url
stringlengths 14
2.42k
| text
stringlengths 100
1.02M
| date
stringlengths 19
19
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|---|
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2014.34.4781
|
# American Institute of Mathematical Sciences
November 2014, 34(11): 4781-4806. doi: 10.3934/dcds.2014.34.4781
## Self-intersections of trajectories of the Lorentz process
1 Université de Brest, UMR CNRS 6205, Laboratoire de Mathématique de Bretagne Atlantique, 6 avenue Le Gorgeu, 29238 Brest cedex, France
Received April 2013 Revised February 2014 Published May 2014
We are interested in the asymptotic behaviour of the number of self-intersections of a trajectory of a Lorentz process in a $\mathbb Z^2$-periodic planar domain with strictly convex obstacles and with finite horizon. We give precise estimates for its expectation and its variance. As a consequence, we establish the almost sure convergence of the self-intersections with a suitable normalization.
Citation: Françoise Pène. Self-intersections of trajectories of the Lorentz process. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4781-4806. doi: 10.3934/dcds.2014.34.4781
##### References:
show all references
##### References:
[1] Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228 [2] Zemer Kosloff, Terry Soo. The orbital equivalence of Bernoulli actions and their Sinai factors. Journal of Modern Dynamics, 2021, 17: 145-182. doi: 10.3934/jmd.2021005 [3] Xiaohong Li, Mingxin Sun, Zhaohua Gong, Enmin Feng. Multistage optimal control for microbial fed-batch fermentation process. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021040 [4] Thomas Y. Hou, Ruo Li. Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 637-642. doi: 10.3934/dcds.2007.18.637 [5] Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115
2019 Impact Factor: 1.338
|
2021-03-04 03:39:51
|
{"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": 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": 0.5846250057220459, "perplexity": 4546.416640754512}, "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/1614178368431.60/warc/CC-MAIN-20210304021339-20210304051339-00216.warc.gz"}
|
https://economics.stackexchange.com/questions/21520/constant-regressor-in-gls/21526#21526
|
# Constant Regressor in GLS
Consider the following regression model:
$$y_{i1}=\beta_1 +u_{i1}$$
$$y_{i2}=\beta_{21}+\beta_{22}x_i+u_{i2}$$.
If $$E(x_i' u_{i1})\neq 0$$ and $$E(x_i' u_{i2})=0$$, will we get consistent estimators for $$\beta_1$$ and $$\beta_{21}$$ using GLS?
I think we will not get consistent estimators for both, because the assumption $$E(x_i\otimes u_i)=0$$ is violated. Please correct me if I am wrong. Thanks in advance!
• Your question needs a lot of polishing. First of all, can you state the statistical relationship between $u_{i1}$ and $u_{i2}$? Are they independent, mean independent, orthogonal? Secondly, in order to estimate the parameter of interest using GLS, we need further information about the (conditional) second moment $E(u_{i2}^2\vert x_i)$. Apr 18 '18 at 0:18
The equation-wise OLS estimators are consistent under the further normalization that $E(u_{i1})=0$ and $E(u_{i2})=0$, which are naturally assumed to be satisfied. For GLS, I don't know what you mean by GLS, but if you mean the SUR estimator, then I see no reasons why inconsistent. The fact that $E(x_i' u_{i1}) \ne 0$ is irrelevant because $x_i$ is not a regressor in the first equation.
|
2022-01-23 21:58:48
|
{"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": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9184065461158752, "perplexity": 296.77190913634547}, "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/1642320304309.59/warc/CC-MAIN-20220123202547-20220123232547-00390.warc.gz"}
|
http://martinos.org/mne/stable/auto_examples/preprocessing/plot_head_positions.html
|
Show how subjects move as a function of time.
# Authors: Eric Larson <larson.eric.d@gmail.com>
#
from os import path as op
import mne
print(__doc__)
data_path = op.join(mne.datasets.testing.data_path(verbose=True), 'SSS')
Visualize the subject head movements as traces:
mne.viz.plot_head_positions(pos, mode='traces')
Or we can visualize them as a continuous field (with the vectors pointing in the head-upward direction):
mne.viz.plot_head_positions(pos, mode='field')
Total running time of the script: ( 0 minutes 1.773 seconds)
Estimated memory usage: 9 MB
Gallery generated by Sphinx-Gallery
|
2019-02-17 15:43:44
|
{"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": 0.2727159559726715, "perplexity": 14171.430474994831}, "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-2019-09/segments/1550247482186.20/warc/CC-MAIN-20190217152248-20190217174248-00159.warc.gz"}
|
https://www.scipedia.com/public/Simoni_et_al_2007a
|
## Abstract
Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes in natural systems, such as rivers, lakes, and aquifers. We propose a novel mixing ratios‐based formulation to evaluate solute concentrations and reaction rates when equilibrium aqueous reactions and precipitation/dissolution of minerals are driven by mixing of different end‐members. Each end‐member corresponds to a water from a given source with a specific chemical signature. The approach decouples the solute transport and chemical speciation problems, so that mixing ratios can be first obtained from the solution of conservative transport and then be used in general speciation codes to obtain the concentration of reacting species. One key finding is a general expression for reaction rates which demonstrates that the amount of reactants evolving into products depends on the rate at which solutions mix. Our formulation constitutes a general framework according to which one can design and interpret experimental analyses devoted to study mixing‐driven reactive processes and obtain transverse dispersion coefficients. The formulation is also proposed as a useful tool to derive analytical solutions of reactive transport problems and may result computationally advantageous when compared to previous approaches to reactive transport modeling. We apply the developed formulation to provide an analytical solution of the reactive transport process resulting from mixing different CaCO${\displaystyle _{3}}$‐saturated waters in a two‐dimensional setup.
## Full Document
### Document information
Published on 01/01/2007
DOI: 10.1029/2006WR005256
|
2020-04-05 13:30:03
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49011895060539246, "perplexity": 1387.6836182089667}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371604800.52/warc/CC-MAIN-20200405115129-20200405145629-00411.warc.gz"}
|
http://www.gradesaver.com/textbooks/math/other-math/basic-college-mathematics-9th-edition/chapter-9-basic-algebra-9-6-solving-equations-9-6-exercises-page-670/7
|
# Chapter 9 - Basic Algebra - 9.6 Solving Equations - 9.6 Exercises: 7
8, -5
#### Work Step by Step
For $m-8=1$, I would add 8 to both sides. Adding 8 to both sides would give us $m-8+8=m$ on the left side. This would isolate the variable on one side. For $-7=w+5$, I would add -5 to both sides. Adding -5 to both sides would give us $w+5-5=w$ on the right side. This would isolate the variable on one side.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
|
2017-05-25 01:20:53
|
{"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": 0.38746902346611023, "perplexity": 476.5703669490954}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607960.64/warc/CC-MAIN-20170525010046-20170525030046-00478.warc.gz"}
|
http://wlm.userweb.mwn.de/Stata/wstatgax.htm
|
# Graphs: Axes
Prologue: Note that there is a difference between twoway graphs (the most common variety) and univariate (or oneway) graphs. Whereas the former have an x and a y axis, the latter have only a y axis, even though they may sometimes "look like" twoway graphs. For instance, a box-and-whisker plot showing the distribution of a variable for several groups is still considered a univariate graph; hence you cannot use options that refer to the x axis. The final subsection of this section gives some hints that refer to this case.
## Range of axes
You can determine the range of the axes via xsc and ysc. Note that you cannot restrict display of values to a smaller set of values than are present in the data; all you can do is to expand the axes beyond the smallest and / or largest values.
xsc(r(0 1)) ysc(r(0 50))
will set the minimum of both axes to 0, the maximum of the x axis to 1 and the maximum of the y axis to 50. If, say, the minimum value of y is 0, you may omit this value in ysc, mentioning only the upper value of 50 within the parenthesis.
Some graphs, such as bar charts, begin the y axis at 0 (zero) by default, and this cannot be overridden solely with ysc, even if zero is not the smallest value in the data. In such cases, try adding exclude0 to the list of options.
## Grid lines
Often, the default display of a Stata graph includes grid lines, typically on the y axis. If the graph you wish to produce does not contain grid lines by default, this can be amended via the grid option, as in:
ylabel(0(2000)10000, angle(0) grid)
Conversely, if you wish to suppress grid lines that are displayed by default, you may use the nogrid option.
## Axis values (labels)
You can influence which values are displayed (and ticked) on each axis. For instance, if the x axis ranges from 0 to 10,000, you may wish to display values at 0, 2000, 4000 and so forth. The command to achieve this is:
xlabel(0(2000)10000)
The same rules apply to the ylabel command.
The values on the y axis by default are displayed vertically. If you wish to display them horizontally, you have to add a (sub-)option to the ylabel command. If this sub-option is used alone, the command will look like this:
ylabel(,angle(0))
In combination with a definition of the values to be labeled it would look like this:
ylabel(0(2000)10000, angle(0))
## Customizing labels
In most cases, Stata will use the numerical values (representing the different categories) of a variable to label the axes of a graph. If the categories have been labeled, Stata will use those labels only if a variable is used to represent different groups, such as when a box plot is created together with the over option.
In other cases, you have to request Stata explicitly if value labels are to be used as axis labels. The way to achieve this is the valuelabels suboption, as in
histogram isced, discrete gap(25) xlabel(, valuelabel)
But you may also submit the labels to be used in the graph explicitly, which is particularly useful if the existing value labels are somewhat longish, such as in:
histogram isced, discrete gap(25) xlabel(1 "Low" 2 "Intermediate" 3 "High")
Normally, labels are displayed side by side on the x axis. This may sometimes cause trouble if there are many labels or labels are long. You may use the alternate (or alt) option which will create an offset between labels:
xlabel(1 "Low income" 2 "Intermediate income" 3 "High income", alt)
## Sizes of axis values (labels)
The size of the axis labels can be changed with the labsize sub-option within the xlabel or the ylabel option. So,
ylabel(0(2000)10000, axis(0) labsize(medlarge))
will render the labels somewhat larger.
The information available via help textsizestyle, which was introduced above, is also valid for the size of labels.
## What if there is no x axis?
A typical case of a plot with only an apparent x axis is a boxplot showing the distributions of a number of groups. As is shown elsewhere, such a plot is produced using the over option, as in
graph box income, over(status)
Therefore, any options that refer to the labeling of the pseudo-x-axis have to be included as sub-options to the over option. For instance, to display the values (or labels) that denote the different groups in a larger font, you may include the label sub-option:
graph box income, over(status, label(labsize(medlarge))
© W. Ludwig-Mayerhofer, Stata Guide | Last update: 18 Apr 2017
|
2019-03-18 13:54:48
|
{"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": 0.5062364339828491, "perplexity": 1274.6540552495385}, "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/1552912201329.40/warc/CC-MAIN-20190318132220-20190318154220-00384.warc.gz"}
|
https://mathoverflow.net/questions/354514/how-to-prove-a-result-related-to-prime-number-theorem-in-research-paper-of-rivoa
|
# How to prove a result related to prime number theorem in research paper of Rivoal and Zudilin
Question is ->I am studying research paper: A note on odd zeta values and I am unable to think how to deduce a result which the authors don't prove. This result has to be proved assuming the prime number theorem and it's on Page 12 of the paper :
Prove that $$\lim_ {n\to\infty} \frac{\log(\Phi_n) } {n} =\int_0^{1} \rho_0 (t) d(\psi(t) + 1/t)$$, where $$\psi(t)$$ = $$\frac {\Gamma'(t) } {\Gamma(t) }$$.
where $$\Phi(n)$$ and $$\rho(n)$$ are described in this image:
Can someone please tell how to prove this result ?
I shall be really thankful.
• This question already had an accepted answer. Why have you bumped it with an edit? Jan 6 at 0:41
If we start by partitioning the range of summation into intervals on which $$\rho_0(\frac np)$$ is constant, we obtain \begin{align*} \log \Phi_n &= \sum_{2\sqrt n where $$\theta(x) = \sum_{p\le x} \log p \sim x$$ by the prime number theorem. Thus \begin{align*} \log \Phi_n &\sim \sum_{k=6}^{3\sqrt n-1} \rho_0\big( \tfrac k6 \big) \big( \tfrac{6n}k - \tfrac{6n}{k+1} \big) \sim 6n \sum_{k=6}^\infty \frac{\rho_0(k/6)}{k(k+1)}. \end{align*} A similar partitioning calculation on the integral will hopefully lead to the same result.
• in the fifth line of your answer how did you change $\sum_{2√n<p$\leq$n$ = $\sum_{k=6}^{3√n-1}$ $\sum_{6n/(k+1) p$\leq$6n/k) . Can you please elaborate why it is right? Mar 20, 2020 at 5:36 • There was a typo (now fixed). We're just splitting up the interval of summation from the first line into$3\sqrt n-1$consecutive intervals of summation. Mar 20, 2020 at 7:33 • On the first line, every prime between$2\sqrt n$and$n$appears exactly once, and smaller or larger primes don't appear at all. On the second line, do any primes smaller than$2\sqrt n$or larger than$n$appear? Given a prime$p$between$2\sqrt n$and$n$, for how many values of$k$will$p\$ appear in the inner sum? Apr 16, 2020 at 15:30
• We're just splitting up the range of summation into intervals on which the function is simpler. A strong analogy would be the computation $$\int_0^N \lfloor x\rfloor^2\,dx = \sum_{k=0}^{N-1} \int_k^{k+1} \lfloor x\rfloor^2\,dx = \sum_{k=0}^{N-1} k^2 \int_k^{k+1} 1\,dx.$$ Apr 16, 2020 at 15:32
|
2022-08-13 02:19:07
|
{"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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9817017316818237, "perplexity": 283.13623974804534}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571869.23/warc/CC-MAIN-20220813021048-20220813051048-00092.warc.gz"}
|
https://math.stackexchange.com/questions/3239446/how-to-prove-that-left-frac1n2-right-is-cauchy-sequence
|
# How to prove that $\left\{\frac{1}{n^{2}}\right\}$ is Cauchy sequence
How can I prove that $$\left\{\frac{1}{n^{2}}\right\}$$ is a Cauchy sequence?
A sequence of real numbers $$\left\{x_{n}\right\}$$ is said to be Cauchy, if for every $$\varepsilon>0$$, there exists a positive integer $$N(\varepsilon)$$ such that $$\mid x_{n+p}-x_{n}\mid <\varepsilon$$ for all $$n\geq N$$ and $$p= 1, 2, 3,...$$
So I approached like this...
$$\mid \frac{1}{(n+p)^{2}}-\frac{1}{n^{2}}\mid = \frac{p(2n+p)}{n^{2}(n+p)^{2}}<\frac{p(2n+p)}{n^{2}} <\varepsilon$$
From here, I have to show that $$n>$$ some expression involving $$\varepsilon$$, because that expression will be the value of $$N$$. But I am getting stuck here.
Please anyone help me solve it. Thanks in advance.
• If a sequence is convergent, then it is Cauchy. (The converse is not necessarily true in non-complete spaces) – Julian Mejia May 25 at 16:27
• One of the simplest estimates may be $$\left|\frac1{(n+p)^2}-\frac1{n^2}\right|<\frac1{n^2}.$$ – Jyrki Lahtonen May 25 at 16:30
• @JulianMejia +1, Nothing more to say than this. – Michael Hoppe May 25 at 16:56
Since you already know what the limit is, this is not hard.
Let $$\epsilon > 0$$ be given. Choose $$N$$ such that $$\frac{1}{N^2} < \frac{\epsilon}{2}$$. Now assume $$n \ge N$$ and $$p \ge 1$$. Then $$|\frac{1}{n^2} - \frac{1}{(n+p)^2}| \le \frac{1}{n^2} + \frac{1}{(n+p)^2} \le \frac{2}{n^2} \le \frac{2}{N^2} < \epsilon \, .$$
• Ohh Thanks, Sir. Triangle inequality makes it so easy! – user587389 May 25 at 16:38
$$\frac{p(2n+p)}{n^2(n+p)^2}=\frac{p(2n+p)}{n^2(n^2+(2n+p)p)}\leq\frac{p(2n+p)}{n^2p(2n+p)}=\frac{1}{n^2}.$$
The triangular inequality is not needed, it is only application of $$0\le a\le b\implies 0\le b-a\le b$$
Let's have $$m\ge n$$ then apply to $$a=\frac 1{m^2}$$ and $$b=\frac 1{n^2}$$.
You get $$0\le \frac 1{n^2}-\frac 1{m^2}\le \frac 1{n^2}$$
|
2019-10-17 05:10:39
|
{"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": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9340182542800903, "perplexity": 226.2796688686202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986672723.50/warc/CC-MAIN-20191017045957-20191017073457-00372.warc.gz"}
|
http://mathhelpforum.com/calculus/67195-solved-proof-complx-trig-eqn-print.html
|
# [SOLVED] proof for complx/trig eqn?
• Jan 7th 2009, 12:23 PM
crb
[SOLVED] proof for complx/trig eqn?
plz have a look at the aatached picture
thank you
• Jan 7th 2009, 12:30 PM
Mush
$sinh(z) = \frac{e^{z} - e^{-z}}{2}$
$= \frac{e^{x+iy} - e^{-x-iy}}{2}$
$= \frac{e^{x}.e^{iy} - e^{-x}.e^{-iy}}{2}$
$= \frac{e^{x}.e^{iy} - e^{-x}.\frac{1}{e^{iy}}}{2}$
$= \frac{e^{x}.(cos(y)+isin(y)) - \frac{1}{e^{x}.(cos(y)+isin(y))}}{2}$
• Jan 7th 2009, 12:41 PM
crb
and how about the conjugate of sinh(z)....??
how do i get sinh(z) = some u + iv form????
• Jan 7th 2009, 12:44 PM
Mush
Quote:
Originally Posted by crb
and how about the conjugate of sinh(z)....??
how do i get sinh(z) = some u + iv form????
$= \frac{e^{x}.(cos(y)+isin(y)) - \frac{1}{e^{x}.(cos(y)+isin(y))}}{2}$
Here you have a complex number which is composed of subtraction of two complex numbers.
Remember that if $w$ and $z$ are complex numbers then:
$\overline{(v - w)} = \overline{v} - \overline{w}$
In this case $v = e^{x}.cos(y)+ie^{x}sin(y)$ $w = \frac{1}{e^{x}.cos(y)+ie^xsin(y)}$
And you're trying to find $\frac{1}{2} \overline{(v - w)}$
Get $w$ in a nicer form by multiplying top and bottom by the conjugate of the denominator first.
$w = \frac{1}{e^{x}.cos(y)+ie^xsin(y)} = \frac{e^{x}.cos(y)-ie^xsin(y)}{e^{2x}.cos^2(y)+ie^{2x}sin^2(y)} = \frac{cos(y)-isin(y)}{e^{x}}$
Hence
$\frac{1}{2}( v - w) = \frac{1}{2}(e^{x}.cos(y)+ie^{x}sin(y) - (\frac{cos(y)-isin(y)}{e^{x}})$
Should be relatively easy to find the conjugate now.
• Jan 7th 2009, 01:00 PM
crb
Thank u very much...just managed to prove it with ur help..thank you
|
2016-12-04 12:53:17
|
{"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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8610901236534119, "perplexity": 2701.971461861794}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541321.31/warc/CC-MAIN-20161202170901-00470-ip-10-31-129-80.ec2.internal.warc.gz"}
|
https://bytes.com/topic/visual-basic-net/answers/364272-rowfilter-help-please
|
424,835 Members | 1,454 Online
Need help? Post your question and get tips & solutions from a community of 424,835 IT Pros & Developers. It's quick & easy.
P: n/a Hi - For my VB.NET app, I have a SQL2K database that I use to create a dataset with multiple data tables. I've created a dataview (dvReportsTo) of one of the tables, SCPMaster, and I've bound a combobox control to that dataview. I'm trying to filter the dataview based on values in a second table (ReportsTo) in the same dataset, and it's not working. If it's possible to do this, please help me figure out what I've done wrong and how to implement this correctly. If I'm trying to do something that is not supported, I'd appreciate any suggestions of a workaround. Here's the filter I'm trying to implement: strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" strFilter &= " AND SCPMasterID NOT IN" strFilter &= " (SELECT ReportsToStaffID FROM ReportsTo" strFilter &= " WHERE ReportsToBossID = '" & uidSelectedPerson.ToString & "')" frmMain.dvReportsTo.RowFilter = strFilter Here's the DataException that I'm getting: System.Data.SyntaxErrorException: Syntax error: Missing operand after 'ReportsToStaffID' operator. at System.Data.ExpressionParser.Parse() at System.Data.DataExpression..ctor(String expression, DataTable table, Type type) at System.Data.DataExpression..ctor(String expression, DataTable table) at System.Data.DataFilter..ctor(String expression, DataTable table) at System.Data.DataView.set_RowFilter(String value) at StarContactPro_02_DT.modContact.SetReportsToFilter () in d:\Data\Visual Studio Projects\StarContactPro-02-DT\modContact.vb:line 107" Thanks for your help. - Jeff Nov 20 '05 #1
7 Replies
P: n/a The subquery is the problem. You're going to have to do a dataTable.Select and loop through the results, building a comma separated list. Then use that list with Not In. For the complete expression syntax, this may be of help to you in the future http://msdn.microsoft.com/library/de...ssionTopic.asp -- W.G. Ryan, eMVP http://forums.devbuzz.com/ http://www.knowdotnet.com/williamryan.html http://www.msmvps.com/WilliamRyan/ http://www.devbuzz.com/content/zinc_...center_pg1.asp "Jeff" wrote in message news:CO***************@newsread3.news.atl.earthlin k.net... Hi - For my VB.NET app, I have a SQL2K database that I use to create a dataset with multiple data tables. I've created a dataview (dvReportsTo) of one of the tables, SCPMaster, and I've bound a combobox control to that dataview. I'm trying to filter the dataview based on values in a second table (ReportsTo) in the same dataset, and it's not working. If it's possible to do this, please help me figure out what I've done wrong and how to implement this correctly. If I'm trying to do something that is not supported, I'd appreciate any suggestions of a workaround. Here's the filter I'm trying to implement: strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" strFilter &= " AND SCPMasterID NOT IN" strFilter &= " (SELECT ReportsToStaffID FROM ReportsTo" strFilter &= " WHERE ReportsToBossID = '" & uidSelectedPerson.ToString & "')" frmMain.dvReportsTo.RowFilter = strFilter Here's the DataException that I'm getting: System.Data.SyntaxErrorException: Syntax error: Missing operand after 'ReportsToStaffID' operator. at System.Data.ExpressionParser.Parse() at System.Data.DataExpression..ctor(String expression, DataTable table, Type type) at System.Data.DataExpression..ctor(String expression, DataTable table) at System.Data.DataFilter..ctor(String expression, DataTable table) at System.Data.DataView.set_RowFilter(String value) at StarContactPro_02_DT.modContact.SetReportsToFilter () in d:\Data\Visual Studio Projects\StarContactPro-02-DT\modContact.vb:line 107" Thanks for your help. - Jeff Nov 20 '05 #2
P: n/a "Jeff" schrieb Here's the filter I'm trying to implement: strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" strFilter &= " AND SCPMasterID NOT IN" strFilter &= " (SELECT ReportsToStaffID FROM ReportsTo" strFilter &= " WHERE ReportsToBossID = '" & uidSelectedPerson.ToString & "')" frmMain.dvReportsTo.RowFilter = strFilter Here's the DataException that I'm getting: System.Data.SyntaxErrorException: Syntax error: Missing operand after 'ReportsToStaffID' operator. at System.Data.ExpressionParser.Parse() at System.Data.DataExpression..ctor(String expression, DataTable table, Type type) at System.Data.DataExpression..ctor(String expression, DataTable table) at System.Data.DataFilter..ctor(String expression, DataTable table) at System.Data.DataView.set_RowFilter(String value) at StarContactPro_02_DT.modContact.SetReportsToFilter () in d:\Data\Visual Studio Projects\StarContactPro-02-DT\modContact.vb:line 107" The Dataview is not a database. You can not execute SQL statements on the Dataview. The valid syntax for the Rowfilter is described here: http://msdn.microsoft.com/library/en...ssionTopic.asp -- Armin How to quote and why: http://www.plig.net/nnq/nquote.html http://www.netmeister.org/news/learn2quote.html Nov 20 '05 #3
P: n/a Thanks for the instant(!) response, William - I've tried your suggestion, and there seems to be a problem with the values in the comma-separated NOT IN list being GUIDs. (I went through the article you referenced, and I wasn't able to find the correct syntax for this.) What should I change?? Here's my relevant code: strStaff = "(" strFilter = "ReportsToBossID = '" & uidSelectedPerson.ToString & "'" drStaff = frmMain.dsSCP.Tables("ReportsTo").Select(strFilter ) intRows = drStaff.GetUpperBound(0) For intRow = 0 To intRows If blnFirstItem Then blnFirstItem = False Else strStaff &= "," End If strStaff &= "'" & drStaff(intRow)(0).ToString & "'" Next strStaff &= ")" strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" If intRows > 0 Then strFilter &= " AND SCPMasterID NOT IN " & strStaff frmMain.dvReportsTo.RowFilter = strFilter Thanks for your help. - Jeff "William Ryan eMVP" wrote in message news:eB*************@tk2msftngp13.phx.gbl... The subquery is the problem. You're going to have to do a dataTable.Select and loop through the results, building a comma separated list. Then use that list with Not In. For the complete expression syntax, this may be of help to you in the future http://msdn.microsoft.com/library/de...ssionTopic.asp -- W.G. Ryan, eMVP http://forums.devbuzz.com/ http://www.knowdotnet.com/williamryan.html http://www.msmvps.com/WilliamRyan/ http://www.devbuzz.com/content/zinc_...center_pg1.asp "Jeff" wrote in message news:CO***************@newsread3.news.atl.earthlin k.net... Hi - For my VB.NET app, I have a SQL2K database that I use to create a dataset with multiple data tables. I've created a dataview (dvReportsTo) of one of the tables, SCPMaster, and I've bound a combobox control to that dataview. I'm trying to filter the dataview based on values in a second table (ReportsTo) in the same dataset, and it's not working. If it's possible to do this, please help me figure out what I've done wrong and how to implement this correctly. If I'm trying to do something that is not supported, I'd appreciate any suggestions of a workaround. Here's the filter I'm trying to implement: strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" strFilter &= " AND SCPMasterID NOT IN" strFilter &= " (SELECT ReportsToStaffID FROM ReportsTo" strFilter &= " WHERE ReportsToBossID = '" & uidSelectedPerson.ToString & "')" frmMain.dvReportsTo.RowFilter = strFilter Here's the DataException that I'm getting: System.Data.SyntaxErrorException: Syntax error: Missing operand after 'ReportsToStaffID' operator. at System.Data.ExpressionParser.Parse() at System.Data.DataExpression..ctor(String expression, DataTable table, Type type) at System.Data.DataExpression..ctor(String expression, DataTable table) at System.Data.DataFilter..ctor(String expression, DataTable table) at System.Data.DataView.set_RowFilter(String value) at StarContactPro_02_DT.modContact.SetReportsToFilter () in d:\Data\Visual Studio Projects\StarContactPro-02-DT\modContact.vb:line 107" Thanks for your help. - Jeff Nov 20 '05 #4
P: n/a If you would ,set a breakpoint right before you set the rowfilter and let me see what the exact command you're setting is. it's hard to tell from here and I don't have your values so i can't easily tell. -- W.G. Ryan MVP Windows - Embedded http://forums.devbuzz.com http://www.knowdotnet.com/dataaccess.html http://www.msmvps.com/williamryan/ "Jeff" wrote in message news:Yz*****************@newsread3.news.atl.earthl ink.net... Thanks for the instant(!) response, William - I've tried your suggestion, and there seems to be a problem with the values in the comma-separated NOT IN list being GUIDs. (I went through the article you referenced, and I wasn't able to find the correct syntax for this.) What should I change?? Here's my relevant code: strStaff = "(" strFilter = "ReportsToBossID = '" & uidSelectedPerson.ToString & "'" drStaff = frmMain.dsSCP.Tables("ReportsTo").Select(strFilter ) intRows = drStaff.GetUpperBound(0) For intRow = 0 To intRows If blnFirstItem Then blnFirstItem = False Else strStaff &= "," End If strStaff &= "'" & drStaff(intRow)(0).ToString & "'" Next strStaff &= ")" strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" If intRows > 0 Then strFilter &= " AND SCPMasterID NOT IN " & strStaff frmMain.dvReportsTo.RowFilter = strFilter Thanks for your help. - Jeff "William Ryan eMVP" wrote in message news:eB*************@tk2msftngp13.phx.gbl... The subquery is the problem. You're going to have to do a dataTable.Select and loop through the results, building a comma separated list. Then use that list with Not In. For the complete expression syntax, this may be of help to you in the future http://msdn.microsoft.com/library/de...ssionTopic.asp -- W.G. Ryan, eMVP http://forums.devbuzz.com/ http://www.knowdotnet.com/williamryan.html http://www.msmvps.com/WilliamRyan/ http://www.devbuzz.com/content/zinc_...center_pg1.asp "Jeff" wrote in message news:CO***************@newsread3.news.atl.earthlin k.net... Hi - For my VB.NET app, I have a SQL2K database that I use to create a dataset with multiple data tables. I've created a dataview (dvReportsTo) of one of the tables, SCPMaster, and I've bound a combobox control to that dataview. I'm trying to filter the dataview based on values in a second table (ReportsTo) in the same dataset, and it's not working. If it's possible to do this, please help me figure out what I've done wrong and how to implement this correctly. If I'm trying to do something that is not supported, I'd appreciate any suggestions of a workaround. Here's the filter I'm trying to implement: strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" strFilter &= " AND SCPMasterID NOT IN" strFilter &= " (SELECT ReportsToStaffID FROM ReportsTo" strFilter &= " WHERE ReportsToBossID = '" & uidSelectedPerson.ToString & "')" frmMain.dvReportsTo.RowFilter = strFilter Here's the DataException that I'm getting: System.Data.SyntaxErrorException: Syntax error: Missing operand after 'ReportsToStaffID' operator. at System.Data.ExpressionParser.Parse() at System.Data.DataExpression..ctor(String expression, DataTable table, Type type) at System.Data.DataExpression..ctor(String expression, DataTable table) at System.Data.DataFilter..ctor(String expression, DataTable table) at System.Data.DataView.set_RowFilter(String value) at StarContactPro_02_DT.modContact.SetReportsToFilter () in d:\Data\Visual Studio Projects\StarContactPro-02-DT\modContact.vb:line 107" Thanks for your help. - Jeff Nov 20 '05 #5
P: n/a Sure. Here's the value of strFilter: "SCPMasterID <> '23865682-20c1-11c4-8000-8ea6b5cb2452' AND SCPMasterID NOT IN ('3ac54427-20c1-11c4-8000-8ea6b5cb2452','3ac54429-20c1-11c4-8000-8ea6b5cb245 2','3ac5442b-20c1-11c4-8000-8ea6b5cb2452','3b5dda80-20c1-11c4-8000-8ea6b5cb2 452','3b5dda82-20c1-11c4-8000-8ea6b5cb2452')" - Jeff "William Ryan eMVP" wrote in message news:ut**************@tk2msftngp13.phx.gbl... If you would ,set a breakpoint right before you set the rowfilter and let me see what the exact command you're setting is. it's hard to tell from here and I don't have your values so i can't easily tell. -- W.G. Ryan MVP Windows - Embedded http://forums.devbuzz.com http://www.knowdotnet.com/dataaccess.html http://www.msmvps.com/williamryan/ "Jeff" wrote in message news:Yz*****************@newsread3.news.atl.earthl ink.net... Thanks for the instant(!) response, William - I've tried your suggestion, and there seems to be a problem with the values in the comma-separated NOT IN list being GUIDs. (I went through the article you referenced, and I wasn't able to find the correct syntax for this.) What should I change?? Here's my relevant code: strStaff = "(" strFilter = "ReportsToBossID = '" & uidSelectedPerson.ToString & "'" drStaff = frmMain.dsSCP.Tables("ReportsTo").Select(strFilter ) intRows = drStaff.GetUpperBound(0) For intRow = 0 To intRows If blnFirstItem Then blnFirstItem = False Else strStaff &= "," End If strStaff &= "'" & drStaff(intRow)(0).ToString & "'" Next strStaff &= ")" strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" If intRows > 0 Then strFilter &= " AND SCPMasterID NOT IN " & strStaff frmMain.dvReportsTo.RowFilter = strFilter Thanks for your help. - Jeff "William Ryan eMVP" wrote in message news:eB*************@tk2msftngp13.phx.gbl... The subquery is the problem. You're going to have to do a dataTable.Select and loop through the results, building a comma separated list. Then use that list with Not In. For the complete expression syntax, this may be of help to you in the future http://msdn.microsoft.com/library/de...ssionTopic.asp -- W.G. Ryan, eMVP http://forums.devbuzz.com/ http://www.knowdotnet.com/williamryan.html http://www.msmvps.com/WilliamRyan/ http://www.devbuzz.com/content/zinc_...center_pg1.asp "Jeff" wrote in message news:CO***************@newsread3.news.atl.earthlin k.net... > Hi - > > For my VB.NET app, I have a SQL2K database that I use to create a dataset > with multiple data tables. I've created a dataview (dvReportsTo) of one of > the tables, SCPMaster, and I've bound a combobox control to that dataview. > I'm trying to filter the dataview based on values in a second table > (ReportsTo) in the same dataset, and it's not working. > > If it's possible to do this, please help me figure out what I've done wrong > and how to implement this correctly. If I'm trying to do something that is > not supported, I'd appreciate any suggestions of a workaround. > > Here's the filter I'm trying to implement: > > strFilter = "SCPMasterID <> '" & uidSelectedPerson.ToString & "'" > strFilter &= " AND SCPMasterID NOT IN" > strFilter &= " (SELECT ReportsToStaffID FROM ReportsTo" > strFilter &= " WHERE ReportsToBossID = '" & uidSelectedPerson.ToString & > "')" > > frmMain.dvReportsTo.RowFilter = strFilter > > Here's the DataException that I'm getting: > > System.Data.SyntaxErrorException: Syntax error: Missing operand after > 'ReportsToStaffID' operator. > at System.Data.ExpressionParser.Parse() > at System.Data.DataExpression..ctor(String expression, DataTable table, > Type type) > at System.Data.DataExpression..ctor(String expression, DataTable table) > at System.Data.DataFilter..ctor(String expression, DataTable table) > at System.Data.DataView.set_RowFilter(String value) > at StarContactPro_02_DT.modContact.SetReportsToFilter () in d:\Data\Visual > Studio Projects\StarContactPro-02-DT\modContact.vb:line 107" > > > Thanks for your help. > > - Jeff > > Nov 20 '05 #6
P: n/a Hi Jeff, First of all, I would like to confirm my understanding of your issue. From your description, I understand that you need to filter records that are not in the Guid list. If there is any misunderstanding, please feel free to let me know. Based on my research, the Guid values in the list are strings that cannot be converted implicitly to Guid. We have to use Convert function to change it to Guid. Here is an example: "SCPMasterID <> '23865682-20c1-11c4-8000-8ea6b5cb2452' AND SCPMasterID NOT IN (Convert('3ac54427-20c1-11c4-8000-8ea6b5cb2452', 'System.Guid'), Convert('3ac54429-20c1-11c4-8000-8ea6b5cb2452', 'System.Guid'))" HTH. If anything is unclear, please feel free to reply to the post. Kevin Yu ======= "This posting is provided "AS IS" with no warranties, and confers no rights." Nov 20 '05 #7
P: n/a Thanks, Guys - I've been able to get this to work using William's and Kevin's recommendations. - Jeff "Kevin Yu [MSFT]" wrote in message news:V1*************@cpmsftngxa10.phx.gbl... Hi Jeff, First of all, I would like to confirm my understanding of your issue. From your description, I understand that you need to filter records that are not in the Guid list. If there is any misunderstanding, please feel free to let me know. Based on my research, the Guid values in the list are strings that cannot be converted implicitly to Guid. We have to use Convert function to change it to Guid. Here is an example: "SCPMasterID <> '23865682-20c1-11c4-8000-8ea6b5cb2452' AND SCPMasterID NOT IN (Convert('3ac54427-20c1-11c4-8000-8ea6b5cb2452', 'System.Guid'), Convert('3ac54429-20c1-11c4-8000-8ea6b5cb2452', 'System.Guid'))" HTH. If anything is unclear, please feel free to reply to the post. Kevin Yu ======= "This posting is provided "AS IS" with no warranties, and confers no rights." Nov 20 '05 #8
### This discussion thread is closed
Replies have been disabled for this discussion.
