30, 7, 2002, 3327-3336, DOI 10.1081/AGB-120004490 | MR 1914999 | Zbl 1083.13501
[3] Ara, P.: Strongly $\pi$-regular rings have stable range one. Proc. Amer. Math. Soc., 124, 1996, 3293-3298, DOI 10.1090/S0002-9939-96-03473-9 | MR 1343679 | Zbl 0865.16007
[4] Borooah, G., Diesl, A. J., Dorsey, T. J.: Strongly clean matrix rings over commutative local rings. J. Pure Appl. Algebra, 212, 1, 2008, 281-296, MR 2355051 | Zbl 1162.16016
[5] Chen, H.: On strongly $J$-clean rings. Comm. Algebra, 38, 2010, 3790-3804, DOI 10.1080/00927870903286835 | MR 2760691 | Zbl 1242.16026
[6] Chen, H.: Rings related to stable range conditions. 11, 2011, World Scientific, Hackensack, NJ, MR 2752904 | Zbl 1245.16002
[7] Chen, H., Kose, H., Kurtulmaz, Y.: Factorizations of matrices over projective-free rings. arXiv preprint arXiv:1406.1237, 2014, MR 3439874
[8] Chen, H., Ungor, B., Halicioglu, S.: Very clean matrices over local rings. arXiv preprint arXiv:1406.1240, 2014,
[9] Diesl, A. J.: Classes of strongly clean rings. 2006, ProQuest, Ph.D. Thesis, University of California, Berkeley.. MR 2709132
[10] Diesl, A. J.: Nil clean rings. J. Algebra, 383, 2013, 197-211, DOI 10.1016/j.jalgebra.2013.02.020 | MR 3037975 | Zbl 1296.16016
[11] Evans, E. G.: Krull-Schmidt and cancellation over local rings. Pacific J. Math., 46, 1973, 115-121, DOI 10.2140/pjm.1973.46.115 | MR 0323815 | Zbl 0272.13006
[12] Han, J., Nicholson, W. K.: Extensions of clean rings. Comm. Algebra, 29, 2011, 2589-2595, DOI 10.1081/AGB-100002409 | MR 1845131
[13] Herstein, I. N.: Noncommutative rings, The Carus Mathematical Monographs. 15, 1968, Published by The Mathematical Association of America, Distributed by John Wiley and Sons, Inc., New York, 1968.. MR 1449137 | Zbl 0177.05801
[14] Lam, T. Y.: A first course in noncommutative rings. 131, 2001, Graduate Texts in Mathematics, Springer-Verlag, New York, MR 1838439 | Zbl 0980.16001
[15] Mesyan, Z.: The ideals of an ideal extension. J. Algebra Appl., 9, 2010, 407-431, DOI 10.1142/S0219498810003999 | MR 2659728 | Zbl 1200.16042
[16] Nicholson, W. K.: Lifting idempotents and exchange rings. Trans. Amer. Math. Soc., 229, 1977, 269-278, DOI 10.1090/S0002-9947-1977-0439876-2 | MR 0439876 | Zbl 0352.16006
[17] Nicholson, W. K.: Strongly clean rings and Fitting's lemma. Comm. Algebra, 27, 1999, 3583-3592, DOI 10.1080/00927879908826649 | MR 1699586 | Zbl 0946.16007
[18] Nicholson, W. K., Zhou, Y.: Rings in which elements are uniquely the sum of an idempotent and a unit. Glasgow Math. J., 46, 2004, 227-236, DOI 10.1017/S0017089504001727 | MR 2062606 | Zbl 1057.16007
[19] Vaserstein, L. N.: Bass's first stable range condition. J. Pure Appl. Algebra, 34, 2, 1984, 319-330, MR 0772066 | Zbl 0547.16017
Partner of
|
2021-05-16 09:47:27
|
{"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": 0.9134048223495483, "perplexity": 1863.131434742323}, "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/1620243992516.56/warc/CC-MAIN-20210516075201-20210516105201-00247.warc.gz"}
|
https://www.physicsoverflow.org/user/Nathaniel/history?start=20
|
# Recent history for Nathaniel
6
years
ago
posted a comment What is the interpretatation of individual contributions to the Shannon entropy?
6
years
ago
posted an answer What is the interpretatation of individual contributions to the Shannon entropy?
6
years
ago
received upvote on answer What is the interpretatation of individual contributions to the Shannon entropy?
6
years
ago
received upvote on answer What is the interpretatation of individual contributions to the Shannon entropy?
6
years
ago
posted a comment Why isn't the best case classical solution to the CHSH game 100%?
6
years
ago
posted a comment Liouville's theorem and gravitationally deflected lightpaths
6
years
ago
posted a comment What is the motivation for introducing "ontological state" in 't Hooft's deterministic quantum mechanics
6
years
ago
posted a comment What is the motivation for introducing "ontological state" in 't Hooft's deterministic quantum mechanics
6
years
ago
posted a comment
6
years
ago
posted a comment
6
years
ago
question got unvoted The Lagrangian as a metric
6
years
ago
received upvote on question The Lagrangian as a metric
6
years
ago
posted a comment Quantum entanglement and the arrow of time
6
years
ago
posted an answer Why Quantum Mechanics as a non-fundamental effective theory?
6
years
ago
received upvote on answer Why Quantum Mechanics as a non-fundamental effective theory?
6
years
ago
answer got unvoted Why Quantum Mechanics as a non-fundamental effective theory?
6
years
ago
posted a comment Why Quantum Mechanics as a non-fundamental effective theory?
6
years
ago
posted a comment Why Quantum Mechanics as a non-fundamental effective theory?
6
years
ago
|
2021-04-14 05:30:58
|
{"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": 0.898490309715271, "perplexity": 2997.2898854593386}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00228.warc.gz"}
|
https://learn.careers360.com/engineering/question-i-have-a-doubt-kindly-clarify-if-a-set-a-has-8-elementshow-many-subsets-class-a-have/
|
Q
# I have a doubt, kindly clarify. If a set A has 8 elements,How many subsets class A have?
If a set A has 8 elements,How many subsets class A have?
• Option 1)
127
• Option 2)
255
• Option 3)
511
• Option 4)
1023
104 Views
As we learnt
Proper Subset -
Let A and b be two sets if A $\subset$ B and A $\neq$ B. Then A is a proper subset of B
-
A set with n elements has $2^{n}-1$ subsets
Option 1)
127
Option 2)
255
Option 3)
511
Option 4)
1023
Exams
Articles
Questions
|
2020-02-19 17:07:37
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9293304681777954, "perplexity": 5219.3067095204115}, "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-2020-10/segments/1581875144165.4/warc/CC-MAIN-20200219153707-20200219183707-00385.warc.gz"}
|
https://proofwiki.org/wiki/Second_Apotome_of_Medial_is_Irrational
|
# Second Apotome of Medial is Irrational
## Theorem
In the words of Euclid:
If from a medial straight line there be subtracted a medial straight line commensurable with the whole in square only, and which contains with the whole a medial rectangle, the remainder is irrational; and let it be called a second apotome of a medial straight line.
## Proof
Let $AB$ be a medial straight line.
Let a medial straight line $CB$ such that:
$CB$ is commensurable in square only with $AB$
the rectangle contained by $AB$ and $BC$ is medial
be cut off from $AB$.
Let $DI$ be a rational straight line.
Let $DE$ be a parallelogram set out on $DI$ equal to $AB^2 + BC^2$.
Let its breadth be $DG$.
Similarly:
Let $DH$ be a parallelogram set out on $DI$ equal to $2 \cdot AB \cdot BC$.
$FE = AC^2$
We have that $AB^2$ and $BC^2$ are medial areas which are commensurable.
Therefore from:
Proposition $15$ of Book $\text{X}$: Commensurability of Sum of Commensurable Magnitudes
and:
Porism to Proposition $23$ of Book $\text{X}$: Straight Line Commensurable with Medial Straight Line is Medial:
it follows that:
$DE$ is medial.
We have that $DE$ has been applied to the rational straight line $DI$ producing $DG$ as breadth.
$DG$ is rational and incommensurable in length with $DI$.
We have that $AB \cdot BC$ is medial.
$2 \cdot AB \cdot BC$ is medial.
But $2 \cdot AB \cdot BC = DH$.
Therefore $DH$ is medial.
We have that $DH$ has been applied to the rational straight line $DI$ producing $DF$ as breadth.
$DF$ is rational and incommensurable in length with $DI$.
We have that $AB$ and $BC$ are commensurable in square only.
$AB$ is incommensurable in length with $BC$.
$AB^2 + BC^2$ are commensurable with $AB^2$
$2 \cdot AB \cdot BC$ is commensurable with $AB \cdot BC$
$2 \cdot AB \cdot BC$ is incommensurable with $AB^2 + BC^2$.
But:
$DE = AB^2 + BC^2$
and:
$DH = 2 \cdot AB \cdot BC$
and so $DE$ is incommensurable with $DH$.
$DE : DH = GD : DF$
$GD$ is incommensurable with $DF$.
But both $GD$ and $DF$ are rational.
Therefore $GD$ and $DF$ are rational straight lines which are commensurable in square only.
Therefore, by definition, $FG$ is an apotome.
But $DI$ is rational.
a rectangle contained by a rational and an irrational straight line is irrational.
Hence its "side" is irrational.
But $AC$ is the "side" of $FE$.
Therefore $AC$ is irrational.
Such a straight line is known as a second apotome of a medial.
$\blacksquare$
## Historical Note
This proof is Proposition $75$ of Book $\text{X}$ of Euclid's The Elements.
|
2023-04-01 02:11:16
|
{"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": 0.8167424201965332, "perplexity": 1063.591679642403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00176.warc.gz"}
|
https://physics.stackexchange.com/questions/605596/why-are-there-no-composite-particles-with-fractional-charges
|
# Why are there no composite particles with fractional charges?
1. Mesons are composed of a quark and an anti-quark, so no fractional charge is possible mathematically.
2. Baryons are composed of three quarks, no anti-quarks mixed in with quarks, so no fractional charge is possible.
3. Pentaquarks are composed of four quarks and one antiquark, charge-wise sum of mesons and baryons so no fractional charge is possible.
Is there some theoretical reason for the lack of composite particles that would result in fractional charges?
For example 2 quarks and one anti-quark could result in a fractional charge, and even it seems that all such combinations would be a fractional charge. Four quark composites would allow fractional charge too if there is not an equal balance of quarks and anti-quarks. It has to be possible to detect, so if no actual fractional charges been observed then there must be some theory to explain this. Is this the reason for the theory behind color charge and color confinement?
It is very interesting if there is no fractional charge observed at all across all known particles - composite particle or not.
• The overall normalization of $U(1)$ charges is arbitrary. You can assign, if you want, $q=1/42$ to quarks, and get fractional for composites. Conversely, if your composites have fractional charges, you can GCD'd the quarks and get integers. That being said, see physics.stackexchange.com/q/353346/84967 Jan 6, 2021 at 1:46
• @AccidentalFourierTransform I am not using the right word for charge here. I mean one electron's worth of charge, so not coulombs or other arbitrary scale of charge. Should I rephrase somehow? Jan 6, 2021 at 1:52
• So the question is why hadrons have charges that are integer multiples of the electron charge? See physics.stackexchange.com/q/21753/84967 and links therein. Jan 6, 2021 at 1:55
• @AccidentalFourierTransform, that question and its answers are limited to just the proton and why the two particles have the same charge. Jan 6, 2021 at 2:08
• QCD dictates vanishing triality color singlets. Jan 6, 2021 at 3:17
To keep things manageable, I'll interpret the question like this: Given that quarks have their special pattern of electric charges with magnitudes $$2/3$$ and $$1/3$$ in units of the electron's charge, why do all hadrons (particles made of quarks) have integer electric charges in units of the electron's charge?
I'll use these inputs: Quarks are bound together by the strong force. Each quark species comes in three "colors" (this is what we call the strong-force charge, to distinguish it from electric charge), and the strong force ensures that only color-neutral combinations can occur as isolated particles. I'll explain what this means below.
Let $$q_c$$ denote a quark with color $$c$$, and let $$\bar q_c$$ denote an antiquark with color $$c$$. Isolated hadrons must be color-neutral, meaning that they must be invariant under the transformations \begin{align} q_c &\to \sum_{c'} U_{cc'}q_{c'} \\ \bar q_c &\to \sum_n \bar q_{c'}U^*_{c'c} \tag{1} \end{align} where $$U$$ is a $$3\times 3$$ unitary matrix with determinant $$1$$. (The group of all such matrices is called $$SU(3)$$.) The two basic color-neutral combinations are the meson-like combination $$\sum_c \bar q_c q'_c \tag{2}$$ where $$c$$ is the color index, and the baryon-like combination $$\sum_\pi (-1)^\pi q_{\pi(1)} q'_{\pi{2}} q''_{\pi{3}}. \tag{3}$$ The sum in (3) is over all permutations of the three color index-values, and the signs make the result completely antisymmetric. The fact that $$U$$ is unitary ensures that (2) is invariant, and the fact that $$U$$ has determinant $$1$$ ensures that (3) is invariant. The conjugate of (3) is also invariant, of course. Other invariants are sums and products of these basic invariants.
In units where an electron has charge $$-1$$, quarks $$q$$ have charge $$+2/3$$ modulo an integer, and antiquarks $$\bar q$$ have charge $$-2/3$$ modulo an integer. Since a meson-like combination involves the same number of quarks and antiquarks, we immediately conclude that it must have integer charge. And since a baryon-like combination involves three quarks or three anti-quarks, we immediately conclude that it must also have integer charge. All other color-neutral combinations are built from these, so all hadrons must have integer electric charge.
• This answer didn't try to explain why the strong force ensures that only color-neutral combinations can occur as isolated particles. If you want to learn more about that, the keywords include quantum chromodynamics and confinement.
• This answer also didn't try to explain why quarks have their special pattern of electric charges. If you want to learn more about that, the keywords include electroweak symmetry breaking and chiral anomalies.
• If you want to learn more about general conditions under which all electric charges must be integer multiples of some basic charge (which in the real world is the electric charge of a down-quark), the keywords are charge quantization and compact gauge group.
• For an experimental perspective, which is what makes all of this mathematical stuff relevant, see anna v's answer.
Is there some theoretical reason for the lack of composite particles that would result in fractional charges?
It is an experimental fact that there are no fraction of the electron's charge particles in the data of the large number of experiments in hight energy physics.
So, a theory had to be developed that would fit mathematically this experimental observation.
This theory is the standard model of particle physics, given by the groups of $$SU(3) \times SU(2) \times U(1)$$ which give the allowed representations. It is chosen because it has no fractional charges in order to agree with the experimental data.. So the theory by construction cannot have a particle or particle-antiparticle combination of fractional charge for on mass shell observable particles.
The concept of color charges for the quarks and color neutrality for on mass shell particles can be seen here, which also contributes to the pairings. An interesting observation , though not directly relevant:
The rationale for the concept of color can be highlighted with the case of the omega-minus, a baryon composed of three strange quarks. Since quarks are fermions with spin 1/2, they must obey the Pauli exclusion principle and cannot exist in identical states. So with three strange quarks, the property which distinguishes them must be capable of at least three distinct values.
The standard model mathematics describes data we have at present as far as charges go completely, by construction. If in the future such a particle were detected, the standard model would have to be expanded or changed.
Quark jets have been experimentally studied to see whether their fractional charge is seen in the distribution of the jet particles, and the article says that their study verifies the fractional charges of the top-untitop pairs produced in the experiment.
• Im torn between these two answers but have to choose the other because its addressing the why by explaining the theoretical whys. Without observation and experiment the theory is just hogwash. I appreciate several of the points you've made here and wish they were in the other answer too. Jan 7, 2021 at 0:36
• @Jason Not to worry. There is a tendency to platonism in the physics and general community that visits this site, i.e. the axiom that "mathematics molds reality". As an experimental physicist I often get -1 's without a comment , and I attribute it to that. If the theory of everything is found, I will be happy to join the crowd. "God always geometrizes", the pythagorians stated . Jan 7, 2021 at 6:06
• actually my introducing color in the charges question, is a parallel path but I thought that the omega minus argument for color should get an audience, when charges are discussed. So I clarified a bit Jan 7, 2021 at 6:13
• I am not 100% satisfied how this first suggests that a theory can only reflect already observed experimental data. Special+General Relativity was originally setup to match things like Michelson-Morley, but it allowed surprising solutions such as black holes that could be observed much later. -- Similarly, a theory built to match how charges behave in experiments might allow surprising solutions under weird situations, thereby suggesting new experiments. In a way, the non-integral charge of quarks is already the black-hole-like surprise result Feb 23, 2021 at 3:15
• @HagenvonEitzen when a theory predicts new phenomena that are found experimentally, that is called validation of the theory. If a theory does not predict new observations or new observations do not invalidate it, then it is a mathematical map of reality and can be thought as the theory of everything. Except, from euclidean times on, we find that theories have to be modified and new ones proposed, when observations become finer. The standard model has such disagreements with experiments, example CP violation cannot be completely accounted. Feb 23, 2021 at 4:55
|
2022-07-01 19:41:00
|
{"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": 23, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7506493926048279, "perplexity": 473.1724779739957}, "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/1656103945490.54/warc/CC-MAIN-20220701185955-20220701215955-00649.warc.gz"}
|
http://dergipark.gov.tr/hujms/issue/38121/439936
|
Yıl 2018, Cilt 47, Sayı 3, Sayfalar 567 - 578 2018-06-01
| | | |
## New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion
#### Hüseyin Budak [1] , Fuat Usta [2] , Mehmet Zeki Sarikaya [3]
##### 30 30
In this paper, we have been introduced and tested some significant new bounds of Ostrowski type integral inequalities. In accordance with this purpose we have taken advantageous of the Taylor expansion for functions. Some numerical experiments have been given to show the applicability and accuracy of the proposed method.
Ostrowski inequality, Taylor expansion
• G. A. Anastassiou and S. S. Dragomir, On some estimates of the remainder in Taylor's formula, J. Math. Anal. Appl. 263 (2001), no. 1, 246263.
• P. Cerone, S. S. Dragomir, J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Res. Rep. Coll., 1 (1998).
• X.-L. Cheng. Improvement of some Ostrowski-Grüss type inequalities, Computers & Mathematics with Applications, 42, 109114, 2001.
• S. S. Dragomir, S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (1997), 1520.
• S. S. Dragomir and S. Wang, An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl. 33 (1997), no. 11, 1520.
• V. N. Huy and Q. A. Ngo, New bounds for the Ostrowski-like type inequalities, Bull. Korean Math. Soc. 48 (2011) 95-104.
• A. R. Kashif, , M. Shoaib, M. A. Latif, Improved version of perturbed Ostrowski type inequalities for n-times dierentiable mappings with three-step kernel and its application, J. Nonlinear Sci. Appl. 9 (2016), 33193332.
• M. E. Kiris and M. Z. Sarikaya, On Ostrowski type inequalities and Ceby²ev type inequalities, Filomat, 29:8 (2015), 16951713.
• Z. Liu, Some OstrowskiGrüss type inequalities and applications, Comput. Math. Appl. 53 (2007) 7379.
• Z. Liu, Some Ostrowski type inequalities, Math. Comput. Modelling 48 (2008) 949960.
• W. Liu, New bounds for the companion of Ostrowski's inequality and applications, Filomat, 28 (2014), 167178.
• A. M. Ostrowski, Über die absolutabweichung einer dierentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
• M. Z. Sarikaya and H. Yaldiz, New generalization fractional inequalities of Ostrowski-Grüss type, Lobachevskii Journal of Math., 2013, Vol. 34, No. 4, pp. 326-331.
• A. Qayyum, S. Hussain, A new generalized Ostrowski Gruss type inequality and applications, Appl. Math. Lett., 25 (2012),1875-1880.
• N. Ujevi¢, New bounds for the rst inequality of Ostrowski-Grüss type and applications, Comput. Math. Appl., 46 (2003), 421427.
Birincil Dil en Matematik Matematik Yazar: Hüseyin Budak Yazar: Fuat Usta (Sorumlu Yazar) Yazar: Mehmet Zeki Sarikaya
Bibtex @araştırma makalesi { hujms439936, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {567 - 578}, doi = {}, title = {New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion}, key = {cite}, author = {Sarikaya, Mehmet Zeki and Budak, Hüseyin and Usta, Fuat} } APA Budak, H , Usta, F , Sarikaya, M . (2018). New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics, 47 (3), 567-578. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/439936 MLA Budak, H , Usta, F , Sarikaya, M . "New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion". Hacettepe Journal of Mathematics and Statistics 47 (2018): 567-578 Chicago Budak, H , Usta, F , Sarikaya, M . "New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion". Hacettepe Journal of Mathematics and Statistics 47 (2018): 567-578 RIS TY - JOUR T1 - New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion AU - Hüseyin Budak , Fuat Usta , Mehmet Zeki Sarikaya Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 567 EP - 578 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion %A Hüseyin Budak , Fuat Usta , Mehmet Zeki Sarikaya %T New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U ISNAD Budak, Hüseyin , Usta, Fuat , Sarikaya, Mehmet Zeki . "New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 567-578.
|
2018-12-10 19:27:39
|
{"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": 0.5842781662940979, "perplexity": 8630.547344629325}, "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-2018-51/segments/1544376823442.17/warc/CC-MAIN-20181210191406-20181210212906-00503.warc.gz"}
|
https://codereview.stackexchange.com/questions/134869/condensing-a-list-of-lists-with-description-lines-in-python/134872
|
# condensing a list of lists with 'description' lines in Python
I have a long list of data pulled in from a csv file that has comments / descriptions scattered throughout the document. I'd like to collapse the descriptions into the last element of each row of data, and my current solution seems slow and overly complex. Rows with data have values in the first index and description rows are empty strings. This gives me a list of lists like so:
data = [
['a', 'this', 'is', 'data', 1, 2, 3, ''],
['', '', '', 'this is a description', '', '', '', ''],
['', '', '', 'that carries onto two lines', '', '', '', ''],
['another', 'row', 'with', 'data', 0, 3, 1, ''],
['', '', '', 'this is a description', '', '', '', ''],
['', '', '', 'that carries onto three lines', '', '', '', ''],
['', '', '', 'like so', '', '', '', ''],
['data', 'with', 'no', 'description', 9, 2, 0, ''],
['b', 'this', 'is', 'data', 1, 2, 3, ''],
['', '', '', '', 'sometimes the description', 'is offset', '', '']
]
Here's what I'd like to see:
desired_data = [
['a', 'this', 'is', 'data', 1, 2, 3,
'this is a description that carries onto two lines'],
['another', 'row', 'with', 'data', 0, 3, 1,
'this is a description that carries onto three lines like so'],
['data', 'with', 'no', 'description', 9, 2, 0, None],
['b', 'this', 'is', 'data', 1, 2, 3, 'sometimes the description is offset']
]
My current solution requires creating whole new lists, one with data and one with descriptions, and then iterating over the data and searching through the descriptions each iteration:
# get numbered rows with data (first element is not '')
actual_data = [(i, x) for i, x in enumerate(data) if x[0] != '']
# get numbered rows with descriptions (first element is '')
descriptions = [(i, ' '.join([j for j in x if j != '']))
for i, x in enumerate(data) if x[0] == '']
# get just the indices of the rows with descriptions
description_indices = {i[0] for i in descriptions}
desired_data_attempt = []
for d in actual_data:
# get data to insert
x = d[1][:]
# get first index to check
n = d[0] + 1
description = []
while n in description_indices:
description.append([i[1] for i in descriptions if i[0] == n][0])
n += 1
# set empty descriptions to None; othewise create one string from list
if description == []:
x[-1] = None
else:
x[-1] = ' '.join(description)
# insert data with description
desired_data_attempt.append(x)
assert desired_data_attempt == desired_data
Ideally, I'd love to be able to construct this new object in one pass through the original data. Any suggestions would be appreciated!