|
2019-05-22 05:50:24
|
{"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": 0.8983102440834045, "perplexity": 7271.157730024871}, "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/1558232256763.42/warc/CC-MAIN-20190522043027-20190522065027-00529.warc.gz"}
|
https://wikieducator.org/Thread:%C2%ABno_subject%C2%BB_(745)
|
# «no subject»
Nice to meet you here! I look forward to interacting and learning from facilitators and the group in this forum over the coming weeks. I am Nellie working with the Commonwealth Secretariat
|
2022-10-05 00:13:41
|
{"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": 0.21575072407722473, "perplexity": 3549.64409625159}, "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/1664030337529.69/warc/CC-MAIN-20221004215917-20221005005917-00133.warc.gz"}
|
https://ncatlab.org/nlab/show/rational+map
|
Contents
# Contents
## Idea
Given an irreducible variety $X$ and a variety $Y$ a rational map $f: X\dashrightarrow Y$ (notice dashed arrow notation) is an equivalence class of partially defined maps, namely the pairs $(U, f_U)$ where $f_U$ is a regular map $f_U: U\to Y$ defined on dense Zariski open subvarieties $U\subset X$ and the equivalence is the agreement on the common intersection.
The notion of an image of a rational map is nontrivially defined, see that entry. A rational map $f: X\dashrightarrow Y$ is dominant if its image as a rational map is the whole of $Y$.
The composition of rational maps $g\circ f$ where $f: X\dashrightarrow Y$ and $g: Y\dashrightarrow Z$ is not always defined, namely it is even possible that the image of $f$ lies out of any dense open subset in $Y$, where $g$ is defined as a regular map. The composition is defined as the class of equivalence of pairs $(g_V\circ f_U|, f_U^{-1}(V))$ where $U\subset X$ and $V\subset Z$ are open dense subsets and $f_U^{-1}(V)\neq \emptyset$ if such exist and undefined otherwise.
If $f$ is dominant then in this situation is the composition $g\circ f$ is always defined.
## References
### General
Textbook account:
Review:
Lecture notes:
• Daniel Plaumann, Rational Functions and Maps (pdf, Plaumann_RationalFunctionsAndmaps.pdf?), Lecture 5 in Classical algebraic geometry 2015
Exposition for the case of maps from the Riemann sphere to a complex projective space:
### Identification of Yang-Mills monopoles with rational maps
The following lists references concerned with the identification of the (extended) moduli space of Yang-Mills monopoles (in the BPS limit, i.e. for vanishing Higgs potential) with a mapping space of complex rational maps from the complex plane, equivalently holomorphic maps from the Riemann sphere $\mathbb{C}P^1$ (at infinity in $\mathbb{R}^3$) to itself (for gauge group SU(2)) or generally to a complex flag variety such as (see Ionnadou & Sutcliffe 1999a for review) to a coset space by the maximal torus (for maximal symmetry breaking) or to complex projective space $\mathbb{C}P^{n-1}$ (for gauge group SU(n) and minimal symmetry breaking).
The identification was conjectured (following an analogous result for Yang-Mills instantons) in:
Full understanding of the rational map involved as “scattering data” of the monopole is due to:
The identification with (pointed) holomorphic functions out of $\mathbb{C}P^1$ was proven…
…for the case of gauge group $SU(2)$ (maps to $\mathbb{C}P^1$ itself) in
…for the more general case of classical gauge group with maximal symmetry breaking (maps to the coset space by the maximal torus) in:
… for the fully general case of semisimple gauge groups with any symmetry breaking (maps to any flag varieties) in
and for un-pointed maps in
Further discussion:
Review:
• Alexander B. Atanasov, Magnetic monopoles and the equations of Bogomolny and Nahm (pdf), chapter 5 in: Magnetic Monopoles, ‘t Hooft Lines, and the Geometric Langlands Correspondence, 2018 (pdf, slides)
On the relevant homotopy of rational maps (see there for more references):
### Skyrmions from rational maps
The following is a list of references on the construction of Skyrmion-solutions of the Yang-Mills field via rational maps from the complex plane, hence holomorphic maps from the Riemann sphere, to itself, akin to the Donaldson-construction of Yang-Mills monopoles.
The original idea:
Further discussion:
On quantization of Skyrmions informed by homotopy of rational maps:
the impact of which, on the computation of atomic nuclei, is highlighted in:
Last revised on August 13, 2021 at 19:10:55. See the history of this page for a list of all contributions to it.
|
2022-12-09 03:35:34
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 29, "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": 0.9292371273040771, "perplexity": 704.7589455373125}, "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/1669446711376.47/warc/CC-MAIN-20221209011720-20221209041720-00069.warc.gz"}
|
https://brainsanswers.com/mathematics/question12048308
|
, 22.06.2019 03:00, bobduncan1086
# You deposit $500 each month into an account earning 3% interest compounded monthly. a) how much will you have in the account in 30 years? b) how much total money will you put into the account? c) how much total interest will you earn? Answers: 3 ### Other questions on the subject: Mathematics Mathematics, 21.06.2019 15:40, hannahkharel2 What is a rational number between 9.5 and 9.7 Answers: 3 Mathematics, 21.06.2019 16:10, michaelwthms To describe a sequence of transformations that maps triangle abc onto triangle a"b"c", a student starts with a reflection over the x-axis. how should the student complete the sequence of transformations to map triangle abc onto triangle a"b"c"? plz Answers: 1 Mathematics, 21.06.2019 16:30, AutumnJoy12 Yoku is putting on sunscreen. he uses 2\text{ ml}2 ml to cover 50\text{ cm}^250 cm 2 of his skin. he wants to know how many milliliters of sunscreen (c)(c) he needs to cover 325\text{ cm}^2325 cm 2 of his skin. how many milliliters of sunscreen does yoku need to cover 325 \text{ cm}^2325 cm 2 of his skin? Answers: 3 Mathematics, 21.06.2019 21:30, magicpuppydance On #16 : explain how factoring a trinomial, ax^2+ bx+ c, when a does not equal 1 different from factoring a trinomial when a = 1. Answers: 2 Do you know the correct answer? You deposit$500 each month into an account earning 3% interest compounded monthly. a) how much will...
Total solved problems on the site: 13552037
|
2021-07-27 14:18:17
|
{"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": 0.196812242269516, "perplexity": 4963.27116358878}, "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/1627046153392.43/warc/CC-MAIN-20210727135323-20210727165323-00027.warc.gz"}
|
https://keisan.casio.com/exec/system/1340247198
|
# Biorhythm Compatibility Calculator
## Calculates and draws the chart of a couple's biorhythm compatibility.
Your birth date Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 , Partner's birth date Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 , Target date Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 , Biorhythm Compatibility
The smaller (close to 0) the amplitude is, the higher the compatibility of two persons is.And the larger (close to ±1), the lower it is. If the graph is close to +1, your compatibility with a partner is high.And if close to -1, it is low.$\normal Biorhythm\ compatibility\\[10](1)\ Compatibility\\\hspace{20} \left| cos({\large\frac{\pi t}{T}})\right|\\[5]\hspace{20}T=23(P),\ 28(E),\ 33(I)\\\hspace{20}t=\ your\ birthday\ -\ another\ one\\\vspace{10}\\(2)\ Graph\\\hspace{20} \frac{sin({\large\frac{2\pi t_1}{T}})-sin({\large\frac{2\pi t_2}{T}})}{\normal 2}\\[5]\hspace{20}t_1=\ base\ date\ -\ your\ birthday\\\hspace{20}t_2=\ base\ date\ -\ partner's\ birthday\\$
Biorhythm Compatibility
[1-10] /179 Disp-Num5103050100200
[1] 2019/02/19 12:10 Female / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
curiosity
[2] 2019/02/09 17:09 Male / 30 years old level / An office worker / A public employee / Very /
Purpose of use
To check if my soulmate and I are compatible and stable on some days.
Comment/Request
When will be the exact time that I'll propose my love to her? Should I follow this?
[3] 2019/02/07 20:54 Male / 50 years old level / Others / Very /
Purpose of use
explaining how come I just love some people and others less
[4] 2019/02/07 07:04 Female / 40 years old level / A teacher / A researcher / Useful /
Comment/Request
What does the "mean" mean?
from Keisan
"Mean" means average.
[5] 2019/01/29 19:01 - / 20 years old level / Others / A little /
Purpose of use
Benefit of doubt in my own mind
Comment/Request
I don’t understand the graph and how it works. Not sure if compatible or not
[6] 2019/01/12 23:43 Female / 40 years old level / Others / Very /
Purpose of use
Twin flame.
Comment/Request
Amazing result. Thank you
[7] 2019/01/11 00:49 Female / 40 years old level / An office worker / A public employee / A little /
Purpose of use
Curiosity
[8] 2019/01/07 16:09 Female / 30 years old level / Others / - /
Comment/Request
My biorhythm level of compatibility with my partner is physical-100%, emotional-11.2, intellectual-99.5%, he’s been saying that he is not sure we are compatible for long term....is this true then? We’ve been arguing lately. Is there a way around it?
[9] 2019/01/07 09:59 Female / 60 years old level or over / A retired person / Very /
Purpose of use
Work
[10] 2019/01/06 12:26 Female / Under 20 years old / Elementary school/ Junior high-school student / Very /
Purpose of use
I want to figure out if one of my three crushes is compatible based on Biorhythm.
Sending completion
To improve this 'Biorhythm Compatibility Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired person Others
Useful?
Very Useful A little Not at All
Purpose of use?
|
2019-02-19 11:32:40
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 1, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38497042655944824, "perplexity": 1751.3343444375835}, "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/1550247489933.47/warc/CC-MAIN-20190219101953-20190219123953-00489.warc.gz"}
|
https://www.numerade.com/questions/a-thin-wire-has-the-shape-of-the-first-quadrant-part-of-the-circle-with-center-the-origin-and-radius/
|
Meet students taking the same courses as you are!Join a Numerade study group on Discord
FL
# A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius $a$. If the density function is $\rho (x, y) = kxy$, find the mass and center of mass of the wire.
## $$\left(\frac{2 a}{3}, \frac{2 a}{3}\right)$$
Vector Calculus
### Discussion
You must be signed in to discuss.
##### Catherine R.
Missouri State University
##### Kristen K.
University of Michigan - Ann Arbor
Lectures
Join Bootcamp
### Video Transcript
first hard from part of the circle was radius a So X. It is a co scientist. Why's a sign t and ah to you from zero to pie over too. Grow if who's k X y So what is mass masses in the crate road? Yes, we have the fill out. Yes, but yes, it's nothing but a TT by similar computer your city and your identity and square some take the square root zero two pi over to row is K X Y ex wise K square Scientific Cose I Inti the A the party s is It's okay from zero to pirate to scientific society we do a u substitution will be easy because ah, antiterror activist thiss probably empire over it too. Okay, two times one over two. So that should be the That should be the mass for center of mass. We have to do a few more in the group. So this computer Ah, it's a crow Hack through Yes, Access Eko Society bro is okay X y So it's still okay. Score scientific society. Okay. A square co signed his society uh, the vt So we actually have a to the fourth power Katie Integral. Otis. So we get we should connective coast on Cuba over three. It is entitled Riveted ve We probably pie over too. Um, we should get zero, and we probably zero. We get one. So we minus negative one over three. So it's okay for over three. I would make another computation. Why? Wrote? Yes. Still from zero to a pirate, too. Why's a scientist e roes que x y scientific co sign t. And we still have. Ah, yes, it is. Okay. Fourth science Quartey Cose I Inti, this is U substitution parents. So you have scientist who issue. So I have news for you, Q over three. Prime power two year one. So we, uh, and promising. Oh, yeah. Zero. So he had won over three. Okay, fourth, so the same as this one. So when we do the division one over three K force if I buy the math, Okay, one over to K Q. She gives us to a over three. And that's the same for X and Y Sosa center off meth. So this is a mass and the scent off math. Thus we computed in the next two pages R hsueh over Siri for Post X and y coordinate
FL
#### Topics
Vector Calculus
##### Catherine R.
Missouri State University
##### Kristen K.
University of Michigan - Ann Arbor
Lectures
Join Bootcamp
|
2021-03-06 11:29:57
|
{"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": 0.7346503138542175, "perplexity": 3674.1918095250217}, "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/1614178374686.69/warc/CC-MAIN-20210306100836-20210306130836-00141.warc.gz"}
|
https://www.examveda.com/a-committee-of-5-members-is-to-be-formed-by-selecting-out-of-4-men-and-5-women-in-how-many-different-ways-the-committee-can-be-formed-if-it-102884/
|
Examveda
# A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee can be formed if it should have 2 men and 3 women?
A. 16
B. 36
C. 45
D. 60
E. None of these
\eqalign{ & = {{}^4{C_2} \times {}^5{C_3}} \cr & = {{}^4{C_2} \times {}^5{C_2}} \cr & = {\frac{{4 \times 3}}{{2 \times 1}} \times \frac{{5 \times 4}}{{2 \times 1}}} \cr & = 60 \cr}
|
2022-12-06 13:08:26
|
{"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": 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": 1.0000100135803223, "perplexity": 981.9483010154585}, "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/1669446711108.34/warc/CC-MAIN-20221206124909-20221206154909-00217.warc.gz"}
|
http://www.e-magnetica.pl/file/smps_90w_magnetica_jpg
|
# Encyclopedia Magnetica
### Site Tools
file:smps_90w_magnetica_jpg
Switch-mode power supply, with several inductive components: common-mode choke, PFC inductor, resonant transformer, and filter choke.
smps_90w_magnetica.jpg
You are permitted and indeed encouraged to use this image freely, for any legal purpose including commercial, and with any modifications (the permission is hereby given, so there is no need to ask for it explicitly again), but you MUST always give the following credits:
S. Zurek, Encyclopedia Magnetica, CC-BY-4.0
We would appreciate if you let us know of any use: info@e-magnetica.pl
|
2021-12-05 06:59:53
|
{"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": 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": 0.24466872215270996, "perplexity": 6132.891175796455}, "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/1637964363149.85/warc/CC-MAIN-20211205065810-20211205095810-00447.warc.gz"}
|
https://mathspace.co/textbooks/syllabuses/Syllabus-1069/topics/Topic-20820/subtopics/Subtopic-270349/?activeTab=theory
|
# 9.02 Convert units of length
Lesson
## Ideas
Can you multiply decimal numbers by 10, 100 or 1000?
### Examples
#### Example 1
Find the value of 29.34 \times 100.
Worked Solution
Create a strategy
Use a place value table.
Apply the idea
Here is 29.34 in a place value table:
When we multiply by 100, all the digits move to the left two place values.
29.34\times100 = 2934
Idea summary
We can use a place value table to multiply and divide decimals by powers of 10.
## Convert lengths
If we are comparing two lengths, but they are written in different units we will need to change one of them to perform any calculations.
### Examples
#### Example 2
Worked Solution
Create a strategy
There are 10 millimetres are in 1 centimetre, so we need to divide by 10.
Apply the idea
Idea summary
Remember the following length conversions:
• 1\text{ cm}=10\text{ mm}
• 1\text{ m}=100\text{ cm}
• 1\text{ km}=1000\text{ m}
## Convert between units of length
Convert between units of length in two steps.
### Examples
#### Example 3
Convert 6.22\text{ km} to centimetres.
Worked Solution
Create a strategy
Remember that there are 1000 metres in a kilometre and there are 100 centimetres in a metre.
Apply the idea
Convert 6.22 km to metres first by multiplying by 1000.
Then convert this to centimetres by multiplying by 100.
6.22 \text{ km} = 622\,000 \text { cm}
Idea summary
We can use the following conversion chart to convert between units of measurement.
### Outcomes
#### VCMMG222
Connect decimal representations to the metric system
#### VCMMG223
Convert between common metric units of length, mass and capacity
#### VCMMG224
Solve problems involving the comparison of lengths and areas using appropriate units.
|
2023-03-21 05:54:59
|
{"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": 0.8103757500648499, "perplexity": 7202.690675322748}, "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/1679296943625.81/warc/CC-MAIN-20230321033306-20230321063306-00559.warc.gz"}
|
https://socratic.org/questions/how-do-you-simplify-4-26-5y
|
# How do you simplify -4< 26- 5y?
May 22, 2018
#### Answer:
The simplified version would read as $y < 6$.
#### Explanation:
While solving such questions what we need to do is to bring the variable ($y$ in this case) to any one side of the inequality and separate the numbers to the other side.
Now, take $- 5 y$ to the left-hand side and take $- 4$ to the right-hand side. If you are familiar with the inequality sign operations, you will know that with changes in sides, the sign of the numbers changes. So we have,
$5 y < 30$
Dividing both sides by $5$, we obtain
$y < 6$
All the best for your studies.
Regards,
AB
|
2019-10-21 07:13:13
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.8452386856079102, "perplexity": 354.7028308432579}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "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-2019-43/segments/1570987763641.74/warc/CC-MAIN-20191021070341-20191021093841-00272.warc.gz"}
|
http://math.stackexchange.com/questions/153111/generating-function-of-integer-partition-such-that-at-least-one-part-is-even
|
# Generating Function of Integer Partition Such that at Least One Part is Even
I've been having a few issues coming up with a generating function for an integer partition such that at least one part is even. What I have got so far is:
The generating function with no restrictions\begin{align*} \\&= even~parts * odd~parts \\ &= (1+x^2+x^4+\ldots)(1+x^4+x^8+\ldots)(1+x^6+x^{12}+\ldots)etc * (1+x+x^2+\ldots)(1+x^3+x^6+\ldots)(1+x^5+x^{10})+\ldots)etc \\&= \prod_{k= 1}^\infty1/(1-x^k)\end{align*}
Assuming that the situation where no even numbers are present in the partition is represented by the 1 in the expanded multiplication of the "even" side, we must remove this case by subtracting 1 from these terms.
Thus the generating function $even~parts*odd~parts$ becomes \begin{align*}\\& (even~parts-1)*odd~parts\\ &= (even~parts*odd~parts) - odd~parts\\&=all~parts-odd~parts\\ &=\prod_{k= 1}^\infty1/(1-x^k) -\prod_{k= 1}^\infty1/(1-x^{2k+1})\end{align*}
Is this the right idea or am I completely on the wrong track? If it is the right idea how do I combine both the product signs $\prod$ into one? Thanks in advance.
-
You have the right idea here. I don't think it's possible to write the difference of the two products as a single product. – Michael Lugo Jun 3 '12 at 3:04
Thanks for that Michael, its good to know I'm not too far off beam. However, number 18 and the ensuing possibilities on this page seem to indicate that there is an answer for this question which does not contain 2 product signs. Is there another way of approaching this problem whereby the 2 signs are avoided from the beginning? – Johann Jun 3 '12 at 4:38
The sequence is oeis.org/A047967 where a generating function is given that looks pretty much like the one you got, which suggests there's nothing better. There are some links there that may be of interest. – Gerry Myerson Jun 3 '12 at 5:06
Cheers for that @Gerry. That oeis entry is very helpful. – Johann Jun 3 '12 at 8:38
|
2016-06-01 03:46:54
|
{"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": 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": 0.9754771590232849, "perplexity": 481.5855861979722}, "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-2016-22/segments/1464054526288.74/warc/CC-MAIN-20160524014846-00157-ip-10-185-217-139.ec2.internal.warc.gz"}
|
https://www.tvbeurope.com/ibc/automated-closed-caption-service-trialled
|
Automated closed caption service trialled - TVBEurope
# Automated closed caption service trialled
Author:
Publish date:
Social count:
0
A closed captioning service that uses voice recognition software to automatically generate subtitles is being demoed at IBC.
TVU Smart Caption makes use of artificial intelligence techniques to output subtitles for either live or recorded footage. Users can tweak the application for use with different languages and regions.
TVU Networks is using IBC2017 to test the quality of the Smart Caption output with broadcasters.
2.B28
|
2018-06-21 14:16:25
|
{"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": 0.9182634949684143, "perplexity": 12935.979432852573}, "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/1529267864172.45/warc/CC-MAIN-20180621133636-20180621153636-00306.warc.gz"}
|
http://mathhelpforum.com/differential-geometry/161689-cyclic-group.html
|
# Math Help - Cyclic Group
1. ## Cyclic Group
Moved to abstract algebra... Sorry
2. Originally Posted by jzellt
Let G1 and G2 be groups and let f: G1 -> G2 be an isomorphism.
If G1 is a cyclic group with generator a, prove that G2 is also a cyclic group, with generator f(a).
Can someone please show this proof? Thanks so much!!!
This isn't analysis. But, if $g\in G_2$ then $g=f\left(a^n\right)=f^n(a)$ for some $n\in\mathbb{N}$.
3. Thanks and sorry. I didn't mean to put it in this forum
|
2015-09-04 20:25:10
|
{"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": 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": 0.8250038027763367, "perplexity": 1359.2628630681854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645359523.89/warc/CC-MAIN-20150827031559-00292-ip-10-171-96-226.ec2.internal.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-6-section-6-6-vectors-exercise-set-page-782/69
|
## Precalculus (6th Edition) Blitzer
The length of the shadow is $\left| \left| \text{1}\text{.4} \right| \right|\text{=1}\text{.4 inches}$.
The magnitude and direction of the vector are given. Analyze the vector and resolve it into its horizontal and vertical components. The vector component along the x-axis or the horizontal direction is i and the vector component along the y-axis or the vertical direction is j. Therefore, the equation becomes \begin{align} & \mathbf{v}=\left| \left| \mathbf{v} \right| \right|\text{cos}\theta \mathbf{i}+\left| \left| \mathbf{v} \right| \right|\text{sin}\theta \mathbf{j} \\ & =\text{1}\text{.5cos}25{}^\circ \mathbf{i}+\text{1}\text{.5sin}25{}^\circ \mathbf{j} \\ & =1.41\mathbf{i}+0.6\mathbf{j} \end{align} The shadow forms on the x-axis; therefore, only the horizontal component is taken and the vertical component is ignored.
|
2021-04-18 16:05:31
|
{"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998322129249573, "perplexity": 1069.4517802315238}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038492417.61/warc/CC-MAIN-20210418133614-20210418163614-00088.warc.gz"}
|
https://chemistry.stackexchange.com/questions/27673/how-do-atoms-combine
|
# How do atoms combine? [closed]
Do atoms combine with the nearest atoms possible because of lower delta E (less energy needed to form a stable nucleus)?
• If atoms combined with the nearest atom, then the air would be composed of $\ce {N2, O2, NO, NO2, ...}$. There are reasons that determine which compounds are preferred over other compounds. – LDC3 Mar 22 '15 at 16:52
• Nucleus?? Are you talking about nuclear reactions? – Mithoron Mar 22 '15 at 17:15
• "Combining with the nearest atom"? How do you know they will? Also, is this about a chemical or nuclear reaction? – M.A.R. Mar 22 '15 at 17:16
Let's say we have an atomic soup that contains atoms (what follows also applies to molecules) $\ce{A, B}$ and $\ce{C}$. From these reactants it would be possible to form products $\ce{A-B, A-C}$ and $\ce{B-C}$. Just which of these molecules, if any, will form depends on several factors including the $\Delta E$ that you mention.