You can do this in one go, just keep a data piece you are going to yield and list of comment items. If you encounter a new comment item - append to list, if you encounter a ata piece - yield one you were holding with all the comments, wipe comments and hold a new data item instead, like this:
def is_comment(item):
return item[0] == ''
def nonempty(item):
return [x for x in item if x]
result = data[0]
for element in data[1:]:
if is_comment(element):
• That's much better, thanks! I made a few tweaks so as to match the desired output exactly (values of 0 in the data were being omitted by nonempty() and empty comments weren't returning None). – Alec Jul 14 '16 at 15:18
|
2020-08-14 03:58:31
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32681286334991455, "perplexity": 6086.687727369748}, "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/1596439739134.49/warc/CC-MAIN-20200814011517-20200814041517-00446.warc.gz"}
|
https://proofwiki.org/wiki/Sequential_Continuity_is_Equivalent_to_Continuity_in_Metric_Space
|
# Sequential Continuity is Equivalent to Continuity in Metric Space
## Theorem
Let $\left({X, d}\right)$ and $\left({Y, e}\right)$ be metric spaces.
Let $f: X \to Y$ be a mapping.
Let $x \in X$.
Then $f$ is continuous at $x$ if and only if $f$ is sequentially continuous at $x$.
### Corollary
$f$ is continuous on $X$ if and only if $f$ is sequentially continuous on $X$.
## Proof
We have that a Continuous Mapping is Sequentially Continuous.
To prove the converse, by the Rule of Transposition we may prove the contrapositive:
If $f$ is not continuous at $x$, then $f$ is not sequentially continuous at $x$.
We suppose therefore that there exists $\epsilon_0 > 0$ such that for all $\delta > 0$ there exists $y \in X$ such that $d \left({x, y}\right) < \delta$ and $e \left({f \left({x}\right), f \left({y}\right)}\right) \ge \epsilon_0$.
For $n \ge 1$, define $\delta_n = \dfrac 1 n$.
For $n \ge 1$, we may choose $y_n \in X$ such that $d \left({x, y_n}\right) < \delta_n$ and $e \left({f \left({x}\right), f \left({y_n}\right)}\right) \ge \epsilon_0$.
Therefore, by definition the sequence $\left\langle{y_n}\right\rangle_{n \ge 1}$ converges to $x$.
However, by definition the sequence $\left\langle{f \left({y_n}\right)}\right\rangle_{n \ge 1}$ does not converge to $f \left({x}\right)$.
That is, $f$ is not sequentially continuous at $x$.
$\blacksquare$
|
2021-04-12 06:30:16
|
{"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": 0.9976506233215332, "perplexity": 50.73549698526927}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038066613.21/warc/CC-MAIN-20210412053559-20210412083559-00397.warc.gz"}
|
https://www.physicsforums.com/threads/basic-math-challenge-june-2018.948674/
|
# FeaturedChallenge Basic Math Challenge - June 2018
1. Jun 1, 2018
### QuantumQuest
Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread!
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all mathematicians". Whether the latter is satisfied will be decided on a case-by-case basis.
3) If you have seen the problem before and remember the solution, you cannot participate in the solution to that problem.
4) You are allowed to use google, wolframalpha or any other resource. However, you are not allowed to search the question directly. So if the question was to solve an integral, you are allowed to obtain numerical answers from software, you are allowed to search for useful integration techniques, but you cannot type in the integral in wolframalpha to see its solution.
5) Mentors, advisors and homework helpers are kindly requested not to post solutions, not even in spoiler tags, for the challenge problems, until 16th of each month. This gives the opportunity to other people including but not limited to students to feel more comfortable in dealing with / solving the challenge problems. In case of an inadvertent posting of a solution the post will be deleted by @fresh_42
$1.$ (resolved in post #62) a) Prove $(e+x)^{e-x}>(e-x)^{e+x}$ for $0<x<e.$
$\space$ $\space$ b) Show that for $0 < b < a$ we have
$\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\dfrac{1}{a} < \dfrac{2}{a+b} < \dfrac{\log (a) - \log (b)}{a-b} < \dfrac{1}{\sqrt{ab}} < \dfrac{1}{b}$
$\space$ $\space$ c) Let $f,g\, : \,[a,b]\longrightarrow \mathbb{R}$ be two monotone integrable functions, either both increasing or both decrasing. $\space$ $\space$ $\space$ $\space$ $\space$ Show that
$\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$$\space$ $\space$ $\int_a^bf(x)g(x)\,dx \ge \int_a^bf(x)\,dx \cdot \int_a^bg(x)\,dx$ $\space$ $\space$ (by @fresh_42)
$2.$ (solved by @PeroK ) One card out of a deck has been lost. The other 51 cards are repeatedly shuffled and then thirteen cards are dealt, face up. The cards are 2 spades, 3 clubs, 4 hearts, and 4 diamonds. What is the chance that the missing card is (a) spade, (b) club, (c) heart, (d)diamond $\space$ $\space$ (by @StoneTemplePython)
$3.$ (solved by @lpetrich ) Farmer Joe bought the blue area for $10,000, the green for$20,000 and the yellow for $30,000. Assuming prices are proportional to the areas, what's the price for his entire field? Figure: (by @fresh_42) $4.$ (solved by @Phylosopher ) Using only geometric reasoning, calculate the average value of $f(x) = \sqrt{2x - x^2}$ on $[0,2]$ (by @QuantumQuest) $5.$ (resolved in post #64) Can one pack 53 bricks, each of dimension $\text{1 x 1 x 4}$ in to a $\text{6 x 6 x 6}$ box? (by @StoneTemplePython) $6.$ (solved by @fishturtle1 ) Show that $a^{13} - a \equiv 0(\mod 2730)$ for all $a \in \mathbb{Z}$ $\space$ $\space$ (by @QuantumQuest) $7.$ (solved by @lpetrich ) The general solution to $y^{(4)}(x)+4y(x)=0$ is given by $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $y(x)=\alpha e^{-x}\cos (x) + \beta e^{-x}\sin (x) + \gamma e^x \sin (x) + \delta e^x \cos (x)$ a) How do we have to choose the initial conditions at $x=0$ in order to get $y(x)=e^{-x}\cos x$ as unique solution? b) Which function do we get for the initial conditions $y'(0)=1 \; , \;y''(0)=0\; , \; y'''(0)=0\; , \; y^{(4)}(0)=0\,$ ? $\space$ $\space$ (by @fresh_42) $8.$ (resolved in post #63) Find the points where the graphs of $f(x) = e^{-x}$ and $g(x) = e^{-x}\cos x$ are tangent to each other. Find another function whose graph is tangent to the graphs of the aforementioned functions in one of the contact points $\space$ $\space$ (by @QuantumQuest) $9.$ (solved by @lpetrich ) Decode: a) ZC ULX QFFY L TBXCFSB FMFS XZYVF ZC RLX AZXVDMFSFA TDSF CULY KZKCB BFLSX LPD, LYA LOO PDDA CUFDSFCZVLO IUBXZVZXCX IHC CUZX YHTQFS HI DY CUFZS RLOO LYA RDSSB LQDHC ZC b) CO PXLIX BPX Y FPRDMCPO MP KPDOM, Y BDRR LIXCAYMCPO PX VXPPB SDFM ZI WCAIO. YOFJIXF JCMU OP VXPPB JCRR ZI CWOPXIL. CM CF BCOI MP DFI OPOMXCACYR XIFDRMF JCMUPDM VXPPB YF RPOW YF EPD KCMI MUIS YOL YF RPOW YF CM CF KPSSPO QOPJRILWI MP YRR SYMUISYMCKCYOF. JUIMUIX MUI RYMMIX CF FYMCFBCIL JCRR ZI LIKCLIL PO Y KYFIZEKYFI ZYFCF. CB EPD UYAI FIIO MUI VXPZRIS ZIBPXI YOL XISISZIX MUI FPRDMCPO, EPD KYOOPM VYXMCKCVYMI CO MUI FPRDMCPO MP MUYM VXPZRIS $\space$ $\space$ (by @fresh_42) $10.$ (solved by @Mr Davis 97 ) Calculate $$\int_{\pi^{-1}}^\pi \dfrac{1}{x}\sin^2 \left( -x-\dfrac{1}{x} \right) \log x\,dx$$ (by @fresh_42) Last edited by a moderator: Jul 18, 2018 2. Jun 1, 2018 ### Wrichik Basu @QuantumQuest cannot view the image for question no. 3. Can you please check? 3. Jun 1, 2018 ### QuantumQuest @Wrichik Basu which browser are you using? I can see it from IE 11, Firefox Quantum 60.0.1 (64-bit) (latest) and Google Chrome 67.0.3396.62 (64-bit) (latest) with no problem. 4. Jun 1, 2018 ### Wrichik Basu Chrome mobile. Not the latest one. 5. Jun 1, 2018 ### QuantumQuest @Wrichik Basu do you see the image now? 6. Jun 1, 2018 ### Wrichik Basu 7. Jun 4, 2018 ### lpetrich My solution for Problem 3: I like to do analytic geometry, so I assign coordinate values to each of the points: E = {0,0}, F = {a1, 0}, A = {a1, b1}, D = {0, b1}, B = {a2, b1+b2}, C = {0, b1+b2}, G = {a2, b1} H is at the intersection of DF and EG, and its location is thus {a1*a2/(a1+a2), a1*b1/(a1+a2)}. Using the shoelace formula, the areas are ABG = (1/2)*(a1-a2)*b2 GBCD = a2*b2 EHD = (1/2)*a1*a2*b1/(a1+a2) ABCD = a1*b1 Total = ABG + GBCD + ABCD From the statement of the problem, GBCD =$20,000 and ABG = $10,000, and that gives us a1*b2 =$40,000
a2*b2 = $20,000 Since we want to find the area of ABCD, we express EHD in terms of it: EHD = (ABCD) * a2/(a1+a2) = (ABCD) * (1/3) Since EHD =$30,000, ABCD = $90,000, and the total price is ABCD + GBCD + ABG =$120,000.
8. Jun 4, 2018
### lpetrich
My solution for Problem 9a:
I will assume a simple letter-substitution code. I will make the encoded letters lowercase and the decoded letters uppercase, for ease of distinction. Initial:
zc ulx qffy l tbxcfsb fmfs xzyvf zc rlx azxvdmfsfa tdsf culy kzkcb bflsx lpd, lya loo pdda cufdsfczvlo iubxzvzxcx ihc cuzx yhtqfs hi dy cufzs rloo lya rdssb lqdhc zc
The frequency counts of letters are
{"f", 14}, {"c", 13}, {"l", 12}, {"z", 11}, {"s", 10}, {"x", 10}, {"d", 9}, {"y", 7}, {"b", 6}, {"u", 6}, {"a", 5}, {"o", 5}, {"h", 4}, {"v", 4}, {"i", 3}, {"q", 3}, {"r", 3}, {"t", 3}, {"k", 2}, {"m", 2}, {"p", 2}
suggesting that one of the first letters is "E". In English spelling, the only letter that occurs alone is "A", and there is a lone l, so l -> A. This gives us
zc uAx qffy A tbxcfsb fmfs xzyvf zc rAx azxvdmfsfa tdsf cuAy kzkcb bfAsx Apd, Aya Aoo pdda cufdsfczvAo iubxzvzxcx ihc cuzx yhtqfs hi dy cufzs rAoo Aya rdssb Aqdhc zc
Trying f -> E (14) and c -> T (13) gives us
zT uAx qEEy A tbxTEsb EmEs xzyvE zT rAx azxvdmEsEa tdsE TuAy kzkTb bEAsx Apd, Aya Aoo pdda TuEdsETzvAo iubxzvzxTx ihT Tuzx yhtqEs hi dy TuEzs rAoo Aya rdssb AqdhT zT
A common two-letter word in English is IT, so we do z->I (11):
"IT uAx qEEy A tbxTEsb EmEs xIyvE IT rAx aIxvdmEsEa tdsE TuAy kIkTb bEAsx Apd, Aya Aoo pdda TuEdsETIvAo iubxIvIxTx ihT TuIx yhtqEs hi dy TuEIs rAoo Aya rdssb AqdhT IT"
The second and third words look like they are either "HAS BEEN" or "HAD BEEN". Trying u->H (6), q->B (3), y->N (7) gives us
IT HAx BEEN A tbxTEsb EmEs xINvE IT rAx aIxvdmEsEa tdsE THAN kIkTb bEAsx Apd, ANa Aoo pdda THEdsETIvAo iHbxIvIxTx ihT THIx NhtBEs hi dN THEIs rAoo ANa rdssb ABdhT IT
The word before THAN looks like it could be MORE. Trying t->M (3), d->O (9), s->R (10) gives us
IT HAx BEEN A MbxTERb EmER xINvE IT rAx aIxvOmEREa MORE THAN kIkTb bEARx ApO, ANa Aoo pOOa THEORETIvAo iHbxIvIxTx ihT THIx NhMBER hi ON THEIR rAoo ANa rORRb ABOhT IT
The words THEORETICAL and NUMBER are almost spelled out, giving v->C (4), o->L (5), h->U (4):
IT HAx BEEN A MbxTERb EmER xINCE IT rAx aIxCOmEREa MORE THAN kIkTb bEARx ApO, ANa ALL pOOa THEORETICAL iHbxICIxTx iUT THIx NUMBER Ui ON THEIR rALL ANa rORRb ABOUT IT
I recognize EVER SINCE, PUT THIS NUMBER UP ON THEIR WALL: m->V (2), x->S (10), i->P (3), r->W (3):
IT HAS BEEN A MbSTERb EVER SINCE IT WAS aISCOVEREa MORE THAN kIkTb bEARS ApO, ANa ALL pOOa THEORETICAL PHbSICISTS PUT THIS NUMBER UP ON THEIR WALL ANa WORRb ABOUT IT
AND WORRY ABOUT IT: a->D (5), b->Y (6):
IT HAS BEEN A MYSTERY EVER SINCE IT WAS DISCOVERED MORE THAN kIkTY YEARS ApO, AND ALL pOOD THEORETICAL PHYSICISTS PUT THIS NUMBER UP ON THEIR WALL AND WORRY ABOUT IT
FIFTY YEARS AGO: k->F (2), p->G (2):
IT HAS BEEN A MYSTERY EVER SINCE IT WAS DISCOVERED MORE THAN FIFTY YEARS AGO, AND ALL GOOD THEORETICAL PHYSICISTS PUT THIS NUMBER UP ON THEIR WALL AND WORRY ABOUT IT
Complete code:
{"l" -> "A", "f" -> "E", "c" -> "T", "z" -> "I", "u" -> "H", "q" -> "B", "y" -> "N", "t" -> "M", "d" -> "O", "s" -> "R", "v" -> "C", "o" -> "L", "h" -> "U", "m" -> "V", "x" -> "S", "i" -> "P", "r" -> "W", "a" -> "D", "b" -> "Y", "k" -> "F", "p" -> "G"}
9. Jun 4, 2018
### lpetrich
My solution for Problem 9b:
I use lowercase for encoded and uppercase for decoded, as before. The letter frequencies:
{"i", 39}, {"p", 38}, {"m", 34}, {"c", 31}, {"y", 26}, {"o", 25}, {"f", 24}, {"x", 20}, {"r", 19}, {"d", 12}, {"u", 12}, {"l", 10}, {"s", 10}, {"b", 9}, {"k", 9}, {"z", 9}, {"j", 7}, {"v", 7}, {"w", 5}, {"a", 4}, {"e", 4}, {"q", 1}}
The lone letter must be A: l->A (10):
co pxlix bpx A fprdmcpo mp kpdom, A bdrr lixcaAmcpo px vxppb sdfm zi wcaio. Aofjixf jcmu op vxppb jcrr zi cwopxil. cm cf bcoi mp dfi opomxcacAr xifdrmf jcmupdm vxppb Af rpow Af epd kcmi muis Aol Af rpow Af cm cf kpsspo qopjrilwi mp Arr sAmuisAmckcAof. juimuix mui rAmmix cf fAmcfbcil jcrr zi likclil po A kAfizekAfi zAfcf. cb epd uAai fiio mui vxpzris zibpxi Aol xisiszix mui fprdmcpo, epd kAoopm vAxmckcvAmi co mui fprdmcpo mp muAm vxpzris
The repeated Af's suggest "as", with f -> S (24):
co pxlix bpx A Sprdmcpo mp kpdom, A bdrr lixcaAmcpo px vxppb sdSm zi wcaio. AoSjixS jcmu op vxppb jcrr zi cwopxil. cm cS bcoi mp dSi opomxcacAr xiSdrmS jcmupdm vxppb AS rpow AS epd kcmi muis Aol AS rpow AS cm cS kpsspo qopjrilwi mp Arr sAmuisAmckcAoS. juimuix mui rAmmix cS SAmcSbcil jcrr zi likclil po A kASizekASi zAScS. cb epd uAai Siio mui vxpzris zibpxi Aol xisiszix mui Sprdmcpo, epd kAoopm vAxmckcvAmi co mui Sprdmcpo mp muAm vxpzris
A kASizekASi zAScS suggests some singular word that ends in -S, and such a word likely has an I before it. Thus, c->I (31):
Io pxlix bpx A SprdmIpo mp kpdom, A bdrr lixIaAmIpo px vxppb sdSm zi wIaio. AoSjixS jImu op vxppb jIrr zi Iwopxil. Im IS bIoi mp dSi opomxIaIAr xiSdrmS jImupdm vxppb AS rpow AS epd kImi muis Aol AS rpow AS Im IS kpsspo qopjrilwi mp Arr sAmuisAmIkIAoS. juimuix mui rAmmix IS SAmISbIil jIrr zi likIlil po A kASizekASi zASIS. Ib epd uAai Siio mui vxpzris zibpxi Aol xisiszix mui SprdmIpo, epd kAoopm vAxmIkIvAmi Io mui SprdmIpo mp muAm vxpzris
Im IS -- a two-letter word starting with I that is likely to be a subject is IT: m->T (34):
Io pxlix bpx A SprdTIpo Tp kpdoT, A bdrr lixIaATIpo px vxppb sdST zi wIaio. AoSjixS jITu op vxppb jIrr zi Iwopxil. IT IS bIoi Tp dSi opoTxIaIAr xiSdrTS jITupdT vxppb AS rpow AS epd kITi Tuis Aol AS rpow AS IT IS kpsspo qopjrilwi Tp Arr sATuisATIkIAoS. juiTuix Tui rATTix IS SATISbIil jIrr zi likIlil po A kASizekASi zASIS. Ib epd uAai Siio Tui vxpzris zibpxi Aol xisiszix Tui SprdTIpo, epd kAoopT vAxTIkIvATi Io Tui SprdTIpo Tp TuAT vxpzris
There are some Tp's, and this means p->O (38):
Io Oxlix bOx A SOrdTIOo TO kOdoT, A bdrr lixIaATIOo Ox vxOOb sdST zi wIaio. AoSjixS jITu oO vxOOb jIrr zi IwoOxil. IT IS bIoi TO dSi oOoTxIaIAr xiSdrTS jITuOdT vxOOb AS rOow AS eOd kITi Tuis Aol AS rOow AS IT IS kOssOo qoOjrilwi TO Arr sATuisATIkIAoS. juiTuix Tui rATTix IS SATISbIil jIrr zi likIlil Oo A kASizekASi zASIS. Ib eOd uAai Siio Tui vxOzris zibOxi Aol xisiszix Tui SOrdTIOo, eOd kAooOT vAxTIkIvATi Io Tui SOrdTIOo TO TuAT vxOzris
lixIaATIOo likely ends in -ATION: o->N (25):
IN Oxlix bOx A SOrdTION TO kOdNT, A bdrr lixIaATION Ox vxOOb sdST zi wIaiN. ANSjixS jITu NO vxOOb jIrr zi IwNOxil. IT IS bINi TO dSi NONTxIaIAr xiSdrTS jITuOdT vxOOb AS rONw AS eOd kITi Tuis ANl AS rONw AS IT IS kOssON qNOjrilwi TO Arr sATuisATIkIANS. juiTuix Tui rATTix IS SATISbIil jIrr zi likIlil ON A kASizekASi zASIS. Ib eOd uAai SiiN Tui vxOzris zibOxi ANl xisiszix Tui SOrdTION, eOd kANNOT vAxTIkIvATi IN Tui SOrdTION TO TuAT vxOzris
Tui SOrdTION is likely THE SOLUTION: u->H (12), i->E (39), r->L (19), d->U (12) -- E is the most frequent one, as one might expect, though the letters after it are somewhat out of the order of their usual frequencies.
IN OxlEx bOx A SOLUTION TO kOUNT, A bULL lExIaATION Ox vxOOb sUST zE wIaEN. ANSjExS jITH NO vxOOb jILL zE IwNOxEl. IT IS bINE TO USE NONTxIaIAL xESULTS jITHOUT vxOOb AS LONw AS eOU kITE THEs ANl AS LONw AS IT IS kOssON qNOjLElwE TO ALL sATHEsATIkIANS. jHETHEx THE LATTEx IS SATISbIEl jILL zE lEkIlEl ON A kASEzekASE zASIS. Ib eOU HAaE SEEN THE vxOzLEs zEbOxE ANl xEsEszEx THE SOLUTION, eOU kANNOT vAxTIkIvATE IN THE SOLUTION TO THAT vxOzLEs
kANNOT -> CANNOT, ANl AS LONw AS -> AND AS LONG AS: "k" -> "C" (9), l->D (10), w->G (5):
IN OxDEx bOx A SOLUTION TO COUNT, A bULL DExIaATION Ox vxOOb sUST zE GIaEN. ANSjExS jITH NO vxOOb jILL zE IGNOxED. IT IS bINE TO USE NONTxIaIAL xESULTS jITHOUT vxOOb AS LONG AS eOU CITE THEs AND AS LONG AS IT IS COssON qNOjLEDGE TO ALL sATHEsATICIANS. jHETHEx THE LATTEx IS SATISbIED jILL zE DECIDED ON A CASEzeCASE zASIS. Ib eOU HAaE SEEN THE vxOzLEs zEbOxE AND xEsEszEx THE SOLUTION, eOU CANNOT vAxTICIvATE IN THE SOLUTION TO THAT vxOzLEs
COssON qNOjLEDGE TO ALL sATHEsATICIANS -> COMMON KNOWLEDGE TO ALL MATHEMATICIANS: s->M (M), q->K (1), j->W (7):
IN OxDEx bOx A SOLUTION TO COUNT, A bULL DExIaATION Ox vxOOb MUST zE GIaEN. ANSWExS WITH NO vxOOb WILL zE IGNOxED. IT IS bINE TO USE NONTxIaIAL xESULTS WITHOUT vxOOb AS LONG AS eOU CITE THEM AND AS LONG AS IT IS COMMON KNOWLEDGE TO ALL MATHEMATICIANS. WHETHEx THE LATTEx IS SATISbIED WILL zE DECIDED ON A CASEzeCASE zASIS. Ib eOU HAaE SEEN THE vxOzLEM zEbOxE AND xEMEMzEx THE SOLUTION, eOU CANNOT vAxTICIvATE IN THE SOLUTION TO THAT vxOzLEM
WHETHEx -> WHETHER, LATTEx -> LATTER, SATISbIED -> SATISFIED, eOU -> YOU: x->R (20), b->F (9), e->Y (4)
IN ORDER FOR A SOLUTION TO COUNT, A FULL DERIaATION OR vROOF MUST zE GIaEN. ANSWERS WITH NO vROOF WILL zE IGNORED. IT IS FINE TO USE NONTRIaIAL RESULTS WITHOUT vROOF AS LONG AS YOU CITE THEM AND AS LONG AS IT IS COMMON KNOWLEDGE TO ALL MATHEMATICIANS. WHETHER THE LATTER IS SATISFIED WILL zE DECIDED ON A CASEzYCASE zASIS. IF YOU HAaE SEEN THE vROzLEM zEFORE AND REMEMzER THE SOLUTION, YOU CANNOT vARTICIvATE IN THE SOLUTION TO THAT vROzLEM
DERIaATION, GIaEN, vROOF, WILL zE: a->V (4), z->B (9):
IN ORDER FOR A SOLUTION TO COUNT, A FULL DERIVATION OR vROOF MUST BE GIVEN. ANSWERS WITH NO vROOF WILL BE IGNORED. IT IS FINE TO USE NONTRIVIAL RESULTS WITHOUT vROOF AS LONG AS YOU CITE THEM AND AS LONG AS IT IS COMMON KNOWLEDGE TO ALL MATHEMATICIANS. WHETHER THE LATTER IS SATISFIED WILL BE DECIDED ON A CASEBYCASE BASIS. IF YOU HAVE SEEN THE vROBLEM BEFORE AND REMEMBER THE SOLUTION, YOU CANNOT vARTICIvATE IN THE SOLUTION TO THAT vROBLEM
vROOF, vROBLEM: v->P (7)
IN ORDER FOR A SOLUTION TO COUNT, A FULL DERIVATION OR PROOF MUST BE GIVEN. ANSWERS WITH NO PROOF WILL BE IGNORED. IT IS FINE TO USE NONTRIVIAL RESULTS WITHOUT PROOF AS LONG AS YOU CITE THEM AND AS LONG AS IT IS COMMON KNOWLEDGE TO ALL MATHEMATICIANS. WHETHER THE LATTER IS SATISFIED WILL BE DECIDED ON A CASEBYCASE BASIS. IF YOU HAVE SEEN THE PROBLEM BEFORE AND REMEMBER THE SOLUTION, YOU CANNOT PARTICIPATE IN THE SOLUTION TO THAT PROBLEM
Complete code:
{"y" -> "A", "f" -> "S", "c" -> "I", "m" -> "T", "p" -> "O", "o" -> "N", "u" -> "H", "i" -> "E", "r" -> "L", "d" -> "U", "k" -> "C", "l" -> "D", "w" -> "G", "s" -> "M", "q" -> "K", "j" -> "W", "x" -> "R", "b" -> "F", "e" -> "Y", "a" -> "V", "z" -> "B", "v" -> "P"}
10. Jun 4, 2018
### Staff: Mentor
This is correct. It is a simple Caesar code: $x \longmapsto 5x+7 (26)$. Do you know who said this?
11. Jun 4, 2018
### Staff: Mentor
Yes, correct, too. Here I used a random, but fixed mapping of letters. The frequency analysis is thus the way to decode it.
12. Jun 4, 2018
### Staff: Mentor
We already have $\,60,000$ for the known area. This means according to your calculation, that the pink area equals the sum of the others. Although the image isn't correctly scaled, I think this can't be true. One difficulty I saw, is the naming of your distances. While the $b_i$ add up, $a_1$ includes $a_2$. That's a bit disturbing and might have caused the error. I couldn't follow your formula for the height of $EHD$, which is the key to the problem.
Btw.: Could you use LaTeX code rather than to write all formulas, esp. the quotients linear?
13. Jun 4, 2018
### Mr Davis 97
Solution to problem 10:
Let $u = \log x$. Then $\displaystyle \int_{\pi^{-1}}^\pi \dfrac{1}{x}\sin^2 \left( -x-\dfrac{1}{x} \right) \log x\,dx = \int_{- \log \pi}^{\log \pi} u\sin^2 (e^u+e^{-u}) \,du$. The integrand can be seen to be an odd function. Since the limits of integration are symmetric about $0$, the value of the integral is $0$.
14. Jun 4, 2018
### Staff: Mentor
Yes, that's correct. You could have left the minus sign in the sine function, because making it a plus isn't necessary and must also be shown. The idea was to demonstrate, that there can also be a multiplicative symmetry in integrals, not only an additive. This can be seen by the substitution $u=x^{-1}$ and proving $\int = -\int \,.$ Taking the logarithm reduces it to the additive case.
15. Jun 4, 2018
### lpetrich
LaTexified version of my solution of Problem 3:
I like to do analytic geometry, so I assign coordinate values to each of the points:
E = {0,0}, F = {a1, 0}, A = {a1, b1}, D = {0, b1}, B = {a2, b1+b2}, C = {0,
b1+b2}, G = {a2, b1}
H is at the intersection of DF and EG, and its location is thus {$\frac{a1 \cdot a2}{a1+a2}$, $\frac{a1 \cdot b1}{a1+a2}$}.
Using the shoelace formula, the areas are
ABG = $\frac12 (a1-a2) \cdot b2$
GBCD = $a2 \cdot b2$
EHD = $\frac12 \frac{a1 \cdot a2 \cdot b1}{a1+a2}$
ABCD = $a1 \cdot b1$
Total = ABG + GBCD + ABCD
From the statement of the problem, GBCD = $20,000 and ABG =$10,000, and that gives us
$a1 \cdot b2$ = $40,000 $a2 \cdot b2$ =$20,000
Since we want to find the area of ABCD, we express EHD in terms of it:
EHD = (ABCD) * $\frac{a2}{a1+a2}$ = (ABCD) * $\frac13$
Since EHD = $30,000, ABCD =$90,000, and the total price is ABCD + GBCD + ABG = $120,000. 16. Jun 4, 2018 ### fresh_42 ### Staff: Mentor You have to prove the coordinates for H, resp. the height of the triangle, and it is asked for the prize of the area of ABCEF which is not$120,000.
17. Jun 6, 2018
### lpetrich
The missing parts of Problem 3, and correction of an error in my original solution:
H is at the intersection of EG and DF. So its location is
(H) = (1-t1)*(E) + (t1)*(G) = (1-t2)*(D) + (t2)*(F)
where t1 and t2 are parameters for points along those two lines.
$$(1-t1)\{0,0\} + (t1)\{a2,b1\} = (1-t2)\{0,b1\} + (t2)\{a1,0\}$$
giving
$$t1 \cdot a2 = t2 \cdot a1 \\ t1 \cdot b1 = (1 - t2) \cdot b1$$
This gives us t2 = 1 - t1 and
$$\frac{t1}{1-t1} = \frac{a1}{a2}$$
Solving for t1 gives us
$$t1 = \frac{a1}{a1 + a2} ,\ t2 = \frac{a2}{a1 + a2}$$
and the coordinates of point H:
$$(H) = \frac{a1}{a1+a2} \{ a2, b1 \}$$
Applying a triangle area formula with (base) = b1 and (height) = first coordinate of above, I find
$$\text{(area of EHD)} = \frac12 \frac{a1 \cdot a2 \cdot b1}{a1 + a2}$$
The total area (ABCEF) = (ABG) + (BCDG) + (ADEF) with
$$\text{(ABG)} = \frac12 (a1 - a2) \cdot b2 ,\, \text{(BCDG)} = a2 \cdot b2 ,\, \text{(ADEF)} = a1 \cdot b1$$
From the problem statement, the area ratio (BCDG)/(ABG) = ($20,000)/($10,000) = 2, and (EHD)/(ABG) = 3, giving
$$a2 \cdot b2 = 2 \cdot \frac12 (a1 - a2) \cdot b2 ,\, \frac12 \frac{a1 \cdot a2 \cdot b1}{a1 + a2} = 3 \cdot \frac12 (a1 - a2) \cdot b2$$
Solving the first one gives a1 = 2*a2, and solving the second one gives b1 = (9/2)*b2. Thus, area (ADEF) = a1*b1 = 9*(a2*b2).
Area (ABG) = (1/2)*(a2*b2), thus (ADEF) = 18 * (ABG), and is thus $180,000. Adding the prices of ABG and BCDG,$10,000 and $20,000, I find$210,000.
18. Jun 6, 2018
### Staff: Mentor
That's better, as one almost actually can read what you've done, and correct. Just a little request for future posts: Please write your variables $a2=a_2$ which is a_2. Otherwise your readers might confuse indices with coefficients. It looks more like code than mathematics.
19. Jun 6, 2018
### lpetrich
Solution for Problem 7:
I will express the general solution of $y^{(4)}(x) + 4y(x) = 0$ as
$$y(x) = c_1 e^x \cos x + c_2 e^x \sin x + c_3 e^{-x} \cos x + c_4 e^{-x} \sin x$$
I calculated the Wronskian of the four terms, and I found it to be 32. So the solutions are linearly independent, and the values of derivatives 0, 1, 2, and 3 at any x value thus suffice to determine the c's.
(a) To find the initial conditions, take the first three derivatives of $y(x) = e^{-x} \cos x$ and find their values at 0.
$$y(x) = e^{-x} \cos x \\ y'(x) = -e^{-x} (\cos x + \sin x) \\ y''(x) = 2e^{-x} \sin x \\ y'''(x) = 2e^{-x} (\cos x - \sin x)$$
giving us
$$y(0) = 1 ,\, y'(0) = -1 \,\ y''(0) = 0, y'''(0) = 2$$
(b) We take four derivatives of the general solution, and then find their value at x = 0.
$$y(x) = c_1 e^x \cos x + c_2 e^x \sin x + c_3 e^{-x} \cos x + c_4 e^{-x} \sin x \\ y'(x) = c_1 e^x (\cos x - \sin x) + c_2 e^x (\cos x + \sin x) - \\ c_3 e^{-x} (\cos x + \sin x) + c_4 e^{-x} (\cos x - \sin x) \\ y''(x) = -2 c_1 e^x \sin x + 2 c_2 e^x \cos x + 2 c_3 e^{-x} \sin x - 2 c_4 e^{-x} \cos x \\ y'''(x) = -2 c_1 e^x (\cos x + \sin x) + 2 c_2 e^x (\cos x - \sin x) + \\ 2 c_3 e^{-x} (\cos x - \sin x) + 2 c_4 e^{-x} (\cos x + \sin x) \\ y^{(4)}(x) = -4 y(x)$$
At x = 0,
$$y(0) = c_1 + c_3 ,\, y'(0) = c_1 + c_2 - c_3 + c_4 ,\, y''(0) = 2 (c_2 - c_4) ,\, \\ y'''(0) = 2(-c_1 + c_2 + c_3 + c_4) ,\, y^{(4)}(0) = -4(c1 + c3)$$
Setting all but the first of them equal to
$$y'(0) = 1 ,\, y''(0) = 0 ,\, y'''(0) = 0 ,\, y^{(4)}(0) = 0$$
gives the solution
$$c_1 = \frac14 ,\, c_2 = \frac14 ,\, c_3 = - \frac14 ,\, c_4 = \frac14$$
and
$$y(x) = \frac14 \left( e^x \cos x + e^x \sin x - e^{-x} \cos x + e^{-x} \sin x \right)$$
20. Jun 6, 2018
### fishturtle1
For 6)
Proof: We make use of Euler's totient function and Euler's theorem through out the proof. Observe, odds are closed under multiplication and evens are closed under multiplication so $a^{13} \equiv a (\operatorname{mod} 2)$. Also, $a^{13} \equiv (a^2)^6\cdot a \equiv a (\operatorname{mod} 3)$. So $a^{13} \equiv a (\operatorname{mod} 3)$. Also, $a^{13} \equiv (a^4)^3\cdot a (\operatorname{mod} 5)$. So $a^{13} \equiv a (\operatorname{mod} 5)$. Also, $a^{13} \equiv (a^6)^2\cdot a \equiv a (\operatorname{mod} 7)$. So $a^{13} \equiv a (\operatorname{mod} 7)$. Finally, $a^{13} \equiv a^{12}\cdot a (\operatorname{mod} 13)$. So $a^{13} \equiv a (\operatorname{mod} 13$.
By Chinese Remainder theorem, we can conclude $a^{13} \equiv a (\operatorname{mod} 2\cdot 3\cdot 5\cdot 7\cdot 13)$ that is, $a^{13} \equiv a (\operatorname{mod} 2730)$.
[\SPOILER]
Last edited: Jun 6, 2018
|
2018-08-17 17:17:04
|
{"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": 0.9996213316917419, "perplexity": 4006.391984121643}, "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-2018-34/segments/1534221212639.36/warc/CC-MAIN-20180817163057-20180817183057-00715.warc.gz"}
|
http://mathhelpforum.com/calculus/212848-integration-partial-fractions-problem.html
|
# Thread: Integration by partial fractions problem
1. ## Integration by partial fractions problem
Hey guys,
I have a homework question that I found a little tricky. I ended up getting an answer but I was hoping for some verification, because I don't feel like I did it correctly. My answer is based on an online integrator, and I know this paper is a bit scattered and difficult to make sense of, so the original equation is on top, the factored version is below the denominator, I did u-substitution to double-check under that, changed it to fractions, and solved for A and B then my answer is on the last line.
Also, if it turns out my answer is correct, I'm a tiny bit confused on how the online integrator got such an answer for both separate integrals and a short explanation of how it ended up being that answer would be great. Any help in general is appreciated, I've been stuck on this problem for two days now so it'd be great to knock it out finally.
2. ## Re: Integration by partial fractions problem
The u in the numerator of your integral should not be there.
$\displaystyle dx=\frac{du}{u}$
3. ## Re: Integration by partial fractions problem
Would that make the integral I'm left with $\displaystyle \int \frac {1}{u^2-3u+2} \,dx$ or would the denominator be affected by my error also?
4. ## Re: Integration by partial fractions problem
Originally Posted by billb91
Would that make the integral I'm left with $\displaystyle \int \frac {1}{u^2-3u+2} \,dx$ or would the denominator be affected by my error also?
Not quite. That dx should be du.
5. ## Re: Integration by partial fractions problem
Oh, sorry, that was what I originally meant. I wasn't being careful when typing it out. :P
Thanks for the help though! I haven't actually gone and solved it yet, but I already know that my new equation will be a LOT easier to solve.
6. ## Re: Integration by partial fractions problem
integral(1/u^2-3y+2)du=?
partial fraction first factor denominator : (u-2)(u-1)... then let A/u-2 +B/(u-1)... then multiply [A(u-2) +B(u-1)]/(u-1)(u-2).... first we concentrate on the numerator.. first expand then collect like terms.. you'll end up with Au-2A+Bu-B... note that Au+Bu=0.. this is because if you look at the original equation that 1/u^2-3u+2.... there is no number with the integer 'u'? right? and the -2A-B=1.. since the constant is 1... then do linear of equation.. to get A and B then substitute.. there you have decompose or split the fraction into two.
7. ## Re: Integration by partial fractions problem
Awesome, thanks for the help! Could anyone verify my answer for this one?
|
2018-03-20 16:19:42
|
{"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": 0.9101296067237854, "perplexity": 550.8283403983427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647498.68/warc/CC-MAIN-20180320150533-20180320170533-00655.warc.gz"}
|
http://h2o-release.s3.amazonaws.com/h2o/master/3888/docs-website/h2o-docs/starting-h2o.html
|
# Starting H2O¶
There are a variety of ways to start H2O, depending on which client you would like to use. The instructions below assume that you already downloaded and installed H2O. If you have not, then please refer to the Downloading & Installing H2O section.
## From R¶
Use the h2o.init() method to initialize H2O. This method accepts the following options. Note that in most cases, simply using h2o.init() is all that a user is required to do.
• nthreads: This launches H2O using all available CPUs and is only applicable if you launch H2O locally using R. If you start H2O locally outside of R or start H2O on Hadoop, the nthreads parameter is not applicable.
• ip: The IP address of the server where H2O is running.
• port: The port number of the H2O server.
• startH2O: (Optional) A logical value indicating whether to try to start H2O from R if no connection with H2O is detected. This is only possible if ip = "localhost" or ip = "127.0.0.1". If an existing connection is detected, R does not start H2O.
• forceDL: (Optional) A logical value indicating whether to force download of the H2O executable. This defaults to FALSE, so the executable will only be downloaded if it does not already exist in the H2O R library resources directory at h2o/java/h2o.jar.
• enable_assertions: (Optional) A logical value indicating whether H2O should be launched with assertions enabled. This is used mainly for error checking and debugging purposes.
• license: (Optional) A character string value specifying the full path of the license file.
• max_mem_size: (Optional) A character string specifying the maximum size, in bytes, of the memory allocation pool to H2O. This value must a multiple of 1024 greater than 2MB. Append the letter m or M to indicate megabytes, or g or G to indicate gigabytes.
• min_mem_size: (Optional) A character string specifying the minimum size, in bytes, of the memory allocation pool to H2O. This value must a multiple of 1024 greater than 2MB. Append the letter m or M to indicate megabytes, or g or G to indicate gigabytes.
• ice_root: (Optional) A directory to handle object spillage. The default varies by OS.
• strict_version_check: (Optional) Setting this to FALSE is unsupported and should only be done when advised by technical support.
• ignore_config: (Optional) This option allows you to specify whether to perform processing of a .h2oconfig file. When h2o.init() is specified, a call to a config reader method is invoked. This call can result in path issues when there is no “root” (for example, with a Windows network drive) because the config file reader searches up to “root.” When there is no “root”, the path to search will continue to expand, eventually result in an error. This value defaults to False.
• proxy: (Optional) A character string specifying the proxy path.
• https: (Optional) Set this to TRUE to use https instead of http.
• insecure: (Optional) Set this to TRUE to disable SSL certificate checking.
• username: (Optional) The username to log in with.
• password: (Optional) The password to log in with.
• cookies: (Optional) Vector (or list) of cookies to add to request.
• context_path: (Optional) The last part of connection URL. For example, http://<ip>:<port>/<context_path>
By default, h2o.init() first checks if an H2O instance is connectible. If it cannot connect and start = TRUE with ip = "localhost", it will attempt to start an instance of H2O at localhost:54321. If an open ip and port of your choice are passed in, then this method will attempt to start an H2O instance at that specified ip and port.
When initializing H2O locally, this method searches for the h2o.jar file in the R library resources (system.file(“java”, “h2o.jar”, package = “h2o”)), and if the file does not exist, it will automatically attempt to download the correct version from Amazon S3. The user must have Internet access for this process to be successful.
Once connected, the h2o.init() method checks to see if the local H2O R package version matches the version of H2O running on the server. If there is a mismatch and the user indicates he/she wants to upgrade, it will remove the local H2O R package and download/install the H2O R package from the server.
Note: You may want to manually upgrade your package rather than waiting until being prompted. This requires that you fully uninstall and reinstall the H2O package and the H2O client package. You must unload packages running in the environment before upgrading. We also recommended that you restart R or R studio after upgrading.
### Example¶
library h2o
h2o.init()
H2O is not running yet, starting it now...
Note: In case of errors look at the following log files:
/var/folders/yl/cq5nhky53hjcl9wrqxt39kz80000gn/T//RtmpKtZXsy/h2o_techwriter_started_from_r.out
/var/folders/yl/cq5nhky53hjcl9wrqxt39kz80000gn/T//RtmpKtZXsy/h2o_techwriter_started_from_r.err
java version "1.8.0_25"
Java(TM) SE Runtime Environment (build 1.8.0_25-b17)
Java HotSpot(TM) 64-Bit Server VM (build 25.25-b02, mixed mode)
Starting H2O JVM and connecting: .. Connection successful!
R is connected to the H2O cluster:
H2O cluster uptime: 2 seconds 812 milliseconds
H2O cluster version: 3.10.4.3
H2O cluster version age: 9 days
H2O cluster name: H2O_started_from_R_techwriter_awt197
H2O cluster total nodes: 1
H2O cluster total memory: 3.56 GB
H2O cluster total cores: 8
H2O cluster allowed cores: 8
H2O cluster healthy: TRUE
H2O Connection ip: localhost
H2O Connection port: 54321
H2O Connection proxy: NA
H2O Internal Security: FALSE
R Version: R version 3.2.2 (2015-08-14)
## From Python¶
Use the h2o.init() function to initialize H2O. This function accepts the following options. Note that in most cases, simply using h2o.init() is all that a user is required to do.
• url: Full URL of the server to connect to. (This can be used instead of ip + port + https.)
• ip: The ip address (or host name) of the server where H2O is running.
• port: Port number that H2O service is listening to.
• https: Set to True to connect via https:// instead of http://.
• insecure: When using https, setting this to True will disable SSL certificates verification.
• username: The username to log in with when using basic authentication.
• password: The password to log in with when using basic authentication.
• cookies: Cookie (or list of) to add to each request.
• proxy: The proxy server address.
• start_h2o: If False, do not attempt to start an H2O server when a connection to an existing one failed.
• nthreads: “Number of threads” option when launching a new H2O server.
• ice_root: The directory for temporary files for the new H2O server.
• enable_assertions: Enable assertions in Java for the new H2O server.
• max_mem_size: Maximum memory to use for the new H2O server.
• min_mem_size: Minimum memory to use for the new H2O server.
• strict_version_check: If True, an error will be raised if the client and server versions don’t match.
### Example¶
python
import h2o
h2o.init(ip="localhost", port=54323)
Checking whether there is an H2O instance running at http://localhost:54323..... not found.
Attempting to start a local H2O server...
Java Version: java version "1.8.0_25"; Java(TM) SE Runtime Environment (build 1.8.0_25-b17); Java HotSpot(TM) 64-Bit Server VM (build 25.25-b02, mixed mode)
Starting server from /Users/techwriter/anaconda/lib/python2.7/site-packages/h2o/backend/bin/h2o.jar
Ice root: /var/folders/yl/cq5nhky53hjcl9wrqxt39kz80000gn/T/tmpN2xfkW
JVM stdout: /var/folders/yl/cq5nhky53hjcl9wrqxt39kz80000gn/T/tmpN2xfkW/h2o_techwriter_started_from_python.out
JVM stderr: /var/folders/yl/cq5nhky53hjcl9wrqxt39kz80000gn/T/tmpN2xfkW/h2o_techwriter_started_from_python.err
Server is running at http://127.0.0.1:54323
Connecting to H2O server at http://127.0.0.1:54323... successful.