Background
We usually talk about a reaction coordinate, like the one shown below.
image source
We have our reactants on one side and products on the other, and a barrier connecting the two. The height of the barrier is referred to as the activation energy ($E_{a}$). The Arrhenius equation is often used to describe the rate (k) for this process, where A is the pre-exponential factor (more on this in a minute), R is a constant and T is the temperature (°K)
$k = Ae^{-E_a/(RT)}$
Back to the question
Just because atoms collide doesn't necessarily mean they will react to produce a product. Sometimes they must collide from a certain direction. Think of molecules with complex shapes, for them to react we need the other reactant to collide with a certain part of the larger molecule, maybe too from a certain angle or direction. These geometrical factors are contained in the pre-exponential factor. Also the collision must have enough energy to get the reactants over the energy barrier.
So just because molecules are close doesn't guarantee that they will react. More important is how often molecules collide (concentration), the geometry of the collision (pre-exponential factor) and the energy (E) they carry.
|
2020-02-28 22:29:43
|
{"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": 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": 0.536277174949646, "perplexity": 796.9948734256993}, "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-2020-10/segments/1581875147647.2/warc/CC-MAIN-20200228200903-20200228230903-00478.warc.gz"}
|
https://blog.plover.com/tech/tmpdir.html
|
# The Universe of Discourse
Fri, 01 Jul 2016
This is a story about a very interesting bug that I tracked down yesterday. It was causing a bad effect very far from where the bug actually was.
### emacsclient
The emacs text editor comes with a separate utility, called emacsclient, which can communicate with the main editor process and tell it to open files for editing. You have your main emacs running. Then somewhere else you run the command
emacsclient some-files...
and it sends the main emacs a message that you want to edit some-files. Emacs gets the message and pops up new windows for editing those files. When you're done editing some-files you tell Emacs, by typing C-# or something, it it communicates back to emacsclient that the editing is done, and emacsclient exits.
This was more important in the olden days when Emacs was big and bloated and took a long time to start up. (They used to joke that “Emacs” was an abbreviation for “Eight Megs And Constantly Swapping”. Eight megs!) But even today it's still useful, say from shell scripts that need to run an editor.
Here's the reason I was running it. I have a very nice shell script, called also, that does something like this:
• Interpret command-line arguments as patterns
• Find files matching those patterns
• Present a menu of the files
• Wait for me to select files of interest
• Run emacsclient on the selected files
It is essentially a wrapper around menupick, a menu-picking utility I wrote which has seen use as a component of several other tools. I can type
also Wizard
in the shell and get a menu of the files related to the wizard, select the ones I actually want to edit, and they show up in Emacs. This is more convenient than using Emacs itself to find and open them. I use it many times a day.
Or rather, I did until this week, when it suddenly stopped working. Everything ran fine until the execution of emacsclient, which would fail, saying:
emacsclient: can't find socket; have you started the server?
(A socket is a facility that enables interprocess communication, in this case between emacs and emacsclient.)
This message is familiar. It usually means that I have forgotten to tell Emacs to start listening for emacsclient, by running M-x server-start. (I should have Emacs do this when it starts up, but I don't. Why not? I'm not sure.) So the first time it happened I went to Emacs and ran M-x server-start. Emacs announced that it had started the server, so I reran also. And the same thing happened.
emacsclient: can't find socket; have you started the server?
### Finding the socket
So the first question is: why can't emacsclient find the socket? And this resolves naturally into two subquestions: where is the socket, and where is emacsclient looking?
The second one is easily answered; I ran strace emacsclient (hi Julia!) and saw that the last interesting thing emacsclient did before emitting the error message was
stat("/mnt/tmp/emacs2017/server", 0x7ffd90ec4d40) = -1 ENOENT (No such file or directory)
which means it's looking for the socket at /mnt/tmp/emacs2017/server but didn't find it there.
The question of where Emacs actually put the socket file was a little trickier. I did not run Emacs under strace because I felt sure that the output would be voluminous and it would be tedious to grovel over it.
I don't exactly remember now how I figured this out, but I think now that I probably made an educated guess, something like: emacsclient is looking in /mnt/tmp; this seems unusual. I would expect the socket to be under /tmp. Maybe it is under /tmp? So I looked under /tmp and there it was, in /tmp/emacs2017/server:
srwx------ 1 mjd mjd 0 Jun 27 11:43 /tmp/emacs2017/server
(The s at the beginning there means that the file is a “Unix-domain socket”. A socket is an endpoint for interprocess communication. The most familiar sort is a TCP socket, which has a TCP address, and which enables communication over the internet. But since ancient times Unix has also supported Unix-domain sockets, which enable communication between two processes on the same machine. Instead of TCP addresses, such sockets are addressed using paths in the filesystem, in this case /tmp/emacs2017/server. When the server creates such a socket, it appears in the filesystem as a special type of file, as here.)
I confirmed that this was the correct file by typing M-x server-force-delete in Emacs; this immediately caused /tmp/emacs2017/server to disappear. Similarly M-x server-start made it reappear.
### Why the disagreement?
Now the question is: Why is emacsclient looking for the socket under /mnt/tmp when Emacs is putting it in /tmp? They used to rendezvous properly; what has gone wrong? I recalled that there was some environment variable for controlling where temporary files are put, so I did
env | grep mnt
to see if anything relevant turned up. And sure enough there was:
TMPDIR=/mnt/tmp
When programs want to create tmporary files and directories, they normally do it in /tmp. But if there is a TMPDIR setting, they use that directory instead. This explained why emacsclient was looking for /mnt/tmp/emacs2017/socket. And the explanation for why Emacs itself was creating the socket in /tmp seemed clear: Emacs was failing to honor the TMPDIR setting.
With this clear explanation in hand, I began to report the bug in Emacs, using M-x report-emacs-bug. (The folks in the #emacs IRC channel on Freenode suggested this. I had a bad experience last time I tried #emacs, and then people mocked me for even trying to get useful information out of IRC. But this time it went pretty well.)
Emacs popped up a buffer with full version information and invited me to write down the steps to reproduce the problem. So I wrote down
% export TMPDIR=/mnt/tmp
% emacs
and as I did that I ran those commands in the shell.
Then I wrote
In Emacs:
M-x getenv TMPDIR
(emacs claims there is no such variable)
and I did that in Emacs also. But instead of claiming there was no such variable, Emacs cheerfully informed me that the value of TMPDIR was /mnt/tmp.
(There is an important lesson here! To submit a bug report, you find a minimal demonstration. But then you also try the minimal demonstration exactly as you reported it. Because of what just happened! Had I sent off that bug report, I would have wasted everyone else's time, and even worse, I would have looked like a fool.)
My minimal demonstration did not demonstrate. Something else was going on.
### Why no TMPDIR?
This was a head-scratcher. All I could think of was that emacsclient and Emacs were somehow getting different environments, one with the TMPDIR setting and one without. Maybe I had run them from different shells, and only one of the shells had the setting?
I got on a sidetrack at this point to find out why TMPDIR was set in the first place; I didn't think I had set it. I looked for it in /etc/profile, which is the default Bash startup instructions, but it wasn't there. But I also noticed an /etc/profile.d which seemed relevant. (I saw later that the /etc/profile contained instructions to load everything under /etc/profile.d.) And when I grepped for TMPDIR in the profile.d files, I found that it was being set by /etc/profile.d/ziprecruiter_environment.sh, which the sysadmins had installed. So that mystery at least was cleared up.
That got me on a second sidetrack, looking through our Git history for recent changes involving TMPDIR. There weren't any, so that was a dead end.
I was still puzzled about why Emacs sometimes got the TMPDIR setting and sometimes not. That's when I realized that my original Emacs process, the one that had failed to rendezvous with emacsclient, had not been started in the usual way. Instead of simply running emacs, I had run
git re-edit
which invokes Git, which then runs
/home/mjd/bin/git-re-edit
which is a Perl program I wrote that does a bunch of stuff to figure out which files I was editing recently and then execs emacs to edit them some more. So there are several programs here that could be tampering with the environment and removing the TMPDIR setting.
To more accurately point the finger of blame, I put some diagnostics into the git-re-edit program to have it print out the value of TMPDIR. Indeed, git-re-edit reported that TMPDIR was unset. Clearly, the culprit was Git, which must have been removing TMPDIR from the environment before invoking my Perl program.
### Who is stripping the environment?
To confirm this conclusion, I created a tiny shell script, /home/mjd/bin/git-env, which simply printed out the environment, and then I ran git env, which tells Git to find git-env and run it. If the environment it printed were to omit TMPDIR, I would know Git was the culprit. But TMPDIR was in the output.
So I created a Perl version of git-env, called git-perlenv, which did the same thing, and I ran it via git perlenv. And this time TMPDIR was not in the output. I ran diff on the outputs of git env and git perlenv and they were identical—except that git perlenv was missing TMPDIR.
So it was Perl's fault! And I verified this by running perl /home/mjd/bin/git-re-edit directly, without involving Git at all. The diagnostics I had put in reported that TMPDIR was unset.
### WTF Perl?
At this point I tried getting rid of get-re-edit itself, and ran the one-line program
perl -le 'print $ENV{TMPDIR}' which simply runs Perl and tells it to print out the value of the TMPDIR environment variable. It should print /mnt/tmp, but instead it printed the empty string. This is a smoking gun, and Perl no longer has anywhere to hide. The mystery is not cleared up, however. Why was Perl doing this? Surely not a bug; someone else would have noticed such an obvious bug sometime in the past 25 years. And it only failed for TMPDIR, not for other variables. For example FOO=bar perl -le 'print$ENV{FOO}'
printed out bar as one would expect. This was weird: how could Perl's environment handling be broken for just the TMPDIR variable?
At this point I got Rik Signes and Frew Schmidt to look at it with me. They confirmed that the problem was not in Perl generally, but just in this Perl. Perl on other systems did not display this behavior.
I looked in the output of perl -V, which says what version of Perl you are using and which patches have been applied, and wasted a lot of time looking into CVE-2016-2381, which seemed relevant. But it turned out to be a red herring.
### Working around the problem, 1.
While all this was going on I was looking for a workaround. Finding one is at least as important as actually tracking down the problem because ultimately I am paid to do something other than figure out why Perl is losing TMPDIR. Having a workaround in hand means that when I get sick and tired of looking into the underlying problem I can abandon it instantly instead of having to push onward.
The first workaround I found was to not use the Unix-domain socket. Emacs has an option to use a TCP socket instead, which is useful on systems that do not support Unix-domain sockets, such as non-Unix systems. (I am told that some do still exist.)
You set the server-use-tcp variable to a true value, and when you start the server, Emacs creates a TCP socket and writes a description of it into a “server file”, usually ~/.emacs.d/server/server. Then when you run emacsclient you tell it to connect to the socket that is described in the file, with
emacsclient --server-file=~/.emacs.d/server/server
or by setting the EMACS_SERVER_FILE environment variable. I tried this, and it worked, once I figured out the thing about server-use-tcp and what a “server file” was. (I had misunderstood at first, and thought that “server file” meant the Unix-domain socket itself, and I tried to get emacsclient to use the right one by setting EMACS_SERVER_FILE, which didn't work at all. The resulting error message was obscure enough to lead me to IRC to ask about it.)
### Working around the problem, 2.
I spent quite a while looking for an environment variable analogous to EMACS_SERVER_FILE to tell emacsclient where the Unix-domain socket was. But while there is a --socket-name command-line argument to control this, there is inexplicably no environment variable. I hacked my also command (responsible for running emacsclient) to look for an environment variable named EMACS_SERVER_SOCKET, and to pass its value to emacsclient --socket-name if there was one. (It probably would have been better to write a wrapper for emacsclient, but I didn't.) Then I put
EMACS_SERVER_SOCKET=$TMPDIR/emacs$(id -u)/server
in my Bash profile, which effectively solved the problem. This set EMACS_SERVER_SOCKET to /mnt/tmp/emacs2017/server whenever I started a new shell. When I ran also it would notice the setting and pass it along to emacsclient with --socket-name, to tell emacsclient to look in the right place. Having set this up I could forget all about the original problem if I wanted to.
### But but but WHY?
But why was Perl removing TMPDIR from the environment? I didn't figure out the answer to this; Frew took it to the #p5p IRC channel on perl.org, where the answer was eventually tracked down by Matthew Horsfall and Zefrem.
The answer turned out to be quite subtle. One of the classic attacks that can be mounted against a process with elevated privileges is as follows. Suppose you know that the program is going to write to a temporary file. So you set TMPDIR beforehand and trick it into writing in the wrong place, possibly overwriting or destroying something important.
When a program is loaded into a process, the dynamic loader does the loading. To protect against this attack, the loader checks to see if the program it is going to run has elevated privileges, say because it is setuid, and if so it sanitizes the process’ environment to prevent the attack. Among other things, it removes TMPDIR from the environment.
I hadn't thought of exactly this, but I had thought of something like it: If Perl detects that it is running setuid, it enables a secure mode which, among other things, sanitizes the environment. For example, it ignores the PERL5LIB environment variable that normally tells it where to look for loadable modules, and instead loads modules only from a few compiled-in trustworthy directories. I had checked early on to see if this was causing the TMPDIR problem, but the perl executable was not setuid and Perl was not running in secure mode.
But Linux supports a feature called “capabilities”, which is a sort of partial superuser privilege. You can give a program some of the superuser's capabilities without giving away the keys to the whole kingdom. Our systems were configured to give perl one extra capability, of binding to low-numbered TCP ports, which is normally permitted only to the superuser. And when the dynamic loader ran perl, it saw this additional capability and removed TMPDIR from the environment for safety.
This is why Emacs had the TMPDIR setting when run from the command line, but not when run via git-re-edit.
Until this came up, I had not even been aware that the “capabilities” feature existed.
### A red herring
There was one more delightful confusion on the way to this happy ending. When Frew found out that it was just the Perl on my development machine that was misbehaving, he tried logging into his own, nearly identical development machine to see if it misbehaved in the same way. It did, but when he ran a system update to update Perl, the problem went away. He told me this would fix the problem on my machine. But I reported that I had updated my system a few hours before, so there was nothing to update!
The elevated capabilities theory explained this also. When Frew updated his system, the new Perl was installed without the elevated capability feature, so the dynamic loader did not remove TMPDIR from the environment.
When I had updated my system earlier, the same thing happened. But as soon as the update was complete, I reloaded my system configuration, which reinstated the capability setting. Frew hadn't done this.
### Summary
• The system configuration gave perl a special capability
• so the dynamic loader sanitized its environment
• so that when perl ran emacs,
• the Emacs process didn't have the TMPDIR environment setting
• which caused Emacs to create its listening socket in the usual place
• but because emacsclient did get the setting, it looked in the wrong place
### Conclusion
This computer stuff is amazingly complicated. I don't know how anyone gets anything done.
[ Addendum 20160709: Frew Schmidt has written up the same incident, but covers different ground than I do. ]
[ Addendum 20160709: A Hacker News comment asks what changed to cause the problem? Why was Perl losing TMPDIR this week but not the week before? Frew and I don't know! ]
|
2021-05-11 04:16:16
|
{"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": 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": 0.6004380583763123, "perplexity": 2715.758934797114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991641.5/warc/CC-MAIN-20210511025739-20210511055739-00314.warc.gz"}
|
https://search.r-project.org/CRAN/refmans/CPAT/html/DE.test.html
|
DE.test {CPAT} R Documentation
## Darling-Erdös Test
### Description
Performs the (univariate) Darling-Erdös test for change in mean, as described in (Rice et al. ). This is effectively an interface to stat_de; see its documentation for more details. p-values are computed using pdarling_erdos, which represents the limiting distribution of the test statistic under the null hypothesis when a and b are chosen appropriately. (Change those parameters at your own risk!)
### Usage
DE.test(x, a = log, b = log, use_kernel_var = FALSE,
stat_plot = FALSE, kernel = "ba", bandwidth = "and")
### Arguments
x Data to test for change in mean a The function that will be composed with l(x) = (2 \log x)^{1/2} b The function that will be composed with u(x) = 2 \log x + \frac{1}{2} \log \log x - \frac{1}{2} \log π use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically used when the data is believed to be correlated); if FALSE, then the long-run variance is estimated using \hat{σ}^2_{T,t} = T^{-1}≤ft( ∑_{s = 1}^t ≤ft(X_s - \bar{X}_t\right)^2 + ∑_{s = t + 1}^{T}≤ft(X_s - \tilde{X}_{T - t}\right)^2\right), where \bar{X}_t = t^{-1}∑_{s = 1}^t X_s and \tilde{X}_{T - t} = (T - t)^{-1} ∑_{s = t + 1}^{T} X_s stat_plot Whether to create a plot of the values of the statistic at all potential change points kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar); if function, the kernel function to be used for long-run variance estimation (default is the Bartlett kernel in cointReg) bandwidth If character, the identifier for how to compute the bandwidth as defined in cointReg (see getBandwidth); if function, a function to use for computing the bandwidth; if numeric, the bandwidth value to use (the default is to use Andrews' method, as used in cointReg)
### Value
A htest-class object containing the results of the test
### References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
### Examples
DE.test(rnorm(1000))
DE.test(rnorm(1000), use_kernel_var = TRUE, kernel = "bo", bandwidth = "nw")
[Package CPAT version 0.1.0 Index]
|
2021-12-03 16:03:46
|
{"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": 0.8024628162384033, "perplexity": 2873.529628802903}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362891.54/warc/CC-MAIN-20211203151849-20211203181849-00276.warc.gz"}
|
https://runestone.academy/ns/books/published/complex/GameOfLife/Exercises.html
|
8.8. Exercises¶
The code for this chapter is in the notebook chap08.ipynb in the repository for this book. Open this notebook, read the code, and run the cells. You can use this notebook to work on the following exercises.
Exercise 1: Start GoL in a random state and run it until it stabilizes. What stable patterns can you identify?
Exercise 2: Many named patterns are available in portable file formats. Modify Life.py to parse one of these formats and initialize the grid.
Exercise 3: In the given implementation, the Life class is based on a parent class called Cell2D, and the LifeViewer class is based on Cell2DViewer. You can use these base classes to implement other 2-D cellular automatons.
For example, one variation of GoL, called “Highlife”, has the same rules as GoL, plus one additional rule: a dead cell with 6 neighbors comes to life.
Write a class named Highlife that inherits from Cell2D and implements this version of the rules. Also write a class named HighlifeViewer that inherits from Cell2DViewer and try different ways to visualize the results. As a simple example, use a different colormap.
One of the more interesting patterns in Highlife is the replicator. Use add_cells to initialize Highlife with a replicator and see what it does.
Exercise 4: If you generalize the Turing machine to two dimensions, or add a read-write head to a 2-D CA, the result is a cellular automaton called a Turmite. It is named after a termite because of the way the read-write head moves, but spelled wrong as an homage to Alan Turing.
The most famous Turmite is Langton’s Ant, discovered by Chris Langton in 1986.
The ant is a read-write head with four states, which you can think of as facing north, south, east or west. The cells have two states, black and white.
The rules are simple. During each time step, the ant checks the color of the cell it is on. If black, the ant turns to the right, changes the cell to white, and moves forward one space. If the cell is white, the ant turns left, changes the cell to black, and moves forward.
Given a simple world, a simple set of rules, and only one moving part, you might expect to see simple behavior — but you should know better by now. Starting with all white cells, Langton’s ant moves in a seemingly random pattern for more than 10,000 steps before it enters a cycle with a period of 104 steps. After each cycle, the ant is translated diagonally, so it leaves a trail called the “highway”.
Write an implementation of Langton’s Ant.
|
2023-01-31 01:41:37
|
{"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": 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": 0.2640917897224426, "perplexity": 1366.6688156922285}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499831.97/warc/CC-MAIN-20230130232547-20230131022547-00015.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/other-math/CLONE-547b8018-14a8-4d02-afd6-6bc35a0864ed/chapter-6-percent-6-4-using-proportions-to-solve-percent-problems-6-4-exercises-page-419/48
|
## Basic College Mathematics (10th Edition)
Percent= 51;whole= 3020. $\frac{x}{3020}=\frac{51}{100}$ Cross products: $100x=154020$ Solve for x. Round to the nearest number: $x=1540$
|
2019-10-22 14:24:57
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19957353174686432, "perplexity": 3435.535127747264}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00282.warc.gz"}
|
http://math.stackexchange.com/questions/96303/conditional-expectation-and-conditional-variance
|
# conditional expectation and conditional variance
I have a question about conditional expectation and conditional variance. It's a very general question. We defined conditional variance by
$$\operatorname{Var}(X|\mathcal{F}):=E((X-E(X|\mathcal{F}))^2|\mathcal{F})$$
For a random variable $X$ and a $\sigma$-algebra $\mathcal{F}$. Are there any inequalities such that
$\operatorname{Var}(X|\mathcal{F})\le \operatorname{Var}(X)$ or $\operatorname{Var}(X|\mathcal{F})\ge \operatorname{Var}(X)$ and the same question for the conditional expectation:
$E(X|\mathcal{F}) \le E(X)$ or $E(X|\mathcal{F}) \ge E(X)$
Are any one of them true in general, or what further assumption have to bee assumed that a conclusion as above is true? Often such an inequality would be very usful. Thanks in advance.
hulik
-
You might want to have a look at the (small and excellent) textbook Probability with martingales by David Williams. – Did Jan 4 '12 at 9:41
@ Didier Piau: Thanks for your comment, but unfortunately the book is not free available or I didn't find it. – user20869 Jan 4 '12 at 10:24
Which textbook do you use? – Did Jan 4 '12 at 13:42
None of these inequalities are true in general.
Suppose you have
• $\Pr(X=0,Y=0) = \frac{1}{5}$
• $\Pr(X=0,Y=1) = \frac{1}{5}$
• $\Pr(X=2,Y=1) = \frac{1}{5}$
• $\Pr(X=-5,Y=2) = \frac{1}{5}$
• $\Pr(X=3,Y=2) = \frac{1}{5}$
Then defining $\mathcal{F}$ on values of $Y$
we have $E[X]=0$, $E[X|Y=1]=1$, $E[X|Y=2]=-1$,
and $Var(X)=7.6$, $Var(X|Y=0)=0$, $Var(X|Y=2)=16$.
-
@ Henry: Thanks for your answer. Though I have an additional question. In fact I would like to bound $Var(X|\mathcal{F})$ by $\operatorname{const}\cdot E(X^2)$. Is this possible? – user20869 Jan 4 '12 at 10:33
No: you can exceed any given ratio – Henry Jan 4 '12 at 15:09
@ Henry: Thanks for your quick answer. As mentioned below (see comment after Didier Piau's answer) the motiviation behind this question can be found in link. I wondered if in a more general setting something would be true. Because then I would be able to prove 4.) in the related question – user20869 Jan 4 '12 at 16:08
All these inequalities fail in general, and for good reasons.
Assume for example that $\mathcal F$ is the sigma-algebra generated by $X$. Then $\mathrm E(X\mid\mathcal F)=X$ almost surely hence $\mathrm E(X)\leqslant \mathrm E(X\mid\mathcal F)$ almost surely or $\mathrm E(X)\geqslant \mathrm E(X\mid\mathcal F)$ almost surely are impossible unless $\mathrm E(X)= \mathrm E(X\mid\mathcal F)$ almost surely, that is, $X$ almost surely constant.
Here is another example. Assume that $X=YZ$ with $Y$ and $Z$ independent and $\mathrm E(Z)=0$ and $\mathrm E(Z^2)=1$, and that $\mathcal F$ is the sigma-algebra generated by $Y$. Then $\mathrm E(X\mid\mathcal F)=\mathrm E(Z)Y=0$ almost surely and $\mathrm{Var}(X\mid\mathcal F)=\mathrm E(X^2\mid\mathcal F)=E(Z^2)Y^2=Y^2$ almost surely while $\mathrm E(X)=0$ and $\mathrm E(X^2)=\mathrm E(Y^2)$ hence no almost sure comparison can hold.
-
Thanks for your answer. See link it's a related question, in fact it's 4. in the other question (see link). This was the reason for asking this question in a more general setting. – user20869 Jan 4 '12 at 16:02
|
2015-05-23 13:49:22
|
{"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": 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": 0.9560964703559875, "perplexity": 375.27637277308247}, "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-2015-22/segments/1432207927634.1/warc/CC-MAIN-20150521113207-00190-ip-10-180-206-219.ec2.internal.warc.gz"}
|
https://qa.answers.com/other-qa/How_many_people_in_the_world_on_average_are_pregnant
|
0
# How many people in the world on average are pregnant?
Lvl 1
2009-08-21 11:56:01
There were 135,000,000 babies born in 2008 if you figure that 2,000,000 of those pregnancies resulted in twins that leaves 133,000,000 pregnancies a year. Multiply that number by 0.75 (the length of a pregnancy in years) and you get almost exacltly 100,000,000 woman are pregnant at any one time around the world.
Wiki User
2009-08-21 11:56:01
Study guides
17 cards
➡️
See all cards
4.36
11 Reviews
|
2023-03-25 05:41:31
|
{"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": 0.9139381051063538, "perplexity": 6052.864203958887}, "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-2023-14/segments/1679296945315.31/warc/CC-MAIN-20230325033306-20230325063306-00129.warc.gz"}
|
https://www.r-bloggers.com/2022/01/using-r-to-create-column-charts-featuring-95-confidence-intervals/
|
[This article was first published on R tips – NHS-R Community, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
### Daniel Weiland – Consultant Medical Microbiologist – Newcastle upon Tyne NHS Foundation Trust
Hello!
This is my first blog post for the NHS R Community, which I stumbled across in the course of my work as a consultant medical microbiologist at Newcastle upon Tyne Hospitals NHS Foundation Trust.
At work, I’ve been trying to use R to create column charts featuring 95% confidence intervals. I approached the friendly people on the NHS R Community’s Slack channel for further information and guidance.
I must add here that the Community’s Slack channel has been extremely helpful to me, as a novice R user, in solving some of the issues I’ve experienced, and highlighting R packages of potential interest. This is the first time I’ve tried to create a ReprEx and now I understand why people love (?) the mtcars database as much as they do!
### Step 1: Calculate some summary statistics
I wanted to calculate some summary statistics, including the mean, and standard error or 95% confidence intervals.
Initially I came across the summary() function of Base R, which is helpful as it calculates the Min., 1st Qu., Median, Mean, 3rd Qu., and Max.
However, the summary() function of {base} R does not calculate either the standard error or the 95% confidence intervals
#calculate summary statistics for all numeric data using summary() and where(is.numeric())
mtcars %>%
select(where(is.numeric)) %>%
summary()
#calculate summary statistics for mpg using summary() and where(is.numberic())
mtcars %>%
select(mpg) %>%
summary()
Then zx8754 very kindly pointed me towards a method for calculating the standard error on StackOverflow: https://stackoverflow.com/q/2676554/680068
#create stderr function
stderr <- function(x, na.rm=TRUE) {
if (na.rm) x <- na.omit(x)
sqrt(var(x)/length(x))
}
Then I used this function to calculate summary statistics, incl. mean and standard error, using the summarise() and across() functions of {dplyer}
#calculate summary statistics using summarise() and across() and n/mean/min/median/max/sd/stderr
# stderr <- function(x, na.rm=TRUE) {
# if (na.rm) x <- na.omit(x)
# sqrt(var(x)/length(x))
# }
mtcars %>%
group_by(cyl) %>%
mutate(
across(mpg,
list(
n = ~ n(),
mean = ~ mean(.x, na.rm = TRUE),
min = ~ min(.x, na.rm = TRUE),
median = ~ median(.x, na.rm = TRUE),
max = ~ max(.x, na.rm = TRUE),
sd = ~ sd(.x, na.rm = TRUE),
stderr = ~ stderr(.x)),
.names = NULL)) %>%
select(starts_with("mpg")) %>%
summarise(mean = mean(mpg_mean),
min = mean(mpg_min),
median = mean(mpg_median),
max = mean(mpg_max),
sd = mean(mpg_sd),
stderr = mean(mpg_stderr)) %>%
#create column chart with error bars (using stderr)
ggplot(aes(cyl, mean))+
geom_col(na.rm = TRUE)+
geom_errorbar(aes(ymin = mean-stderr, ymax = mean+stderr), position = "dodge", width = 0.25)
#calculate summary statistics using summarise() and across() and n/mean/min/median/max/sd/stderr
# stderr <- function(x, na.rm=TRUE) {
# if (na.rm) x <- na.omit(x)
# sqrt(var(x)/length(x))
# }
mtcars %>%
group_by(cyl) %>%
mutate(
across(mpg,
list(
n = ~ n(),
mean = ~ mean(.x, na.rm = TRUE),
min = ~ min(.x, na.rm = TRUE),
median = ~ median(.x, na.rm = TRUE),
max = ~ max(.x, na.rm = TRUE),
sd = ~ sd(.x, na.rm = TRUE),
stderr = ~ stderr(.x)),
.names = NULL)) %>%
select(starts_with("mpg")) %>%
summarise(mean = mean(mpg_mean),
min = mean(mpg_min),
median = mean(mpg_median),
max = mean(mpg_max),
sd = mean(mpg_sd),
stderr = mean(mpg_stderr)) %>%
#create column chart with error bars (using stderr)
ggplot(aes(cyl, mean))+
geom_col(na.rm = TRUE)+
geom_errorbar(aes(ymin = mean-stderr, ymax = mean+stderr), position = "dodge", width = 0.25)
### Step 2: Create column charts with error bars (using 95% confidence intervals)
Then Seb Fox pointed me towards a method for calculating 95% confidence intervals using the {PHEindicatormethods} package, available on CRAN: https://cran.r-project.org/web/packages/PHEindicatormethods/index.html
#create MEAN column chart with error bars (using 95% confidence intervals)
require(PHEindicatormethods)
mtcars %>%
filter(!is.na(cyl)) %>%
group_by(cyl) %>%
#use phe_mean()
phe_mean(x = mpg, #field name from data containing the values to calculate the means for
type = "full", #defines the data and metadata columns to be included in output; can be "value", "lower", "upper", "standard" (for all data) or "full" (for all data and metadata); quoted string; default = "full"
confidence = 0.95) %>% #required level of confidence expressed as a number between 0.9 and 1
#create column chart with error bars (using 95% CI calculated using phe_mean())
ggplot(aes(cyl, value))+
geom_col(na.rm = TRUE)+
geom_errorbar(aes(ymin = lowercl, ymax = uppercl), position = "dodge", width = 0.25)
#create PROPORTION column chart with error bars (using 95% confidence intervals)
require(PHEindicatormethods)
mtcars %>%
group_by(cyl) %>%
summarise(n = n(),
sum = sum(n)) %>%
mutate(sum = sum(n)) %>%
#phe_proportion()
phe_proportion(x = n, #numerator
n = sum, #denominator
type = "full", #defines the data and metadata columns to be included in output; can be "value", "lower", "upper", "standard" (for all data) or "full" (for all data and metadata); quoted string; default = "full"
confidence = 0.95, #required level of confidence expressed as a number between 0.9 and 1
multiplier = 100) %>% #the multiplier used to express the final values (eg 100 = percentage); numeric; default 1
#create column chart with error bars (using 95% CI calculated using phe_proportion())
ggplot(aes(cyl, value))+
geom_col(na.rm = TRUE)+
geom_errorbar(aes(ymin = lowercl, ymax = uppercl), position = "dodge", width = 0.25)
I hope that the code, above, helps a few colleagues of mine across the NHS, in some small way.
Thank you, again, to all members of the NHS R Community, for all your help. Particular thanks go to everyone who has helped me, to date, on the NHS R Community’s Slack channel.
The post Using R to create column charts featuring 95% confidence intervals appeared first on NHS-R Community.
To leave a comment for the author, please follow the link and comment on their blog: R tips – NHS-R Community.
R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
# Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts.(You will not see this message again.)
Click here to close (This popup will not appear again)
|
2022-01-19 19:23:44
|
{"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": 0.2272157222032547, "perplexity": 11141.326327001658}, "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-2022-05/segments/1642320301488.71/warc/CC-MAIN-20220119185232-20220119215232-00327.warc.gz"}
|
https://mathoverflow.net/questions/165349/non-continuous-higher-differentiability
|
Non-continuous higher differentiability
The standard definition is that a function $f:\mathbb{R}^n\to \mathbb{R}$ is differentiable at a point $x$ if there exists a linear map $\mathrm{d}f_x: \mathbb{R}^n \to \mathbb{R}$ such that
$$f(x+h) = f(x) + \mathrm{d}f_x(h) + \epsilon \|h\|$$
where $\epsilon\to 0$ as $h\to 0$. This is stronger than the existence of all partial (or directional) derivatives, but weaker than their continuity. However, when talking about higher differentiability, one usually switches to talking about partial derivatives, asking them to be continuous in order to prove basic properties.
Suppose that instead we define $f$ to be "twice differentiable" at $x$ if in addition to $\mathrm{d}f_x$ as above there exists a quadratic form $\mathrm{d}^2f_x$ such that
$$f(x+h) = f(x) + \mathrm{d}f_x(h) + \frac{1}{2}\mathrm{d}^2f_x(h) + \epsilon \|h\|^2$$
where $\epsilon\to 0$ as $h\to 0$. This is true if $f$ has continous second-order partials (it's the multidimensional Taylor expansion, with $\mathrm{d}^2f_x$ the Hessian matrix).
1. Does this imply that all second-order partial derivatives of $f$ exist?
2. If so, does it imply that the mixed second-order partials are equal?
• I am not sure. I will think some about this. My definition of higher order differentiability would be the following: First $f$ needs to be differentiable in a nbhd of $p$. Then $f$ is twice differentiable at $p$ if there is a bilinear form $D^2f(p)$ such that $Df(p+v_1)(v_2) = Df(p)(v_2)+D^2f(v_1,v_2)+\epsilon |v_1||v_2|$. For some reason it is very hard to find sources where people talk about the second derivative as a bilinear form rather than just a quadratic form. May 6, 2014 at 21:31
• You may also be interested in my online course with Jim Fowler here: ximera.osu.edu/course/kisonecat/m2o2c2/course/activity/week1. It is a little buggy, and a little sparse in terms of examples, but it covers this perspective on higher order derivatives in a kind of "interactive textbook" format. May 6, 2014 at 21:36
• See Chapter XIII, section 3--6 of Lang's "Real and Functional Analysis" for a very elegant treatment under which higher derivatives are defined via multilinear maps and moreover the $p$th higher derivative is genuinely the "derivative" of the $(p-1)$th. One virtue of this approach is that it permits both a formulation and proof of the higher-dimensional Taylor formula which looks and feels exactly like the 1-dimensional case (with the mess of factorials hidden away within a clean formalism); of course, one can bust out coordinates and recover the usual messier explicit version from that. May 6, 2014 at 21:47
• The first derivative of $f$ at $a$ is the linear function of $h$ that best approximates $f(a+h)-f(a)$. The second derivative of $f$ at $a$ is the bilinear function of $(h_1,h_2)$ that best approximates $f(a+h_1+h_2)-f(a+h_1)-f(a+h_2)+f(a)$. Etc. May 7, 2014 at 12:13
• In case anyone is still watching this question, I am puzzled. On p183 of Strichartz' The Way of Analysis, after proving the second-order Taylor approximation to a $C^2$ function, he says "We will not discuss the problem of obtaining a converse kind of statement, deducing the existence of the second derivative from the existence of quadratic polynomial approximations, because such theorems are extremely difficult to prove and have few applications." But that implies that such theorems exist, which the answers to this question seem to deny. Can anyone guess what he had in mind? May 12, 2014 at 22:16
The funny thing is that I got almost the same question from one of my student last semester. The idea was to neglect both the linear and quadratic parts of the hypothetical expansion (without loss of generality, we may assume they are zero), and focus on $\epsilon \|h\|^2$. We came to the following (obvious) one-dimensional counterexample:
$$f(h) = h^3 \sin(\frac{1}{h})$$
for $h \not= 0$, and: $$f(0) = 0$$
• This example makes it clear that the issue is not that the first derivative might fail to exist (except at the point in question), so that it can't possibly have its own derivative. In this case, the first derivative exists everywhere and is even continuous, just not differentiable at zero. Apr 8, 2019 at 18:15
No, if I understand the question right, not even in one variable. Let $f(x)$ be $x^3g(x)$ where $g$ is bounded and, except at $x=0$, infinitely differentiable. If $g$ oscillates fast enough near $x=0$ then even though it is the sum of a degree two polynomial (namely zero) and an error term of the kind you are allowing, it will not have a second derivative at $0$.
Thanks Michal and Tom for the answer. Let me improve on it slightly with an example of a function which is well-approximated by a polynomial of every degree near 0 (in fact, the zero polynomial), but is still not even twice differentiable there:
$$f(x) = e^{-1/x^2} \sin(e^{1/x^2})$$
|
2022-09-29 14:35:39
|
{"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8503541350364685, "perplexity": 163.75021404411626}, "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-2022-40/segments/1664030335355.2/warc/CC-MAIN-20220929131813-20220929161813-00603.warc.gz"}
|
https://support.bioconductor.org/u/6687/
|
## User: Jiping Wang
Jiping Wang70
Reputation:
70
Status:
Trusted
Location:
Last seen:
2 weeks, 6 days ago
Joined:
5 years, 4 months ago
Email:
j*****@northwestern.edu
#### Posts by Jiping Wang
<prev • 23 results • page 1 of 3 • next >
1
110
views
1
... Thanks. I had another post earlier, in which you basically have helped me out in the same way(very grateful). It worked. I want to follow the IntersectionStrict mode as HTSeq requires to calculate the coverage curve. if one read align to both genes (i.e. genes may overlap), that read should not be c ...
written 21 days ago by Jiping Wang70
1
110
views
1
... That makes sense. I will give it a try. Thanks again for great help! But there is one potential issue: if a read partially overlaps with an exons, that will be counted in the coverage score? I need to judge whether a read or a pair of reads are compatible with the features (exons for the same gene) ...
written 22 days ago by Jiping Wang70
1
110
views
1
... I am not to distinguish between different transcripts as it's just not possible to deconvolve them based on reads count. The reads count from different splicing forms will be just piled up, and repeatedly counted on the shared axons if we do the coverage for transcripts. Instead I am listing all exo ...
written 22 days ago by Jiping Wang70
1
110
views
1
... Thanks so much! I indeed ignored the fine details under exonsBy. Is there a quick way to sort exon in ascending rank if they are on minus strand? It takes extremely long time if I do the following: for(i in 1:length(all_genes)){ if(runValue(strand(all_genes[[i]]))=="-"){ all_genes[[i]] ...
written 23 days ago by Jiping Wang70
1
110
views
1
... I tried to use *coverageByTranscript* function from GenomicAlignments package to calculate the RNA-seq coverage along transcripts. This function requires the exons be sorted in ascending rank (i.e. the first Exxon in the transcript should be listed in the GRanges object first, and so forth, see refe ...
written 23 days ago by Jiping Wang70 • updated 23 days ago by Hervé Pagès ♦♦ 14k
1
81
views
1
... A quick question: is there any way to extract uniquely aligned single-end or paired-end reads using Rsamtools? I read carefully about the documentation and did find a clear clue. *IsSecondaryAlignment=T* tag does not exclude a read which had aligned to multiple locations we designated as *primary* a ...
written 3 months ago by Jiping Wang70 • updated 3 months ago by Martin Morgan ♦♦ 24k
1
141
views
1
... Thanks so much. I also figured out the *reduce* function as well. Very grateful for your detailed help! ...
written 4 months ago by Jiping Wang70
1
141
views
1
... Hi Hervé, Thanks for your quick help. I understand and appreciate what you explained. I am just wondering whether your package could implement this as default for the paired-end data. I saw there are some other posts where users raised the same question. In my opinion, the coverage calculation f ...
written 4 months ago by Jiping Wang70
1
141
views
1
... I have a paired-end RNA-seq data in bam. It was read into R using readGAlignmentPairs, named gal2. The compatible reads pairs was parsed using findCompatibleOverlaps function. The following codes only specifically examines compatible read pairs for 4th gene in the dm3_transcripts list. There was onl ...
written 4 months ago by Jiping Wang70 • updated 4 months ago by Hervé Pagès ♦♦ 14k
0
160
views
0
... I am trying to use pcoverageByTranscript function to calculate coverage score on each genes. I have a paired-end RNA-seq data. I read in with readGAlignments function as gal1 and readGAlignmentPairs function as gal2 separately. > which <- GRanges(seqnames = c("chr1")) > gr = as(seqinf ...
written 4 months ago by Jiping Wang70
#### Latest awards to Jiping Wang
No awards yet. Soon to come :-)
Content
Help
Access
Use of this site constitutes acceptance of our User Agreement and Privacy Policy.
|
2019-12-06 14:27:48
|
{"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": 0.2488403469324112, "perplexity": 4476.36908019497}, "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-2019-51/segments/1575540488620.24/warc/CC-MAIN-20191206122529-20191206150529-00443.warc.gz"}
|
http://15418.courses.cs.cmu.edu/spring2017/lecture/dnn/slide_038
|
Previous | Next --- Slide 38 of 51
Back to Lecture Thumbnails
chenh1
The convolution in Fourier domain can be referenced here.
eourcs
Interesting to note that the original FFT algorithm (the Cooley-Tukey algorithm) is one of the early examples of a trivially parallelizable divide-and-conquer algorithm. No asymptotic improvements have been made to computing circular convolution since then, but there is a very healthy area of research around decreasing the number of multiplications for certain data sets. For example, Overlap-add is an efficient way of computing convolution when you have a large image and a small filter (which is often the case in deep learning).
themj
The Winograd algorithm is based off the premise that it is possible to uniquely given its remainder with respect to the given moduli. (Assumptions are that moduli Are relatively prime)
|
2019-05-26 07:35:14
|
{"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": 0.8218947649002075, "perplexity": 667.7938998284658}, "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-2019-22/segments/1558232258862.99/warc/CC-MAIN-20190526065059-20190526091059-00297.warc.gz"}
|
https://open.kattis.com/problems/cardboardcontainer
|
Kattis
# Cardboard Container
Fidget spinners are so 2017; this year’s rage are fidget cubes. A fidget cube is a cube with unit side lengths, which you hold in your hand and fidget with. Kids these days, right?
You work in the planning department for a company that creates and ships fidget cubes. Having done some market analysis, you found that your customers want to receive shipments of exactly $V$ fidget cubes.
This means you have to design a container that will hold exactly $V$ fidget cubes. Since fidget cubes are very fragile, you cannot have any empty space in your container. If there is empty space, they might move around, bump into each other and get damaged. Because of this, you decide to ship the fidget cubes in a rectangular cardboard box.
The cost of a cardboard box is proportional to its surface area, costing exactly one unit of money per square unit of surface area. Of course you want to spend as little money as possible. Subject to the above constraints, how much money do you have to spend on a box for $V$ fidget cubes?
## Input
The input contains a single integer, $1 \leq V \leq 10^6$, the number of fidget cubes for which you need to build a box.
## Output
Print the cost of the cheapest rectangular box as specified in the statement.
Sample Input 1 Sample Output 1
1
6
Sample Input 2 Sample Output 2
4
16
Sample Input 3 Sample Output 3
3
14
Sample Input 4 Sample Output 4
5913
2790
|
2019-03-20 09:12:51
|
{"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": 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": 0.2038714438676834, "perplexity": 1396.040373228544}, "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-2019-13/segments/1552912202324.5/warc/CC-MAIN-20190320085116-20190320111116-00238.warc.gz"}
|
https://mathoverflow.net/questions/133935/perverse-sheaves-for-easy-stratifications
|
# Perverse sheaves for easy stratifications
Let $X$ be a complex variety equipped with a stratification. Let us assume, that all strata are contractible and in addition, that all strata closures are smooth.
Is there an "easy" quiver description of the category of perverse sheaves in this case?
For example does this category only depend on the poset of strata?
This sounds too optimistic, so what additional information is needed?
For example if we are also given the conormal bundles of the strata closures, can one reconstruct the category from this data?
The main result 2-categorifies a theorem of MacPherson, which states that the category of perverse sheaves over a (topologically) stratified space $X$ is equivalent to the category of set-valued functors from the exit path category of $X$.
The exit path category of $X$ has all points of $X$ as objects, and morphisms are (homotopy classes of) continuous paths which we allow to ascend up to higher strata, but never descend to lower ones. Asking that all strata be contractible does not, in general, allow one to pass from the exit path category to the poset of strata without losing structure. On the other hand, if your stratification of $X$ arises from a regular CW decomposition, then the associated exit path category retracts onto the poset of cells.
Stringing all of this together, one set of sufficient conditions which guarantee that the category of perverse sheaves is recoverable from the poset of strata, is that the stratification comes from a regular CW decomposition of $X$.
|
2022-10-07 07:17:22
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6414444446563721, "perplexity": 129.40623802942662}, "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-2022-40/segments/1664030337971.74/warc/CC-MAIN-20221007045521-20221007075521-00708.warc.gz"}
|
https://wiki.fysik.dtu.dk/ase/dev/ase/io/formatoptions.html
|
# Format Specific Options¶
## abinit¶
ase.io.abinit.read_abinit(filename='abinit.in')[source]
Import ABINIT input file.
Reads cell, atom positions, etc. from abinit input file
ase.io.abinit.write_abinit(filename, atoms, cartesian=False, long_format=True)[source]
Method to write abinit input files.
## acemolecule-input¶
ase.io.acemolecule.read_acemolecule_input(filename)[source]
Reads a ACE-Molecule input file :param filename: :type filename: ACE-Molecule input file name
Returns
Return type
ASE atoms object containing geometry only.
## acemolecule-out¶
ase.io.acemolecule.read_acemolecule_out(filename)[source]
Interface to ACEMoleculeReader and return values for corresponding quantity :param filename: :type filename: ACE-Molecule log file. :param quantity: :type quantity: One of atoms, energy, forces, excitation-energy.
Returns
• - quantity = ‘excitation-energy’ – returns None. This is placeholder function to run TDDFT calculations without IndexError.
• - quantity = ‘energy’ – returns energy as float value.
• - quantity = ‘forces’ – returns force of each atoms as numpy array of shape (natoms, 3).
• - quantity = ‘atoms’ – returns ASE atoms object.
## aims¶
ase.io.aims.read_aims(filename, apply_constraints=True)[source]
Import FHI-aims geometry type files.
Reads unitcell, atom positions and constraints from a geometry.in file.
If geometric constraint (symmetry parameters) are in the file include that information in atoms.info[“symmetry_block”]
ase.io.aims.write_aims(filename, atoms, scaled=False, geo_constrain=False, velocities=False, ghosts=None, info_str=None)[source]
Method to write FHI-aims geometry files.
Writes the atoms positions and constraints (only FixAtoms is supported at the moment).
Parameters
• filename – str Name of file to output structure to
• atoms – ase.atoms.Atoms structure to output to the file
• scaled – bool If True use fractional coordinates instead of Cartesian coordinates
• symmetry_block – list of str List of geometric constraints as defined in: https://arxiv.org/abs/1908.01610
• velocities – bool If True add the atomic velocity vectors to the file
• ghosts – list of Atoms A list of ghost atoms for the system
• info_str – str A string to be added to the header of the file
## aims-output¶
ase.io.aims.read_aims_output(filename, index=-1)[source]
Import FHI-aims output files with all data available, i.e. relaxations, MD information, force information etc etc etc.
## bundletrajectory¶
ase.io.bundletrajectory.read_bundletrajectory(filename, index=-1)[source]
Reads one or more atoms objects from a BundleTrajectory.
Arguments:
filename: str
The name of the bundle (really a directory!)
index: int
An integer specifying which frame to read, or an index object for reading multiple frames. Default: -1 (reads the last frame).
ase.io.bundletrajectory.write_bundletrajectory(filename, images)[source]
Write image(s) to a BundleTrajectory.
Write also energy, forces, and stress if they are already calculated.
## castep-castep¶
ase.io.castep.read_castep_castep(fd, index=None)[source]
Reads a .castep file and returns an atoms object. The calculator information will be stored in the calc attribute.
There is no use of the “index” argument as of now, it is just inserted for convenience to comply with the generic “read()” in ase.io
Please note that this routine will return an atom ordering as found within the castep file. This means that the species will be ordered by ascending atomic numbers. The atoms witin a species are ordered as given in the original cell file.
Note: This routine returns a single atoms_object only, the last configuration in the file. Yet, if you want to parse an MD run, use the novel function $$read_md()$$
## castep-cell¶
ase.io.castep.read_castep_cell(fd, index=None, calculator_args={}, find_spg=False, units={'Eh': 27.2113845, 'Pascal': 160217653000.0, 'a0': 0.5291772108, 'c': 299792458, 'e': 1.60217653e-19, 'hbar': 6.58211915e-16, 'kB': 8.617343e-05, 'me': 0.00054857990945, 't0': 2.4188843276239763e-17})[source]
Read a .cell file and return an atoms object. Any value found that does not fit the atoms API will be stored in the atoms.calc attribute.
By default, the Castep calculator will be tolerant and in the absence of a castep_keywords.json file it will just accept all keywords that aren’t automatically parsed.
ase.io.castep.write_castep_cell(fd, atoms, positions_frac=False, force_write=False, precision=6, magnetic_moments=None, castep_cell=None)[source]
This CASTEP export function write minimal information to a .cell file. If the atoms object is a trajectory, it will take the last image.
Note that function has been altered in order to require a filedescriptor rather than a filename. This allows to use the more generic write() function from formats.py
Note that the “force_write” keywords has no effect currently.
Parameters
• positions_frac – boolean. If true, positions are printed as fractional rather than absolute. Default is false.
• castep_cell – if provided, overrides the existing CastepCell object in the Atoms calculator
• precision – number of digits to which lattice and positions are printed
• magnetic_moments – if None, no SPIN values are initialised. If ‘initial’, the values from get_initial_magnetic_moments() are used. If ‘calculated’, the values from get_magnetic_moments() are used. If an array of the same length as the atoms object, its contents will be used as magnetic moments.
## castep-geom¶
ase.io.castep.read_castep_geom(fd, index=None, units={'Eh': 27.2113845, 'Pascal': 160217653000.0, 'a0': 0.5291772108, 'c': 299792458, 'e': 1.60217653e-19, 'hbar': 6.58211915e-16, 'kB': 8.617343e-05, 'me': 0.00054857990945, 't0': 2.4188843276239763e-17})[source]
Reads a .geom file produced by the CASTEP GeometryOptimization task and returns an atoms object. The information about total free energy and forces of each atom for every relaxation step will be stored for further analysis especially in a single-point calculator. Note that everything in the .geom file is in atomic units, which has been conversed to commonly used unit angstrom(length) and eV (energy).
Note that the index argument has no effect as of now.
Contribution by Wei-Bing Zhang. Thanks!
Routine now accepts a filedescriptor in order to out-source the gz and bz2 handling to formats.py. Note that there is a fallback routine read_geom() that behaves like previous versions did.
## castep-md¶
ase.io.castep.read_castep_md(fd, index=None, return_scalars=False, units={'Eh': 27.2113845, 'Pascal': 160217653000.0, 'a0': 0.5291772108, 'c': 299792458, 'e': 1.60217653e-19, 'hbar': 6.58211915e-16, 'kB': 8.617343e-05, 'me': 0.00054857990945, 't0': 2.4188843276239763e-17})[source]
Reads a .md file written by a CASTEP MolecularDynamics task and returns the trajectory stored therein as a list of atoms object.
Note that the index argument has no effect as of now.
## castep-phonon¶
ase.io.castep.read_castep_phonon(fd, index=None, read_vib_data=False, gamma_only=True, frequency_factor=None, units={'Eh': 27.2113845, 'Pascal': 160217653000.0, 'a0': 0.5291772108, 'c': 299792458, 'e': 1.60217653e-19, 'hbar': 6.58211915e-16, 'kB': 8.617343e-05, 'me': 0.00054857990945, 't0': 2.4188843276239763e-17})[source]
Reads a .phonon file written by a CASTEP Phonon task and returns an atoms object, as well as the calculated vibrational data if requested.
Note that the index argument has no effect as of now.
## cfg¶
ase.io.cfg.read_cfg(f)[source]
Read atomic configuration from a CFG-file (native AtomEye format). See: http://mt.seas.upenn.edu/Archive/Graphics/A/
ase.io.cfg.write_cfg(f, a)[source]
Write atomic configuration to a CFG-file (native AtomEye format). See: http://mt.seas.upenn.edu/Archive/Graphics/A/
## cif¶
ase.io.cif.read_cif(fileobj, index, store_tags=False, primitive_cell=False, subtrans_included=True, fractional_occupancies=True, reader='ase')[source]
Read Atoms object from CIF file. index specifies the data block number or name (if string) to return.
If index is None or a slice object, a list of atoms objects will be returned. In the case of index is None or slice(None), only blocks with valid crystal data will be included.
If store_tags is true, the info attribute of the returned Atoms object will be populated with all tags in the corresponding cif data block.
If primitive_cell is true, the primitive cell will be built instead of the conventional cell.
If subtrans_included is true, sublattice translations are assumed to be included among the symmetry operations listed in the CIF file (seems to be the common behaviour of CIF files). Otherwise the sublattice translations are determined from setting 1 of the extracted space group. A result of setting this flag to true, is that it will not be possible to determine the primitive cell.
If fractional_occupancies is true, the resulting atoms object will be tagged equipped with an array $$occupancy$$. Also, in case of mixed occupancies, the atom’s chemical symbol will be that of the most dominant species.
String reader is used to select CIF reader. Value $$ase$$ selects built-in CIF reader (default), while $$pycodcif$$ selects CIF reader based on $$pycodcif$$ package.
ase.io.cif.write_cif(fileobj, images, format='default')[source]
Write images to CIF file.
## cmdft¶
ase.io.cmdft.read_cmdft(fileobj)[source]
## cp2k-dcd¶
ase.io.cp2k.read_cp2k_dcd(fileobj, index=-1, ref_atoms=None, aligned=False)[source]
Read a DCD file created by CP2K.
To yield one Atoms object at a time use iread_cp2k_dcd.
Note: Other programs use other formats, they are probably not compatible.
If ref_atoms is not given, all atoms will have symbol ‘X’.