-------------------------- ---------------------------------
H2O cluster uptime: 02 secs
H2O cluster version: 3.10.4.3
H2O cluster version age: 9 days
H2O cluster name: H2O_from_python_techwriter_pu6lbs
H2O cluster total nodes: 1
H2O cluster free memory: 3.556 Gb
H2O cluster total cores: 8
H2O cluster allowed cores: 8
H2O cluster status: accepting new members, healthy
H2O connection url: http://127.0.0.1:54323
H2O connection proxy:
H2O internal security: False
Python version: 2.7.12 final
-------------------------- ---------------------------------
### From Anaconda¶
This section describes how run H2O in an Anaconda Cloud environment. This section assumes that you have installed H2O on Anaconda using the instructions in the Install on Anaconda Cloud section.
#### Launching Jupyter Notebook¶
1. Open a Terminal window and launch jupyter notebook.
user\$ jupyter notebook
2. Create a new Python notebook by selecting the New button in the upper left corner. At this point, you can begin using Jupyter Notebook to run H2O Python commands. An example notebook follows.
#### GBM Example¶
After you successfully launch Jupyter notebook, enter the following commands to run a GBM example.
1. Import the H2O and GBM modules.
1. Initialize H2O using h2o.init().
1. Import the Airlines dataset. This dataset will be used to classify whether a flight will be delayed.
1. Convert columns to factors.
1. Set the predictor names and the response column name.
1. Split the dataset into training and validation sets.
1. Specify the number of bins that will be included in the historgram and then split.
1. Train the models.
1. Print the AUC scores for the training data and the validation data.
#### Troubleshooting¶
If your system includes two versions of Anaconda (a global installation and a user-specific installation), be sure to use the User Anaconda. Using the Global Anaconda will result in an error when you attempt to run commands in Jupyter Notebook. You can verify the version that you are using by running which pip (Mac) or where pip (Windows). If your system shows that your environment is set up to use Global Anaconda by default, then change the PATH environment variable to use the User Anaconda.
## From the Command Line¶
You can use Terminal (OS X) or the Command Prompt (Windows) to launch H2O.
When you launch from the command line, you can include additional instructions to H2O 3.0, such as how many nodes to launch, how much memory to allocate for each node, assign names to the nodes in the cloud, and more.
Note: H2O requires some space in the /tmp directory to launch. If you cannot launch H2O, try freeing up some space in the /tmp directory, then try launching H2O again.
For more detailed instructions on how to build and launch H2O, including how to clone the repository, how to pull from the repository, and how to install required dependencies, refer to the developer documentation.
There are three different argument types:
• JVM options
• H2O options
• Authentication options
The arguments use the following format: java <JVM Options> -jar h2o.jar <H2O Options>.
### JVM Options¶
• -version: Display Java version info.
• -Xmx<Heap Size>: To set the total heap size for an H2O node, configure the memory allocation option -Xmx. By default, this option is set to 1 Gb (-Xmx1g). When launching nodes, we recommend allocating a total of four times the memory of your data.
Note: Do not try to launch H2O with more memory than you have available.
### H2O Options¶
• -h or -help: Display this information in the command line output.
• -version: Specify to print version information and exit.
• -name <H2OCloudName>: Assign a name to the H2O instance in the cloud (where <H2OCloudName> is the name of the cloud). Nodes with the same cloud name will form an H2O cloud (also known as an H2O cluster).
• -flatfile <FileName>: Specify a flatfile of IP address for faster cloud formation (where <FileName> is the name of the flatfile).
• -ip <IPnodeAddress>: Specify an IP for the machine other than the default localhost, for example:
• IPv4: -ip 178.16.2.223
• IPv6: -ip 2001:db8:1234:0:0:0:0:1 (Short version of IPv6 with :: is not supported.) Note: If you are selecting a link-local address fe80::/96, it is necessary to specify the zone index (e.g., %en0 for fe80::2acf:e9ff:fe15:e0f3%en0) in order to select the right interface.
• -port <#>: Specify a PORT used for REST API. The communication port will be the port with value +1 higher.
• -baseport: Specifies the starting port to find a free port for REST API, the internal communication port will be port with value +1 higher.
• -network <ip_address/subnet_mask>: Specify an IP addresses with a subnet mask. The IP address discovery code binds to the first interface that matches one of the networks in the comma-separated list; to specify an IP address, use -network. To specify a range, use a comma to separate the IP addresses: -network 123.45.67.0/22,123.45.68.0/24. For example, 10.1.2.0/24 supports 256 possibilities. IPv4 and IPv6 addresses are supported.
• IPv4: -network 178.0.0.0/8
• IPv6: -network 2001:db8:1234:0:0:0:0:0/48 (short version of IPv6 with :: is not supported.)
• -ice_root <fileSystemPath>: Specify a directory for H2O to spill temporary data to disk (where <fileSystemPath> is the file path).
• -log_dir <fileSystemPath>\: Specify the directory where H2O writes logs to disk. (This usually has a good default that you need not change.
• -log_level <TRACE,DEBUG,INFO,WARN,ERRR,FATAL>: Specify to write messages at this logging level, or above. The default is INFO.
• -flow_dir <server-side or HDFS directory>: Specify a directory for saved flows. The default is /Users/h2o-<H2OUserName>/h2oflows (where <H2OUserName> is your user name).
• -nthreads <#ofThreads>: Specify the maximum number of threads in the low-priority batch work queue (where <#ofThreads> is the number of threads).
• -client: Launch H2O node in client mode. This is used mostly for running Sparkling Water.
• -context_path <context_path>: The context path for jetty.
### Authentication Options¶
• -jks <filename>: Specify a Java keystore file.
• -jks_pass <password>: Specify the Java keystore password.
• -hash_login: Specify to use Jetty HashLoginService. This defaults to False.
• -ldap_login: Specify to use Jetty LdapLoginService. This defaults to False.
• -kerberos_login: Specify to use Kerberos LoginService. This defaults to False.
• -pam_login: Specify to use the Pluggable Authentication Module (PAM) LoginService. This defaults to False.
• -login_conf <filename>: Specify the LoginService configuration file.
• -form_auth: Enables Form-based authentication for Flow. This defaults to Basic authentication.
• -session_timeout <minutes>: Specifies the number of minutes that a session can remain idle before the server invalidates the session and requests a new login. Requires -form_auth. This defaults to no timeout.
• -internal_security_conf <filename>: Specify the path (absolute or relative) to a file containing all internal security related configurations.
### H2O Internal Communication¶
By default, H2O selects the IP and PORT for internal communication automatically using the following this process (if not specified):
1. Retrieve a list of available interfaces (which are up).
2. Sort them with “bond” interfaces put on the top.
3. For each interface, extract associated IPs.
4. Pick only reachable IPs (that filter IPs provided by interfaces, such as awdl):
• If there is a site IP, use it.
• Otherwise, if there is a link local IP, use it. (For IPv6, the link IP 0xfe80/96 is associated with each interface.)
• Or finally, try to find a local IP. (Use loopback or try to use Google DNS to find IP for this machine.)
Notes: The port is selected by looking for a free port starting with port 54322. The IP, PORT and network selection can be changed by the following options:
• -ip
• network
• -port
• -baseport
### Cloud Formation Behavior¶
New H2O nodes join to form a cloud during launch. After a job has started on the cloud, it prevents new members from joining.
• To start an H2O node with 4GB of memory and a default cloud name: java -Xmx4g -jar h2o.jar
• To start an H2O node with 6GB of memory and a specific cloud name: java -Xmx6g -jar h2o.jar -name MyCloud
• To start an H2O cloud with three 2GB nodes using the default cloud names: java -Xmx2g -jar h2o.jar & java -Xmx2g -jar h2o.jar & java -Xmx2g -jar h2o.jar &
Wait for the INFO: Registered: # schemas in: #mS output before entering the above command again to add another node (the number for # will vary).
### Clouding Up: Cluster Creation¶
H2O provides two modes for cluster creation:
• Multicast based
• Flatfile based
#### Multicast¶
In this mode, H2O is using IP multicast to announce existence of H2O nodes. Each node selects the same multicast group and port based on specified shared cloud name (see -name option). For example, for IPv4/PORT a generated multicast group is 228.246.114.236:58614 (for cloud name michal), for IPv6/PORT a generated multicast group is ff05:0:3ff6:72ec:0:0:3ff6:72ec:58614 (for cloud name michal and link-local address which enforce link-local scope).
For IPv6 the scope of multicast address is enforced by a selected node IP. For example, if IP the selection process selects link-local address, then the scope of multicast will be link-local. This can be modified by specifying JVM variable sys.ai.h2o.network.ipv6.scope which enforces addressing scope use in multicast group address (for example, -Dsys.ai.h2o.network.ipv6.scope=0x0005000000000000 enforces the site local scope. For more details please consult the class water.util.NetworkUtils).
For more information about scopes, see the following image.
#### Flatfile¶
The flatfile describes a topology of a H2O cluster. The flatfile definition is passed via the -flatfile option. It needs to be passed at each node in the cluster, but definition does not be the same at each node. However, transitive closure of all definitions should contains all nodes. For example, for the following definition
Nodes nodeA nodeB nodeC Flatfile A,B A, B B, C
The resulting cluster will be formed by nodes A, B, C. The node A transitively sees node C via node B flatfile definition, and vice versa.
The flatfile contains a list of nodes in the form IP:PORT that are going to compose a resulting cluster (each node on a separated line, everything prefixed by # is ignored). Running H2O on a multi-node cluster allows you to use more memory for large-scale tasks (for example, creating models from huge datasets) than would be possible on a single node.
IPv4:
# run two nodes on 108
10.10.65.108:54322
10.10.65.108:54325
IPv6:
0:0:0:0:0:0:0:1:54321
0:0:0:0:0:0:0:1:54323
### Web Server¶
The web server IP is auto-configured in the same way as internal communication IP, nevertheless the created socket listens on all available interfaces. A specific API can be specified with the -web_ip option.
#### Options¶
• -web_ip: specifies IP for web server to expose REST API
### Dual Stacks¶
Dual stack machines support IPv4 and IPv6 network stacks. Right now, H2O always prefer IPV4, however the preference can be changed via JVM system options java.net.preferIPv4Addresses and java.net.preferIPv6Addresses. For example:
• -Djava.net.preferIPv6Addresses=true -Djava.net.preferIPv4Addresses=true - H2O will try to select IPv4
• -Djava.net.preferIPv6Addresses=true -Djava.net.preferIPv4Addresses=false - H2O will try to select IPv6
## On Spark¶
Refer to the Getting Started with Sparkling Water section for information on how to launch H2O on Spark.
|
2019-04-26 11:46:30
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17693930864334106, "perplexity": 9392.120171314087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578770163.94/warc/CC-MAIN-20190426113513-20190426135513-00195.warc.gz"}
|
https://codefreshers.com/make-palindrome-2-solution-codechef/
|
# [Solution] Make Palindrome 2 solution codechef
Make Palindrome 2 solution codechef – You are given a binary string SS of length NN. You want to obtain a palindrome from SS by applying the following operation at most N2⌊N2⌋ times:
• Choose an index i(1i|S|)i(1≤i≤|S|), delete the character SiSi from SS and concatenate the remaining parts of the string. Here |S||S| denotes the current length of string SS.
## [Solution] Make Palindrome 2 solution codechef
For example, if S=S= 11010, then applying the operation on index i=2i=2 makes S=S= 1010.
Note that after each operation, the length of the string SS decreases by one.
Find any palindrome you can obtain after the operations. It can be proved that it is always possible to obtain a palindrome from SS under the given constraints.
Here, N2⌊N2⌋ denotes floor division of the integer NN by 22. For example, 52=2⌊52⌋=282=4⌊82⌋=4. A binary string is a string that consists of only the characters 0 and 1.
### Input Format
• The first line of input contains an integer TT, denoting the number of test cases. The TT test cases then follow:
• The first line of each test case contains an integer NN, denoting the length of the binary string SS.
• The second line of each test case contains the binary string SS.
## [Solution] Make Palindrome 2 solution codechef
For each test case, print on a separate line any palindromic string that can be obtained from SS by applying the given operation at most N2⌊N2⌋ times.
### Constraints
• 1T10001≤T≤1000
• 1N1001≤N≤100
• SS contains only the characters 0 and 1.
### Sample Input 1
4
3
101
3
001
4
1011
6
010011
## [Solution] Make Palindrome 2 solution codechef
101
00
111
1001
### Explanation
Test case 11: The given string is already a palindrome.
Test case 22: Applying the operation on index i=3i=3 makes S=S= 00 which is a palindrome.
Test case 33: Applying the operation on index i=2i=2 makes S=S= 111 which is a palindrome.
Test case 44: Applying the operation on index i=1i=1 makes S=S= 10011. Then applying the operation on index i=5i=5 makes S=S= 1001 which is a palindrome.
|
2022-08-10 23:34:35
|
{"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": 0.6782417893409729, "perplexity": 602.0280120425539}, "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/1659882571222.74/warc/CC-MAIN-20220810222056-20220811012056-00767.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-8-section-8-4-circumference-and-area-of-a-circle-exercises-page-373/16
|
## Elementary Geometry for College Students (6th Edition)
Given the area of the circle = 56.35 $in^{2}$ to find the approximate lengths of the radius and the diameter of a circle The area A of a circle whose radius has length r is given by A = $\pi r^{2}$ 56.35 = $\pi r^{2}$ $r^{2}$ = $\frac{56.35}{3.14}$ r = $\sqrt 17.94$ = 4.23 in The radius of the circle r = 4.23 in The diameter of the circle = 2 * r = 2 * 4.23 = 8.470 in
|
2021-03-01 20:12:49
|
{"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": 0.7282505631446838, "perplexity": 147.26235065902156}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362899.14/warc/CC-MAIN-20210301182445-20210301212445-00100.warc.gz"}
|
https://solvedlib.com/n/an-dirline-gt-rcvcnuc-r-functionthe-numbct-otnull-price,1156659
|
# An dirline > rcvcnuc, R,functionthe numbct otnull-price tckelInt; numbcrdisounc cicketsscla_ valtes R=jk"table below.Numbtr pllull-orc licrctsZi 20m) 75M I0,Uu 145,0 S0,(KM
###### Question:
An dirline > rcvcnuc, R, function the numbct otnull-price tckel Int; numbcr disounc cickets scla_ valtes R=jk" table below. Numbtr pllull-orc licrcts Zi 20m) 75M I0,Uu 145,0 S0,(KM Number IS,( 150,QU 185 (UO 220,(uU discount tckets 6uQ 155,(0 190,000 225,000 260,00 Xu) 195,() 230,(KMI 265,() SO) (K) ICM) 235,Un 270.u0O 305,U00 340,000 Eydlual (3(X), G(XV) , and Interpret Vout ansmct f (Ju0, 6uu)
#### Similar Solved Questions
##### Which of the following GC 9 ?detectors called catherometer (&bii 1.5)flame ionization detectorelectron capture detectormass spectrometer detectorthermal conductivity detectoratomic emission detector
Which of the following GC 9 ?detectors called catherometer (&bii 1.5) flame ionization detector electron capture detector mass spectrometer detector thermal conductivity detector atomic emission detector...
##### DESIGN. For Exercises $36-38,$ use the following information. Jill is designing a picture frame for an art project. She plans to have a square piece of glass in the center and surround it with a decorated ceramic frame, which will also be a square. The dimensions of the glass and frame are shown in the diagram at the right. jill determines that she needs 27 square inches of material for the frame.What are the dimensions of the glass piece?
DESIGN. For Exercises $36-38,$ use the following information. Jill is designing a picture frame for an art project. She plans to have a square piece of glass in the center and surround it with a decorated ceramic frame, which will also be a square. The dimensions of the glass and frame are shown in ...
##### Question 1(2 01 30 Separe deiecuve ofthe computers are selected random without replacement: What _ the probabil certain shipment of /8 computers Trartior decima numde qundeg rour decima places_ that 4 of the computers are delective? Express Your answerTablesKeypdERiant hawEntethpaint
Question 1(2 01 30 Sep are deiecuve ofthe computers are selected random without replacement: What _ the probabil certain shipment of /8 computers Trartior decima numde qundeg rour decima places_ that 4 of the computers are delective? Express Your answer Tables Keypd ERiant haw Enteth paint...
##### 2. UART (10 pts) Draw the UART protocol data exchange for the data (Ox C5, 0x 29) using 8E1 (8 bi...
2. UART (10 pts) Draw the UART protocol data exchange for the data (Ox C5, 0x 29) using 8E1 (8 bits of data, even parity, 1 stop bit). Label the frames. If the baud rate is 300 bps, what is the data rate? Why does the receiver have to sample this data? 2. UART (10 pts) Draw the UART protocol data e...
##### Complete the reaction H, H Dula C sourte
complete the reaction H, H Dula C sourte...
##### Calculus1. Determine the limits: lin(3-5 (T33]Jin (+9 2+1 (T3]
Calculus 1. Determine the limits: lin(3-5 (T33] Jin (+9 2+1 (T3]...
##### Cleze J: G,2,0 &F,6 Sixplc : 6 , € ,69 E) H po sYJ^ :8, € ) E only Unsu X8& 1 kec ! E pe Ts D Sinple 0 [ ( Polraen 8
cleze J: G,2,0 &F,6 Sixplc : 6 , € ,69 E) H po sYJ^ :8, € ) E only Unsu X8& 1 kec ! E pe Ts D Sinple 0 [ ( Polraen 8...
##### Part A Review What is the final temperature of the cylinder? Express your answer to two...
Part A Review What is the final temperature of the cylinder? Express your answer to two significant figures and include the appropriate unit:s A 12 cm -diameter cylinder contains argon gas at 10 atm pressure and a temperature of 55 piston can slide in and out of the cylinder. The cylinder's init...
##### Score: 0 of pt10 of 13 (5 complete)HW Score: 26.92%, 3.5 of 13 pts5.2.15Question HelpGraph the solution of the following systemX -3y 2 2x+y <Use the graphing tool to graph the systemClick to enlarge graph
Score: 0 of pt 10 of 13 (5 complete) HW Score: 26.92%, 3.5 of 13 pts 5.2.15 Question Help Graph the solution of the following system X -3y 2 2x+y < Use the graphing tool to graph the system Click to enlarge graph...
##### What is the mass of 0.76 moles of the cupric sulfate salt CuSO4.5H2O?
What is the mass of 0.76 moles of the cupric sulfate salt CuSO4.5H2O?...
##### N galvanometer of range sv. 2) The deflection of galvanometre falls from s-o division to 10...
n galvanometer of range sv. 2) The deflection of galvanometre falls from s-o division to 10 division Whag a shunt in of 15r is used to calculate the gavanometre resistance ?...
##### (Note: select all correct answers) The optimal risky portfolio can be identified by finding the minimum...
(Note: select all correct answers) The optimal risky portfolio can be identified by finding the minimum variance point on the efficient frontier the maximum return point on the efficient frontier the tangency point of the capital market line and the efficient frontier the line with the steepest slop...
##### PA 12-3 Joe Birra needs to purchase malt for his_Birra needs purchase malt lor his micro-brow produclion_ His supplier charges 535 per dolivery (no maller how much is delivered) and $1. par gallon: Joc$ annua holding cosl is 25% of Ihe price per gallon: Joe uses 275 gallons malt per week.Suppose Joe orders 125 gallons each unie What is nIs average inventory?gallons(Round your answer decimal placos ) Suppose. Joe orders 1250 gallons each UMc Hon many orders does he place with his supplier each y
PA 12-3 Joe Birra needs to purchase malt for his_ Birra needs purchase malt lor his micro-brow produclion_ His supplier charges 535 per dolivery (no maller how much is delivered) and $1. par gallon: Joc$ annua holding cosl is 25% of Ihe price per gallon: Joe uses 275 gallons malt per week. Suppose ...
##### (3) You told that" 99% confidence interval for the population mean is 173 to 24.5. How large would you need sample generale 99" confidence interval with half the margin of error, if the population standard deviation is 252
(3) You told that" 99% confidence interval for the population mean is 173 to 24.5. How large would you need sample generale 99" confidence interval with half the margin of error, if the population standard deviation is 252...
|
2022-09-28 23:35:36
|
{"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": 3, "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": 0.4901354908943176, "perplexity": 14389.905251941787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335286.15/warc/CC-MAIN-20220928212030-20220929002030-00054.warc.gz"}
|
https://stats.stackexchange.com/questions/505794/counting-biased-coins-2-estimating-bias-imbalance
|
# Counting Biased Coins 2: Estimating Bias Imbalance
This is a continuation of another question I have asked recently. The setup and the question itself are sufficiently different (and likely more complicated) to warrant a separate question.
Setup: There is a device that produces coins. Most of the time it makes unbiased coins, but sometimes it makes biased coins. Let
• $$p$$ be the probability of producing a Heads-biased coin (P[Heads] > P[Tails])
• $$q$$ be the probability of producing a Tails-biased coin (P[Heads] < P[Tails])
• $$1-p-q$$ thus be the probability of producing an unbiased coin (P[Heads] = P[Tails])
Biased coins can have different bias. There is no prior knowledge about the distribution of these biases. However, in practice we frequently see strongly-biased coins.
We use the device to produce $$N=100$$ coins. Then we toss each coin $$M=200$$ times and record the results.
Questions:
1. We would like to test if $$p > q$$
2. We would like to estimate $$p$$ and $$q$$, and have some error bars or confidence regions.
Attempt: I have attempted a non-parametric approach.
1. For each coin, perform a binomial test in each direction
2. Count the number of significantly heads-biased and tails biased coins $$N_H$$ and $$N_T$$ given confidence threshold of $$5\%$$
3. Perform another binomial test on the two numbers, with the null hypothesis that the probabilities of producing a heads-biased and tails-biased coins are equal.
The good things about this solution is that it seems to look reasonable for actual data and that it gives us estimates for $$\hat p = \frac{N_H}{N}$$ and $$\hat q = \frac{N_T}{N}$$. The bad things are that I'm not not sure how solid the math is, the confidence threshold is somewhat arbitrary, and I don't have a confidence interval.
It would be cool to alternatively try a model-based approach, addressing the hierarchical nature of this random process directly. However, I know nothing at all about the parametric methods used to tackle such problems. Any suggestions, names, links to literature are appreciated.
Note: This is a minimal example of a problem I have encountered in experimental design in neuroscience. I have judged that further details are unnecessary to make progress on this problem.
• Re "clearly the problem is unsolvable:" that isn't clear at all. The problem is solvable; you just can't expect high accuracy or confidence unless $M$ is sufficiently large. But that's a characteristic of most statistical questions. Thus, your sense of "unsolvabilty" isn't adequate justification for the "strongly biased" convention. If you have another reason to invoke that definition, then fine; but please don't complicate the problem for this reason alone.