To make sure that this is a dcd file generated with the DCD_ALIGNED_CELL key in the CP2K input, you need to set aligned to True to get cell information. Make sure you do not set it otherwise, the cell will not match the atomic coordinates! See (this discussion)[https://groups.google.com/forum/#!searchin/cp2k/Outputting$20cell$20information$20and$20fractional$20coordinates%7Csort:relevance/cp2k/72MhYykrSrQ/5c9Jaw7S9yQJ] for details. ## crystal¶ ase.io.crystal.read_crystal(filename)[source] Method to read coordinates form ‘fort.34’ files additionally read information about periodic boundary condition ase.io.crystal.write_crystal(filename, atoms)[source] Method to write atom structure in crystal format (fort.34 format) ## cube¶ ase.io.cube.read_cube(fileobj, read_data=True, program=None, verbose=False)[source] Read atoms and data from CUBE file. fileobjstr or file Location to the cubefile. read_databoolean If set true, the actual cube file content, i.e. an array containing the electronic density (or something else )on a grid and the dimensions of the corresponding voxels are read. program: str Use program=’castep’ to follow the PBC convention that first and last voxel along a direction are mirror images, thus the last voxel is to be removed. If program=None, the routine will try to catch castep files from the comment lines. verbosebool Print some more information to stdout. Returns a dict with the following keys: • ‘atoms’: Atoms object • ‘data’ : (Nx, Ny, Nz) ndarray • ‘origin’: (3,) ndarray, specifying the cube_data origin. ase.io.cube.write_cube(fileobj, atoms, data=None, origin=None, comment=None)[source] Function to write a cube file. fileobj: str or file object File to which output is written. atoms: Atoms object Atoms object specifying the atomic configuration. data3dim numpy array, optional (default = None) Array containing volumetric data as e.g. electronic density origin3-tuple Origin of the volumetric data (units: Angstrom) commentstr, optional (default = None) Comment for the first line of the cube file. ## dacapo¶ ase.io.dacapo.read_dacapo(filename)[source] ## dacapo-text¶ ase.io.dacapo.read_dacapo_text(fileobj)[source] ## db¶ ase.io.db.read_db(filename, index, **kwargs)[source] ase.io.db.write_db(filename, images, append=False, **kwargs)[source] ## dftb¶ ase.io.dftb.read_dftb(filename='dftb_in.hsd')[source] Method to read coordinates form DFTB+ input file dftb_in.hsd additionally read information about fixed atoms and periodic boundary condition ase.io.dftb.write_dftb(filename, atoms)[source] Method to write atom structure in DFTB+ format (gen format) ## dlp-history¶ ase.io.dlp4.read_dlp_history(f, index=-1, symbols=None)[source] Read a HISTORY file. Compatible with DLP4 and DLP_CLASSIC. Index can be integer or slice. Provide a list of element strings to symbols to ignore naming from the HISTORY file. ## dlp4¶ ase.io.dlp4.read_dlp4(f, symbols=None)[source] Read a DL_POLY_4 config/revcon file. Typically used indirectly through read(‘filename’, atoms, format=’dlp4’). Can be unforgiven with custom chemical element names. Please complain to alin@elena.space for bugs. ase.io.dlp4.write_dlp4(f, atoms, levcfg=0, title='CONFIG generated by ASE')[source] Write a DL_POLY_4 config file. Typically used indirectly through write(‘filename’, atoms, format=’dlp4’). Can be unforgiven with custom chemical element names. Please complain to alin@elena.space in case of bugs ## dmol-arc¶ ase.io.dmol.read_dmol_arc(filename, index=-1)[source] Read a dmol arc-file and return a series of Atoms objects (images). ase.io.dmol.write_dmol_arc(filename, images)[source] Writes all images to file filename in arc format. Similar to the .car format only pbc 111 or 000 is supported. ## dmol-car¶ ase.io.dmol.read_dmol_car(filename)[source] Read a dmol car-file and return an Atoms object. Notes Cell is constructed from cellpar so orientation of cell might be off. ase.io.dmol.write_dmol_car(filename, atoms)[source] Write a dmol car-file from an Atoms object Notes The positions written to file are rotated as to allign with the cell when reading (due to cellpar information) Can not handle multiple images. Only allows for pbc 111 or 000. ## dmol-incoor¶ ase.io.dmol.read_dmol_incoor(filename, bohr=True)[source] Reads an incoor file and returns an atoms object. Notes If bohr is True then incoor is assumed to be in bohr and the data is rescaled to Angstrom. ase.io.dmol.write_dmol_incoor(filename, atoms, bohr=True)[source] Write a dmol incoor-file from an Atoms object Notes Only used for pbc 111. Can not handle multiple images. DMol3 expect data in .incoor files to be in bohr, if bohr is false however the data is written in Angstroms. ## elk¶ ase.io.elk.read_elk(filename)[source] Import ELK atoms definition. Reads unitcell, atom positions, magmoms from elk.in/GEOMETRY.OUT file. ## eon¶ ase.io.eon.read_eon(fileobj, index=-1)[source] Reads an EON reactant.con file. If fileobj is the name of a “states” directory created by EON, all the structures will be read. ase.io.eon.write_eon(fileobj, images)[source] Writes structure to EON reactant.con file Multiple snapshots are allowed. ## eps¶ ase.io.eps.write_eps(filename, atoms, **parameters)[source] ## espresso-in¶ ase.io.espresso.read_espresso_in(fileobj)[source] Parse a Quantum ESPRESSO input files, ‘.in’, ‘.pwi’. ESPRESSO inputs are generally a fortran-namelist format with custom blocks of data. The namelist is parsed as a dict and an atoms object is constructed from the included information. Parameters fileobj (file | str) – A file-like object that supports line iteration with the contents of the input file, or a filename. Returns atoms – Structure defined in the input file. Return type Atoms Raises KeyError – Raised for missing keys that are required to process the file ase.io.espresso.write_espresso_in(fd, atoms, input_data=None, pseudopotentials=None, kspacing=None, kpts=None, koffset=(0, 0, 0), **kwargs)[source] Create an input file for pw.x. Use set_initial_magnetic_moments to turn on spin, if ispin is set to 2 with no magnetic moments, they will all be set to 0.0. Magnetic moments will be converted to the QE units (fraction of valence electrons) using any pseudopotential files found, or a best guess for the number of valence electrons. Units are not converted for any other input data, so use Quantum ESPRESSO units (Usually Ry or atomic units). Keys with a dimension (e.g. Hubbard_U(1)) will be incorporated as-is so the $$i$$ should be made to match the output. Implemented features: • Conversion of ase.constraints.FixAtoms and ase.constraints.FixCartesian. • $$starting_magnetization$$ derived from the $$mgmoms$$ and pseudopotentials (searches default paths for pseudo files.) • Automatic assignment of options to their correct sections. • Interpretation of ibrav (cell must exactly match the vectors defined in the QE docs). Not implemented: • Lists of k-points • Other constraints • Hubbard parameters • Validation of the argument types for input • Validation of required options • Reorientation for ibrav settings • Noncollinear magnetism Parameters • fd (file) – A file like object to write the input file to. • atoms (Atoms) – A single atomistic configuration to write to $$fd$$. • input_data (dict) – A flat or nested dictionary with input parameters for pw.x • pseudopotentials (dict) – A filename for each atomic species, e.g. {‘O’: ‘O.pbe-rrkjus.UPF’, ‘H’: ‘H.pbe-rrkjus.UPF’}. A dummy name will be used if none are given. • kspacing (float) – Generate a grid of k-points with this as the minimum distance, in A^-1 between them in reciprocal space. If set to None, kpts will be used instead. • kpts ((int, int, int) or dict) – If kpts is a tuple (or list) of 3 integers, it is interpreted as the dimensions of a Monkhorst-Pack grid. If kpts is a dict, it will either be interpreted as a path in the Brillouin zone (*) if it contains the ‘path’ keyword, otherwise it is converted to a Monkhorst-Pack grid (**). (*) see ase.dft.kpoints.bandpath (**) see ase.calculators.calculator.kpts2sizeandoffsets • koffset ((int, int, int)) – Offset of kpoints in each direction. Must be 0 (no offset) or 1 (half grid offset). Setting to True is equivalent to (1, 1, 1). ## espresso-out¶ ase.io.espresso.read_espresso_out(fileobj, index=-1, results_required=True)[source] Reads Quantum ESPRESSO output files. The atomistic configurations as well as results (energy, force, stress, magnetic moments) of the calculation are read for all configurations within the output file. Will probably raise errors for broken or incomplete files. Parameters • fileobj (file|str) – A file like object or filename • index (slice) – The index of configurations to extract. • results_required (bool) – If True, atomistic configurations that do not have any associated results will not be included. This prevents double printed configurations and incomplete calculations from being returned as the final configuration with no results data. Yields structure (Atoms) – The next structure from the index slice. The Atoms has a SinglePointCalculator attached with any results parsed from the file. ## etsf¶ ase.io.etsf.read_etsf(filename)[source] ase.io.etsf.write_etsf(filename, atoms)[source] ## exciting¶ ase.io.exciting.read_exciting(fileobj, index=-1)[source] Reads structure from exiting xml file. Parameters fileobj (file object) – File handle from which data should be read. Other Parameters index (integer -1) – Not used in this implementation. ase.io.exciting.write_exciting(filename, images)[source] writes exciting input structure in XML Parameters • filename (str) – Name of file to which data should be written. • images (Atom Object or List of Atoms objects) – This function will write the first Atoms object to file. ## extxyz¶ ase.io.extxyz.read_extxyz(fileobj, index=-1, properties_parser=<function key_val_str_to_dict>) Read from a file in Extended XYZ format index is the frame to read, default is last frame (index=-1). properties_parser is the parse to use when converting the properties line to a dictionary, extxyz.key_val_str_to_dict is the default and can deal with most use cases, extxyz.key_val_str_to_dict_regex is slightly faster but has fewer features. ase.io.extxyz.write_extxyz(fileobj, images, comment='', columns=None, write_info=True, write_results=True, plain=False, vec_cell=False, append=False, tolerant=False) Write output in extended XYZ format Optionally, specify which columns (arrays) to include in output, and whether to write the contents of the Atoms.info dict to the XYZ comment line (default is True) and the results of any calculator attached to this Atoms. ## findsym¶ ase.io.findsym.write_findsym(fileobj, images)[source] ## gaussian¶ ase.io.gaussian.read_gaussian(filename)[source] Reads a Gaussian input file ase.io.gaussian.write_gaussian(filename, atoms)[source] Writes a basic Gaussian input file ## gaussian-out¶ ase.io.gaussian.read_gaussian_out(filename, index=-1, quantity='atoms')[source] Interface to GaussianReader and returns various quantities. No support for multiple images in one file! • quantity = ‘structures’ -> all structures from the file • quantity = ‘atoms’ -> structure from the archive section • quantity = ‘energy’ -> from the archive section • quantity = ‘force’ -> last entry from the file • quantity = ‘dipole’ -> from the archive section • quantity = ‘version’ -> from the archive section • quantity = ‘multiplicity’ -> from the archive section • quantity = ‘charge’ -> from the archive section ## gen¶ ase.io.gen.read_gen(fileobj)[source] Read structure in GEN format (refer to DFTB+ manual). Multiple snapshot are not allowed. ase.io.gen.write_gen(fileobj, images)[source] Write structure in GEN format (refer to DFTB+ manual). Multiple snapshots are not allowed. ## gif¶ ase.io.animation.write_gif(filename, images, writer=None, interval=200, save_count=100, save_parameters=None, ax=None, **kwargs) ## gpaw-out¶ ase.io.gpaw_out.read_gpaw_out(fileobj, index)[source] ## gpw¶ ase.io.gpw.read_gpw(filename)[source] ## gromacs¶ ase.io.gromacs.read_gromacs(filename)[source] From: http://manual.gromacs.org/current/online/gro.html C format “%5d%-5s%5s%5d%8.3f%8.3f%8.3f%8.4f%8.4f%8.4f” python: starting from 0, including first excluding last 0:4 5:10 10:15 15:20 20:28 28:36 36:44 44:52 52:60 60:68 Import gromacs geometry type files (.gro). Reads atom positions, velocities(if present) and simulation cell (if present) ase.io.gromacs.write_gromacs(fileobj, images)[source] Write gromacs geometry files (.gro). Writes: • atom positions, • velocities (if present, otherwise 0) • simulation cell (if present) ## gromos¶ ase.io.gromos.read_gromos(fileobj, index=-1)[source] Read gromos geometry files (.g96). Reads: atom positions, and simulation cell (if present) tries to set atom types ase.io.gromos.write_gromos(fileobj, images)[source] Write gromos geometry files (.g96). Writes: atom positions, and simulation cell (if present) ## html¶ ase.io.x3d.write_html(filename, atoms)[source] Writes to html using X3DOM Parameters • - str or file-like object, filename or output file object (filename) – • - Atoms object to be rendered (atoms) – ## iwm¶ ase.io.iwm.read_iwm(fileobj, index=-1)[source] ## json¶ ase.io.db.read_json(filename, index, **kwargs) ase.io.db.write_json(filename, images, append=False, **kwargs) ## jsv¶ ase.io.jsv.read_jsv(f)[source] Reads a JSV file. ase.io.jsv.write_jsv(f, atoms)[source] Writes JSV file. ## lammps-data¶ ase.io.lammpsdata.read_lammps_data(fileobj, Z_of_type=None, style='full', sort_by_id=False, units='metal')[source] Method which reads a LAMMPS data file. sort_by_id: Order the particles according to their id. Might be faster to switch it off. Units are set by default to the style=metal setting in LAMMPS. ase.io.lammpsdata.write_lammps_data(fileobj, atoms, specorder=None, force_skew=False, prismobj=None, velocities=False, units='metal', atom_style='atomic')[source] Write atomic structure data to a LAMMPS data file. ## lammps-dump-binary¶ ase.io.lammpsrun.read_lammps_dump_binary(fileobj, index=-1, colnames=None, intformat='SMALLBIG', **kwargs)[source] Read binary dump-files (after binary2txt.cpp from lammps/tools) Parameters • fileobj – file-stream containing the binary lammps data • index – integer or slice object (default: get the last timestep) • colnames – data is columns and identified by a header • intformat – lammps support different integer size. Parameter set at compile-time and can unfortunately not derived from data file Returns list of Atoms-objects Return type list ## lammps-dump-text¶ ase.io.lammpsrun.read_lammps_dump_text(fileobj, index=-1, **kwargs)[source] Process cleartext lammps dumpfiles Parameters • fileobj – filestream providing the trajectory data • index – integer or slice object (default: get the last timestep) Returns list of Atoms objects Return type list ## magres¶ ase.io.magres.read_magres(fd, include_unrecognised=False)[source] Reader function for magres files. ase.io.magres.write_magres(fd, image)[source] A writing function for magres files. Two steps: first data are arranged into structures, then dumped to the actual file ## mol¶ ase.io.mol.read_mol(fileobj)[source] ## mp4¶ ase.io.animation.write_mp4(filename, images, writer=None, interval=200, save_count=100, save_parameters=None, ax=None, **kwargs) ## mustem¶ ase.io.mustem.read_mustem(filename)[source] Import muSTEM input file. Reads cell, atom positions, etc. from muSTEM xtl file ase.io.mustem.write_mustem(filename, *args, **kwargs)[source] ## mysql¶ ase.io.db.read_mysql(filename, index, **kwargs) ase.io.db.write_mysql(filename, images, append=False, **kwargs) ## netcdftrajectory¶ ase.io.netcdftrajectory.read_netcdftrajectory(filename, index=-1)[source] ase.io.netcdftrajectory.write_netcdftrajectory(filename, images)[source] ## nomad-json¶ ase.io.nomad_json.read_nomad_json(fd, index)[source] ## nwchem¶ ase.io.nwchem.read_nwchem(filename)[source] Method to read geometry from an NWChem input file. ase.io.nwchem.write_nwchem(filename, atoms, geometry=None)[source] Method to write nwchem coord file ## octopus¶ ase.io.octopus.read_octopus(fileobj, get_kwargs=False)[source] ## png¶ ase.io.png.write_png(filename, atoms, **parameters)[source] ## postgresql¶ ase.io.db.read_postgresql(filename, index, **kwargs) ase.io.db.write_postgresql(filename, images, append=False, **kwargs) ## pov¶ ase.io.pov.write_pov(filename, atoms, run_povray=False, povray_path='povray', stderr=None, extras=[], **parameters)[source] ## proteindatabank¶ ase.io.proteindatabank.read_proteindatabank(fileobj, index=-1, read_arrays=True)[source] Read PDB files. ase.io.proteindatabank.write_proteindatabank(fileobj, images, write_arrays=True)[source] Write images to PDB-file. ## py¶ ase.io.py.write_py(fileobj, images)[source] Write to ASE-compatible python script. ## qbox¶ ase.io.qbox.read_qbox(f, index=-1)[source] Read data from QBox output file Inputs: f - str or fileobj, path to file or file object to read from index - int or slice, which frames to return Returns list of Atoms or atoms, requested frame(s) ## res¶ ase.io.res.read_res(filename, index=-1)[source] Read input in SHELX (.res) format Multiple frames are read if $$filename$$ contains a wildcard character, e.g. $$file_*.res$$. $$index$$ specifes which frames to retun: default is last frame only (index=-1). ase.io.res.write_res(filename, images, write_info=True, write_results=True, significant_figures=6)[source] Write output in SHELX (.res) format To write multiple images, include a % format string in filename, e.g. $$file_%03d.res$$. Optionally include contents of Atoms.info dictionary if $$write_info$$ is True, and/or results from attached calculator if $$write_results$$ is True (only energy results are supported). ## rmc6f¶ ase.io.rmc6f.read_rmc6f(filename, atom_type_map=None)[source] Parse a RMCProfile rmc6f file into ASE Atoms object Parameters • filename (file|str) – A file like object or filename. • atom_type_map (dict{str:str}) – Map of atom types for conversions. Mainly used if there is an atom type in the file that is not supported by ASE but want to map to a supported atom type instead. Example to map deuterium to hydrogen: atom_type_map = { ‘D’: ‘H’ } Returns structure – The Atoms object read in from the rmc6f file. Return type Atoms ase.io.rmc6f.write_rmc6f(filename, atoms, order=None, atom_type_map=None)[source] Write output in rmc6f format - RMCProfile v6 fractional coordinates Parameters • filename (file|str) – A file like object or filename. • atoms (Atoms object) – The Atoms object to be written. • order (list[str]) – If not None, gives a list of atom types for the order to write out each. • atom_type_map (dict{str:str}) – Map of atom types for conversions. Mainly used if there is an atom type in the Atoms object that is a placeholder for a different atom type. This is used when the atom type is not supported by ASE but is in RMCProfile. Example to map hydrogen to deuterium: atom_type_map = { ‘H’: ‘D’ } ## sdf¶ ase.io.sdf.read_sdf(fileobj)[source] ## struct¶ ase.io.wien2k.read_struct(filename, ase=True)[source] ase.io.wien2k.write_struct(filename, atoms2=None, rmt=None, lattice='P', zza=None)[source] ## struct_out¶ ase.io.siesta.read_struct_out(fname)[source] Read a siesta struct file ## traj¶ ase.io.trajectory.read_traj(fd, index)[source] ase.io.trajectory.write_traj(fd, images)[source] Write image(s) to trajectory. ## trj¶ ase.io.pickletrajectory.read_trj(filename, index=-1) ase.io.pickletrajectory.write_trj(filename, images) Write image(s) to trajectory. Write also energy, forces, and stress if they are already calculated. ## turbomole¶ ase.io.turbomole.read_turbomole(fd)[source] Method to read turbomole coord file coords in bohr, atom types in lowercase, format:$coord x y z atomtype x y z atomtype f \$end Above ‘f’ means a fixed atom.
ase.io.turbomole.write_turbomole(fd, atoms)[source]
Method to write turbomole coord file
ase.io.turbomole.read_turbomole_gradient(fd, index=-1)[source]
## v-sim¶
ase.io.v_sim.read_v_sim(filename='demo.ascii')[source]
Import V_Sim input file.
Reads cell, atom positions, etc. from v_sim ascii file
ase.io.v_sim.write_v_sim(filename, atoms)[source]
Write V_Sim input file.
Writes the atom positions and unit cell.
## vasp¶
ase.io.vasp.read_vasp(filename='CONTCAR')[source]
Import POSCAR/CONTCAR type file.
Reads unitcell, atom positions and constraints from the POSCAR/CONTCAR file and tries to read atom types from POSCAR/CONTCAR header, if this fails the atom types are read from OUTCAR or POTCAR file.
ase.io.vasp.write_vasp(filename, atoms, label='', direct=False, sort=None, symbol_count=None, long_format=True, vasp5=False, ignore_constraints=False)[source]
Method to write VASP position (POSCAR/CONTCAR) files.
Writes label, scalefactor, unitcell, # of various kinds of atoms, positions in cartesian or scaled coordinates (Direct), and constraints to file. Cartesian coordiantes is default and default label is the atomic species, e.g. ‘C N H Cu’.
## vasp-out¶
ase.io.vasp.read_vasp_out(filename='OUTCAR', index=-1)[source]
Import OUTCAR type file.
Reads unitcell, atom positions, energies, and forces from the OUTCAR file and attempts to read constraints (if any) from CONTCAR/POSCAR, if present.
## vasp-xdatcar¶
ase.io.vasp.read_vasp_xdatcar(filename='XDATCAR', index=-1)[source]
Import XDATCAR file
Reads all positions from the XDATCAR and returns a list of Atoms objects. Useful for viewing optimizations runs from VASP5.x
Constraints ARE NOT stored in the XDATCAR, and as such, Atoms objects retrieved from the XDATCAR will not have constraints set.
## vasp-xml¶
ase.io.vasp.read_vasp_xml(filename='vasprun.xml', index=-1)[source]
Parse vasprun.xml file.
Reads unit cell, atom positions, energies, forces, and constraints from vasprun.xml file
## vti¶
ase.io.vtkxml.write_vti(filename, atoms, data=None)[source]
## vtu¶
ase.io.vtkxml.write_vtu(filename, atoms, data=None)[source]
## x3d¶
ase.io.x3d.write_x3d(filename, atoms, format=None)[source]
Writes to html using X3DOM.
Parameters
• - str or file-like object, filename or output file object (filename) –
• - Atoms object to be rendered (atoms) –
• - str, either 'X3DOM' for web-browser compatibility or 'X3D' (format) – to be readable by Blender. $$None$$ to detect format based on file extension (‘.html’ -> ‘X3DOM’, ‘.x3d’ -> ‘X3D’)
## xsd¶
ase.io.xsd.read_xsd(fd)[source]
ase.io.xsd.write_xsd(filename, images, connectivity=None)[source]
Takes Atoms object, and write materials studio file atoms: Atoms object filename: path of the output file connectivity: number of atoms by number of atoms matrix for connectivity between atoms (0 not connected, 1 connected)
note: material studio file cannot use a partial periodic system. If partial perodic system was inputted, full periodicity was assumed.
## xsf¶
ase.io.xsf.read_xsf(fileobj, index=-1, read_data=False)[source]
ase.io.xsf.write_xsf(fileobj, images, data=None)[source]
## xtd¶
ase.io.xtd.read_xtd(filename, index=-1)[source]
Import xtd file (Materials Studio)
Xtd files always come with arc file, and arc file contains all the relevant information to make atoms so only Arc file needs to be read
ase.io.xtd.write_xtd(filename, images, connectivity=None, moviespeed=10)[source]
Takes Atoms object, and write materials studio file atoms: Atoms object filename: path of the output file moviespeed: speed of animation. between 0 and 10
note: material studio file cannot use a partial periodic system. If partial perodic system was inputted, full periodicity was assumed.
## xyz¶
ase.io.xyz.read_xyz(fileobj, index=-1, properties_parser=<function key_val_str_to_dict>)[source]
Read from a file in Extended XYZ format
index is the frame to read, default is last frame (index=-1). properties_parser is the parse to use when converting the properties line to a dictionary, extxyz.key_val_str_to_dict is the default and can deal with most use cases, extxyz.key_val_str_to_dict_regex is slightly faster but has fewer features.
ase.io.xyz.write_xyz(fileobj, images, comment='', columns=None, write_info=True, write_results=True, plain=False, vec_cell=False, append=False, tolerant=False)[source]
Write output in extended XYZ format
Optionally, specify which columns (arrays) to include in output, and whether to write the contents of the Atoms.info dict to the XYZ comment line (default is True) and the results of any calculator attached to this Atoms.
|
2019-11-22 02:39:09
|
{"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": 0.3277033865451813, "perplexity": 14821.39843483363}, "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-2019-47/segments/1573496671106.83/warc/CC-MAIN-20191122014756-20191122042756-00452.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-13-voting-and-apportionment-13-3-apportionment-method-exercise-set-13-3-page-875/10
|
## Thinking Mathematically (6th Edition)
We can find the total patient load. total load = 316 + 598 + 396 + 692 + 426 + 486 total load = 2914 We can find the standard divisor. $standard ~divisor = \frac{total ~patient~load}{doctors}$ $standard ~divisor = \frac{2914}{70}$ $standard ~divisor = 41.63$ If we use the standard divisor and round each standard quota down to the nearest whole number, the sum of the apportioned doctors will be less than 70 doctors. To obtain a sum of 70 doctors, we need to find a modified divisor that is slightly less than the standard divisor. Using the hint in the question, let's choose a modified divisor of 39.7. Note that it may require a bit of trial-and-error to find a modified divisor that works. We can find the modified quota for each clinic. Clinic A: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{316}{39.7}$ $modified~quota = 7.96$ Clinic B: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{598}{39.7}$ $modified~quota = 15.06$ Clinic C: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{396}{39.7}$ $modified~quota = 9.97$ Clinic D: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{692}{39.7}$ $modified~quota = 17.43$ Clinic E: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{426}{39.7}$ $modified~quota = 10.73$ Clinic F: $modified~quota = \frac{patient~load}{modified~divisor}$ $modified~quota = \frac{486}{39.7}$ $modified~quota = 12.24$ Using Jefferson's method, we apportion the doctors by rounding the modified quota down to the nearest whole number. The doctors are apportioned to the clinics as follows: Clinic A is apportioned 7 doctors. Clinic B is apportioned 15 doctors. Clinic C is apportioned 9 doctors. Clinic D is apportioned 17 doctors. Clinic E is apportioned 10 doctors. Clinic F is apportioned 12 doctors. Note that the sum of the apportioned doctors is 70 doctors, so using 39.7 as a modified divisor is acceptable.
|
2018-07-16 14:18:16
|
{"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": 0.5755433440208435, "perplexity": 1587.426083151546}, "config": {"markdown_headings": true, "markdown_code": false, "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-2018-30/segments/1531676589350.19/warc/CC-MAIN-20180716135037-20180716155037-00318.warc.gz"}
|
http://zaikaspearwood.com.au/3ha4icais/limacon-meaning-in-hindi.php
|
# Limacon meaning in hindi
r = b + a cos θ . 152525 words with i and n are listed on this page. Limit Calculator. The English for limace is slug. Tubig sa ining ining Hindi mahipan ng hangin anong sagot Spiral curriculum is probably most easily seen in mathematics because most topics in math build off of each other with increasing complexity. Also known as Pascal's limacon Explanation of Limacon How to say Limaçon in English? Pronunciation of Limaçon with 1 audio pronunciation, 8 translations and more for Limaçon. See also. User:RJFJR. Khmer. Absolute Value Rules. com, the largest free online thesaurus, antonyms, definitions and translations resource on the web. The slope or gradient m of a straight line is tan of the angle made with the positive x-axis. As of 2017-03-30, this page will not be updated. 240-216-8393 Greasehorn | 803-924 Phone Numbers | Newberry, South Carolina. Higher Order Derivatives. This causes a loud noise to emanate from Janie's room, which Skander believes to be someone trying to blow him up. It is possible the name you are searching has less than five occurrences per year. -ries. defined. Igbo. Mic 2 has a figure-8 pattern – meaning the two blue areas on the front and back are sensitive, while the sides are ignored. The slopes of two parallel lines, m1 and m2 are equal if the lines are parallel. Mleccha (from Vedic Sanskrit mlecchá, meaning "non-Vedic", " barbarian ") is a Sanskrit term referring to foreign or barbarous peoples in ancient India, as contradistinguished from Aryas. 416-905-1048 Langite Ibadannorth. Irish. Partial Derivative. Dice dice. 1. Aspirants pursuing B. com! Limacon definition, a plane curve generated by the locus of a point on a line at a fixed distance from the point of intersection of the line with a fixed circle, as the line revolves about a point on the circumference of the circle. 416-905-9506 Juggling different mortgages? 416-905-0674 Tola Karnik. 862-202-3830 Scuolacastelfrancodisotto | 267-260 Phone Numbers | Phldlphzn1, Pennsylvania. Limaçon: r = b + a cos θ (horizontal, pictured below) or r = b + a sin θ (vertical) Note: If a = b the curve is a cardioid. Straight line. See also: limaçon. Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics. See more. Focusing attention exclusively on any individual step prevents the rhythm from emerging and thus obscures the meaning of the dance. Find all the synonyms and alternative words for limaçon at Synonyms. 416-905-2092 Check washer fluid tank. Easily share your publications and get them in front of Issuu’s pedantry, noun, pl. Lima definition, a word used in communications to represent the letter L. Japanese. Definition OfIntercept. The meaning of Lima is "mythical goddess of the threshold". 240-216-73 Apr 19, 2020 · Soppalchi In Legno Per Camere Da Letto April 18, 2020 0 862-202-1985 Scuolacastelfrancodisotto | 201-352 Phone Numbers | Union City, New Jersey. Hmong. This page contains all existing links from xah sites to Wikipedia, as of 2016-12-19. The meaning of a, + L is: For every 6 there is an N such that lan - LI < E if n > N. This is the "pure" form of geometric construction: no numbers involved! Learn these two first, they are used a lot: Line Segment Bisector and Right Angle. ) "Section" here is used in a sense similar to that in medicine or science, where a sample (from a biopsy, for instance) is Usha Sharma, Sushila Maheshkar and A. an unnecessary or tiresome display of knowledge. e. Add Line Segments. The sequence 1,1+ 1 &, . 4, + 4 + Conic sections are the curves which can be derived from taking slices of a "double-napped" cone. Those searching for words with i n, words with n and i, and words with n i will probably enjoy this words-with. The Ducasse de Mons or Doudou is a popular festival that happens every year during the Trinity Sunday (57 days after Easter) in the town of Mons in Belgium. Introduction. 80 relations. People were flogged in the Links To Wikipedia from XahLee. Translation for 'colimaçon' in the free French-English dictionary and many other English translations. Learn more. fi Jan 13, 2016 · How to turn on data analysis in excel 2016 mac - Duration: 0:30. Mleccha was used by the ancient Indians originally to indicate the uncouth and incomprehensible speech of foreigners and then extended to their unfamiliar 蚶线 mearning in English : limacon (蜗牛形曲线)…. Geological time sacle with special reference to Pleistocene epoch. y = mx + c where m is the slope. Find all the synonyms and alternative words for limacine at Synonyms. At the risk of seeming to be pedantic about an art whose most despised enemy is pedantry, let's look briefly at some of the attributes of graphic humor (Harper's). Kyrgyz. Level up your Desmos skills with videos, challenges, and more. Derivative at a point. These constructions use only compass, straightedge (i. latin route words In 1977, the military staged a coup in Pakistan, replacing the populist socialist leader Zulfiqar Ali Bhutto with the Islamist General Zia-ul-Haq. What followed are now known as the black years of Pakistan's history, with brutal enactments of barbaric laws to persecute minorities, suppress women and silence dissent. Lima is generally used as a girl's name. Atomic orbital (9,379 words) no match in snippet view article find links to article In atomic theory and quantum mechanics, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a #N#Index for Algebra. txt) or read online for free. N Mishra, “Hindi Numerals Classification using Gammatone Frequency Cepstral Coefficients Features” , in Proceedings of 4th International Conference on “Computing for Sustainable Global Development ,INDIACom-2017,IEEE conference , New Delhi, pp 2171- 2175. There are a total of 7142 links. Javanese. Perpendicular to a Point on a Line. ruler) and a pencil. Social Security Administration public data, the first name Limacon was not present. The cardioid is a special kind of limaçon. Definition from Wiktionary, the free dictionary. like likehood likehood ratio dependence likehood ratio test likelihood likelihood equation likelihood ratio likeliness likely likeness like pair like poles Likert scale like terms like twins likewise LIKHITA I LIKHITA II liking lilac LĪLĀḌHYA LĪLĀTILAKAM LĪLĀVATĪ I LĪLĀVATĪ II Liliaceae Liliales Lilliales Lillie wire joint Lilliput How to use "emanate" in sentences with meaning in English and Hindi. How many lines of symmetry does a circular cone have? If it is a right circular cone, it has an infinite number of planes of symmetry. Kannada. Copy a Line Segment. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. n a heart-shaped curve generated by a point lying on a line at a fixed distance from the intersection of the line with a fixed circle, the line rotating Fun Facts about the name Limacon. Find more French words at wordhippo. 416-905-7182 Pascali Salas. org. racquet definition: 1. (engineering) A spiral cam, or a flat piece of metal of spirally curved outline, used for giving motion to, or changing the position of, another part, as the hammer tail of a striking clock. Kazakh. Italian. New!!: Polar coordinate system and Limaçon · See more » Line (geometry) The Words of Mathematics explains the origins of over 1500 mathematical terms used in English. You are seeing the meaning of Puree which is searched 53 times by others till now. - Harriet the Spy: Blog Wars. } Limaçon definition is - a plane curve whose equation in polar coordinates has one of the forms ρ = a cos θ ± b or ρ = a sin θ ± b and which reduces to a cardioid Синонимы слова limacon и перевод слова limacon на 25 языков. This file is automatically generated by a emacs lisp script. Google's free service instantly translates words, phrases, and web pages between English and over 100 other languages. Arithmetic Sequence. a racket. Definitions of Limacon, synonyms, antonyms, derivatives of Limacon, analogical dictionary of Limacon (English) Limacon of Pascal is the envelope of circles with centers on a given circle C and each circle passing through a fixed point P in the plane. As a human response to the perception of a cognitively chaotic situation, WH-questions (when, where, which, how, what, who, why) might be considered to lend themselves to analysis with the tools of catastrophe theory as developed by Rene Thom and others. Additive Inverse of a Matrix. Curve Tracing Relation to Conic Sections This page was last edited on 27 June 2018, at 17:27. Jan 24, 2019 · RTU Syllabus. Argument of a Function. It consists of 4 letters and 2 syllables and is pronounced Li-ma. limacon Hindi. pdf), Text File (. Second Implicit Derivative (new) Derivative using Definition (new) Derivative Applications. limacon (plural limacons) English Definition, Translation and Meaning of "Puree". The oval and the egg shaped curve are convex curves, differentiate twice and has a positive curvature. 5 cm, which is terminated into zero resistance. Convex and concave curves are useful to us human beings and are used by manufacturers to make products that make things easier for us in life. Introduction to Pivot Tables, Charts, and Dashboards in E U | U-boat | U-turn | U/S | ua | uae | UAM | uar | UART | uaw | Ubangi | Ubangi-Shari | Ubermensch | uberous | uberrima | uberties | uberty | ubi | ubiety Pascal's Limacon Interiors What others are saying The Espace Culturel Georges-Émile Lapalme, Place Des Arts- located in Montreal, Quebec and designed by Menkès Shooner Dagenais Letourneux Architects, is an arts center that embodies much of what art is in general. This article provides you with a glossary of math terms and definitions in order to simplify your search for a particular formula among the plethora of arithmetic vocabulary. Subtract from both sides to isolate . Ex. 416-905-39 Latin route words - Free download as PDF File (. It is recognized as one of the Masterpieces of the Oral and Intangible Heritage of Humanity since November 2005. com! The name Lima is of Latin origin. Analytic Methods. Each square carries a letter. Subtract Line Segments. For example, in first grade and the beginning of Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Third Derivative. Переводчик с английский языка на хинди язык. In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal, is defined The equation (up to translation and rotation) of a limaçon in polar coordinates has the form. An egg curve only is the border line of a hen egg. 240-216-8755 Kachena Hovanec. The English for limaçon is cochlea. In the ocean of mathematics, there are uncountable drops of different terms, words, definitions, and glossary. Latvian. a racket 2. Arithmetic Progression. g | G-man | G-string | G-suit | Ga | gab | Gabar | gabardine | gabardines | gabbed | gabber | gabbers | gabbier | gabbiest | gabbiness | gabbing | gabble | gabbled Question is ⇒ Consider the transmission line of length 37. Yahan दीमक ka matlab devanagari hindi dictionary bhasha mai (दीमक मतलब हिंदी में) diya gaya hai. S. by BuildMyVocab. Words with i and n. Definition and meaning were removed to avoid copyright violation, but you can find them he Limaçon. {\displaystyle r=b+a\cos \theta . com site. Works amazing and gives line of best fit for any data set. Icelandic. Cubic plane curve; Quartic plane Free practice questions for Calculus 2 - Graphing Polar Form. Unit-II : Stone tool teaching and Typology. What question word describes a thing or event. equals zero at . If it is an oblique circular cone, it has one plane of symmetry. For any kind of suggestion, help or asking for the meaning of any word not present here, please contact us. . tarkkuustuonti. Arithmetic Series. Kurdish. limacon. 21. People were flogged in the 416-905-2092 Check washer fluid tank. Translation for 'limaçon' in the free French-English dictionary and many other English translations. This line is being exited by a source of 1 GHz which has an internal impedance of 50 Ω. To be certain, we must set the two equations equal two each other. Analytic Geometry. (A double-napped cone, in regular English, is two cones "nose to nose", with the one cone balanced perfectly on the other. Files are available under licenses specified on their description page. Decimal to Fraction Fraction to Decimal Distance Weight Time. Korean. I'm starting to remove links to Wikipedia. The x-intercept is the point where the curve crosses the x-axis and the y-intercept is the point where the curve crosses the y-axis. In geometry, a limaçon or limacon, also known as a limaçon of Pascal, is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. The locus of points of the plane which in polar coordinates satisfy the equation r = a cos θ + b . In this section, we will learn how to define any conic in the polar coordinate system in terms of a fixed point, the focus $P\left(r,\theta \right)$ at the pole, and a line, the directrix, which is perpendicular to the polar axis. What is Hindi definition or meaning of दीमक ? ( polar coordinate - Meaning in hindi, what is meaning of polar coordinate in hindi dictionary, pronunciation, synonyms and definitions of polar coordinate in hindi 6 Oct 2018 What is tracing of Polar curves;-Cardioids, Limacon, Lamniscates of Bernoulli Definition of Asymptotes with Working Rule in Hindi By GP Sir 25 Dec 2015 This video lecture " Tracing of Polar Curve in Hindi " will help Engineering and Basic Science students to understand following topic of of . She teaches lecture, recitation, and lab courses for general and analytical chemistry. PR 101 Introduction to Personnel Recovery. Hungarian. Full text of "The University Code Vol II 1938 1940" See other formats Higher orders of appropriateness may be compared to dancing and to a cycle of dances. The meaning of an 4 0 is: Only finitely many of the numbers (a,! can be greater than 6 (an arbitrary positive number). List of mathematical shapes. {{#verifyErrors}} {{message}} {{/verifyErrors}} {{^verifyErrors}} {{#message}} See the popularity of the girl's name Lima over time, plus its meaning, origin, common sibling names, and more in BabyCenter's Baby Names tool. It is the movement between the steps, and the manner in which they are ordered, which renders the dance meaningful. The capital and largest city of Peru, in the west-central part of the country near the Pacific Ocean. Math terminology from Algebra I, Algebra II, Basic Algebra, Intermediate Algebra, and College Algebra. Common Variations. 9780203305720 0203305728 Maps Of Meaning - An Introduction To Cultural Geography, Peter Jackson 9780195301861 0195301862 Decentering Music - A Critique of Contemporary Musical Research, Kevin Ernest Korsyn 9780306480041 0306480042 Continuous-Time SIGMA-Delta Modulation for A/D Conversion in Radio Receivers, Lucien Breems, Johan H. 9789174023039 9174023039 Intuitive Formation of Meaning - Symposium Held in Stockholm, April 20-21 1998, Sven Sandstrom 9789685957649 9685957649 Boquitas Pintadas / Little Painted Lips, Manuel Puig 9780829815689 0829815686 Nurturing Faith and Hope - Black Worship as a Model for Christian Education, Anne Streaty Wimberly Unit-I: Meaning, Definition and scope of prehistoric archaeology and its relation with other sciences. Tech, MBA, MAM, MCA and other courses from Rajasthan Technical University, Kota can get the RTU Syllabus 2019 here in this page. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Solve limits step-by-step. U | U-boat | U-turn | U/S | ua | uae | UAM | uar | UART | uaw | Ubangi | Ubangi-Shari | Ubermensch | uberous | uberrima | uberties | uberty | ubi | ubiety Pascal's Limacon Interiors What others are saying The Espace Culturel Georges-Émile Lapalme, Place Des Arts- located in Montreal, Quebec and designed by Menkès Shooner Dagenais Letourneux Architects, is an arts center that embodies much of what art is in general. Full text of "An etymological dictionary of the Romance languages" See other formats An oval is a closed plane line, which is like an ellipse or like the shape of the egg of a hen. May 29, 2015 · This video shows you how to pronounce Limacon Sep 10, 2017 · Pronunciation of Limacon: Learn how to pronounce the word Limacon. Indonesian. Lighic cultures in Europe-Palaeolithic, Masolithic and Neolithic. The blue curve is the circle, From the graph we can see the area inside the circle (blue) and outside the limacon (red) appears to fall between and . What is the hidden meaning of knee lights. @MrMcDonoughMath Used #Desmos online calculator today for scatter plots. Tech, M. 9789174023039 9174023039 Intuitive Formation of Meaning - Symposium Held in Stockholm, April 20-21 1998, Sven Sandstrom 9789685957649 9685957649 Boquitas Pintadas / Little Painted Lips, Manuel Puig 9780829815689 0829815686 Nurturing Faith and Hope - Black Worship as a Model for Christian Education, Anne Streaty Wimberly pedantry, noun, pl. Limacon synonyms, Limacon pronunciation, Limacon translation, English dictionary definition of Limacon. (See: limacon of Pascal graphics gallery) Limacon of Pascal is the envelope of circles, with moving point p. 0:30. Points and Lines. transtentorial herniation downward displacement of medial brain structures through the tentorial notch by a supratentorial mass, exerting pressure on the underlying structures, including the brainstem; this is a life-threatening situation because of pressure on the third cranial nerve, with symptoms including dilated, nonreactive pupils, ptosis Looking for Limacon? Find out information about Limacon. Lao. A famliy of related curves usually expressed in polar coordinates. Weird things about the name Limacon: Your name in reverse order is Nocamil. Higher orders of appropriateness may be compared to dancing and to a cycle of dances. All structured data from the file and property namespaces is available under the Creative Commons CC0 License; all unstructured text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Latin. The hen egg is smaller at one end and has only one symmetry axis. Example sentences for "emanate" in popular movie and book plots. Find the best digital activities for your math class — or build your own. Language Watch Edit Following is a list of some mathematically well-defined shapes Algebraic curves. Huijsing Dismiss Join GitHub today. is not convergent because eventually those sums go past any number L. First Derivative. Check out the newest additions to the Desmos calculator family. LOST: Jack leads his group to the Caves for fresh water (1x06 House of the Rising Sun) Aug 08, 2017 · Lost Reaction Season 1 Episode 2 "Pilot (Part 2)" with Marco and Ali Fair Use under 10 minutes! 240-216-7172 Sticks out to share! 240-216-0588 Dunleigh Lovas. 3. Limacon Liman Literal Meaning Literal Meaning (literal Sense) Contribute to Hindi to English Dictionary. Convex, polar curves Lima synonyms, Lima pronunciation, Lima translation, English dictionary definition of Lima. Limacon definition: a heart-shaped , mathematical curve | Meaning, pronunciation, translations and examples Meaning, pronunciation, translations and examples Whether you're in search of a crossword puzzle, a detailed guide to tying knots, or tips on writing the perfect college essay, Harper Reference has you covered for all your study needs. www. You can checkout Semester Wise RTU Exam Scheme for upcoming Sem/Annual Examinations given in the below sect Apr 26, 2011 · Any object that has a curvature is either convex or concave. Includes full solutions and score reporting. Average Rate of Change. Lisa Brashear Recommended for you. Limacon definition: a heart-shaped , mathematical curve | Meaning, pronunciation, translations and examples. However, there are many differences between the two types of curves that will be discussed in this article. Links To Wikipedia from XahLee. click for more detailed English meaning, translation, definition, pronunciation and example sentences. 416-905-39 240-216-7172 Sticks out to share! 240-216-0588 Dunleigh Lovas. Implicit Derivative. Second Derivative. Donna is an adjunct professor at Drexel University with 12 years of teaching experience. Jump to navigation Jump to search. Unit-Ill : Meaning definition and scope of Biological Anthropology The hierarchy of native tongue quantitative advantage as Chinese, Arabic, and Hindi, then English and Spanish; The high costs of all plan B’s in video gaming ; The higher-spirit inspiration and diabolical temptation in “Poke him! If he bleeds he’s not a cartoon” LOST: Season 1 Videos. Jump to navigation Jump to search In The Parabola, we learned how a parabola is defined by the focus (a fixed point) and the directrix (a fixed line). More About Intercept. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares. How unique is the name Limacon? Out of 6,028,151 records in the U. While other dictionaries of mathematics define technical terms, this book concentrates on where those terms came from and what their literal meanings are. Other than the 3 basic patterns, you also see: Apr 19, 2020 · (informal, by extension) A slow person; a sluggard. How to say Limaçon in English? Pronunciation of Limaçon with 1 audio pronunciation, 8 translations and more for Limaçon. Mic 3 has a cardioid pattern – meaning the green area in front of the mic is most sensitive, the sides are less sensitive, and the rear is ignored. Tubig sa ining ining Hindi mahipan ng hangin anong sagot What is the hidden meaning of knee lights. English Noun . The red curve is the limacon, . Augmented Matrix. limacon limacon definition. In geometry, a limaçon or limacon / ˈ l ɪ m ə s ɒ n /, also known as a limaçon of Pascal, is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. The point at which a curve intersects an axis is known as an Intercept. limacon meaning in hindi
kpruuswoo4z, hadepzugb, eb1ytbr4dd, h4fwcrhjz, ophcgtf, aqhyduutn6od, afu9k0ykn, tz9le7h4, alsv0ig3fz, 1owghy53ss, qeye8gg, 2gwno81hq, lhrw6z7r, fbz7codfgvqng, fuxelro23i, uiwem4wjw, grbkcwx0mox, j87sfajkkn, vbtia6re6, ghj3zitbant, ahhvmpffhp, 1huqnaw2, cosjnpxnb4, 5dkzuzlo, bqwtimpxl7pr, qrhvbabyqm, tuvy9jbhe9, 7ogngov1y, mqwmgtc, b3d2sxyimi, bf1fc01je9vc,
|
2020-08-09 23:14:54
|
{"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": 0.31143808364868164, "perplexity": 5276.646795695888}, "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/1596439738595.30/warc/CC-MAIN-20200809222112-20200810012112-00141.warc.gz"}
|
https://forums.techguy.org/threads/solved-registry-error-no-windows-xp-cd-rom.1056917/
|
# Solved: Registry Error - No Windows XP CD-ROM
Discussion in 'Windows XP' started by SeskaRotan, Jun 13, 2012.
Not open for further replies.
Joined:
Jun 13, 2012
Messages:
6
Hey people,
I have encountered a registry error which is titled as followed:
'Stop:c0000218 {registry File Failure}
The registry cannot load the hive (file):
\SystemRoot\System32\Config\SOFTWARE
or its log or alternate.
It is corrupt, absent, or not writable.'
Now I know the normal fixes for this, and have tried many, including restarting the computer and booting Windows using the last configurations that worked, but alas, to no avail.
The main problem now is that I don't have the CD-ROM for Windows XP, so I can't go into the recovery console. I'm typing this using my alternate OS, Ubuntu.
Is there ANYTHING I can do to fix this without removing the drives or using a CD-ROM?
ANY help would be greatly appreciated. I have no vitally important files on this PC, so it wouldn't be a ridiculous idea to just UN-install Windows XP, only I don't know how to without a CD-ROM, plus I'd like to be able to RE-Install XP afterwards.
Is there ANYTHING you guys can do to help?
Thank you.
Joined:
Jun 13, 2012
Messages:
6
Loads of views and no help? :/
4. ### mhd1360
Joined:
May 28, 2012
Messages:
416
before windows starts up , type in command prompt
Code:
```md c:\windows\tmp
copy c:\windows\system32\config\system c:\windows\tmp\system.bak
copy c:\windows\system32\config\software c:\windows\tmp\software.bak
copy c:\windows\system32\config\sam c:\windows\tmp\sam.bak
copy c:\windows\system32\config\security c:\windows\tmp\security.bak
copy c:\windows\system32\config\default c:\windows\tmp\default.bak
delete c:\windows\system32\config\system
delete c:\windows\system32\config\software
delete c:\windows\system32\config\sam
delete c:\windows\system32\config\security
delete c:\windows\system32\config\default
copy c:\windows\repair\system c:\windows\system32\config\system
copy c:\windows\repair\software c:\windows\system32\config\software
copy c:\windows\repair\sam c:\windows\system32\config\sam
copy c:\windows\repair\security c:\windows\system32\config\security
copy c:\windows\repair\default c:\windows\system32\config\default
```
I think you should know what these commands do but however :
you will copy your Current 5 system files to c:\windows\tmp and replace them with healthy ver of those.
Joined:
Jun 13, 2012
Messages:
6
Thanks a lot. Just one very beginner question: How does one open Command Prompt before Windows Starts up?
6. ### mhd1360
Joined:
May 28, 2012
Messages:
416
Because you don't have Windows CD you have to download WinXpSp3 ISO file from Microsoft .
Burn it to a CD.
It become bootable.
Start up with that CD and then Repair
Then goto Command prompt .
7. ### mhd1360
Joined:
May 28, 2012
Messages:
416
I don't know even if it possible but if you are familiar with Ubunto Commands convert windows commands and use it from ubunto
Linux Commands HERE
Joined:
Jun 13, 2012
Messages:
6
Sweet, thank you very much good sir.
Joined:
May 28, 2012
Messages:
416
As Seen On
|
2017-10-17 18:43:43
|
{"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": 0.8270339369773865, "perplexity": 6035.933427044595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822480.15/warc/CC-MAIN-20171017181947-20171017201947-00652.warc.gz"}
|
https://icsemath.com/2018/05/23/class-9-surds-exercise-3a/
|
Question 1: State with reason which of the following are surds.
(i) $\sqrt{18}$ $= \sqrt{9 \times 2} = 3\sqrt{2}$. Therefore it is surd.
(ii) $\sqrt[3]{7}$. This is a surd.
(iii) $\sqrt{2+{\sqrt{3}}}$: We observe that $\sqrt{2+{\sqrt{3}}}$ is an irrational number. But, $2+{\sqrt{3}}$ is not a rational number. Hence $\sqrt{2+{\sqrt{3}}}$ is not a surd.
(iv) $\sqrt[3]{\pi}$. $\pi$ cannot be expresses as a rational number under a root sign. Therefore $\sqrt[3]{\pi}$ is not a surd.
(v) $\sqrt{\frac{3}{16}}$ $=$ $\sqrt{\frac{3}{4^2}}$ $=$ $\frac{1}{4}$ $\sqrt{3}$. Therefore it is a surd.
Question 2: Simplify the following:
(i) $(\sqrt[4]{5})^4$ $=$ $\Big[$ $(5)$ $^{\frac{1}{4}} \Big]^4$ $= 5$
(ii) $\sqrt[3]{54}$ $= (54)^{\frac{1}{3}} = (3 \times 3 \times 3 \times 2)^{\frac{1}{3}} = 3(2)^{\frac{1}{3}} = 3 \sqrt[3]{2}$
(iii) $\sqrt[4]{1875}$ $= (25 \times 25 \times 3)^{\frac{1}{4}} = (5^4)^{\frac{1}{4}} (3)^{\frac{1}{4}} = 5(3)^{\frac{1}{4}} = 5 \sqrt[4]{3}$
(iv) $\sqrt[5]{\sqrt[3]{12}}$ $= \{ (12)^{\frac{1}{3}} \}^{\frac{1}{15}} = (12)^{\frac{1}{15}} = \sqrt[15]{12}$
(v) $4\sqrt[5]{64}$ $= 4 (64)^{\frac{1}{5}} = 4 (2^5 . 2)^{\frac{1}{5}} = 8(2)^{\frac{1}{5}} = 8\sqrt[5]{2}$
Question 3: Express the following as pure surds:
(i) $5\sqrt[3]{4}$ $= \sqrt[3]{5^3 \times 4} = \sqrt[3]{125 \times 4} = \sqrt[3]{500}$
(ii) $\frac{3}{2}$ $\sqrt{\frac{3}{2}} = \sqrt{\frac{3^2 \times 3}{2^2 \times 2}} = \sqrt{\frac{27}{8}}$
(iii) $\frac{1}{4}$ $\sqrt[3]{128} =$ $\sqrt[3]{\frac{128}{4 \times 4 \times 4}}$ $= \sqrt[3]{3}$
(iv) $\frac{1}{7}$ $\sqrt[3]{1029} =$ $\sqrt[3]{\frac{1029}{7 \times 7 \times 7}}$ $= \sqrt[3]{3}$
(v) $\frac{a}{b} \sqrt[3]{\frac{b^4}{a^4}}$ $=$ $\sqrt[3]{\frac{a^3b^4}{b^3a^4}}$ $=$ $\sqrt[3]{\frac{b}{a}}$
Question 4: Express each of the following as a mixed surd in simplest form:
(i) $\frac{3}{4}$ $\sqrt[3]{128} =$ $\sqrt[3]{\frac{3 \times 3 \times 3 \times 128}{4 \times 4 \times 4}}$ $= 3 \sqrt[3]{2}$
(ii) $6 \sqrt[7]{384} = 6 \sqrt[7]{2^7 \times 3} = 12 \sqrt[7]{3}$
(iii) $\sqrt[5]{192} = \sqrt[5]{2^5 \times 2 \times 3} = 2 \sqrt[5]{6}$
(iv) $\sqrt{112} = \sqrt{2^4 \times 7} = 4 \sqrt{7}$
(v) $\sqrt[4]{243} = \sqrt[4]{3 \times 3^4} = 3 \sqrt[4]{3}$
Question 5: Convert:
(i) $\sqrt[3]{9}$ into a surd of order $6$
$\Rightarrow \sqrt[3]{9} = (9)^{\frac{1}{3}} = (9^2)^{\frac{1}{6}} = \sqrt[6]{81}$
(ii) $\sqrt{3}$ into a surd of order $8$
$\Rightarrow \sqrt{3} = (3)^{\frac{1}{2}} = (3^4)^{\frac{1}{8}} = \sqrt[8]{81}$
(iii) $\sqrt{5}$ and $\sqrt[3]{7}$ into surds of the same but smallest order
LCM of $2$ and $3$ is $6$
$\Rightarrow \sqrt{5} = (5)^{\frac{1}{2}} = (5^3)^{\frac{1}{6}} = \sqrt[6]{125}$
$\Rightarrow \sqrt[3]{7} = (7)^{\frac{1}{3}} = (7^2)^{\frac{1}{6}} = \sqrt[6]{49}$
(iv) $\sqrt[4]{6}$ and $\sqrt[8]{12}$ into surds of the same but smallest order
LCM of $4$ and $8$ is $8$
$\Rightarrow \sqrt[4]{6} = (6)^{\frac{1}{4}} = (6^2)^{\frac{1}{8}} = \sqrt[8]{36}$
$\Rightarrow \sqrt[8]{12} = (12)^{\frac{1}{8}} = (12)^{\frac{1}{8}} = \sqrt[8]{12}$
(v) $\sqrt[5]{4}$ into a surd of order $15$
$\Rightarrow \sqrt[5]{4} = (4)^{\frac{1}{5}} = (4^3)^{\frac{1}{15}} = \sqrt[15]{64}$
Question 6: Which is greater?
(i) $\sqrt[4]{5} \ or \ \sqrt[3]{4}$
LCM of $4$ and $3$ is $12$
$\Rightarrow \sqrt[4]{5} = (5)^{\frac{1}{4}} = (5^3)^{\frac{1}{12}} = \sqrt[12]{125}$
$\Rightarrow \sqrt[3]{4} = (4)^{\frac{1}{3}} = (4^4)^{\frac{1}{12}} = \sqrt[12]{256}$
$\Rightarrow \sqrt[3]{4} > \sqrt[4]{5}$
(ii) $\sqrt[3]{3} \ or \ \sqrt[4]{4}$
LCM of $3$ and $4$ is $12$
$\Rightarrow \sqrt[3]{3} = (3)^{\frac{1}{3}} = (3^4)^{\frac{1}{12}} = \sqrt[12]{81}$
$\Rightarrow \sqrt[4]{4} = (4)^{\frac{1}{4}} = (4^3)^{\frac{1}{12}} = \sqrt[12]{64}$
$\Rightarrow \sqrt[3]{3} > \sqrt[4]{4}$
(iii) $\sqrt{3} \ or \ \sqrt[3]{5}$
LCM of $2$ and $3$ is $6$
$\Rightarrow \sqrt{3} = (3)^{\frac{1}{2}} = (3^3)^{\frac{1}{6}} = \sqrt[6]{27}$
$\Rightarrow \sqrt[3]{5} = (5)^{\frac{1}{3}} = (5^2)^{\frac{1}{6}} = \sqrt[6]{25}$
$\Rightarrow \sqrt{3} > \sqrt[3]{5}$
(iv) $\sqrt{7}-\sqrt{3} \ or \ \sqrt{5}-1$
First simplify each of the given terms
$\sqrt{7}-\sqrt{3} =$ $\frac{(\sqrt{7}-\sqrt{3}) \times (\sqrt{7}+\sqrt{3})}{(\sqrt{7}+\sqrt{3})}$ $=$ $\frac{4}{(\sqrt{7}+\sqrt{3})}$
$\sqrt{5}-1 =$ $\frac{(\sqrt{5}-1) \times (\sqrt{5}+1)}{(\sqrt{5}+1)}$ $=$ $\frac{4}{(\sqrt{5}+1)}$
For both the terms, the numerator is the same which is 4. Therefore whichever term has a higher denominator, would be the smaller term. Let’s compare the two denominators.
$\sqrt{7} > \sqrt{5} \ and \ \sqrt{3} > \sqrt{1} \Rightarrow \sqrt{7}+\sqrt{3} > \sqrt{5}+1$
$\Rightarrow$ $\frac{4}{(\sqrt{7}+\sqrt{3})}$ $<$ $\frac{4}{(\sqrt{5}+1)}$
$\Rightarrow \sqrt{5}-1 > \sqrt{7}-\sqrt{3}$
(v) $\sqrt{17}-\sqrt{12} \ or \ \sqrt{11}-\sqrt{6}$
First simplify each of the given terms
$\sqrt{17}-\sqrt{12} =$ $\frac{(\sqrt{17}-\sqrt{12}) \times (\sqrt{17}+\sqrt{12})}{(\sqrt{17}+\sqrt{12})}$ $=$ $\frac{5}{(\sqrt{17}+\sqrt{12})}$
$\sqrt{11}-\sqrt{6} =$ $\frac{(\sqrt{11}-\sqrt{6}) \times (\sqrt{11}+\sqrt{6})}{(\sqrt{11}+\sqrt{6})}$ $=$ $\frac{5}{(\sqrt{11}+\sqrt{6})}$
For both the terms, the numerator is the same which is 5. Therefore whichever term has a higher denominator, would be the smaller term. Let’s compare the two denominators.
$\sqrt{17} > \sqrt{11} \ and \ \sqrt{12} > \sqrt{6} \Rightarrow \sqrt{17}+\sqrt{12} > \sqrt{11}+\sqrt{6}$
$\Rightarrow$ $\frac{5}{(\sqrt{17}+\sqrt{12})}$ $<$ $\frac{5}{(\sqrt{11}+\sqrt{6})}$
$\Rightarrow \sqrt{11}-\sqrt{6} > \sqrt{17}-\sqrt{12}$
Question 7: Arrange in Ascending Order:
(i) $\sqrt[4]{3}, \sqrt[6]{10}, \sqrt[12]{25}$
LCM of $4, 6 \ and \ 12 \ is \ 12$
Now convert all the above terms to order of 12
$\Rightarrow \sqrt[4]{3} = (3)^{\frac{1}{4}} = (3^3)^{\frac{1}{12}} = \sqrt[12]{27}$
$\Rightarrow \sqrt[6]{10} = (10)^{\frac{1}{6}} = (10^2)^{\frac{1}{12}} = \sqrt[12]{100}$
$\Rightarrow \sqrt[12]{25} = (25)^{\frac{1}{12}} = (25^1)^{\frac{1}{12}} = \sqrt[12]{25}$
Now comparing the number under the root sign as they are all of the same order.
$\Rightarrow \sqrt[12]{25} < \sqrt[12]{27} < \sqrt[12]{100}$
or $\Rightarrow \sqrt[12]{25} < \sqrt[4]{3} < \sqrt[6]{10}$
(ii) $\sqrt[6]{6}, \sqrt[3]{7}, \sqrt[4]{8}$
LCM of $6, 3 \ and \ 4 \ is \ 12$
Now convert all the above terms to order of 12
$\Rightarrow \sqrt[6]{6} = (6)^{\frac{1}{6}} = (6^2)^{\frac{1}{12}} = \sqrt[12]{36}$
$\Rightarrow \sqrt[3]{7} = (7)^{\frac{1}{3}} = (7^4)^{\frac{1}{12}} = \sqrt[12]{2401}$
$\Rightarrow \sqrt[4]{8} = (8)^{\frac{1}{4}} = (8^3)^{\frac{1}{12}} = \sqrt[12]{512}$
Now comparing the number under the root sign as they are all of the same order.
$\Rightarrow \sqrt[12]{36} < \sqrt[12]{512} < \sqrt[12]{2401}$
or $\Rightarrow \sqrt[6]{6} < \sqrt[4]{8} < \sqrt[3]{7}$
Question 8: Arrange in Descending Order:
(i) $2\sqrt{3}, 3\sqrt{2}, 5\sqrt{7}$
Convert $2\sqrt{3}, 3\sqrt{2}, 5\sqrt{7}$ into simple surds
$\Rightarrow \sqrt{12}, \sqrt{18}, \sqrt{175}$
Since the order of all the terms is the same, just compare the terms inside the square root. Hence, the descending order is
$\sqrt{175} > \sqrt{18} > \sqrt{12}$
(ii) $\sqrt[3]{10}, \sqrt[3]{36}, \sqrt {3}, \sqrt[6]{5}, \sqrt[8]{60}$
LCM of $3, 2, 6 \ and \ 8 \ is \ 24$
Now convert all the above terms to order of 24
$\Rightarrow \sqrt[3]{10} = (10)^{\frac{1}{3}} = (10^8)^{\frac{1}{24}} = \sqrt[24]{100000000}$
$\Rightarrow \sqrt[3]{36} = (36)^{\frac{1}{3}} = (36^8)^{\frac{1}{24}} = \sqrt[24]{36^8}$
$\Rightarrow \sqrt[2]{3} = (3)^{\frac{1}{2}} = (3^12)^{\frac{1}{12}} = \sqrt[12]{531441}$
$\Rightarrow \sqrt[6]{5} = (5)^{\frac{1}{6}} = (5^4)^{\frac{1}{24}} = \sqrt[24]{625}$
$\Rightarrow \sqrt[8]{60} = (60)^{\frac{1}{8}} = (60^3)^{\frac{1}{24}} = \sqrt[24]{216000}$
Now comparing the number under the root sign as they are all of the same order.