– whuber
Jan 20, 2021 at 23:28
• @whuber I see your point. I thought there was no way around it. I dislike it anyway. Thanks for your input, I will get rid of it Jan 20, 2021 at 23:31
• Are you at all interested in a Bayesian methodology? The model I posted in your last question could perhaps be extended, but I'm not going to commit the time unless you're serious about it. Jan 20, 2021 at 23:50
• @DemetriPananos Maybe wait a few days. I promise to read about it and try to understand it myself. Jan 21, 2021 at 8:07
• You have two questions that can be tackled in multiple ways and there will be options that are optimal in one sense but not in another. What is the overall target of the analysis? What should be optimized? Jan 22, 2021 at 13:10
In your last question, I provided a hierarchical Bayesian mixture model. That model can be generalized quite easily (to my surprise) to accommodate your changes here. The extension is not intended to be a legitimate solution to your problem, considering you're not familiar with Bayesian modelling. In any case, I'm posting it here for posterity.
I'll first present the full model and comment on its structure after. The model is
$$\mathbf{p} \sim \operatorname{Dirichlet}(\mathbf{1})$$
$$\mu_l \sim \operatorname{Uniform(0, 0.5)}$$
$$\mu_r \sim \operatorname{Uniform(0.5,1)}$$
$$\kappa_l \sim \operatorname{Half Cauchy}(0,1)$$
$$\kappa_r \sim \operatorname{Half Cauchy}(0,1)$$
$$b_1 \vert \mu_r, \kappa_r \sim \operatorname{Beta}\Big(\mu_r \times \kappa_r, (1-\mu_r) \times \kappa_r \Big)$$
$$b_2 \vert \mu_l, \kappa_l \sim \operatorname{Beta}\Big(\mu_l \times \kappa_l,(1-\mu_l) \times \kappa_l \Big)$$
$$b_3 = 0.5$$
$$y_i \sim \sum_{i=1}^3 \mathbf{p}_i \operatorname{Binomial}(b_i;200)$$
The probability of drawing a biased coin ($$p$$ in the previous model, $$\mathbf{p}$$ in the present model) is now generalized to be a draw from a Dirichlet distribution. You can think of the elements of this vector as probabilities $$p$$, $$q$$, and $$1-p-q$$ from your description.
Each of the two biases are modeled as coming from a binomial distribution parameterized by the mean $$\mu$$ and the "precision" parameter $$\kappa$$. The means $$\mu_l$$ and $$\mu_r$$ are forced to be below and above 0.5 respectively.
The model is easy to write down, but challenging to fit in Stan. The Stan model is
data{
int n;
int y[n];
}
parameters{
simplex[3] prob_of_bias;
real<lower=0, upper=1> mu_left;
real<lower=0> kappa_left;
vector<lower = 0, upper = 0.5>[n] b_left;
real<lower=0, upper=1> mu_right;
real<lower=0> kappa_right;
vector<lower = 0.5, upper = 1>[n] b_right;
}
model{
real lp[3];
prob_of_bias ~ dirichlet(rep_vector(1, 3));
mu_left ~ beta(1, 1);
mu_right ~ beta(1,1);
kappa_left ~ cauchy(0, 1);
kappa_right ~ cauchy(0, 1);
// the prior below takes a parameterization in terms of mu and kappa
// and turns it into alpha beta parameterization
b_left ~ beta_proportion(mu_left, kappa_left);
b_right ~ beta_proportion(mu_right, kappa_right);
for (i in 1:n){
lp[1] = log(prob_of_bias[1]) + binomial_lpmf(y[i] | 200, b_left[i]);
lp[2] = log(prob_of_bias[2]) + binomial_lpmf(y[i] | 200, 0.5);
lp[3] = log(prob_of_bias[3]) + binomial_lpmf(y[i] | 200, b_right[i]);
target += log_sum_exp(lp);
}
}
generated quantities{
matrix[n,3] ps;
for (i in 1:n) {
vector[3] pn;
// log-probability that there is bias
pn[1] = log(prob_of_bias[1]) + binomial_lpmf(y[i] | 200, b_left[i]);
// log-probability that there is no bias
pn[2] = log(prob_of_bias[2]) + binomial_lpmf(y[i] | 200, 0.5);
pn[3] = log(prob_of_bias[3]) + binomial_lpmf(y[i] | 200, b_right[i]);
// posterior probabilities for bias and no bias
ps[i,] = to_row_vector(softmax(pn));
}
}
The model experiences divergences using sensible default parameters for Stan's samplers. I've had to decrease the step size of the integrator, thereby increasing the time required to sample the model. I can get the model to fit, but only just barely. My code could stand to be optimized. I make no attempt to optimize it at this time.
## Simulation
I've simulated the process here. I have a 60% probability to drawing a fair coin, and a 25% probability to drawing a coin with bias less than 50%. Here is some code to generate some data:
# Simulate the data
ncoins = 100
nflips = 200
which_bias = sample(1:3, replace = T, size = ncoins, prob = c(0.25, 0.6, 0.15))
bias = matrix(rep(0, 3*ncoins), ncol = 3)
bias[,1] = rbeta(ncoins, 20, 80)
bias[,2] = 0.5
bias[,3] = rbeta(ncoins, 900, 100 )
theta = rep(0, ncoins)
for (i in 1:ncoins){
theta[i] = bias[i, which_bias[i]]
}
y = rbinom(ncoins, nflips, theta)
Fitting the model with the simulated data results in the following marginal posterior distributions for the elements of $$\mathbf{p}$$. I've added the true values in red. Not bad for 100 coins and 200 flips.
Again, we can compute the posterior probability that any given coin is has a bias in a particular direction. Here are the probabilities first 10 coins
P(Left Bias) P(No Bias) P(Right Bias)
[1,] 0.000 1.000 0.000
[2,] 0.000 0.000 1.000
[3,] 0.001 0.999 0.000
[4,] 0.000 1.000 0.000
[5,] 0.002 0.998 0.000
[6,] 0.000 1.000 0.000
[7,] 0.000 0.000 1.000
[8,] 0.000 1.000 0.000
[9,] 1.000 0.000 0.000
[10,] 0.000 1.000 0.000
To compare, the first 10 coins have the following biases:
1 Fair
2 Right Bias
3 Fair
4 Fair
5 Fair
6 Fair
7 Right Bias
8 Fair
9 Left Bias
10 Fair
So the probabilities are more are less bang on. That is only because $$\mu_l$$ an $$\mu_r$$ were very extreme biases.
Again, I'm not saying this is the solution you should use. It is a solution, and its a solution which could use a lot of optimization. If readers have extensions to the model or improvements, please feel free to add them.
|
2022-07-02 01:27:55
|
{"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": 34, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7000410556793213, "perplexity": 1263.5774615947817}, "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/1656103983398.56/warc/CC-MAIN-20220702010252-20220702040252-00070.warc.gz"}
|
https://xphysics.wordpress.com/2010/11/01/rybczyk-transformations/
|
## Rybczyk transformations
It is well known that the Lorentz transformations lead to Einstein’s velocity addition equation. Rybczyk however, does not consider a transformation, but does have an alternative velocity addition equation. In this post, we shall derive the transformations that are associated with the Rybczyk velocity addition equation.
Consider two systems of reference, denoted as $\mathcal{S}$ and $\mathcal{S}'$, the velocity of $\mathcal{S}'$ with respect to $\mathcal{S}$ is denoted as $v$. A particular body $\mathcal{B}$ is in motion and the velocity of body $\mathcal{B}$ with respect to $\mathcal{S}$ is denoted as $u_\mathcal{B}$ and the velocity of body $\mathcal{B}$ with respect to $\mathcal{S}'$ is denoted as $u'_\mathcal{B}$. The Rybczyk addition equation can be written as
(1) $u_\mathcal{B} = v + u'_\mathcal{B} \sqrt{1 - v^2/c^2}$ (Rybczyk)
that can be found at (Millennium Relativity Velocity Composition, © 2002 Joseph A. Rybczyk). We ask the question, what is the co-ordinate transformation that is associated with the Rybczyk velocity addition? Such transformations I call Rybczyk transformations, named after Joseph A. Rybczyk, who proposed the Rybczyk velocity addition. The general linear co-ordinate transformation from $\mathcal{S}$ to $\mathcal{S}'$ can be written as
(2) $\left[\begin{array}{rcl}t' &=& k(v) t + l(v) x\\x' &=& p(v) t + q(v) x\end{array}\right.$
where $(t,x)$ is defined for $\mathcal{S}$ and $(t',x')$ is defined for $\mathcal{S}'$. For the body $\mathcal{B}$ we can write $x=u_\mathcal{B} t$ but also $x' = u'_\mathcal{B} t'$, thus
(3) $p(v) t + q(v) \left( v + u'_\mathcal{B} \sqrt{1 - v^2/c^2} \right) t = u'_\mathcal{B} \left( k(v) t + l(v) \left( v + u'_\mathcal{B} \sqrt{1 - v^2/c^2} \right) t \right)$
that is rewritten as
(4) $\left( l(v) \sqrt{1-v^2/c^2} \right) {u'_\mathcal{B}}^2 + \left( k(v) + l(v) - q(v) \sqrt{1-v^2/c^2} \right) u'_\mathcal{B} = \left( p(v) + v q(v) \right)$
This has the form $A(v) {u'_\mathcal{B}}^2 + B(v) u'_\mathcal{B} = C(v)$ and this is true for any arbitrary value of $u'_\mathcal{B}$ (within a certain domain), thus $A(v)=0$, $B(v)=0$ and $C(v)=0$. Therefore we obtain
(5) $\left[\begin{array}{rcl}l(v) &=& 0\\ k(v) &=& q(v) \sqrt{1-v^2/c^2}\\p(v) &=& - v(q)v\end{array}\right.$
The Rybczyk transformation can be written as
(6) $\left[\begin{array}{rcl}t' &=& q(v) \sqrt{1-v^2/c^2} t\\x' &=& q(v) (x-vt) \end{array}\right.$
A quick verification gives
(7) $\displaystyle u' = \frac{x'}{t'} = \frac{q(v) (x-vt)}{q(v) \sqrt{1-v^2/c^2} t} = \frac{u-v}{\sqrt{1-v^2/c^2}}$
thus $u = v + u' \sqrt{1-v^2/c^2}$ which is the Rybczyk addition equation. The Rybczyk transformation can also be written in the matrix-form as
(7) $\left(\begin{array}{c}t'\\x'\end{array}\right) = q(v) \left(\begin{array}{cc}\sqrt{1-v^2/c^2}&0\\-v&1\end{array}\right) \left(\begin{array}{c}t\\x\end{array}\right)$
It is clear that this has a different form then the Lorentz transformations.
Hope you like the post!
|
2018-06-23 12:02:35
|
{"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": 35, "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": 0.9343668222427368, "perplexity": 381.4355082830425}, "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/1529267864958.91/warc/CC-MAIN-20180623113131-20180623133131-00525.warc.gz"}
|
https://unlearningmath.com/2009/03/06/notes-on-representation-copying/
|
## Notes on Representation – Copying
In this blog, I’ve surveyed a number of different representation systems for quantities, including the decimal number system, the number line, tally marks, and prime bags, and I’ve tried to see and say something interesting and fresh about each. When I think of the suitability of different representations for quantities, I tend to think of their suitability for operations like counting, adding, multiplying, comparing. That is, I think of representations in relationship to common or important actions. I want to see if in a given system of representation it is easy to see which quantity is larger, and I want to see if in a given system of representation it is easy to multiply.
Yet there is one important action that I had completely overlooked until I started to look into tally marks more deeply. And that is the action of copying. For sure, it is not common to think of copying as having anything to do with arithmetic or mathematics or with representation of quantity. And indeed, for many representation systems, copying of quantities is largely transparent. In the decimal number system, you need a lot of digits to make copying a number something you’d even be concerned about. But even in the decimal number system, we resort to various tricks when the numbers get larger. If I asked you to write down a phone number, 3105551212, so you could call it, it suddenly wouldn’t look so easy. We’re used to seeing a phone number split in smaller chunks, 310-555-1212, and we do a similar thing with social security numbers. You can copy down the un-split large number, but you might find yourself doing it by tracing the number with your finger. Using your finger to mark progress is not something to be ashamed about – I see middle schoolers use their fingers routinely when trying to find the median of a set of numbers. It is simple, and it works.
Each system of representation has its own issues with copying, some trivial, some not so much. The act of copying a decimal number is quite straightforward: you can copy one digit at a time, while tracing the digits carefully. As I mentioned, it is rarely something we pause about and mention its difficulty. It also helps that most numbers we encounter don’t have that many digits. It is rare to be asked to write down 30 digits of $\sqrt{5}$ or of $\pi$. And when you encounter really big numbers, such as the speed of light in miles per second, or Avogadro’s number in chemistry, you use an approximation with few “real” digits. For the speed of light, you use 187,000 miles per second, or you use 300,000 kilometers per second. The more precise 299,792.458 kilometers per second is not something you’d likely be asked to quote (i.e. copy).
If you represent quantity by a distance on the number line, copying a number comes down to approximating the distance on a different line. The number 1.5 is easy to copy precisely, the number 1.5178 not so easy.
With tally marks, copying isn’t particularly hard, but it can be quite cumbersome. A hundred tally marks, done as 20 groups of five, can be copied one group at a time, while tracing your progress with your finger or by other means. When larger groupings are allowed, as in our fanciful proposal here, it may be easier to keep track, but it still requires a considerable amount of writing to copy the number from one place to another. Of course, the niche in which tally marks are used is almost exclusively for counting. You rarely copy a number in tally mark representation, you convert it to a number in decimal representation. The cumbersome nature of copying tally marks is surely one of the reasons its use is restricted to such a narrow niche.
This entry was posted in Uncategorized and tagged , , , , , , . Bookmark the permalink.
|
2019-12-07 03:41:56
|
{"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": 2, "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": 0.8064181208610535, "perplexity": 659.5973238124296}, "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/1575540495263.57/warc/CC-MAIN-20191207032404-20191207060404-00216.warc.gz"}
|
https://centront.com/simple-truth-ytytddu/ac4f10-hall-coefficient-for-insulator
|
A theory is developed for the T = 0 Mott - Hubbard insulating phases of the Hubbard model at -filling, including both the antiferromagnetic (AF) and paramagnetic (P) insulators. It essentially refers to the product of magnetic induction and current density when a magnetic field works perpendicular to the current flow associated with a thin film. Sorry!, This page is not available for now to bookmark. Using angle-resolved photoemission, we have mapped out the Fermi surface (FS) of single crystal Nd[sub 2[minus][ital x]]Ce[sub [ital x]]CuO[sub 4[minus][delta]] when doped as a superconductor ([ital x]=0.15) and overdoped as a metal ([ital x]=0.22). we define the Hall coefficient as: € R H = E y J x B z = 1 ep (10) for p-type semiconductors. 1. The model describes the effect of dynamical, local orbital correlations arising from local quantum chemistry of the material. An additional anisotropic component to the usual dc conductivity is nonvanishing for certain types of spirals. 3. We treat the low- and high-temperature limits analytically and explore some aspects of the intermediate-temperature regime numerically. As an application of interest, we compute the dielectric figure-of-merit (DFOM), a quantity that is of potential importance for microwave device applications. What is the expression of Hall coefficient? We study the optical, Raman, and ac Hall response of the doped Mott insulator within the dynamical mean-field theory (d=∞) for strongly correlated electron systems. The interplay of film stoichiometry and strain on the metal-insulator transition (MIT) and Hall coefficient of NdNiO 3 films grown under different conditions is investigated. S2), ... Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films. What is Fleming’s Left-Hand Rule? The Hall coefficient, R H, is in units of 10-4 cm 3 /C = 10-10 m 3 /C = 10-12 V.cm/A/Oe = 10-12. ohm.cm/G. . However, if you want to know more on this topic, stick around on this page. Hall effect is more effective in semiconductor. In particular, essential features of systems in d = 3, and even lower dimensions, are very well described by the results in d = ∞ or expansions around this limit. takes into account the factors as stated below –, 1. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. However, the I component within the Hall effect calculation stands for –nevA. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). Comment: 9 pages, 7 figures, accepted for publication in Phys. You can also download our Vedantu app to benefit from a personalized learning experience. We find that Kohler's rule is neither obeyed at high nor at intermediate temperatures. However, we should note that in the region of maximum Hall coefficient, there can be large fluctuations in the measured R 0 for different samples with nearly the same composition x , and small deviations from x =0.51 can decrease R 0 by a factor of 2 or more. An intriguing pressure-induced ferromagnetic to antiferromagnetic transition is predicted. Our results are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers. Since the mobilities µh and µe are not constants but functions of T, the Hall coefficient given by Eq. The calculated ac Hall constant and Hall angle also exhibit the isosbectic points. 10-61 of your textbook, the Hall voltage can be written as: where B is the magnetic field applied to the sample, I is the current flowing perpendicular to the magnetic field, and t is the thickness of the sample. Dynamical coupling of single-particle processes to the, Charge dynamics in the two-dimensional Hubbard model is investigated by quantum Monte Carlo simulations. Near the metal-insulator transition, the Hall coefficient of metal-insulator composites (MR -I composite) can be up to 104 times larger than that in the pure metal called Giant Hall effect. 3 correction to ρ and R ... insulator transition and will be temperature independent. t R BI V H H = nq RH 1 = Similarly, it is negative when electrons are more than holes. By contrast, the isostructural, Strongly correlated electronic materials such as the high-$T_c$ cuprates are expected to feature unconventional transport properties, where charge, spin and heat conduction are potentially independent probes of the dynamics. A path-integral field-theoretic derivation of electromagnetic linear response for the two-dimensional Hubbard model is given. Easy online ordering for the ones who get it done along with 24/7 customer service, free technical support & more. In this case, ‘I’ stands for an electric current, ‘n’ signifies the number of electrons per unit volume, and ‘A’ is the conductor’s cross-sectional area. We find that for strong interactions, spin diffusion is driven by super-exchange and strongly violates the quantum limit of charge diffusion. Hall Effect was discovered by Edwin Hall in 1879.The voltage or electric field produced due to the application of magnetic field is also referred to as Hall voltage or Hall field In the weak coupling regime ${R}_{H}$ is electronlike. Results for thermodynamic quantities (specific heat, entropy, . The Hall effect in a weak magnetic field of an excitonic insulator in the semimetallic limit is investigated by the use of the Green function formalism developed recently. . These results are also compared with those obtained for a non-FL metal in d=∞. We discuss the physical ideas underlying this theory and its mathematical derivation. The Hall effect in a weak magnetic field of an excitonic insulator in the semimetallic limit is investigated by the use of the Green function formalism developed recently. In semiconductors , R H is positive for the hole and negative for free electrons. The hall coefficient is positive if the number of positive charges is more than the negative charges. However, the measurement of spin transport in such materials is - in contrast to charge transport - highly challenging. The temperature scale T*, decreasing with increasing hole concentration, provides a link between transport and magnetic properties. Proc. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals. 3. Future directions are suggested for both theoretical and experimental studies. At high field, the ordinary Hall effect dominates as is seen by the linear dependence of ρ xy whereas at low fields anomalous Hall effect dominates. Strictly speaking, this method should work only for homogeneous materials, which is not the case in VO2because of the SPS. We have studied the charge to spin conversion in Bi1− x Sb x /CoFeB heterostructures. (iii) We can take some typical values for copper and silicone to see the order of magnitude of V H.For copper n=10 29 m-3 and for Si, n = 1= 25 m-3.Hence the Hall voltage at B = 1T and i=10A and t = 1 mm for copper and Silicone are, 0.6µV and 6 mV respectively. Hall effect formula enables one to determine whether a material serves as a semiconductor or an insulator. RH is the Hall coefficient: where n is the density of charge carriers and q is their sign (-e for electrons, +e for holes). Access scientific knowledge from anywhere. magnetic field divided by the sample thickness. The components of Hall effect derivation are Hall Voltage (VH), Hall field (EH), drift velocity (v), width of the material (d), magnetic field (B), and the force acting on an electron (Bev). These materials are particularly interesting because of similarities to the high-$T_c$ cuprate superconductors including unconventional metallic properties and competition between antiferromagnetism and superconductivity. Correlations between electrons are treated under the Hartree-Fock approximation with only a dominant term and the effect of impurity scattering is considered. We present an overview of the rapidly developing field of applications of this method to other systems. A brief review of the state-of-the-art is presented. Login . A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. We compute the Raman response, which probes the fluctuations of the “stress tensor,” and show that the scattering is characterized by appreciable incoherent contributions. The material is a) Insulator b) Metal c) Intrinsic semiconductor d) None of the above. It extends the standard mean-field construction from classical statistical mechanics to quantum problems. What are the Applications of Hall Effect? However, this derivation stipulates that the force is downward facing because of the magnetic field (equal to the upward electric force), in the case of equilibrium. The normal state transport properties (resistivity, Hall effect) of La2-xSrxCuO4 have been studied over wide ranges of Sr doping and temperature. The change in sign is not affected by short-range magnetic domains. That value is uniquely associated with the single Dirac cone on the surface of topological insulators. Using the $d=\infty$ solution for our effective model, we show how many experimental observations for the well-doped ($x\simeq 0.3$) three-dimensional manganites $La_{1-x}Sr_{x}MnO_{3}$ can be qualitatively explained by invoking the role of orbital degeneracy in the DE model. The observed FS shape suggests that a model Hamiltonian with only nearest-neighbor interactions is not sufficient to describe the electronic structure near [ital E][sub [ital F]]; next-nearest-neighbor interactions should be considered. They are consistent with a low effective Fermi energy and the unconventional temperature dependence of many of the properties of the metallic phase. What are the components of Hall effect derivation? The carrier Appropriate parameter values for the model imply that the electronic correlations are strong, significant magnetic frustration is present, and the system is close to a metal-insulator transition. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. In particular, there appears to be an effective Fermi energy of the order of 100 K which is an order of magnitude smaller than predicted by band structure calculations. ), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. Near the metal-insulator transition, the Hall coefficient R of metal-insulator composites (M-I composite) can be up to 104 times larger than that in the pure metal called Giant Hall effect. Here we observe spin diffusion in a Mott insulator of. For the square lattice, the sign of the latter is found to be holelike (while the Fermi surface is electronlike) for fillings close to half, and electronlike for almost empty bands. Assume that, the indoor and the outdoor temperatures are 22°C and -8°C, and the convection heat transfer coefficients on the inner and the outer sides are h 1 = 10 W/m 2 K and h 2 = 30 W/m 2 K, respectively. 2. 1. We calculate with quantum Monte Carlo methods the Hall coefficient ${R}_{H}$ for the 2D Hubbard model at small hole doping near half filling. In beryllium, cadmium and tungsten, however, the coefficient is positive. Hall Co efficien t in the doped Mott Insulator Pinaki Ma jumdar and H. R. Krishnam urthy Dep artment of Physics, Indian Inst itute of Scienc e, Bangalor e 560 012, India. 1Q: What hall effect experiment signifies? For the t-J model on the square lattice in two dimensions the change of sign occurs at roughly 1/3 hole filling in good agreement with measurements on La2-xSrxCuO4 compounds, and is weakly temperature dependent. Inspired by a theoretical prediction of the quantum anomalous Hall (QAH) effect in magnetically doped topological insulator thin films, Chang et al. What is the Quantity of 1/(ne) Where ‘n’ is the Number Density of Charge Carriers and ‘e’ is the Electric Charge? Therefore, RH = - $\frac{1}{{ne}}$μ = $\frac{v}{E}$= $\frac{J}{{neE}}$ = σRH = $\frac{{RH}}{\rho }$ (v). Sci. What is a prominent application for the Hall effect? II, Faraday rotation and the Hall constant in strongly correlated Fermi systems, Fermi surface and electronic structure of Nd[sub 2[minus][ital x]]Ce[sub [ital x]]CuO[sub 4[minus][delta]], Charge dynamics in (La, Sr) 2 CuO 4 : from underdoping to overdoping, Correlated Lattice Fermions in d = ∞ Dimensions, Positive Hall coefficient observed in single-crystal Nd2-xCexCuO4- at low temperatures, Physical properties of the half-filled Hubbard model in infinite dimensions, Hall Coefficient for the Two-Dimensional Hubbard Model, Bosonic fluctuations in Strongly Correlated Systems, theoretical study of strongly correlated system, Insulating Ferromagnetism in L a 4 B a 2 C u 2 O 10 : An Ab Initio Wannier Function Analysis, Spin Transport in a Mott Insulator of Ultracold Fermions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. The role of low-energy coherence (FL) or incoherence (non-FL) in determining the finite frequency response of strongly correlated metals in d=∞ is discussed in detail. Which Factor is the Hall Coefficient RH for a Conductor Independent of? Acad. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. Hall effect helps in the measurement of the magnetic field around an electric charge and differentiate a semiconductor from an insulator. Grainger's got your back. Orbital correlations in the ferromagnetic half-metal CrO2, Magneto-optical Sum Rules Close to the Mott Transition, Optical and Magneto-optical Response of a Doped Mott Insulator, Dynamical Mean-Field Theory of Strongly Correlated Fermion Systems and the Limit of Infinite Dimensions, Transport properties of strongly correlated metals: A dynamical mean-field approach, Magnetotransport in the doped Mott insulator, A strongly correlated electron model for the layered organic superconductors kappa-(BEDT-TTF)2X, Role of Orbital Degeneracy in Double Exchange Systems, Conductivity and Hall effect in the two-dimensional Hubbard model, Mott-Hubbard transition in infinite dimensions. The Hall coefficient enhancement observed in those materials is about 100 or less. Are you looking to get in contact with one of our New York Local Unions? Computer programs for the numerical implementation of this method are also provided with this article. It is essentially the ratio between density (signified by x-axis) and current density (denoted by the y-axis). We report measurements of the conductivity and Hall coefficient of insulating n-type CdSe with dopant concentrations near the critical concentration for the metal-insulator transition. In 1D, the metallic phase off half-filling'' is a Luttinger liquid with pseudospin-charge separation. Comment: 8 pages, 2 figures, submitted to Phys. The Origin of the Giant Hall Effect in Metal-Insulator Composites. E H J B. We find, remarkably, that changes in the Fermi-surface topology associated with incommensurate planar spin-density-wave saddle points induce a change in sign of the Hall coefficient at dopings deltaH=0.02-0.5 for U/t=2-10. We find quantitative agreement of our $R_H^*$ with the QMC results obtained in two dimensions by Assaad and Imada [Phys. B. Applying the physical model for alloys with phase separation developed in [1] [2], we conclude that the Giant Hall effect is caused by an electron transfer away from the metallic phase to the insulating … In general µe > µh so that inversion may happen only if p > n; thus "Hall coefficient inversion" is characteristic of … Local moments are introduced explicitly from the outset, enabling ready identification of the dominant low-energy scales for insulating spin-flip excitations. Pro Lite, Vedantu The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. Also, you should be aware of the fact that the Hall angle in Hall effect stands for the angle between electric field and drift velocity. Contrary to the common belief of concurrent magnetic and metal-insulator … The expression for Hall coefficient is EH/JB. The Hall coefficient is just the reciprocal of the total current-carrying charge in the conductor, and has the same sign as the sign of this charge. 2. © 2008-2021 ResearchGate GmbH. This coupled problem is solved numerically. For a particular material the Hall coefficient was found to be zero. With a brief light shed on its applications, let us move on to how you can make the Hall effect derivation from scratch. On top of that, Hall resistance or R = $\frac{{VH}}{i} = \frac{B}{{net}}$. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and … B. Besides, Hall coefficient (RH) implies the ratio between the product of current density and magnetic field and the induced electric field. Join ResearchGate to find the people and research you need to help your work. implies the ratio between the product of current density and magnetic field and the induced electric field. mechanism resolved by the Hall coefficient parallels the Slater picture, but without a folded Brillouin zone, and contrasts sharply with the behavior of Mott insulators and spin density waves, where the electronic gap opens above and at T N, respectively. The occurrence of the isosbectic point in the optical conductivity is shown to be associated with the frequency dependence of the generalized charge susceptibility. Which Factor is the Hall Coefficient R, Vedantu We investigate the role of orbital degeneracy in the double exchange (DE) model. The present limitations of the approach, and possible extensions of the formalism are finally discussed. 1B and fig. For the AF case, the resultant theory is applicable over the entire U-range, and is discussed in some detail. Correlations between electrons are treated under the Hartree-Fock approximation with only a dominant term and the effect of impurity scattering is considered. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported. Theoretically, in addition to ρ, the Hall coefficient (R H) is another quantity that is expected to get modified due to e-e interactions10. Nd4Ba2Cu2O10 develops the observed antiferromagnetic order via its characteristics of a 1D chain. Hall Co-efficient: The hall coefficient can be defined as the Hall’s field per unit current density per unit magnetic field. Looking for AURALEX Wall Insulation, 2 ft Width, 4 ft Length, 1.0 Noise Reduction Coefficient (NRC), Mineral Wool (19MP40)? impact of the resulting dynamics on the electronic constituents. The temperature dependence of electrical transport, optical, and nuclear magnetic resonance properties deviate significantly from those of a conventional metal. In this case, ‘I’ stands for an electric current, ‘n’ signifies the number of electrons per unit volume, and ‘A’ is the conductor’s cross-sectional area. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model. All content in this area was uploaded by H. R. Krishnamurthy on May 08, 2013. Lett. We suggest that the high frequency Hall constant can be directly measured in a Faraday rotation experiment. $$\frac{E_{H}}{JB}$$: Hall coefficient (R H) is defined as the ratio between the induced electric field and to the product of applied magnetic field and current density. The fascinating electronic properties of the family of layered organic molecular crystals kappa-(BEDT-TTF)2X where X is an anion (e.g., X=I3, Cu[N(CN)2]Br, Cu(SCN)2) are reviewed. In a similar manner it can be shown that for an n-type semiconductor, in which the charge carriers are electrons with charge -e, the Hall coefficient is € R H = 1 − en =− 1 (11) Note that the Hall coefficient has opposite signs for n and p-type semiconductors. We determine the region where metallic and insulating solutions coexist using second-order perturbation theory and we draw the phase diagram of the Hubbard model at half filling with a semicircular density of states. In the $J_{H}\to\infty$ limit, an effective generalized Hubbard'' model incorporating orbital pseudospin degrees of freedom is derived. This limit — which is wellknown in the case of classical as well as localized quantum spin models — is found to be very helpful also in the case of quantum mechanical models with itinerant degrees of freedom. Although RH is sample dependent in sign above ∼100 K, it increases steeply to positive values in all crystals studied below ∼80 K. RH remains T (temperature) dependent at 2 K, in contrast to the resistivity ρa which saturates to a constant below 30 K. Using a two-band model, we account for the observed profiles of RH vs T and ρa vs T. The analysis reveals that the scattering processes for the electronlike and holelike bands have vastly different temperature scales. Login into Examveda with. The system realizes the Fermi-Hubbard model, believed to capture the essence of the cuprate phenomenology. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. 6 is also a function of T and it may become zero and even change sign. We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. $\frac{{ - Bi}}{{net}}\frac{{EH}}{{JB}} = - \frac{1}{{ne}}$. ) The charge dynamics changes significantly in the non-superconducting overdoped range with RH(T) becoming constant above a characteristic temperature T*, and p(T) ? For the P phase, we consider in particular the destruction of the Mott insulator, the resultant critical behaviour of which is found to stem inherently from proper inclusion of the spin-flip excitations. Surprisingly, the in-plane order of both cases is not controlled by coupling between nearest neighbors. {\bf 74}, 3868 (1995)]. We deduce a model relevant for the description of the ferromagnetic half-metal chromium dioxide (CrO2), widely used in magnetic recording technology. Rev. The dominant magnetic coupling, revealed through evaluated parameters (t, U, and J), turns out to be the intersite direct exchange, a currently ignored mechanism that overwhelms the antiferromagnetic superexchange. Dynamical mean-field theory, which maps the Hubbard model onto a single impurity Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. Natl. The paper extends the Bloch-Boltzmann theory to the case of untraditional Fermi liquids where the damping of the quasiparticles is Gamma(ε)~max(kBT,ε). We observe that a bipartite-lattice condition is responsible for the high-temperature result $\sigma_{xy}\sim 1/T^2$ obtained by various authors, whereas the general behavior is $\sigma_{xy}\sim 1/T$, as for the longitudinal conductivity. The Hall coefficient RH has been measured in superconducting single crystals of Nd2-xCexCuO4-δ(x∼0.15). This crossover leads to a non-monotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. is discussed, which makes use of the limit of high spatial dimensions. Distinguished Professor Sarachik has published extensively in professional journals on her work in superconductivity, disordered metallic alloys, metal-insulator transitions in doped semiconductors, hopping transport in solids, properties of strongly interacting electrons in two dimensions, and spin dynamics in molecular magnets. Pro Lite, Vedantu We demonstrate that the Mott transition at finite temperatures has a first-order character. The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling are calculated. The familiar T-linear resistivity and the strongly T dependent Hall effect RH(T) are found only near the optimal hole concentration (x ˜ 0.15–0.18). spin-flip excitations leads to a renormalized self-consistent description of the single-particle propagators that is shown to be asymptotically exact in strong coupling, for both the AF and P phases. (p. The model possesses an exact solution in one- and in infinite dimensions. Unlike insulators or semiconductors derived from simple metals such as sodium We observe that the semiclassical Hall constant for a strongly correlated Fermi system is most directly related to the high frequency Hall conductivity. Hall effect physics involves a metal body which contains a single form of charge carriers, like electrons. Hall effect definition finds immense application in integrated circuits (ICs) in the form of Hall effect sensors. We discuss the Mott-Hubbard transition in light of the Hubbard model in infinite dimensions with special emphasis on the finite-temperature aspects of the problem. Hall effect principle, on the other hand, states that the magnetic field through which current passes exerts a transverse force. ultracold fermionic atoms with single-atom resolution. Insulation R-values generally met code, but the quality of the insulation This, in turn, relocates the electrical charge to a specific side of the conducting body. (Rapid Communication) B49: 14039 (1994), with Peihua Dai and Youzhu Zhang. In the strong coupling regime, where the mapping to the $t$- $J$ model is justified, ${R}_{H}$ is electronlike with small amplitude in the temperature regime $T>U$, $T 1 ; n ˜ 1.5±0.1 ) Co-efficient: the Hall coefficient RH has been in. A numerical solution of the transport properties ( response to a specific side of the are. Particular material the Hall coefficient /CoFeB heterostructures and imaginary parts of the SPS electrical,. Scattering experiments Hall effect physics involves a metal body which contains a single form of carriers! Occurrence of the material is a prominent application for the description of the ferromagnetic half-metal chromium dioxide CrO2. A link between transport and magnetic properties ( resistivity, Hall coefficient is positive from recent of. Field per unit current density and magnetic properties, 2 figures, submitted to Phys that Hall effect from. Established that the Mott transition at finite temperatures has a first-order character quantities ( heat... All content in this limit approach, and possible extensions of the puzzling insulating of! Contrast to charge transport - highly challenging even change sign its initial level involves an explanation on hypercubic. Onto a single-impurity model supplemented by a band-filling scenario density ( signified by x-axis ) and current density ( by. A personalized learning experience app to benefit from a personalized learning experience suggested both... In one- and in infinite dimensions circuits ( ICs ) in the measurement of spin in! In infinite dimensions with special emphasis on the surface of topological insulators from coherent Fermi liquid excitations at temperatures! And a Hall-insulator phase near the superconductor-to-insulator transition in light of the conducting body a first-order character obeyed! Real and imaginary parts of the ferromagnetic half-metal chromium dioxide ( CrO2 ),... Self-duality a! Involves a metal body which contains a single form of charge diffusion strains are evaluated for films under. The present limitations of the metallic phase of a 1D chain H }$ is electronlike tn n. Intrinsic semiconductor d ) None of the infinite-dimensional Hubbard model using a dynamical approximation! Those obtained for a proper understanding of the metallic phase of CrO2 antiferromagnetic order via its of. Semiconductor from an insulator in-plane order of both cases is not the case in VO2because the! On may 08, 2013 side of the intermediate-temperature regime numerically half-filled La4Ba2Cu2O10 elucidated! For –nevA to spin conversion in Bi1− x Sb x /CoFeB heterostructures the method makes use of an mapping! Lattice mismatch strains are evaluated for films grown under a range of growth pressures on! By Assaad and Imada [ Phys of this method should work only for homogeneous materials, are...
|
2021-06-16 15:14:36
|
{"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": 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": 0.6206890940666199, "perplexity": 1144.8911459801768}, "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/1623487623942.48/warc/CC-MAIN-20210616124819-20210616154819-00601.warc.gz"}
|
https://environmentalcomputing.net/statistics/linear-models/linear-regression/
|
# Linear Regression
Linear regression is the one of the most widely used statistical techniques in the life and earth sciences. It is used to model the relationship between a response (also called dependent) variable $y$ and one or more explanatory (also called independent or predictor) variables $x_{1}$,$x_{2}$$x_{n}$. For example, we could use linear regression to test whether temperature (the explanatory variable) is a good predictor of plant height (the response variable).
In simple linear regression, with a single explanatory variable, the model takes the form:
$y = \alpha + \beta x + \varepsilon$
where $\alpha$ is the intercept (value of $y$ when $x$ = 0), $\beta$ is the slope (amount of change in $y$ for each unit of $x$), and $\varepsilon$ is the error term. It is inclusion of the error term, also called the stochastic part of the model, that makes the model statistical rather than mathematical. The error term is drawn from a statistical distribution that captures the random variability in the response. In standard linear regression this is assumed to be a normal (Gaussian) distribution.
Note that the linear in linear model does not imply a straight-line relationship but rather that the response is a linear (additive) combination of the effects of the explanatory variables. However, because we tend to start by fitting the simplest relationship, many linear models are represented by straight lines.
Note that a linear regression is just a special case of a linear model, where both the response and predictor variables are continuous.
### Running the analysis
The goal in linear regression is obtain the best estimates for the model coefficients ($\alpha$ and $\beta$). In R you can fit linear models using the function lm.
For this worked example, download a data set on plant heights around the world, Plant_height.csv, and import into R.
Plant_height <- read.csv(file = "Plant_height.csv", header = TRUE)
The main argument to lm is the model formula y ~ x, where the response variable is on the left of the tilde (~) and the explanatory variable is on the right. lm also has an optional data argument that lets you specify a data frame from which the variables will be taken.
To test whether plant height is associated with temperature, we would model height as the dependent variable (in this case we are using the log of plant height) and temperature as the predictor variable.
lm(loght ~ temp, data = Plant_height)
### Interpreting the results
To obtain detailed output (e.g., coefficient values, R2, test statistics, p-values, confidence intervals etc.), assign the output of the lm function to a new object in R and use the summary function to extract information from that model object.
model <- lm(loght ~ temp, data = Plant_height)
summary(model)
##
## Call:
## lm(formula = loght ~ temp, data = Plant_height)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.97903 -0.42804 -0.00918 0.43200 1.79893
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.225665 0.103776 -2.175 0.031 *
## temp 0.042414 0.005593 7.583 1.87e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6848 on 176 degrees of freedom
## Multiple R-squared: 0.2463, Adjusted R-squared: 0.242
## F-statistic: 57.5 on 1 and 176 DF, p-value: 1.868e-12
The estimates for the coefficients give you the slope and intercept. In this example, the regression equation for (log) plant height as a function of temperature is:
$log(plant height) = -0.22566 +0.0421.temperature + \varepsilon$
Calling summary on a model object produces a lot of useful information but one of the main things to look out for are the t-statistics and p-values for each coefficient. These test the null hypothesis that the true value for the coefficient is 0.
For the intercept we usually don’t care if it is zero or not, but for the other coefficient (the slope), a value significantly differing from zero indicates that there is an association between that explanatory variable and the response. In this example, an increase in temperature is associated with an increase in plant height.
Whilst the t-statistics and p-values indicate a significant association, the strength of the association is captured by the R2 value, the proportion of variance in the response that is explained by the explanatory variable(s).
The F-statistic and associated p-value indicates whether the model as a whole is significant. The model will always be significant if any of the coefficients are significant. With only one predictor variable, the probability associated with the t test, that tests whether the slope differs from zero, is identical to the probability associated with the F statistic.
We can also obtain 95% confidence intervals for the two parameters. Showing that the intervals for the slope do not include zero is another way of showing that there is an association between the dependent and predictor variable.
confint(model)
## 2.5 % 97.5 %
## (Intercept) -0.43047074 -0.02085828
## temp 0.03137508 0.05345215
### Assumptions to check
Linearity. There is no point trying to fit a staight line to data that are curved! Curvilinear relationships produce U-shaped patterns in plots of the residuals vs the fitted values. Using the plot function on a model object provides a series of four graphical model diagnostics, the first of which is a plot of residuals versus fitted values.
plot(model, which = 1)
The absence of strong patterning in the above plot indicates the assumption of linearity is valid. If there is strong patterning, one potential solution is to log-transform the response. Note in the above example plant height had already been log-transformed. An alternative solution is to fit a linear model of the response as a polynomial function (e.g. quadratic) of the response. The simplest way to do this in R is to use the poly function.
Click here to see a nice interactive app that shows you what patterns of residuals you would expect with curved relationships
Constant variance. An even spread of data around the regression line is desirable. If the plot of residuals versus fitted values is fan-shaped the assumption of constant variance (aka homogeneity of variance) is violated. A log-transformation of the response variable may fix this problem, but if it doesn’t the best solution is to use a different error distribution in a generalised linear model framework (GLM). See the Generalised linear models 1 for more information.
Normality. Checks of whether the data are normally distributed are usually performed by either plotting a histogram of the residuals or via a quantile plot where the residuals are plotted against the values expected from a normal distribution (the second of the figures obtained by plot(model). If the points in the quantile plot lie mostly on the line, the residuals are normally distributed. Violations of normality can be fixed via transformations or by using a different error-distribution in a GLM. Note, however, that linear regression is reasonably robust against violations of normality.
par(mfrow = c(1, 2)) # This code put two plots in the same window
hist(model\$residuals) # Histogram of residuals
plot(model, which = 2) # Quantile plot
Independence. The observations of the response should be independent of each other. Non-independent observations are those that are in some way associated with each other beyond that which is explained by the predictor variable(s). For instance, samples collected from the same site, or repeatedly from the same object, may be more alike due to some additional factor other than the measured explanatory variable. Ensuring independence is an issue of experimental and sampling design and we usually know if the data are independent or not in advance of our analysis.
There are a variety of measures for dealing with non-independence. These include ensuring all important predictors are in the model; averaging across nested observations; or using a mixed-model (see Mixed models 1).
### Communicating the results
Written The results of linear regression may be presented in the text in a number of different ways, but a short sentence is often adequate, e.g., “plant height exhibited a significant (F = 57.5, p < 0.01) negative relationship with temperature”. However, if you have run several analyses (or if there is more than one predictor), it may be useful to present the results as a table with coefficient values, standard errors and p-values for each explanatory variable.
Visual For a linear regression with a single explanatory variable, it is useful to present the results as a scatter plot. The line of best fit derived from the model can be added with the abline function.
plot(loght ~ temp, data = Plant_height, xlab = "Temperature (C)", ylab = "log(Plant height)", pch = 16)
abline(model, col = "red")
### Further help
Type ?lm to get the R help for this function.
Quinn and Keough (2002) Experimental design and data analysis for biologists. Cambridge University Press. Ch. 5 Correlation and regression.
McKillup (2012) Statistics explained. An introductory guide for life scientists. Cambridge University Press. Ch. 17 Regression.
More advice on interpreting coefficients in linear models
Author: Andrew Letten
Year: 2016
Last updated: Feb 2022
|
2022-07-06 20:15:25
|
{"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": 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": 0.6665719747543335, "perplexity": 1287.4954308445745}, "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/1656104676086.90/warc/CC-MAIN-20220706182237-20220706212237-00501.warc.gz"}
|
https://wiki.bnl.gov/eic/index.php?title=Special:MobileDiff/3739
|
# BEGIN ANSIBLE MANAGED BLOCK WIKIEDITOR #17.01.14-> wfLoadExtension( 'WikiEditor' ); # ## Enables/disables use of WikiEditor by default but still allow users to disable it in preferences #$wgDefaultUserOptions['usebetatoolbar'] = 1; #$wgDefaultUserOptions['usebetatoolbar-cgd'] = 1; # ## Displays the Preview and Changes tabs #$wgDefaultUserOptions['wikieditor-preview'] = 0; # ## Displays the Publish and Cancel buttons on the top right side #$wgDefaultUserOptions['wikieditor-publish'] = 0; #17.01.14<- # END ANSIBLE MANAGED BLOCK WIKIEDITOR Changes - EIC
# Changes
, 15:14, 3 August 2013
Line 32: Line 32:
These protons cannot be detected in the main detector. The standard detectors used to detect the scattered proton are roman pots placed at different distances from the IR.
These protons cannot be detected in the main detector. The standard detectors used to detect the scattered proton are roman pots placed at different distances from the IR.
Using this detector technology poses an other requirement on the machine performance. To reach as small scattering angles as possible a small emittance of the beam is crucial as there is also an additional requirement of 10 sigma clearance from the core of the beam.
Using this detector technology poses an other requirement on the machine performance. To reach as small scattering angles as possible a small emittance of the beam is crucial as there is also an additional requirement of 10 sigma clearance from the core of the beam.
+
To have good acceptance at low scattering angle the beam needs to be cooled and we need
== Detector Space and Magnetic Field ==
== Detector Space and Magnetic Field ==
2,105
edits
|
2022-12-01 03:06:23
|
{"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": 0.42348960041999817, "perplexity": 3264.992337892985}, "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-20221201021257-20221201051257-00092.warc.gz"}
|
https://math.stackexchange.com/questions/2106252/why-is-1-2-3-neq-1-2-3-emptyset
|
# Why is $\{1,2,3\} \neq \{1,2,3,\emptyset \}?$
I understand why this is the case comparatively , if a set is looked at as being a 'box', then the empty set is considered to be an empty box. So the set $\{1,2,3\}=A$ is considered to be a 'box' containing elements $1,2,3$, and $\{1,2,3,\emptyset \}=B$ is the set containing the elements $1,2,3$ and an 'empty box'?