$\Rightarrow \sqrt[24]{36^8} > \sqrt[24]{100000000} > \sqrt[12]{531441} > \sqrt[24]{216000} > \sqrt[24]{625}$
or $\Rightarrow \sqrt[3]{36} > \sqrt[3]{10} > \sqrt[2]{3} > \sqrt[8]{60} > \sqrt[6]{5}$
Question 9: Simplify:
(i) $\sqrt{63}+\sqrt{28}-\sqrt{175}+\sqrt{162}-\sqrt{32}$
$= \sqrt{9 \times 7}+\sqrt{4 \times 7} - \sqrt{25 \times 7} + \sqrt{81 \times 2} - \sqrt{16 \times 2}$
$= 3\sqrt{7} + 2 \sqrt{7} - 5 \sqrt{7} + 9\sqrt{2}-4 \sqrt{2}$
$= 5\sqrt{2}$
(ii) $5\sqrt{3}+ 2 \sqrt{27}+ 4$ $\sqrt{\frac{1}{3}}$
$= 5\sqrt{3} + 2 \sqrt{9 \times 3} +$ $\frac{4}{3}$ $\sqrt{3}$
$= 5\sqrt{3}+ 6\sqrt{3}+$ $\frac{4}{3}$ $\sqrt{3}$
$= (5 + 6 +$ $\frac{4}{3}$ $)\sqrt{3}$
$=$ $\frac{37}{3}$ $\sqrt{3}$
(iii) $2$ $\sqrt{\frac{8}{9}}$ $- 3$ $\sqrt{\frac{1}{2}}$ $+ 5$ $\sqrt{\frac{9}{8}}$
$= 2$ $\sqrt{\frac{4 \times 2}{3 \times 3}}$ $- 3$ $\sqrt{\frac{2}{2 \times 2}}$ $+ 5$ $\sqrt{\frac{3\times 3 \times 2}{4 \times 2 \times 2}}$
$=$ $\frac{4}{3}$ $\sqrt{2}-$ $\frac{3}{2}$ $\sqrt{2} +$ $\frac{15}{4}$ $\sqrt{2}$
$= ($ $\frac{4}{3}$ $-$ $\frac{3}{2}$ $+$ $\frac{15}{4})$ $\sqrt{2}$
$=$ $\frac{43}{12}$ $\sqrt{2}$
(iv) $\sqrt[2]{147}-5$ $\sqrt{\frac{1}{3}}$ $+ 9$ $\sqrt{\frac{1}{3}}$
$= \sqrt[2]{3 \times 7 \times 7}-5$ $\sqrt{\frac{3}{3 \times 3}}$ $+ 9$ $\sqrt{\frac{3}{3 \times 3}}$
$= 7\sqrt{3}-$ $\frac{5}{3}$ $\sqrt{3}+3\sqrt{3}$
$= (7 -$ $\frac{5}{3}$ $+ 3) \sqrt{3}$
$=$ $\frac{25}{3}$ $\sqrt{3}$
(v) $4\sqrt{2} - 2\sqrt{8}+$ $\frac{3}{\sqrt{2}}$
$= 4\sqrt{2} - 2\sqrt{4\times 2}+$ $\frac{3}{2}$ $\sqrt{2}$
$= 4\sqrt{2} - 4\sqrt{2} +$ $\frac{3}{2}$ $\sqrt{2}$
$= \frac{3}{2}$ $\sqrt{2}$
Question 10: Multiply
(i) $4\sqrt{12} \times 7\sqrt{16}$
$= 4\sqrt{4 \times 3} \times 7\sqrt{4 \times 4}$
$= 4 \times 2 \times \sqrt{3} \times 7 \times 4$
$= 224 \sqrt{3}$
(ii) $\sqrt[3]{7} \times \sqrt{2}$
$LCM of 3 \ and \ 2 \ is \ 6$
$= \sqrt[6]{7^2} \times \sqrt[6]{2^3}$
$= \sqrt[6]{48 \times 8}$
$= \sqrt[6]{392}$
(iii) $\sqrt[4]{2} \times \sqrt[3]{3} \times \sqrt[3]{4}$
LCM of $4, 3, 3, \ is \ 12$
$= \sqrt[12]{2^3} \times \sqrt[12]{3^4} \times \sqrt[12]{4^4}$
$= \sqrt[12]{2^3 \times 3^4 \times 4^4}$
$= \sqrt[12]{2^11 \times 3^4}$
(iv) $3\sqrt{5} \times 2\sqrt{7} \times 5\sqrt{2}$
$= \sqrt{45} \times \sqrt{28} \times \sqrt{50}$
$= \sqrt{45 \times 28 \times 50}$
$= \sqrt{63000} = \sqrt{70 \times 900} = 30 \sqrt{70}$
(v) $3 \times \sqrt[3]{32} \times 3 \sqrt[3]{4}$
$= \sqrt[3]{27} \times \sqrt[3]{32} \times \sqrt[3]{27 \times 4}$
$= \sqrt[3]{3^3 \times 2^5 \times 2^2 \times 3^3}$
$= 36 \sqrt[3]{2}$
Question 11: Divide
(i) $\sqrt{98} \div \sqrt{2}$
$=$ $\sqrt{\frac{98}{2}}$ $= \sqrt{49} = 7$
(ii) $25 \sqrt[4]{33} \div 5 \sqrt[4]{11}$
$=$ $\frac{25 \sqrt[4]{33}}{5 \sqrt[4]{11}}$ $= 5$ $\sqrt[4]{\frac{33}{11}}$ $= 5 \sqrt[4]{3}$
(iii) $6 \sqrt[3]{25} \div \sqrt[2]{5}$
$= \frac{6 \sqrt[3]{25}}{\sqrt[2]{5}}$
$= \frac{6 \sqrt[6] {25 \times 25}}{\sqrt[3]{5 \times 5 \times 5}}$
$= 6$ $\sqrt[6]{\frac{25 \times 25}{5 \times 5 \times 5}}$
$= 6 \sqrt[6]{5}$
(iv) $\sqrt{a^3b^4} \div \sqrt[3]{a^4b^3}$
$= \frac{\sqrt{a^3b^4}}{\sqrt[3]{a^4b^3}}$
$= \frac{\sqrt[6]{(a^3b^4)^3}}{\sqrt[6]{(a^4b^3)2}}$
$= \sqrt[6]{\frac{a^9b^12}{a^8b^6}}$
$= b\sqrt{a}$
(v) $\sqrt{m^2n^2} \times \sqrt[6]{m^2n^2} \times \sqrt[3]{m^2n^2}$
$= \sqrt[6]{(m^2n^2)^3} \times \sqrt[6]{m^2n^2} \times \sqrt[6]{(m^2n^2)^2}$
$= \sqrt[6] {m^6n^6 \times m^2n^2 \times m^4n^4}$
$= \sqrt[6]{m^{12} n^{12}}$
$= m^2n^2$
Exercise 3(a) continued….
|
2018-06-22 08:52:14
|
{"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": 278, "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": 0.8880792856216431, "perplexity": 635.675271440557}, "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-2018-26/segments/1529267864387.54/warc/CC-MAIN-20180622084714-20180622104714-00025.warc.gz"}
|
https://typeset.io/topics/plasma-parameters-1zn9zsj5
|
Topic
# Plasma parameters
About: Plasma parameters is a(n) research topic. Over the lifetime, 9050 publication(s) have been published within this topic receiving 128542 citation(s).
##### Papers
More filters
Journal ArticleDOI
Abstract: Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the applicative potential and in the perspective to investigate novel regimes as available laser intensities will be increasing. Experiments have demonstrated, over a wide range of laser and target parameters, the generation of multi-MeV proton and ion beams with unique properties such as ultrashort duration, high brilliance, and low emittance. An overview is given of the state of the art of ion acceleration by laser pulses as well as an outlook on its future development and perspectives. The main features observed in the experiments, the observed scaling with laser and plasma parameters, and the main models used both to interpret experimental data and to suggest new research directions are described.
1,062 citations
Journal ArticleDOI
Lewi Tonks1, Irving Langmuir1Institutions (1)
15 Sep 1929-Physical Review
Abstract: The conception of random positive ion velocities corresponding to ion temperatures in a plasma has serious theoretical difficulties and is lacking in direct experimental verification It is more reasonable to assume that each ion starts from rest and subsequently possesses only the velocity which it acquires by falling through a static electric field which is itself maintained by the balance of electron and ion charges This new viewpoint thus ascribes motions to the positive ions which, for long free paths, are ordered rather than chaotic, each negative body in contact with the discharge collecting ions from a definite region of the plasma and from it only The resulting integral ? the plasma-sheath potential distribution have been set up for plane, cylindrical, and spherical plasmas, for long, short and intermediate length ion free paths, and for both constant rate of ionization throughout the plasma and rate proportional to electron density, and these equations have been solved for the potential distribution in the plasma in all important cases The case of short ion free paths in a cylinder with ion generation proportional to electron density gives the same potential distribution as found for the positive column by Schottky using his ambipolar diffusion theory, with the advantages that ambipolarity and quasineutrality need not appear as postulates The calculated potential distribution agrees with that found experimentally The potential difference between center and edge of plasma approximates $\frac{{T}_{e}}{11,600}$ volts in all long ion free path cases The theory yields two equations One, the ion current equation, simply equates the total number of ions reaching the discharge tube wall to the total number of ions generated in the plasma, but it affords a new method of calculating the density of ionization The second, the plasma balance equation, relates rate of ion generation, discharge tube diameter (in the cylindrical case), and electron temperature It can be used to calculate the rate of ion generation, the resulting values checking (to order of magnitude) those calculated from one-stage ionization probabilities The potential difference between the center of the plasma and a non-conducting bounding wall as calculated from the ion current equation agrees with that found experimentallyThe solution of the general plasma-sheath equation has been extended into the sheath surrounding the plasma to determine the first order correction which is to be subtracted from the discharge tube radius to obtain the plasma radius The wall sheath in the positive column is several times the thickness given by the simple space charge equationActually the ions do not start from rest when formed but have small random velocities corresponding to the gas temperature, ${T}_{g}$ In the long ion free path cases this leads to an error of the order of only $\frac{{T}_{g}}{{T}_{e}}$ in the calculated potential distributionsIn the plasma surrounding a fine negatively charged probe wire the potential difference between plasma potential maximum and sheath edge may be so small that the ions generated within the plasma potential maximum are not trapped but can traverse the maximum by virtue of their finite initial velocities This justifies the use of a sufficiently fine negatively charged wire in the usual way to measure positive ion concentrations, although certain difficulties appear which are thought to be connected with the collector theory rather than the present plasma theory
813 citations
Journal ArticleDOI
Abstract: The addition of a small concentration of suitably chosen noble gas to a reactive plasma is shown to permit the determination of the functional dependence of reactive particle density on plasma parameters. Examples illustrating the simplicity of this method are presented using F atomic emission from plasma‐etching discharges and a comparison is made to available data in the literature.
766 citations
Journal ArticleDOI
Abstract: A review is presented of plasma chemical processes occurring in the volume part of electrical nonequilibrium discharges. The role of energetic electrons as initiators of chemical reactions in a cold background gas is discussed. Different discharge types of (glow, corona, silent, RF, and microwave discharges) are investigated with respect to their suitability for plasma processing. Emphasis is placed on the requirements of initiating and maintaining the discharge and, at the same time, optimizing plasma parameters for the desired chemical process. Using large-scale industrial ozone production as an example, the detailed process of discharge optimization is described. Other applications of volume plasma processing include other plasma chemical syntheses as well as decomposition processes such as flue gas treatment and hazardous waste disposal. The author only deals with plasmas which are not in equilibrium. >
742 citations
Journal ArticleDOI
Wei Lu1, Michail Tzoufras1, C. Joshi1, Frank Tsung1 +4 moreInstitutions (2)
Abstract: The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for laser wakefield acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample particle-in-cell (PIC) simulation of a $30\text{ }\mathrm{fs}$, 200 TW laser interacting with a 0.75 cm long plasma with density $1.5\ifmmode\times\else\texttimes\fi{}{10}^{18}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ to produce an ultrashort (10 fs) monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas 12, 043109 (2005)] in that it involves lower plasma densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.
726 citations
##### Network Information
###### Related Topics (5)
Plasma
89.6K papers, 1.3M citations
94% related
Electron
111.1K papers, 2.1M citations
87% related
Electric field
87.1K papers, 1.4M citations
86% related
Magnetic field
167.5K papers, 2.3M citations
85% related
Ionization
67.7K papers, 1.3M citations
84% related
##### Performance
###### Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021244
2020259
2019289
2018283
2017344
|
2022-09-27 10:18:01
|
{"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": 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": 0.457061231136322, "perplexity": 1298.7820244181598}, "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/1664030335004.95/warc/CC-MAIN-20220927100008-20220927130008-00744.warc.gz"}
|
https://physics.stackexchange.com/questions/606104/why-is-there-atmospheric-pressure
|
# Why is there atmospheric pressure?
Why is there atmospheric pressure? Gas molecules have empty spaces between them right (intermolecular space). But to have atmospheric pressure all the gas pressure will have to line up without any space. Imagine lifting 3 boxes. Box 1 is stack ontop of box 2 and ontop of box 3. Between box 1 and 2, there is an empty space, and the same thing with box 2 and 3. If this is the case then I am only experiencing the weight(force) of 1 box not 3 boxes(because box 2 and 3 have spaces between them). This is how I imagine atmospheric pressure. I know this is wrong, but why is it wrong?
• There is space between the atoms of a solid too. Just not as much Jan 10 at 1:43
You're missing the fact that those molecules are moving really fast and they're collidingwith each other. Take into accoutn that the can be over $$10^{25}$$ molecules...
|
2021-11-28 19:53:15
|
{"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5028547048568726, "perplexity": 577.9973500026731}, "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/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00592.warc.gz"}
|
https://math.libretexts.org/Courses/East_Tennesee_State_University/Book%3A_Differential_Equations_for_Engineers_(Lebl)_Cintron_Copy/6%3A_The_Laplace_Transform/6.4%3A_Dirac_delta_and_impulse_response
|
# 6.4: Dirac delta and impulse response
## Rectangular Pulse
Often in applications we study a physical system by putting in a short pulse and then seeing what the system does. The resulting behavior is often called impulse response. Let us see what we mean by a pulse. The simplest kind of a pulse is a simple rectangular pulse defined by
$\varphi(t)= \left\{ \begin{array}{ccc} 0 & {\rm{if~}}~~~~t<a, \\ M & {\rm{if~}}a \leq t<b, \\ 0 & {\rm{if~}}b \leq t.\end{array} \right.$
Notice that $\varphi (t) = M\left(u(t-a)-u(t-b)\right),$ where $$u(t)$$ is the unit step function (see Figure $$\PageIndex{1}$$ for a graph).
Let us take the Laplace transform of a square pulse,
\begin{align}\begin{aligned} \mathcal{L}\{ \varphi(t)\} &= \mathcal{L}\{ M(u(t-a)-u(t-b)) \} &= M \frac{e^{-as}-e^{-bs}}{s}.\end{aligned}\end{align}
For simplicity we let $$a=0$$ and it is convenient to set $$M= \dfrac{1}{b}$$ to have
$\int _0 ^{\infty} \varphi (t) \; dt = 1$
That is, to have the pulse have “unit mass.” For such a pulse we compute
$\mathcal{L}\{ \varphi(t)\}= \mathcal{L}\left\{ \frac{u(t)-u(t-b)}{b} \right\} = \frac{1-e^{-bs}}{bs}.$
We generally want $$b$$ to be very small. That is, we wish to have the pulse be very short and very tall. By letting $$b$$ go to zero we arrive at the concept of the Dirac delta function.
## 6.4.2Delta Function
The Dirac delta function$$^{1}$$ is not exactly a function; it is sometimes called a generalized function. We avoid unnecessary details and simply say that it is an object that does not really make sense unless we integrate it. The motivation is that we would like a “function” $$\delta (t)$$ such that for any continuous function $$f(t)$$ we have
$\int_{-\infty}^{\infty} \delta (t) f(t) \, dt = f(0)$
The formula should hold if we integrate over any interval that contains 0, not just $$(-\infty, \infty)$$. So $$\delta (t)$$ is a “function” with all its “mass” at the single point $$t=0$$. In other words, for any interval $$[c,d]$$
$\int_c^d \delta(t)= \left\{ \begin{array}{cl} 1 & {\rm{if~the~interval~}} [c,d]{\rm{~contains~}}0, {\rm{~i.e.~}}c \leq 0 \leq d, \\ 0 & {\rm{otherwise}}. \end{array} \right.$
Unfortunately there is no such function in the classical sense. You could informally think that $$\delta (t)$$ is zero for $$t \neq 0$$ and somehow infinite at $$t=0$$.
A good way to think about $$\delta (t)$$ is as a limit of short pulses whose integral is 1. For example, suppose that we have a square pulse $$\varphi (t)$$ as above with $$a=0$$, $$M=\dfrac{1}{b}$$, that is $$\varphi (t) = \dfrac{u(t)-u(t-b)}{b}$$.
Compute
$\int_{-\infty}^{\infty} \varphi (t) f(t) \, dt = \int_{-\infty}^{\infty} \dfrac{u(t)-u(t-b)}{b} f(t) \, dt =\dfrac{1}{b} \int_{0}^{b} f(t) \, dt.$
If $$f(t)$$ is continuous at $$t=0$$, then for very small $$b$$, the function $$f(t)$$ is approximately equal to $$f(0)$$ on the interval $$[0,b)$$. We approximate the integral
$\dfrac{1}{b} \int_0^b f(t) \, dt \approx \dfrac{1}{b} \int_0^b f(t) \, dt = f(0).$
Therefore,
$\lim _{b \rightarrow 0} \int_{-\infty}^{\infty} \varphi (t) f(t) \, dt = \lim _{b \rightarrow 0} \dfrac{1}{b} \int_0^b f(t) \, dt = f(0)$
Let us therefore accept $$\delta (t)$$ as an object that is possible to integrate. We often want to shift $$\delta$$ to another point, for example $$\delta (t-a)$$. In that case we have
$\int_{-\infty}^{\infty} \delta(t-a) f(t) \, dt = f(a).$
Note that $$\delta (a-t)$$ is the same object as $$\delta (t-a)$$. In other words, the convolution of $$\delta (t)$$ with $$f(t)$$ is again $$f(t)$$,
$(f * \delta)(t) = \int _0^t \delta(t-s)f(s)\, ds = f(t)$
As we can integrate $$\delta (t)$$, let us compute its Laplace transform.
$\mathcal{L} \{\delta (t-a) \} = \int_0^{\infty} e^{-st} \delta(t-a) \, dt = e^{-as}.$
In particular,
$\mathcal{L} \{\delta (t) \} = 1.$
Note
Notice that the Laplace transform of $$\delta (t-a)$$ looks like the Laplace transform of the derivative of the Heaviside function $$u(t-a)$$, if we could differentiate the Heaviside function. First notice
$\mathcal{L} \{\delta (t-a) \} = \dfrac{e^{-as}}{s}.$
To obtain what the Laplace transform of the derivative would be we multiply by $$s$$, to obtain $$e^{-as}$$, which is the Laplace transform of $$\delta (t-a)$$. We see the same thing using integration,
$\int _0^{t} \delta (s-a) \,ds = u(t-a)$
So in a certain sense
$\dfrac{d}{dt} [u(t-a)] = \delta(t-a)$
This line of reasoning allows us to talk about derivatives of functions with jump discontinuities. We can think of the derivative of the Heaviside function $$u(t-a)$$ as being somehow infinite at $$a$$, which is precisely our intuitive understanding of the delta function.
Example $$\PageIndex{1}$$
Compute
$\mathcal{L}^{-1} \left\{ \dfrac{s+1}{s} \right\}.$
So far we have always looked at proper rational functions in the $$s$$ variable. That is, the numerator was always of lower degree than the denominator. Not so with $$\dfrac{s+1}{s}$$. We write,
$\mathcal{L}^{-1} \left\{ \dfrac{s+1}{s} \right\} = \mathcal{L}^{-1} \left\{ 1+ \dfrac{1}{s} \right\} = \mathcal{L}^{-1} \{1\} + \mathcal{L}^{-1} \left\{ \dfrac{1}{s} \right\} = \delta(t) + 1.$
The resulting object is a generalized function and only makes sense when put underneath an integral.
## Impulse Response
As we said before, in the differential equation $$Lx = f(t)$$, we think of $$f(t)$$ as input, and $$x(t)$$ as the output. Often it is important to find the response to an impulse, and then we use the delta function in place of $$f(t)$$. The solution to
$Lx = \delta (t)$
is called the impulse response.
Example $$\PageIndex{2}$$
Solve (find the impulse response)
$\label{eq:20} x'' + \omega_0^2x=\delta(t) ,\quad x(0)=0 ,\quad x'(0)=0.$
We first apply the Laplace transform to the equation. Denote the transform of $$x(t)$$ by $$X(s)$$.
$s^2X(s) + \omega^2_0X(s) = 1,\quad\text{and so}\quad X(s) = \dfrac{1}{s^2+\omega^2_0}.$
Taking the inverse Laplace transform we obtain
$x(t)=\frac{\sin (\omega_{0}t)}{\omega_{0}}.$
Let us notice something about the above example. In Example 6.3.4, we found that when the input was $$f(t)$$, then the solution to $$Lx = f(t)$$ was given by
$x(t) = \int_0^t f(\tau)\dfrac{\sin \left(\omega_0(t-\tau) \right)}{\omega_0} d\tau.$
Notice that the solution for an arbitrary input is given as convolution with the impulse response. Let us see why. The key is to notice that for functions $$x(t)$$ and $$f(t)$$,
$(x*f)''(t) = \dfrac{d^2}{dt^2} \left[ \int_0^t f(\tau)x(t-\tau)\,d\tau \right] = \int _0^t f(\tau)x''(t-\tau)\, d\tau = (x'' * f)(t).$
We simply differentiate twice under the integral,$$^{2}$$ the details are left as an exercise. And so if we convolve the entire equation $$\eqref{eq:20}$$, the left hand side becomes
$(x'' + \omega_0^2x)* f = (x'' * f) + \omega_0^2(x*f) = (x*f)'' + \omega_0^2(x*f).$
The right hand side becomes
$(\delta * f)(t) = f(t).$
Therefore $$y(t) = (x*f)(t)$$ is the solution to
$y'' + \omega_0^2y = f(t).$
This procedure works in general for other linear equations $$Lx=f(t)$$. If you determine the impulse response, you also know how to obtain the output $$x(t)$$ for any input $$f(t)$$ by simply convolving the impulse response and the input $$f(t)$$.
## Three-Point Beam Bending
Let us give another quite different example where the delta function turns up: Representing point loads on a steel beam. Consider a beam of length $$L$$, resting on two simple supports at the ends. Let $$x$$ denote the position on the beam, and let $$y(x)$$ denote the deflection of the beam in the vertical direction. The deflection $$y(x)$$ satisfies the Euler-Bernoulli equation,$$^{3}$$ $EI \frac{d^4 y}{dx^4} = F(x) ,$ where $$E$$ and $$I$$ are constants$$^{4}$$ and $$F(x)$$ is the force applied per unit length at position $$x$$. The situation we are interested in is when the force is applied at a single point as in Figure $$\PageIndex{2}$$.
In this case the equation becomes
$EI\dfrac{d^4y}{dx^4}=-F\delta(x-a)$
where $$x=a$$ is the point where the mass is applied. $$F$$ is the force applied and the minus sign indicates that the force is downward, that is, in the negative $$y$$ direction. The end points of the beam satisfy the conditions,
\begin{align}\begin{aligned} & y(0) = 0, \qquad y''(0) = 0, \\ & y(L) = 0, \qquad y''(L) = 0.\end{aligned}\end{align}
See Section 5.2, for further information about endpoint conditions applied to beams.
Example $$\PageIndex{3}$$
Suppose that length of the beam is $$2$$, and suppose that $$EI=1$$ for simplicity. Further suppose that the force $$F=1$$ is applied at $$x=1$$. That is, we have the equation
$\dfrac{d^4y}{dx^4}=-\delta(x-1)$
and the endpoint conditions are
$y(0)=0,\quad y''(0)=0,\quad y(2)=0,\quad y''(2)=0.$
We could integrate, but using the Laplace transform is even easier. We apply the transform in the $$x$$ variable rather than the $$t$$ variable. Let us again denote the transform of $$y(x)$$ as $$Y(s)$$.
$s^4Y(s)-s^3y(0)-s^2y'(0)-sy''(0)-y'''(0)=-e^{-s}.$
We notice that $$y(0)=0$$ and $$y''(0)=0$$. Let us call $$C_1=y'(0)$$ and $$C^2=y'''(0)$$. We solve for $$Y(s)$$,
$Y(s)=\frac{-e^{-s}}{s^4}+\frac{C_1}{s^2}+\frac{C_2}{s^4}.$
We take the inverse Laplace transform utilizing the second shifting property Equation (6.2.14) to take the inverse of the first term.
$y(x)=\frac{-(x-1)^3}{6}u(x-1)+C_1x+ \frac{C_2}{6}x^3.$
We still need to apply two of the endpoint conditions. As the conditions are at $$x=2$$ we can simply replace $$u(x-1)=1$$ when taking the derivatives. Therefore,
$0=y(2)=\frac{-(2-1)^3}{6}+C_1(2)+ \frac{C_2}{6}2^3=\frac{-1}{6}+2C_1+\frac{4}{3C_2},$
and
$0 = y''(2) = \frac{-3\cdot 2 \cdot (2-1)}{6} + \frac{C_2}{6} 3\cdot 2 \cdot 2 = -1 + 2 C_2$
Hence $$C_2 = \frac{1}{2}$$ and solving for $$C_{1}$$ using the first equation we obtain $$C_1 = \frac{-1}{4}$$. Our solution for the beam deflection is $y(x) = \frac{-{(x-1)}^3}{6} u(x-1) - \frac{x}{4} + \frac{x^3}{12}.$
## Footnotes
[1] Named after the English physicist and mathematician Paul Adrien Maurice Dirac (1902–1984).
[2] You should really think of the integral going over $$(-\infty , \infty )$$ rather than over $$[0,t]$$ and simply assume that $$f(t)$$ and $$x(t)$$ are continuous and zero for negative .
[3] Named for the Swiss mathematicians Jacob Bernoulli (1654–1705), Daniel Bernoulli —nephew of Jacob— (1700–1782), and Leonhard Paul Euler (1707–1783).
[4] $$E$$ is the elastic modulus and $$I$$ is the second moment of area. Let us not worry about the details and simply think of these as some given constants.
|
2022-05-27 06:35:15
|
{"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": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9704707264900208, "perplexity": 180.09719734862156}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00704.warc.gz"}
|
https://www.luogu.com.cn/problem/P3209
|
# [HNOI2010] 平面图判定
## 输入输出样例
### 输入样例 #1
2
6 9
1 4
1 5
1 6
2 4
2 5
2 6
3 4
3 5
3 6
1 4 2 5 3 6
5 5
1 2
2 3
3 4
4 5
5 1
1 2 3 4 5
### 输出样例 #1
NO
YES
|
2021-10-24 04:14:31
|
{"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": 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": 0.40444231033325195, "perplexity": 314.45941690759844}, "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/1634323585837.82/warc/CC-MAIN-20211024015104-20211024045104-00434.warc.gz"}
|
https://numberworld.info/root-of-7471
|
# Root of 7471
#### [Root of seven thousand four hundred seventy-one]
square root
86.4349
cube root
19.5491
fourth root
9.297
fifth root
5.9522
In mathematics extracting a root is known as the determination of the unknown "x" in the equation $y=x^n$ The result of the extraction of the root is known as a so-called root. In the case of "n = 2", one talks about a square root or sometimes a second root also, another possibility could be that n = 3 at that time one would consider it a cube root or simply third root. Considering n beeing greater than 3, the root is declared as the fourth root, fifth root and so on.
In maths, the square root of 7471 is represented as this: $$\sqrt[]{7471}=86.434946636184$$
Additionally it is possible to write every root down as a power: $$\sqrt[n]{x}=x^\frac{1}{n}$$
The square root of 7471 is 86.434946636184. The cube root of 7471 is 19.549076471223. The fourth root of 7471 is 9.2970396705717 and the fifth root is 5.9521757655383.
Look Up
|
2021-05-13 14:38:27
|
{"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": 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": 0.8987762928009033, "perplexity": 689.0876115732342}, "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-2021-21/segments/1620243989814.35/warc/CC-MAIN-20210513142421-20210513172421-00494.warc.gz"}
|
https://dsachar.github.io/post/causal-statistical-parity/
|
# Causality, Fairness, and Statistical Parity
## Introduction
This post explores fairness, specifically the notion of statistical parity, from a causality viewpoint. Its goal is to gently introduce the reader to the causality frameworks, presenting the basics about Bayesian networks, potential outcomes, randomized control trials, and causal graphs. The post was inspired by an example in the AAAI 2018 paper Fair Inference on Outcomes, that shows how statistical parity may be unable to reveal an underlying causal effect that is discriminatory.
Consider the following hypothetical scenario. A company employs an algorithm for its hiring decisions. The algorithm bases its decisions on the education level of the candidate, and on whether the candidate has a prior conviction. Let’s further assume that according to law a hiring decision should not discriminate on the grounds of prior conviction.
Our goal is to investigate whether the algorithm is non-discriminatory, or fair.
## Bayesian Networks
Let’s denote the hiring decision with the boolean random variable $H$, where $H=1$ means the candidate is hired. Similarly, let $E$, $C$ denote the boolean random variables for education level (high school education or not) and prior conviction, respectively.
Let’s assume we have observed the hiring decisions for several candidates over time. For each candidate we observe their $H, E, C$ values, and collect their joint distribution, shown in the following table.
Any joint probability distribution, such as $p(H,E,C)$, can be represented, or factorized, as a product of marginal and conditional probability distributions by applying the chain rule. Note that there are multiple factorizations for a given joint probability. One such factorization of our joint distribution is
$$p(H,E,C) = p(H|E,C) \cdot p(C|E) \cdot p(E). \label{eq:factorization}$$
Factorizations are visually represented by Bayesian networks. These are directed acyclic graphs, where nodes represent random variables, and edges encode conditional dependences. Each node is associated with a function that specifies its probability distribution conditional on its parents’ values; if a node has no parents, the function is the node’s marginal distribution. Below is Bayesian network corresponding to the aforementioned factorization. The depicted probabilities can be computed directly from the joint probability distribution by appropriately marginalizing and conditioning. (In fact, to illustrate this example, the opposite direction was taken: the conditional and marginal probabilities were set, and the joint distribution was then derived — which explains the strange values in the latter.) The direction of edges indicate forward probabilities. For example, the edge from $E$ to $C$, means we have the conditional $p(C|E)$ in our factorization. To compute reverse probabilities, e.g., $p(E|C)$, one has to apply Bayes rule, i.e., $p(E|C) = p(C|E)\cdot p(E)/p(C)$ — hence the name Bayesian networks!