What I struggle with is how this intuition would make sense given the empty set is a subset of every other set.
Also, I know that $\{\emptyset \} \neq \emptyset$, so would it be the case that for the given set $A$, $\emptyset \subset A$, but that $\emptyset \notin A$, as the set containing no elements is not in the set $A$, but $\emptyset \in B$ is true, right?
In the midst of forming this question I thought of a way of looking at this question, but I am not sure whether it is correct:
So continuing with the comparison of looking at a set being a 'box', $\emptyset \subset A$ simply means that the the set $A$ has some 'free space' in the box, and so the set could be visualised by $A=\{1,2,3,\qquad\}$?, and every set\'box' has some 'empty space', whereby the 'empty box' represents simply the collection of that void.
Does this analogy capture the true picture of Why $\{1,2,3\} \neq \{1,2,3,\emptyset \}$ and $\emptyset \subset A$?
Just a very quick question,
Is the power set of $C=\{1,\emptyset\}$,
$$\mathcal{P}(C)=\{\{1\},\{ \emptyset \},\{1, \emptyset \},\emptyset \}?$$
• Using "more tags" doesn't help when you're using the wrong tags. – Asaf Karagila Jan 20 '17 at 16:40
• Also, an empty box might have nothing inside, but it's not nothing. It's still a box. – Asaf Karagila Jan 20 '17 at 16:40
• I'm not sure this is a duplicate. The OP says he knows the technical explanation in the suggested duplicate, but is after intuition instead. I believe a better answer to this question would perhaps be, "don't take the box analogy too seriously". – hmakholm left over Monica Jan 20 '17 at 16:55
Don't take the box analogy too seriously. It captures some of the aspects of the mathematical concept of a set, but not all of them. For example, we can easily imagine two boxes that are both empty, but set theory nevertheless holds that there is one and only one empty set.
Boxes have some value in explaining how $A \in B$ and $A \subseteq B$ are two different claims (which are unfortunately both expressed as "$B$ contains $A$" in common mathematical English, so one has to guess which is meant from the context). Beyond that, their value diminishes somewhat.
The real technical reality of sets is simply that they are something that either are, or are not, in the $\in$ relation to each other, such that they satisfy the Axiom of Extensionality:
A set is fully given by what its elements are. More precisely, whenever $A$ and $B$ are different sets, there must be either an $x$ such that $x\in A$ and $x\notin B$, or an $y$ such that $y\notin A$ and $y\in B$, or possibly both. If such an $x$ or $y$ does not exist, then it can only be because $A$ and $B$ are the same set.
Viewed like this, what your $A$ and $B$ are is simply the totality of answers to "is this an element of $A$?" and "is this an element of $B$?".
Because the answer to "is $\varnothing$ an element of $A$?" is different from the answer to "is $\varnothing$ an element of $B$?", the two sets are different.
• Okay, is my intuition regarding the 'empty space' technically correct? – Gurjinder Jan 20 '17 at 18:28
• @Gurjinder: I don't know what it means for intuition to be "technically correct". I don't think your image of empty space feels very useful, though. – hmakholm left over Monica Jan 20 '17 at 18:46
• Okay cool, your explanation seems to make sense, thanks. – Gurjinder Jan 20 '17 at 18:48
|
2021-03-02 03:17:49
|
{"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": 0.7574806809425354, "perplexity": 294.21042236653375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363211.17/warc/CC-MAIN-20210302003534-20210302033534-00282.warc.gz"}
|
https://plainmath.net/13934/industrial-cooling-process-circulated-pressure-diameter-pressure-diameter
|
# In an industrial cooling process, water is circulated through a system. If the water is pumped with a speed of 0.45 m/s under a pressure of 400 torr from the first floor through a 6.0-cm diameter pipe, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?
Question
Other
In an industrial cooling process, water is circulated through a system. If the water is pumped with a speed of 0.45 m/s under a pressure of 400 torr from the first floor through a 6.0-cm diameter pipe, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?
2021-02-20
In an industrial cooling process, water is circulated through a system.
If the water is pumped with a speed of($$\displaystyle{v}_{{{1}}}={0.45}\frac{{m}}{{s}}$$)
under a pressure of ($$\displaystyle{P}_{{{1}}}$$ = 400 torr) from the first floor througha($$\displaystyle{D}_{{{1}}}$$ = 6.0cm) diameter pipe,
Let '$$\displaystyle{P}_{{{2}}}$$' be the pressure on the next floor ( h = 4.0 m ) above in a pipe with adiameter of ($$\displaystyle{D}_{{{2}}}$$ = 2.0 cm)
Density of water = $$\displaystyle{1000}{k}\frac{{g}}{{m}^{{{3}}}}$$
From the equation of continuity we have
The rate is $$\displaystyle{A}_{{{1}}}{v}_{{{1}}}={A}_{{{2}}}{v}_{{{2}}}$$
Or, $$\displaystyle{v}_{{{2}}}={A}_{{{1}}}\frac{{v}_{{{1}}}}{{A}_{{{2}}}}$$
Or, $$\displaystyle{v}_{{{2}}}={\left(\frac{{D}_{{{1}}}}{{D}_{{{2}}}}\right)}^{{{2}}}{v}_{{{1}}}$$
Apply; Bernoulli's Theorem
$$\displaystyle{P}_{{{1}}}+{\left(\frac{{1}}{{2}}\right)}{{v}_{{{1}}}^{{{2}}}}+{0}={P}_{{{2}}}+{\left(\frac{{1}}{{2}}\right)}\cdot{{v}_{{{2}}}^{{{2}}}}+{h}\cdot{g}$$
Put the above given values in the above expression , to get'$$\displaystyle{P}_{{{2}}}$$'
### Relevant Questions
Water at a pressure of $$\displaystyle{3.00}\times{10}^{{5}}$$ Pa flows through a horizontal pipe at a speed of 1.00 m/s. the pipe narrows to 1/4 its original diameter. Find the following:
A. The flow speed in the narrow section
B. the pressure in the narrow section
A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.
a) what is the speed at the instant his feet touch theground?
b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?
c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.
Look Out! A snowball rolls off a barn roof that slopes downward at an angle of 40 degrees . The edge of the roof is 14.0 m above the ground, and the snowball has a speed of 7.00 m/s as it rolls off the roof. Ignore air resistance.
A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?
A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing a rope attached to a chandelier, heswings down to grapple with the movie's villian (mass 70.0 kg), whois standing directly under the chandelier.(assume that thestuntman's center of mass moves downward 5.0 m. He releasesthe rope just as he reaches the villian).
a) with what speed do the entwined foes start to slide acrossthe floor?
b) if the coefficient of kinetic friction of their bodies withthe floor is 0.250, how far do they slide?
An electron is fired at a speed of $$\displaystyle{v}_{{0}}={5.6}\times{10}^{{6}}$$ m/s and at an angle of $$\displaystyle\theta_{{0}}=–{45}^{\circ}$$ between two parallel conductingplates that are D=2.0 mm apart, as in Figure. Ifthe potential difference between the plates is $$\displaystyle\triangle{V}={100}\ {V}$$, determine (a) how close d the electron will get to the bottom plate and (b) where the electron will strike the top plate.
As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is $$\displaystyle\mu_{{k}}$$, the coefficient of kinetic friction between the chair and the waxed floor? Use $$\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}$$ for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for $$\displaystyle\mu_{{k}}$$, since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.
The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with $$\displaystyle\mu={1.5}$$ and $$\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}$$.
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $$\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$$.
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $$\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$$? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X?
|
2021-06-13 12:19:51
|
{"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": 0.5618412494659424, "perplexity": 955.9259143334402}, "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/1623487608702.10/warc/CC-MAIN-20210613100830-20210613130830-00033.warc.gz"}
|
https://puzzling.stackexchange.com/questions/2079/how-many-squares-can-you-find-in-the-picture
|
# How many squares can you find in the picture?
How many sqares can you draw in given pattern, when each corner of a sqare has to lie in the exact center of one of the 20 colored circles?
There are an infinite number of squares whose sides pass through exactly four circles. In fact, there are an infinite number of squares passing through the top four circles alone.
Each frame of the above gif represents one possible square you can draw through those circles. In addition to the 90 squares represented in these 90 frames, there are infinitely many more. For example, "the square that lies halfway between frame 1 and frame 2".
Edit: If we add the additional constraint that the corners of the square must lie on a circle, then there are 17, as originally determined by kaine.
• Note that this answer applies to "how many squares are there whose lines pass through these circles?", but not "how many squares are there whose corners lie on these circles?". I wasn't sure how to interpret the question, so I went with the former. – Kevin Aug 13 '14 at 13:21
• wrong answer, it seems you didn't get the question,look at kaine's answer. – Masoud Mohammadi Aug 13 '14 at 13:52
• @Riddle, What's wrong with it? All of my squares satisfy the criteria "your square shouldn't have more than 4 or less than 4 circles. and your lines should pass the 4 circles." Please clarify your question. – Kevin Aug 13 '14 at 14:13
• +1. The infinite answer should be kept. That is the reason how people should formulate their question very precisely :) – justhalf Aug 14 '14 at 5:41
• Even with "The Corners lie on four circles" you still have infinite squares by tilting and moving. The question should be "Which corners are at the exact centers of one of the 20 colored circles" – Falco Aug 18 '14 at 9:21
9 squares that are $1$x$1$ (trivial)
4 squares that are $\sqrt{2}$x$\sqrt{2}$ (Diamonds centered at the 4 central circles)
2 squares that are $\sqrt{5}$x$\sqrt{5}$ (Each starts at a yellow circle. Move like a knight: example 2 right 1 up, 2 up 1 left, 2 left 1 down, 2 down 1 right)
2 squares that are $\sqrt{13}$x$\sqrt{13}$ (Each starts at the orange circles. Move 3 right 2 up or 3 left 2 up and then keep going)
Are there more than that?
• I can only see nine $1 \times 1$ squares. There are also four $\sqrt{8} \times \sqrt{8}$ squares – squeamish ossifrage Aug 13 '14 at 13:21
• Thank you, miscounted. Don't the $\sqrt 8$ squares go through additional circles? 8 is made from 2 square numbers by 4+4 and the 4 squares with those dimensions I found go through 3 more circles each. – kaine Aug 13 '14 at 13:26
• can you show √5 and √13 in picture? – Masoud Mohammadi Aug 13 '14 at 13:54
• @kaine According to the current wording of the puzzle there is nothing wrong with the squares intersecting additional circles. – aaaaaaaaaaaa Aug 27 '14 at 17:25
I found 21
• 9 variations of black square
• 2 variations of orange square
• 4 variations of brown square
• 4 variations of gray square
• 2 variations of red square
• actually, i told in question that each square must be exactly on 4 circles ,but one of your square is on 8 circles, but my question was edited. so your answer is correct, but other answeres are correct too, because they answered before the edit happens. – Masoud Mohammadi Aug 28 '14 at 17:31
My answer is 21. It break down as follows:
9: Square from dots right next to each other
4: Squares with 1 dot in the middle
2: Squares with central 4 dots in the middle
2: Squares with previous 2 squares in the middle (The above can be more easily visualized from watching Kevin's answer)
4: From the 4 squares with 1 dot in the middle, extend out 1 more dot on each corner to make another square.
The total of 9 + 4 + 2 + 2 + 4 = 21.
• Given the recent change to the question, this answer appears to be the most correct now (addition of 4 squares that previously were considered incorrect). – Joel Rondeau Aug 28 '14 at 15:59
I have found 21 Squares, too.
As Kevin illustrated in his beautiful answer there are 17 squares. PLUS there are 4 more squares.
all the squares are as follows:
Dimensions How many
• Nine × [1x1]
• Four × [√2×√2]
• Two × [√5×√5]
• Four × [√8×√8]
• Two × [√13×√13]
• TOTAL of 21 squares
|
2019-05-24 15:54:29
|
{"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": 0.6257383227348328, "perplexity": 1312.0647462539798}, "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-2019-22/segments/1558232257660.45/warc/CC-MAIN-20190524144504-20190524170504-00484.warc.gz"}
|
https://tex.stackexchange.com/questions/274393/how-to-hyperref-prefixed-urls
|
# How to hyperref prefixed URLs?
Is it possible to define URL prefixes and correctly provide hyperrefs for them?
For example:
\defineprefix{dbo}{http://dbpedia.org/ontology/}
\prefixurl{dbo:City}
Should have the same effect as:
\href{http://dbpedia.org/ontology/City}{dbo:City}
Edit: This is the MWE of the accepted code where it causes an error:
\documentclass{article}
\usepackage{hyperref}
\makeatletter
\newcommand\defineprefix[2]{%
\def\urlprefixabbrv@#1{#2}}
\newcommand\prefixurl[2]{%
\href{\urlprefixabbrv@#1/#2}{#1:#2}}
\makeatother
\begin{document}
\defineprefix{owl}{http://www.w3.org/2002/07/owl\#}
\defineprefix{xsd}{http://www.w3.org/2001/XMLSchema\#}
\prefixurl{owl}{Class}
\prefixurl{xsd}{string}
\end{document}
• Is your syntax for \prefixurl flexible? It would be somewhat easier to code if you allow the syntax \prefixurl{dbo}{City}. – Willie Wong Oct 22 '15 at 14:47
• Yes the syntax is flexible, the second one would equally useful. – Konrad Höffner Oct 22 '15 at 14:49
The following should work
\documentclass{article}
\usepackage{hyperref}
\makeatletter
\newcommand\defineprefix[2]{%
\expandafter\def\csname urlprefixabbrv@#1\endcsname{#2}}
\newcommand\prefixurl[2]{%
\href{\csname urlprefixabbrv@#1\endcsname/#2}{#1:#2}}
\makeatother
\begin{document}
\defineprefix{dbo}{http://dbpedia.org/ontology/}
\prefixurl{dbo}{City}
\end{document}
You are responsible yourself for keeping track you don't define the same prefix twice and overwrite each other.
• Thank you very much, this will be very useful for Semantic Web papers! – Konrad Höffner Oct 22 '15 at 14:57
• Unfortunately this only works with one defined prefix, how can I modify this so that I can define multiple prefixes? The error message is: "! Use of \urlprefixabbrv@ doesn't match its definition." – Konrad Höffner Dec 10 '15 at 11:48
• @KonradHöffner: it works for me. Can you past your code? The command \urlprefixabbrv@ should never be called by itself: the defined command should be \urlprefixabbrv@string where string is the class of prefix (in the example above, the command defined is \urlprefixabbrv@dbo). If you can construct a minimum non-working example, please edit it into the question and ping me again, and I'll see if I can debug. Right now I cannot reproduce your error so I don't know what it is that went wrong. – Willie Wong Dec 10 '15 at 14:30
• I added an MWE of the problem to the question. – Konrad Höffner Dec 11 '15 at 12:31
• @KonradHöffner: Ah, I sort-of see the problem. Try the version I am about to put up in 5 minutes. Some veterans however may come by and chide me for my poor code form. – Willie Wong Dec 11 '15 at 17:36
|
2019-11-21 18:11:32
|
{"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": 0.8174870610237122, "perplexity": 1815.8175918145323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670948.64/warc/CC-MAIN-20191121180800-20191121204800-00088.warc.gz"}
|
https://copyme.github.io/publication/2016-04-09-bijective-rigid-motions-of-the-2d-cartesian-grid
|
# Bijective Rigid Motions of the 2D Cartesian Grid
Published in DGCI, 2016
Recommended citation: Pluta K., Romon P., Kenmochi Y., Passat N. (2016) Bijective Rigid Motions of the 2D Cartesian Grid. In: Normand N., Guédon J., Autrusseau F. (eds) Discrete Geometry for Computer Imagery. DGCI 2016. Lecture Notes in Computer Science, vol 9647. Springer, pp 359-371, doi:10.1007/978-3-319-32360-2_28
Author(s): K. Pluta, P. Romon, Y. Kenmochi, N. Passat
Abstract: Rigid motions are fundamental operations in image processing. While they are bijective and isometric in $\mathbb{R}^2$, they lose these properties when digitized in $\mathbb{Z}^2$. To investigate these defects, we first extend a combinatorial model of the local behavior of rigid motions on $\mathbb{Z}^2$, initially proposed by Nouvel and Rémila for rotations on $\mathbb{Z}^2$. This allows us to study bijective rigid motions on $\mathbb{Z}^2$, and to propose two algorithms for verifying whether a given rigid motion restricted to a given finite subset of $\mathbb{Z}^2$ is bijective.
File(s): Pre-print (PDF), BibTeX
Errata is not provided but several typos and mistakes were corrected in the journal version of this paper (see Bijective Digitized Rigid Motions on Subsets of the Plane)
|
2018-12-12 18:42:33
|
{"extraction_info": {"found_math": true, "script_math_tex": 6, "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": 0.7489026188850403, "perplexity": 2223.4017246467192}, "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-2018-51/segments/1544376824115.18/warc/CC-MAIN-20181212181507-20181212203007-00513.warc.gz"}
|
https://chapel-lang.org/docs/usingchapel/chplenv.html
|
Setting up Your Environment for Chapel¶
To get started with Chapel, there are four environment settings that are strongly recommended for effective use of the release, and a few other optional settings that are useful for cross-compiling or overriding the default settings. To check the values of the Chapel environment variables that are set or can be inferred, run the script:
$CHPL_HOME/util/printchplenv The setchplenv.* source scripts in the $CHPL_HOME/util/quickstart/ and $CHPL_HOME/util/ directories contain commands that set the following variables for various shells and host platforms when they are sourced from the $CHPL_HOME directory. Frequent Chapel users may want to add such settings to their shell's dotfile(s); but for getting started the setchplenv.* scripts can be convenient.
Optional Settings¶
CHPL_TARGET_PLATFORM¶
If you are cross-compiling for a platform other than your $CHPL_HOST_PLATFORM, set the CHPL_TARGET_PLATFORM environment variable to describe that platform. See CHPL_HOST_PLATFORM above for legal values (though whether or not a given setting will support cross-compilation depends on your specific environment). Note If CHPL_TARGET_PLATFORM is not set, the target platform defaults to the same value as $CHPL_HOST_PLATFORM.
CHPL_*_COMPILER¶
Optionally, you can set CHPL_HOST_COMPILER and/or CHPL_TARGET_COMPILER to indicate the compiler suite to use in building the sources. CHPL_HOST_COMPILER is the compiler used to build the Chapel compiler itself so that it will run on CHPL_HOST_PLATFORM. CHPL_TARGET_COMPILER is the compiler used to build the runtime libraries and generated code for CHPL_TARGET_PLATFORM. Currently supported values are as follows:
Value Description
allinea The Allinea ARM compiler suite -- clang and clang++
clang The Clang compiler suite -- clang and clang++
clang-included The Clang compiler in third-party/llvm
cray-prgenv-allinea The Cray PrgEnv compiler using the Allinea backend
cray-prgenv-cray The Cray PrgEnv compiler using the Cray CCE backend
cray-prgenv-gnu The Cray PrgEnv compiler using the GNU backend
cray-prgenv-intel The Cray PrgEnv compiler using the Intel backend
cray-prgenv-pgi The Cray PrgEnv compiler using the PGI backend
gnu The GNU compiler suite -- gcc and g++
ibm The IBM compiler suite -- xlc and xlC
intel The Intel compiler suite -- icc and icpc
pgi The PGI compiler suite -- pgcc and pgc++
The default for CHPL_*_COMPILER depends on the value of the corresponding CHPL_*_PLATFORM environment variable:
Platform Compiler
cray-x*
• gnu (for CHPL_HOST_COMPILER)
• cray-prgenv-$PE_ENV (for CHPL_TARGET_COMPILER, where PE_ENV is set by PrgEnv-* modules) darwin clang if available, otherwise gnu pwr6 ibm other gnu If CHPL_HOST_PLATFORM == CHPL_TARGET_PLATFORM and is not cray-x*, CHPL_TARGET_COMPILER will default to the same value as CHPL_HOST_COMPILER. Note Note that builds with LLVM Support (i.e. when CHPL_LLVM=llvm) will build the runtime twice: once with the compiler as described above and once with clang-included. We do this in order to avoid issues in linking objects built by different compilers. CHPL_TARGET_ARCH¶ Optionally, set the CHPL_TARGET_ARCH environment variable to indicate that the target executable should be specialized to the given architecture when using --specialize (and --fast). Valid options are: Value Description native The C compiler will attempt to detect the architecture on the machine that is compiling the target executable. This is a good choice if you will be running on the same machine that you are compiling on. If you are not, see the options below. unknown No specialization will be performed none No specialization will be performed (will not warn) Architecture-specific values intel amd arm core2 k8 aarch64 nehalem k8sse3 thunderx westmere barcelona thunderx2t99 sandybridge bdver1 ivybridge bdver2 haswell bdver3 broadwell bdver4 skylake knl These values are defined to be the same as in GCC 7: If you do not want CHPL_TARGET_ARCH to have any effect, you can set it to either unknown or none. Both will disable specialization, but the latter will not warn if --specialize is used. Setting CHPL_TARGET_ARCH to an incorrect value for your processor may result in an invalid binary that will not run on the intended machine. Special care should be taken to select the lowest common denominator when running on machines with heterogeneous processor architectures. The default value for this setting will vary based on settings in your environment, in order of application these rules are: • If CHPL_TARGET_COMPILER is cray-prgenv-* you do not need to set anything in CHPL_TARGET_ARCH. One of the craype-* modules (e.g. craype-sandybridge) should be loaded to provide equivalent functionality. Once the proper module is loaded, CRAY_CPU_TARGET will have the architecture being used in it. • If CHPL_TARGET_COMPILER is cray, pgi, or ibm, CHPL_TARGET_ARCH will be set to none and no specialization will occur. • If CHPL_COMM is set, no attempt to set a useful value will be made, CHPL_TARGET_ARCH will be unknown. • If CHPL_TARGET_PLATFORM is darwin, linux*, or cygwin* CHPL_TARGET_ARCH will be native, passing the responsibility off to the backend C compiler to detect the specifics of the hardware. CHPL_MAKE¶ Optionally, set the CHPL_MAKE environment variable to indicate the GNU-compatible make utility that you want the compiler back-end to invoke when compiling the generated C code. If not set, this will default to a value based on $CHPL_HOST_PLATFORM:
platform make utility
cygwin*, darwin make
linux32, linux64 gmake if available, otherwise make
other gmake
CHPL_MODULE_PATH¶
Optionally, set the CHPL_MODULE_PATH environment variable to provide a list of directories to be added to the Module Search Paths. The value of this environment variable should be a colon-separated list of directory paths.
The module search path is used to satisfy 'use' statements in the Chapel program. The complete search path can be displayed using the compiler option --print-search-dirs. It will also include the compiler's standard module search paths, those introduced by the -M flag on the command line and directories containing the .chpl files named explicitly on the compiler command line.
CHPL_LOCALE_MODEL¶
Optionally, set the CHPL_LOCALE_MODEL environment variable to indicate the locale model you want to use. Current options are:
Value Description
flat top-level locales are not further subdivided
numa top-level locales are further subdivided into sublocales, each one a NUMA domain
knl a processor-specific locale model for the self-hosted Xeon Phi (Knight's Landing) which includes NUMA support and access to the tightly-coupled high-bandwidth memory
If unset, CHPL_LOCALE_MODEL defaults to flat.
Optionally, set the CHPL_TASKS environment variable to indicate what tasking layer you want to use to implement intra-locale parallelism (see Chapel Tasks for more information on this option). Current options are:
Value Description
If CHPL_TASKS is not set it defaults to qthreads in all cases except for a few specific configurations in which it defaults to fifo:
• target platform is cygwin*
• target platform is netbsd*
Note
Note that the Chapel util/quickstart/setchplenv.* source scripts set CHPL_TASKS to fifo to reduce build-time and third-party dependences, while the util/setchplenv.* versions leave it unset, resulting in the behavior described just above.
See Chapel Tasks for more information about executing using the various CHPL_TASKS options.
CHPL_COMM¶
Optionally, set the CHPL_COMM environment variable to indicate what communication layer you want to use to implement inter-locale communication. Current options are:
Value Description
none only supports single-locale execution
gasnet use the GASNet-based communication layer
ugni Cray-specific native communication layer
If unset, CHPL_COMM defaults to none in most cases. On Cray XE and XC systems it defaults to ugni. On Cray CS systems it defaults to gasnet. See Multilocale Chapel Execution for more information on executing Chapel programs using multiple locales. See Using Chapel on Cray Systems for more information about Cray-specific runtime layers.
CHPL_MEM¶
Optionally, the CHPL_MEM environment variable can be used to select a memory management layer. Current options are:
Value Description
cstdlib use the standard C malloc/free commands
jemalloc use Jason Evan's memory allocator
If unset, CHPL_MEM defaults to jemalloc for most configurations. If the target platform is cygwin* it defaults to cstdlib
Note
Certain CHPL_COMM settings (e.g. ugni and gasnet segment fast/large) register the heap to improve communication performance. Registering the heap requires special allocator support that not all allocators provide. Currently only jemalloc is capable of supporting configurations that require a registered heap.
CHPL_LAUNCHER¶
Optionally, the CHPL_LAUNCHER environment variable can be used to select a launcher to get your program up and running. See Chapel Launchers for more information on this variable's default and possible settings.
CHPL_ATOMICS¶
Optionally, the CHPL_ATOMICS environment variable can be used to select an implementation for atomic operations in the runtime. Current options are:
Value Description
cstdlib implement Chapel atomics as a wrapper around C standard atomics (from C11)
intrinsics implement atomics using target compiler intrinsics (which typically map down to hardware capabilities)
locks implement atomics by using mutexes to protect normal operations
If unset, CHPL_ATOMICS defaults to intrinsics for most configurations. On some 32 bit platforms, or if the target compiler is pgi or cray-prgenv-pgi it defaults to locks. In a future release, cstdlib will become the default whenever possible. At this time, though, most C compilers either do not support standard atomics or have bugs in their implementation.
Note
gcc 4.8.1 added support for 64 bit atomics on 32 bit platforms. We default to intrinsics for 32 bit platforms when using the target compiler gnu with a recent enough version of gcc. For older versions or other target compilers we default to locks
CHPL_TIMERS¶
Optionally, the CHPL_TIMERS environment variable can be used to select an implementation for Chapel's timers. Current options are:
generic
use a gettimeofday()-based implementation
If unset, CHPL_TIMERS defaults to generic
CHPL_GMP¶
Optionally, the CHPL_GMP environment variable can select between no GMP support, using the GMP distributed with Chapel in third-party, or using a system GMP. Current options are:
Value Description
system use a system install of GMP (#include gmp.h, -lgmp)
none do not build GMP support into the Chapel runtime
gmp use the GMP distribution bundled with Chapel in third-party
If unset, Chapel will attempt to build GMP using CHPL_TARGET_COMPILER (noting that the bundled version may not be supported by all compilers). Based on the outcome, Chapel will default to:
Value Description
gmp if the build was successful
system if unsuccessful and CHPL_TARGET_PLATFORM is cray-x*
none otherwise
Note
Note that the Chapel util/quickstart/setchplenv.* source scripts set CHPL_GMP to none while the util/setchplenv.* versions leave it unset, resulting in the behavior described just above.
CHPL_HWLOC¶
Optionally, the CHPL_HWLOC environment variable can select between no hwloc support or using the hwloc package distributed with Chapel in third-party.
Value Description
none do not build hwloc support into the Chapel runtime
hwloc use the hwloc distribution bundled with Chapel in third-party
If unset, CHPL_HWLOC defaults to hwloc if CHPL_TASKS is qthreads. In all other cases it defaults to none. In the unlikely event the bundled hwloc distribution does not build successfully, it should still be possible to use qthreads. To do this, manually set CHPL_HWLOC to none and rebuild (and please file a bug with the Chapel team.) Note that building without hwloc will have a negative impact on performance.
CHPL_REGEXP¶
Optionally, the CHPL_REGEXP environment variable can be used to enable regular expression operations as defined in Regexp. Current options are:
Value Description
re2 use the re2 distribution in third-party
none do not support regular expression operations
If unset, Chapel will attempt to build RE2 using CHPL_TARGET_COMPILER (noting that the bundled version may not be supported by all compilers). Based on the outcome, Chapel will default to:
Value Description
re2 if the build was successful
none otherwise
Note
Note that the Chapel util/quickstart/setchplenv.* source scripts set CHPL_REGEXP to 'none while the util/setchplenv.* versions leave it unset, resulting in the behavior described just above.
CHPL_AUX_FILESYS¶
Optionally, the CHPL_AUX_FILESYS environment variable can be used to request that runtime support for filesystems beyond the usual Linux one be present. Current options are:
Value Description
none only support traditional Linux filesystems
hdfs also support HDFS filesystems using Apache Hadoop libhdfs
hdfs3 support for HDFS filesystems using Pivotal libhdfs3
curl also support CURL as a filesystem interface
If unset, CHPL_AUX_FILESYS defaults to none.
See Auxiliary I/O Systems, HDFS, and Curl for more information about HDFS and CURL support.
CHPL_LLVM¶
Optionally, the CHPL_LLVM environment variable can be used to enable support for the LLVM back-end to the Chapel compiler (see LLVM Support) or to support extern blocks in Chapel code via the Clang compiler (see C Interoperability). Current options are:
Value Description
llvm use the llvm/clang distribution in third-party
system find a compatible LLVM in system libraries; note: the LLVM must be a version supported by Chapel
none do not support llvm-/clang-related features
If unset, CHPL_LLVM defaults to llvm if you've already installed llvm in third-party and none otherwise.
Chapel currently supports LLVM 6.0. Earlier versions of LLVM required the use of internal Clang header files. LLVM 5.0 has a known optimization bug that affects Chapel.
Note
We have had success with this procedure to install LLVM 6.0 dependencies on Ubuntu.
First, place the appropriate lines from https://apt.llvm.org into /etc/apt/sources.list.d/llvm-toolchain.list, then do the following.
apt-get install llvm-6.0-dev llvm-6.0 llvm-6.0-tools clang-6.0 libclang-6.0-dev libedit-dev
CHPL_UNWIND¶
Optionally, the CHPL_UNWIND environment variable can be used to select an unwind library for stack tracing. Current options are:
Value Description
libunwind use the libunwind bundled with Chapel in third-party
system assume libunwind is already installed on the system
none don't use an unwind library, disabling stack tracing
If unset, CHPL_UNWIND defaults to none
Compiler Command Line Option Defaults¶
Most of the compiler's command line options support setting a default value for the option via an environment variable. To see a list of the environment variables that support each option, run the compiler with the --help-env flag. For boolean flags and toggles, setting the environment variable to any value selects that flag.
Chapel Configuration File¶
The Chapel configuration file is a file named either chplconfig or .chplconfig that can store overrides of the inferred environment variables listed as a result of executing printchplenv.
Syntax¶
Below are the valid forms of syntax for Chapel configuration files. All other usages will result in a syntax error.
Definitions
Users can define variables with the following format:
CHPL_ENV=value
Above, the default value of CHPL_ENV will be overridden to be value. All white space is stripped away from definitions.
Ignored Lines
Any lines containing nothing or only white space will be ignored. Comments, which are denoted by the # character, similar to bash or python, are also ignored.
Example¶
Below is an example of a Chapel configuration file with comments:
# ~/.chplconfig
# Default to multi-locale
CHPL_COMM=gasnet
# System GMP is available on these machines
CHPL_GMP=system
To confirm the configuration file is written correctly, you can run printchplenv --all --overrides, which will show a list of variables that are currently being overridden. Values followed by a + have been overridden by the Chapel configuration file, whereas values followed by a * have been overridden by an environment variable.
Generating Configuration Files¶
To generate a configuration file based on the current configuration, use printchplenv or ./configure.
When using printchplenv, run it with the --simple format flag to get a format compatible with Chapel configuration files.
The --overrides filter flag can be used to print only the variables currently overridden by either environment variables or Chapel configuration file.
For example, to save the current overrides into a Chapel configuration file:
printchplenv --all --simple --overrides > ~/.chplconfig
The printchplenv --all --simple flag can be used to print all the variables of the current configuration. For example:
printchplenv --all --simple > ~/.chplconfig
For more information on using printchplenv, see the printchplenv -h output.
Alternatively, the ./configure script will generate a chplconfig file. See Installing Chapel.
Search Paths and File Names¶
Though you can put your Chapel configuration file anywhere by setting the $CHPL_CONFIG environment variable to its enclosing directory, you can also place it in your $HOME or $CHPL_HOME directory and Chapel will be able to find it. The search priority for Chapel configuration files is as follows: 1. $CHPL_CONFIG
2. $HOME (~/) 3. $CHPL_HOME
When both a chplconfig and .chplconfig are present, the visible chplconfig will be prioritized.
Only a single chplconfig file will be used. That is, as soon as a valid Chapel configuration file is found, the definitions of that file are used.
Note
The \$CHPL_CONFIG variable is the path to the enclosing directory - not the full path including chplconfig itself.
Variable Priority¶
Variable precedence goes in the following order:
1. Explicit compiler flags: chpl --env=value
2. Environment variables: CHPL_ENV=value
3. Chapel configuration file: ~/.chplconfig
4. Inferred environment variables: printchplenv
|
2019-01-19 20:45:49
|
{"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": 0.17617295682430267, "perplexity": 12007.764738215546}, "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-2019-04/segments/1547583681597.51/warc/CC-MAIN-20190119201117-20190119223117-00488.warc.gz"}
|
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2008_v45n6_1623
|
DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES
Title & Authors
DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES
Cho, Jung-R.; Gould, Ronald J.;
Abstract
The complete multipartite graph $\small{K_{n(2t)}}$ having n partite sets of size 2t, with $\small{n\;{\geq}\;6}$ and $\small{t\;{\geq}\;1}$, is shown to have a decomposition into gregarious 6-cycles, that is, the cycles which have at most one vertex from any particular partite set. Complete sets of differences of numbers in $\small{{\mathbb{Z}}_n}$ are used to produce starter cycles and obtain other cycles by rotating the cycles around the n-gon of the partite sets.
Keywords
multipartite graph;graph decomposition;gregarious cycle;difference set;
Language
English
Cited by
1.
ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES,;
East Asian mathematical journal , 2013. vol.29. 3, pp.337-347
2.
CIRCULANT DECOMPOSITIONS OF CERTAIN MULTIPARTITE GRAPHS INTO GREGARIOUS CYCLES OF A GIVEN LENGTH,;
East Asian mathematical journal , 2014. vol.30. 3, pp.311-319
1.
CIRCULANT DECOMPOSITIONS OF CERTAIN MULTIPARTITE GRAPHS INTO GREGARIOUS CYCLES OF A GIVEN LENGTH, East Asian mathematical journal , 2014, 30, 3, 311
2.
A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES, Bulletin of the Korean Mathematical Society, 2007, 44, 4, 709
3.
ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES, East Asian mathematical journal , 2013, 29, 3, 337
4.
Some gregarious kite decompositions of complete equipartite graphs, Discrete Mathematics, 2013, 313, 5, 726
References
1.
B. Alspach and H. Gavlas, Cycle decompositions of $K_{n}$ and $K_{n}$ − I, J. Combin. Theory Ser. B 81 (2001), no. 1, 77-99
2.
E. Billington and D. G. Hoffman, Decomposition of complete tripartite graphs into gregarious 4-cycles, Discrete Math. 261 (2003), no. 1-3, 87-111
3.
E. Billington, D. G. Hoffman, and C. A. Rodger, Resolvable gregarious cycle decompositions of complete equipartite graphs, Preprint
4.
N. J. Cavenagh and E. J. Billington, Decomposition of complete multipartite graphs into cycles of even length, Graphs Combin. 16 (2000), no. 1, 49-65
5.
J. R. Cho, M. J. Ferrara, R. J. Gould, and J. R. Schmitt, Difference sets generating gregarious 4-cycle decomposition of complete multipartite graphs. Preprint
6.
J. Liu, A generalization of the Oberwolfach problem and $C_{t}$-factorizations of complete equipartite graphs, J. Combin. Des. 8 (2000), no. 1, 42-49
7.
M. Sajna, Cycle decompositions. III. Complete graphs and fixed length cycles, J. Combin. Des. 10 (2002), no. 1, 27-78
8.
M. Sajna, On decomposing $K_{n}$ I into cycles of a fixed odd length, Discrete Math. 244 (2002), no. 1-3, 435-444
9.
D. Sotteau, Decomposition of $K_{m,n}$($K^{*}_{m,n}$) into cycles (circuits) of length 2$\kappa$, J. Combin. Theory Ser. B 30 (1981), no. 1, 75-81
|
2017-07-20 22:49:16
|
{"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": 4, "/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": 0.5581536889076233, "perplexity": 2588.9910674381076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423512.93/warc/CC-MAIN-20170720222017-20170721002017-00291.warc.gz"}
|
https://irzu.org/research/bugs-mate-panel-package-ubuntu/
|
Bugs : mate-panel package : Ubuntu
Steps to reproduce:
1) sudo apt install virtualbox
2) See that it doesn’t appear in the menus
3) To make it appear, run any ONE of the following actions:
3b) Or run: mate-panel –reset
3c) Or fake any menu file modification to cause a rescan:
sudo sed ‘s/a/a/’ -i /usr/share/applications/mate-calc.desktop
This isn’t a problem in the VirtualBox packaging. All other desktop environments correctly show its menu. It’s a race condition that affects other packages as well; I’ll try to explain it below.
When installing virtualbox, the following things happen:
1) The virtualbox package is unpacked and it provides a binary at /usr/share/virtualbox/VBox.sh.
2) The virtualbox-qt package is unpacked and it provides the menu at /usr/share/applications/virtualbox.desktop.
3) MATE scans for menu changes. It sees that virtualbox.desktop contains this line: TryExec=VirtualBox
It tries to locate a VirtualBox binary, and fails because it doesn’t exist yet. It marks that menu as invalid.
4) A split second later the virtualbox-qt installation continues and the debhelper code that corresponds to debian/virtualbox-qt.links creates the /usr/share/virtualbox/VBox.sh /usr/bin/VirtualBox symlink and makes the VirtualBox binary available.
So the menu doesn’t show up because it was marked as “missing executable” at step (3); it will show up if we ping the backend to scan the menus once more.
The solution would be to postpone the backend scanning for a second, when the symlink will exist.
Note that even though brisk-menu defines BRISK_RELOAD_TIME 2000, I think this isn’t appropriate because it re-uses the wrong backend information from 2 seconds ago, when the symlink was missing.
|
2022-11-27 12:31:47
|
{"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": 0.25169292092323303, "perplexity": 7480.277225061753}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710237.57/warc/CC-MAIN-20221127105736-20221127135736-00031.warc.gz"}
|
http://mathhelpforum.com/trigonometry/120370-trigonometric-identity.html
|
# Thread: Trigonometric identity
1. ## Trigonometric identity
Can somebody solve this and give detailed description ?
I get stuck on this part 1/2 sin18..
2. ## sin 18 degrees
Hello ldx2
Welcome to Math Help Forum!
Originally Posted by ldx2
Can somebody solve this and give detailed description ?
I get stuck on this part 1/2 sin18..
I agree: $\sin^224^o-\sin^26^o = \tfrac12\sin 18^o$.
There are various ways of deriving $\sin18^o$. Here's one. And here's my version:
$\sin 18^o = \cos 72^o = 2\cos^236^o-1=2(1-2\sin^218)^2-1$
So if we put $x = \sin18^o, x$ is the root of the equation:
$x = 2(1-2x^2)^2-1$
for which $0.
$\Rightarrow x=2(1-4x^2+4x^4)-1$
$\Rightarrow 8x^4-8x^2-x+1=0$
Noting that $x = 1$ satisfies this equation, we can factorise:
$(x-1)(8x^3+8x^2-1)=0$
and then discard the factor $(x-1)$, since $0.
We then note that $x = -\tfrac12$ is also a root. Hence $(2x+1)$ is a factor, which again we discard for the same reason; leaving us with the remaining factor:
$4x^2+2x-1=0$
the positive root of which is:
$x = \frac{\sqrt5-1}{4}=\sin18^o$
Hence $\sin^224^o-\sin^26^o = \frac{\sqrt5-1}{8}$
Grandad
3. Thanks for the quick reply and solving it. EDIT: I understood until the part where you say x=-1/2 is also a root and how you found out (2x+1) is also a factor. Could you explain that part in more detail ?
4. Hello ldx2
Originally Posted by ldx2
Thanks for the quick reply and solving it. EDIT: I understood until the part where you say x=-1/2 is also a root and how you found out (2x+1) is also a factor. Could you explain that part in more detail ?
By inspection (which is a posh word for 'trial and error'), when $x = -\tfrac12, 8x^3+8x^2-1= -1+2-1=0$. So, using the remainder theorem, $(2x+1)$ is a factor.
Grandad
5. LOL 'trial and error' ! Thank you for clearing it up. Could you please take a look at my other thread where i posted 2 trig. problems !
|
2017-06-28 14:38:01
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9339509606361389, "perplexity": 1091.674343303814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323682.21/warc/CC-MAIN-20170628134734-20170628154734-00397.warc.gz"}
|
https://datascience.stackexchange.com/questions/25152/why-svm-classifier-error-is-much-smaller-than-knn-classifier-error
|
# Why SVM classifier error is much smaller than KNN classifier error?
I have a dataset with a binary classification, on which I train a kNN algorithm and a SVM algorithm.
On the tests set I get approximately 75% error when using kNN, but only approximately a 20% error using an SVM.
What does this tell me about the dataset?
|
2021-11-30 03:11:59
|
{"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": 0.805578351020813, "perplexity": 1229.390417316578}, "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/1637964358903.73/warc/CC-MAIN-20211130015517-20211130045517-00358.warc.gz"}
|
https://byjus.com/question-answer/if-the-value-of-principal-quantum-number-is-3-the-total-possible-values-for-magnetic/
|
Question
# If the value of principal quantum number is 3, the total possible values for magnetic quantum number will be?
A
5
B
9
C
8
D
10
Solution
## The correct option is C 5The azimuthal quantum number $$(l) =n-1$$$$=3-1$$$$=2$$Therefore, the total possible values of magnetic quantum number (m) are$$m= 2l+1$$$$=2(2)+1$$$$=4+1$$$$m=5$$Chemistry
Suggest Corrections
0
Similar questions
View More
People also searched for
View More
|
2022-01-17 20:40:06
|
{"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": 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": 0.2912590503692627, "perplexity": 3591.4428275679065}, "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-2022-05/segments/1642320300616.11/warc/CC-MAIN-20220117182124-20220117212124-00022.warc.gz"}
|
https://www.rdocumentation.org/packages/brms/versions/2.4.0/topics/make_standata
|
make_standata
0th
Percentile
Data for brms Models
Generate data for brms models to be passed to Stan
Usage
make_standata(formula, data, family = gaussian(), prior = NULL,
autocor = NULL, cov_ranef = NULL, sample_prior = c("no", "yes", "only"),
stanvars = NULL, knots = NULL, check_response = TRUE,
only_response = FALSE, control = list(), ...)
Arguments
formula
An object of class formula, brmsformula, or mvbrmsformula (or one that can be coerced to that classes): A symbolic description of the model to be fitted. The details of model specification are explained in brmsformula.
data
An object of class data.frame (or one that can be coerced to that class) containing data of all variables used in the model.
family
A description of the response distribution and link function to be used in the model. This can be a family function, a call to a family function or a character string naming the family. Every family function has a link argument allowing to specify the link function to be applied on the response variable. If not specified, default links are used. For details of supported families see brmsfamily. By default, a linear gaussian model is applied. In multivariate models, family might also be a list of families.
prior
One or more brmsprior objects created by set_prior or related functions and combined using the c method or the + operator. See also get_prior for more help.
autocor
An optional cor_brms object describing the correlation structure within the response variable (i.e., the 'autocorrelation'). See the documentation of cor_brms for a description of the available correlation structures. Defaults to NULL, corresponding to no correlations. In multivariate models, autocor might also be a list of autocorrelation structures.
cov_ranef
A list of matrices that are proportional to the (within) covariance structure of the group-level effects. The names of the matrices should correspond to columns in data that are used as grouping factors. All levels of the grouping factor should appear as rownames of the corresponding matrix. This argument can be used, among others to model pedigrees and phylogenetic effects. See vignette("brms_phylogenetics") for more details.
sample_prior
Indicate if samples from all specified proper priors should be drawn additionally to the posterior samples (defaults to "no"). Among others, these samples can be used to calculate Bayes factors for point hypotheses. If set to "only", samples are drawn solely from the priors ignoring the likelihood. In this case, all parameters must have proper priors.
stanvars
An optional stanvars object generated by function stanvar to define additional variables for use in Stan's program blocks.
knots
Optional list containing user specified knot values to be used for basis construction of smoothing terms. See gamm for more details.
check_response
Logical; check validity of the response?
only_response
Logical; extract data related to the response only?
control
A named list currently for internal usage only
...
Other potential arguments
Value
A named list of objects containing the required data to fit a brms model with Stan.
Aliases
• make_standata
Examples
# NOT RUN {
data1 <- make_standata(rating ~ treat + period + carry + (1|subject),
data = inhaler, family = "cumulative")
names(data1)
data2 <- make_standata(count ~ log_Age_c + log_Base4_c * Trt_c
+ (1|patient) + (1|visit),
data = epilepsy, family = "poisson")
names(data2)
# }
Documentation reproduced from package brms, version 2.4.0, License: GPL (>= 3)
Community examples
Looks like there are no examples yet.
|
2018-08-15 08:57:21
|
{"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": 0.17478738725185394, "perplexity": 3580.555972176975}, "config": {"markdown_headings": false, "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-2018-34/segments/1534221210040.24/warc/CC-MAIN-20180815083101-20180815103101-00102.warc.gz"}
|