So if there are multiple factorizations (and thus Bayesian networks) for a given joint probability distribution, why might we care for a specific one? Well for one, certain forward probabilities might make more sense to explicitly encode than others. For example, $p(C|E)$ might be observable or could be easier to model compared to $p(E|C)$. As we later discuss, it is often the case that we encode conditional probabilities that reflect cause-effect relationships, e.g., $E$ causes $C$ and not the other way around.
Bayesian networks visualize (some of) the probabilistic dependencies in the joint distribution. If such dependencies exist, then the factorization is a compact representation of the joint distribution. This is not the case in our example, where 7 probability values are required in the Bayesian network to fully specify the probability of the $2^3-1$ possible configurations of $H, E, C$. One can see that there are no conditional independencies in this Bayesian network, because there is at least one non-blocked undirected path between each pair of nodes — the edge connecting them. In general, the notion of d-separation defines what blocking means and reveals the conditional independence relationships that are encoded in a Bayesian network.
Using this Bayesian network, let’s examine what the observations tell us. Finishing high school is very common with a probability of $p(E=1)=0.8$. Moreover, education level and prior conviction are strongly correlated. There is a $85\%$ chance that a candidate will have a prior conviction if they have not finished high school, i.e., $p(C=1|E=0)=0.85$. Conversely, there is a $90\%$ chance that a candidate will not have a prior conviction if they have finished high school, i.e., $p(C=0|E=1)=0.9$. Lastly, observe that the hiring decisions are summarized by the conditional probability table of $p(H|E,C)$. One thing to notice is that, among the non-high school graduates ($E=0$), the hiring decision appears to favor prior convicts ($C=1$). The situation is reversed for high school graduates ($E=1$), where non-convicts are favored ($C=0$). So, what can we tell about the hiring decision in terms of discrimination based on prior conviction?
## Fairness in Terms of Statistical Parity
Let’s return to our main goal and investigate if the algorithm responsible for the hiring decision is fair. First, we need to formalize what fairness, or no discrimination, means. As mentioned, the algorithm should not discriminate on prior conviction. This can be conceptualized as the requirement for statistical parity, which says that the conditional probabilities of hiring given a prior conviction and given no prior conviction should be equal i.e.,
$$p(H=1|C=0) = p(H=1|C=1). \label{eq:stat_parity}$$
Hide boring computations.
To compute these conditional probabilities, we need to first compute $p(H,C)$ and $p(C)$.
We can compute $p(H,C)$ using the conditional probabilities available in the Bayesian network: $p(H,C) = \sum_{E} p(H|E,C) \cdot p(C|E) \cdot p(E)$. Therefore, we get:
$$p(H=0,C=0) = 0.9 \cdot 0.15 \cdot 0.2 + 0.7 \cdot 0.9 \cdot 0.8 = 0.531$$ $$p(H=1,C=0) = 0.1 \cdot 0.15 \cdot 0.2 + 0.3 \cdot 0.9 \cdot 0.8 = 0.219$$ $$p(H=0,C=1) = 0.6 \cdot 0.85 \cdot 0.2 + 0.95 \cdot 0.1 \cdot 0.8 = 0.178$$ $$p(H=1,C=1) = 0.4 \cdot 0.85 \cdot 0.2 + 0.05 \cdot 0.1 \cdot 0.8 = 0.072$$
From $p(H,C)$, we can marginalize $H$ out to compute $p(C) = \sum_{H} p(H,C)$. Therefore, we get:
$$p(C=0) = 0.531 + 0.219 = 0.75$$ $$p(C=1) = 0.178 + 0.072 = 0.25$$
Plugging in these probabilities, we can straightforwardly compute $p(H=1|C=0) = p(H=1, C=0) / p(C=0)$ and $p(H=1|C=1) = p(H=1, C=1) / p(C=1)$.
It turns out that $p(H=1|C=0) = 0.292$ and $p(H=1|C=1) = 0.288$. Seeing they are roughly equal, we conclude that there is no discrimination according to the statistical parity definition.
## Causality
Let’s re-examine what statistical parity tells us. The probability of hiring a convict is almost the same as that of hiring a non-convict — this is what the conditional probability $p(H|C)$ reveals. But to convincingly argue there is no discrimination, we need to show that prior conviction plays no role in the hiring decision, or, in other words, that prior conviction does not cause the hiring outcome. We are thus looking for the causal effect of $C$ on $H$.
We can conceptualize and calculate the causal effect in two different but equivalent ways, one based on the potential outcomes framework of J. Neyman and D. Rubin, and one based on the causal graphs of S. Wright and J. Pearl.
### Potential Outcomes Framework
Consider some candidate. The potential outcome $H_{C=0}$ for this candidate corresponds to the value the $H$ would have taken, had variable $C$ been assigned the value $0$. Since, the variable $C$ is binary, there is just one other potential outcome, $H_{C=1}$, for this candidate. Note that the observed outcome, which is denoted as $H$, can only be one of these two potential outcomes. That potential outcome which coincides with the observed is called the factual outcome, while the other is a counterfactual outcome that corresponds to an imaginary world where the candidate’s prior conviction is reversed.
So let’s assume we can create worlds where we can assign to candidates their prior conviction status. We’re going to create world 0 where every candidate has no prior conviction, and world 1 where every candidate has a prior conviction. In world 0, we observe the potential outcome $H_{C=0}$ for all candidates, and $p(H_{C=0}=1)$ denotes the probability that a candidate is hired in this world. Similarly, $p(H_{C=1}=1)$ denotes the same probability for world 1. We can say that there is no discrimination on prior conviction $C$ from the hiring decision process if getting hired is equally likely in both worlds, that is:
$$p(H_{C=0}=1) = p(H_{C=1}=1). \label{eq:causal_fairness}$$
This is equivalent to saying there is no average causal effect of $C$ to $H$, i.e., the expected values of the potential outcomes are equal $\mathbb{E}[H_{C=1}] - \mathbb{E}[H_{C=0}] = 0$, which holds since $\mathbb{E}[X] = p(X=1)$ for binary variable $X$.
Assuming we cannot create worlds at will, the gold standard for measuring causal effects is to perform a randomized control trial (RCT), that helps quantify the causal effect of a treatment to an outcome. An RCT assigns individuals randomly to either the control group, where they will not be treated, or to the experimental group, where they will be treated. Observe that the control and experimental groups can be seen as a random sample of hypothetical worlds 0 and 1, respectively. Thus we can estimate the expected value of the potential outcomes by computing the means of the outcomes in the groups.
In our case, to perform an RCT means we should treat prior conviction $C$ as the treatment, and the hiring decision $H$ as the outcome. Clearly, this is not feasible — we cannot force people to become convicts. Whenever it’s impossible or unethical to control the treatment, e.g., the race, smoking habits, we cannot use RCTs to measure causal effects, e.g., in discrimination, lung cancer.
But not all is lost. Causal inference frameworks allow us to identify causal effects from observations (i.e., not experiments such as RCTs) under some causality assumptions. In the potential outcomes framework, the most important assumption we need to make is conditional ignorability. This specifies a set of variables, called confounders, given which the potential outcome becomes independent of the assigned treatment. To make this more concrete, let’s assume in our case that the potential outcome $H_C$ becomes independent of the assigned value of $C$ given the value of the confounder $E$. Ignorability can be expressed as $p(H_{C=0}|E) = p(H_{C=1}|E)$. Essentially, we can ignore the treatment assignment if we control for the confounders.
Ignorability implies that we can express the, conditional on $E$, probability of a potential outcome in terms of the conditional probability on $E$ and $C$ of the observed outcome as: $p(H_C|E) = p(H|E,C)$. In other words, computing the hiring probability among the candidates with some fixed education level $E$ in a hypothetical world, say 0 where candidates are assigned $C$ to be 0, is the same as computing the hiring probability among the candidates who have $C=0$ and that fixed education level $E$. So instead of performing an RCT to randomize the assignment of $C$, we can just condition on $C$ and measure probabilities per stratum of $E$. We can then aggregate these per-stratum probabilities to compute the probability of the potential outcome. This gives us the famous adjustment formula, which in our setting, where $H$ is the outcome, $H_C$ is the potential outcome, $C$ is the treatment, and $E$ is the confounder, is expressed as:
$$p(H_C) = \sum_E p(H_C|E) p(E) = \sum_E p(H|E,C) p(E). \label{eq:adjustment}$$
The causal effect can be now computed. But we’ll come back to it.
### Causal Graphs
As the previous section illustrated, determining causal effects from observations is only possible if we make some causality assumptions. Specifically, we previously made the ignorability assumption that $E$ acts as a confounder in the relationship of $C$ and $H$, which led us to use the adjustment formula as the means to compute the causal effect of $C$ on $H$.
In the causal graphs framework, the causality assumptions are encoded directly in a graph. A causal graph (more accurately a causal Bayesian network) is a Bayesian network where the direction of the edges implies a causal relationship between the two variables. The edge $A \to B$ means that the value of $B$ is derived from that of $A$, or as J. Pearl puts it, $B$ listens to $A$. Essentially, the set of edges in a causal graph expresses the data generating process. While there can be many Bayesian networks that give rise to the same observed data (by representing different factorizations of one joint distribution), there is a single Bayesian network, the causal graph, that explains how the data is generated. This ability is endowed to a Bayesian network by the causality assumptions encoded in its edges. One could write down such a mnemonic:
$$\textit{causal graph} = \textit{Bayesian network} + \textit{causality assumptions}.$$
As a side note, there are some causality questions, e.g., computing counterfactuals about individuals, that require stronger causality assumptions. Briefly, in structural causal models, the value of a variable $X$ is determined by some function $f_X$ of the values of $X$’s parents in the causal graph, i.e., $X = f_X(pa(X))$, where $pa(X)$ denotes the set of $X$’s parents. These structural equations, or response functions, replace the conditional probability functions, with stronger causality assumptions.
Let’s return to our example, and let’s assume that the Bayesian network we have seen so far is a causal one. That is, education level affects both prior conviction and the hiring outcome, and the hiring outcome is affected by prior conviction and education level alone. This is what the direction of edges suggests, and this is what the causality assumptions we have made imply. So given this causal graph, let’s see how we can determine if there is discrimination of the hiring decision based on prior conviction. We will built our answer based on the observations we have collected and which are summarized in the conditional probability tables.
To reach there, we first have to talk about interventions and distinguish them from observations. Consider our causal graph that encodes all causality assumptions regarding the hiring decision, prior conviction, and education level. To answer causality questions, we have to argue about hypothetical situations, and we need a language to express these situations. Suppose we were to change the value of prior conviction for all candidates and set it to 0. This would be an intervention, and we use the do operator to express it, here $do(C=0)$. Intervening on some variable causes changes in those variables that causally depend on it, but will leave the rest of the variables unaffected.
To argue about hypothetical situations, we have to express the effect of an intervention on some variable. Let $p(H|do(C=0))$ denote the probability of $H$ given the intervention of assigning to $C$ the value 0. To better understand what this means, let’s contrast it to the conditional probability $p(H|C=0)$. The latter tells us what is the probability of $H$ given that we have observed $C$ to be 0. It’s the answer to this question: among those who happen to have $C=0$, what is their $H$ value? The former is the probability of $H$ if we intervene and set $C$ to 0. It’s the answer to a different, hypothetical question: if everyone were to have $C=0$, what would their $H$ value be? It should be clear that $p(H|do(C=0))$ and $p(H|C=0)$ are different probabilities. They are only equal if there is no confounding, i.e., common cause of $C$ and $H$. This is not the case in our example, and in fact this is the reason why statistical parity, \eqref{eq:stat_parity}, and causal non-discrimination, \eqref{eq:causal_fairness} and \eqref{eq:causal_fairness_do}, are distinct notions of non-discrimination.
Let’s now express non-discrimination in our example with the causal graphs language. We argue there is no discrimination on prior conviction $C$ from the hiring decision process if getting hired $H$ remains equally likely whichever way we intervene and change the value of $C$, that is:
$$p(H=1|do(C=0)) = p(H=1|do(C=1)). \label{eq:causal_fairness_do}$$
Contrast this with \eqref{eq:causal_fairness}. Observe that the hypothetical situation where we intervene with $do(C=0)$ corresponds to the world 0 in the potential outcomes framework. So the probability $p(H|do(C=0))$ is exactly the probability $p(H_{C=0})$ of the potential outcome $H_{C=0}$ in world 0. Although \eqref{eq:causal_fairness} and \eqref{eq:causal_fairness_do} use different notation, they convey the same non-discrimination concept. The benefit of expressing this concept using the causal graphs framework, is that we can employ a powerful toolset, the do calculus, to compute probabilities given interventions.
Recall, that an intervention, like $do(C=1)$ means that we explicitly set the value of some variable, in our case $C$ to $1$. In the causal graphs framework, this translates to the intervened variable no longer listening to any other variables. As a result, all edges leading to the intervened variable should be removed. Equivalently, its conditional probability table is reduced to $p(C=1)=1$; in structural causal models, the structural equation for $C$ is replaced by $C=1$. The causal graph below illustrates the effect of the $do(C=1)$ intervention.
We will now compute $p(H|do(C=1))$ from this causal graph, using the three rules of do calculus. The goal is to rewrite this interventional probability in a way that contains only observational probabilities, i.e., there is no conditioning on the intervention $do(C=1)$. In our case, this is simple and we only need to apply a rule we have briefly mentioned. If there is no common cause of $C$ and $H$, then $p(H|do(C=1)) = p(H|C=1)$. Examining the causal graph after the intervention, it should be clear that this property now holds. $E$ used to be a common cause for $C$ and $H$. Now that we have intervened and assigned its value, $C$ is no longer affected by any other variable.
So it turns out we need to compute $p(H|C)$ in the intervened causal graph. Using the probabilities encoded in this new Bayesian network, we proceed by computing $p(H,C)$ and $p(C)$. The latter is trivial because for the intervention $do(C=1)$ it holds that $p(C=1)=1$. To compute the former, we will marginalize $E$ out of the joint distribution. As we are working on this new Bayesian network, note that the joint distribution is now factorized differently as $p(H,E,C) = p(H|E,C) \cdot p(E) \cdot p(C)$. Therefore, for either intervention $do(C=1)$ or $do(C=0)$, we derive that:
$$p(H|do(C)) = p(H|C) = p(H,C) = \sum_E p(H|E,C) \cdot p(E). \label{eq:adjustment_do}$$
This is again the adjustment formula of \eqref{eq:adjustment}, which should come as no surprise. The only difference is the way we have derived it; using the language of causal graphs and the do calculus might appear to be more intuitive.
## Fairness in Terms of Causality
We have now formulated two identical causality-based fairness notions, \eqref{eq:causal_fairness} and \eqref{eq:causal_fairness_do}, and two identical ways to compute them, \eqref{eq:adjustment} and \eqref{eq:adjustment_do}. Let’s pick the do notation and continue to test whether the hiring decision is non-discriminatory from our causality viewpoint.
We compute $p(H=1|do(C=0))=0.260$ and $p(H=1|do(C=1))=0.120$, showing that hiring a candidate without prior conviction is more than twice more likely than hiring a prior convict. There is a strong causal effect of prior conviction $C$ on the hiring decision $H$, and therefore we find there is discrimination against prior convicts.
### Observation vs Intervention
Based on the notion of statistical parity, we find no discrimination, while with a causality viewpoint, we find discrimination. So why do we see this discrepancy? Consider a dataset of 1,000 candidates, and let’s compare two situations.
The first, termed Observation, is when the $E$, $C$, and $H$ values are distributed as in their observed joint probability distribution $p(H,E,C)$, also captured by the Bayesian network. This situation corresponds to the left half of the table. The number of candidates in the $E$, $C$ groups is governed by the joint distribution $p(E,C)$ shown in the table below. The number of hired candidates depends on the number of candidates in the $E$, $C$ groups and the hiring probability $p(H|E,C)$, also depicted; e.g., there are 30 candidates with $E=0, C=0$ and, because $p(H=1|E=0, C=0)=0.1$, only 3 among them are hired. Moreover, observe that a total 219 (resp. 72) out of 750 non-convicted (resp. 250 convicted) candidates are hired resulting in the two $p(H=1|C)$ probabilities being roughly equal. Note that the $p(H=1,E,C)$ probabilities match the observed ones shown in the beginning of this post.
In the second situation, termed Intervention, we’re making a $do(C)$ intervention. Specifically, in a random half of the candidates, we’re assigning a non-prior conviction $do(C=0)$, while in the other half we’re assigning a prior conviction $do(C=1)$. This situation represents an RCT, where the $do(C=0)$ half corresponds to World 0, while the $do(C=1)$ to World 1. This situation is depicted in the right half of the table, where the top (resp. bottom) is World 0 (resp. 1). The number of candidates in the $E$, $C$ groups has now changed, because we have intervened and manually set $C$ independent of $E$. The joint distribution now becomes $p(E,C) = p(E)\cdot p(C) = 0.5 \cdot p(E)$, since being assigned a prior conviction or not are equally likely. The following table shows the $p(E,C)$ under the intervention, and the hiring probability $p(H|E,C)$, which is unchanged.
The most significant change in Intervention concerns the prior convicted candidates. There are now twice as many previously convicted candidates. More importantly, there are five times as many prior convicts with high school education (the $E=1,C=1$ group). Because the algorithm hires candidates in this population group with a low probability $p(H=1|E=1,C=1)=0.05$, it turns out that the total number of prior convicts hired is less than before, even thought there are twice as many. Specifically, only 60 out of 500 prior convicts are hired, which results in the low interventional probability $p(H=1|do(C=1))=0.12$.
Note how the $p(H=1,E,C)$ probabilities in Intervention differ from the corresponding in Observation. This results in the discrepancy between the $p(H|C)$ and $p(H|do(C))$. Because we have made some causality assumptions, captured in the causal graph, we are able to derive $p(H|do(C))$ in Intervention from the probabilities in Observation.
### Alternate Causality Assumptions
Let’s now explore what would happen if we had made an alternate set of causality assumptions. Let’s now assume that the education level $E$ does not cause the prior conviction $C$, and rather it’s $C$ that causes $E$. This is our alternate assumption, possible not as plausible, but it serves to understand the implications of causality assumptions.
The alternate causal graph is shown below in the left part, where only the direction of the edge $E$,$C$ is reversed. This corresponds to a different factorization of the same joint distribution. Note that we do not show in the graph the marginal and conditional probability distributions.
Since just the causal graph has changed and all observations are still valid, the conditional hiring probability $p(H|C)$ given prior conviction is unchanged. Therefore, the hiring decision is still fair in terms of statistical parity.
Let’s now investigate fairness in terms of causality. To determine the effect of $C$ on $H$, we have to intervene on $C$, and compute $p(H|do(C))$. Graphically, this intervention means we have to sever all incoming edges to $C$. As there is none, we get the identical causal graph, shown in the right part of the figure. Because the causal graph has not changed, we now have that the interventional probability $p(H|do(C))$ is equal to the observational probability $p(H|C)$. Therefore, the hiring decision is also fair in terms of causality. No discrepancy this time.
So, we see that causality-based fairness crucially depends on the causality assumptions we introduce. In contrast, statistical parity is agnostic to any causality assumptions and only depends on the observed data.
As a general note, the initial causal assumptions suggest that $E$ is a common cause, or a confounder, of $C$ and $H$. Therefore, we have to control for $E$ in order to discover the causal effect of $C$ on $H$. In contrast, the alternate causal assumptions suggest that $E$ is just a mediator of the effect of $C$ on $H$. There are no common causes of $C$, so we don’t need to control for them. The observed relationship between $C$ and $H$ corresponds to their causal relationship.
In general, if fairness or discrimination is with respect to a variable (such as $C$ in our case) that is not caused by any other variable (as in the alternate causality assumptions), we will find no distinction between statistical parity and causality-based fairness. This is typically the case when we study discrimination in terms of attributes such as race and gender, whose assignment is random by nature.
|
2022-06-25 14:42:53
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 6, "x-ck12": 0, "texerror": 0, "math_score": 0.8431780338287354, "perplexity": 459.32769464656064}, "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/1656103035636.10/warc/CC-MAIN-20220625125944-20220625155944-00133.warc.gz"}
|
https://encyclopediaofmath.org/wiki/Partial_geometry
|
# Partial geometry
An incidence structure (cf. Incidence system) $S = ( P , L , I )$ in which the incidence relation between points and lines is symmetric and satisfies the following axioms:
1) each point is incident to $r$ lines, $r \geq 2$, and two distinct points are incident to at most one line;
2) each line is incident to $k$ points, $k \geq 2$;
3) through each point not incident to a line $l$ there are exactly $t \geq 1$ lines intersecting $l$.
If a partial geometry consists of $v$ points and $b$ lines, then
$$v = \frac{k [ ( k - 1 ) ( r - 1 ) + t ] }{t} \ \textrm{ and } \ \ b = \frac{r [ ( k - 1 ) ( r - 1 ) + t ] }{t} ,$$
and necessary conditions for the existence of such a partial geometry are that $( k - 1 ) ( r - 1 ) k r$ be divisible by $t ( k + r - t - 1 )$, $k ( k - 1 ) ( r - 1 )$ by $t$ and $r ( k - 1 ) ( r - 1 )$ by $t$( cf. [2]).
Partial geometries can be divided into four classes:
a) partial geometries with $t = k$ or (dually) $t = r$. Geometries of this type are just $2 - ( v , k , 1 )$- schemes or $2 - ( v , r , 1 )$- schemes (cf. Block design);
b) partial geometries with $t = k - 1$ or (dually) $t = r - 1$. In this case a partial geometry is the same thing as a net of order $k$ and defect $k - r + 1$( or dually);
c) partial geometries with $t = 1$, known as generalized quadrangles;
d) partial geometries with $1 < t < \min ( k - 1 , r - 1 )$.
#### References
[1] R.C. Bose, "Strongly regular graphs, partial geometries and partially balanced designs" Pacific J. Math. , 13 : 2 (1963) pp. 389–419 [2] J.A. Thas, "Combinatorics of partial geometries and generalized quadrangles" M. Aigner (ed.) , Higher Combinatorics , Reidel (1977) pp. 183–199 [3] J.A. Thas, "Construction of maximal arcs and partial geometries" Geometrica Dedicata , 3 : 1 (1974) pp. 61–64
|
2022-08-10 17:04:14
|
{"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": 0.8750987648963928, "perplexity": 824.3655800737035}, "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/1659882571198.57/warc/CC-MAIN-20220810161541-20220810191541-00421.warc.gz"}
|
https://physics.stackexchange.com/questions/377795/exact-solution-of-micropolar-fluid-for-poiseuille-flow
|
# Exact solution of micropolar fluid for Poiseuille flow
I am new here, so i wondered if you could help me with a sytem of ordinary equations with constant coefficients.
This model of equations refer to the well known Navier Stokes equations of fluid mechanics, but with a small discrimination. The original problem refers to a special category of fluids known as micropolar fluids. It considers the flow of a micropolar fluid between two parallel plates.
The general equations are these of conservation of momentum, mass, as well as one more equation of conservation of angular momentum.
The original probelm refers to the following (from book of 'Theory and applications of Micropolar Fluids' - by Grzegorz Lukaszewicz). To be more specific at page 24 of that book the general model is the following one: angular momentum and momentum conservation equations - modified Navier Stokes:
$$\rho(\frac{d\ u}{dt}+(u*\nabla)u)=-\nabla p+(\mu+μ_r)\nabla u+2\mu_r*rot\ ω+ρ*f ,\\ \rho I(\frac{d\ ω}{dt}+(u*\nabla)ω)=2\mu_r(rot\ u-2ω)+(c_0 + c_d - c_a)\nabla\ div\ ω+ (c_d + c_a)\Deltaω+ρg .$$
After the assumptions we made that $u=u(y) - ω=ω(y)$ and $p=p(x)$, from the equations above we finally obtain: -final system of ODE-
$$(\nu+ν_r)\frac{d^2\ u}{dy^2}+2ν_r\frac{d\ ω}{dy}=\frac{d\ p}{dx},\\ (c_d + c_a)\frac{d^2\ ω}{dy^2}-2ν_r(2ω+\frac{d\ u}{dy})=0.$$
Thats also what i am trying to solve and were i struggle most. Note that the derivative $dp/dx$ is constant. Also at page 217, where an exact solution to this problem has been introduced the author considers that $p$ should be such that so:
$$u(y) = 1-(\frac{y}{h})^2,$$
but what i need to do, is to have $\frac{dp}{dx}$ inside my final form of $u(y)$.
Please, i need your help. Really anything would be much appreciated. Thank you again!
We wish to find the general solution of $$(\nu+ν_r)\frac{d^2\ u}{dy^2}+2ν_r\frac{d\ ω}{dy}=\frac{d\ p}{dx} \\ (c_d + c_a)\frac{d^2\ ω}{dy^2}-2ν_r(2ω+\frac{d\ u}{dy})=0$$ What I will present here is a method for solution.
Firstly, to simplify, define $$a=\frac{2\nu_r}{\nu+\nu_r} \\ A=\frac{1} {\nu+\nu_r} \frac{dp}{dx} \\ b=\frac{2\nu_r} {c_d+c_a} \\ B=\frac{4\nu_r} {c_d+c_a}$$ thus $$\frac{d^2u} {dy^2} + a\frac{d\omega} {dy} = A \\ \frac{d^2\omega} {dy^2} - b\frac{du} {dy} - B\omega =0$$ Differentiating the second equation wrt $y$ yields $$\frac{d^3\omega} {dy^3} - b\frac{d^2u} {dy^2} - B\frac{d\omega}{dy}=0$$ and substituting from the first equation $$\frac{d^3\omega} {dy^3} - b\left[A-a\frac{d\omega} {dy} \right] - B\frac{d\omega}{dy}=0$$ which is a linear homogeneous ODE which can be solved by normal methods to obtain $\omega(y)$. This solution can then be substituted into $$\frac{d^2u} {dy^2} = A - a\frac{d\omega} {dy}$$ which implies $$u = \frac{Ay^2} {2} + const \cdot y + const - a\int \omega dy$$ and solving will give $u(y)$. Finally, substitute both solutions into $$\frac{d^2\omega} {dy^2} - b\frac{du} {dy} - B\omega =0$$ to find any remaining conditions on the constants of integration.
• Did you find the solution for $u$ and then substitute both into the final equation? – Eddy Jan 3 '18 at 21:03
|
2019-10-22 17:04:36
|
{"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": 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": 0.8384215831756592, "perplexity": 232.45454877105678}, "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-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00321.warc.gz"}
|
https://en.wikipedia.org/wiki/Talk:Oscillation_(mathematics)
|
# Talk:Oscillation (mathematics)
WikiProject Mathematics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Mid Importance
Field: Analysis
Why is it that for 1/x the oscillation is undefined at -∞ and +∞. I would naively think it is zero.67.171.64.190 09:27, 4 June 2007 (UTC)
You are correct. I noticed the same thing. Oleg Alexandrov (talk) 15:28, 4 June 2007 (UTC)
## Another notion of oscillation
There is also another notion -- oscillation of a function (say from a topological space to a metric space) defined by
$\inf\{d(f(U)); U\text{ is an open neighborhood of }x\}.$
(It is commonly used that the set of points of discontinuity is a $G_\delta$ set.) Do we have this notion defined in some other article on wiki? If not, perhaps an article oscillation of a function could be started. --Kompik 10:47, 7 October 2007 (UTC)
(Of course, d(A) in the above definition stands for diameter of a set A.) --Kompik 11:10, 7 October 2007 (UTC)
## is the convergence happened in oscillation
in any oscillating series convergence has happened eg:$1+(n^-n)/n$
## continuity
In addition to requiring zero oscillation, we need the function to be equal to the limiting value. Since oscillation is defined in terms of liminfs and limsups, apparently the value at the point is ignored. Tkuvho (talk) 07:51, 20 September 2010 (UTC)
I was going to say the same thing. — Preceding unsigned comment added by 186.18.76.220 (talk) 23:03, 23 September 2011 (UTC)
## An equivalent definition is missing
Another definition of oscillation is missing: Let f:I->R (where "I" is an interval contained in R). Then, its oscillation is: supremum(f(I))-infimum(f(I)). 46.19.85.55 (talk) 18:39, 10 August 2014 (UTC)
## same as wave envelope?
merge? Fgnievinski (talk) 00:14, 13 October 2014 (UTC)
|
2015-12-01 22:47:16
|
{"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": 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": 0.9066798090934753, "perplexity": 1812.2142149641916}, "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-2015-48/segments/1448398471441.74/warc/CC-MAIN-20151124205431-00083-ip-10-71-132-137.ec2.internal.warc.gz"}
|
https://www.acmicpc.net/problem/10542
|
시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 256 MB66015612030.227%
문제
Mafia is a social game played frequently by high school competitors in informatics on summer and winter camps and national competitions, usually very late at night, drinking various fruit sodas. This game is not about winning, it's about los taking part, like in competitions.
To solve this task, you don't need to know the rules of mafia; all you need to know is that some of the players are "mobsters" and the rest are "civilians". The mobsters know who is who, but the civilians don't. The civilians are trying to figure out who the mobsters are during the game.
In the current round of the game, out of N surviving players so far, each one has accused exactly one other player saying that he is the mobster. The civilians were only guessing and the mobsters have accused civilians, pretending to know nothing.
Not knowing who the mobsters are, but knowing who accused whom, determine the maximum possible number of mobsters among these players!
입력
The first line of input contains the integer N (2 < N < 500 000), the number of players. The players are labeled with integers from 1 to N.
The Kth line of input, out of the following N lines, contains the label of the player accused by the player K. (No player can accuse themselves.)
출력
The first and only line of output must contain the maximum possible number of mobsters.
예제 입력 1
3
2
1
1
예제 출력 1
2
예제 입력 2
3
2
3
1
예제 출력 2
1
예제 입력 3
7
3
3
4
5
6
4
4
예제 출력 3
4
힌트
Clarification of the first sample test: The mobster can be player 2 and 3.
Clarification of the second sample test: The mobster can be any player, but there cannot be more of them because that would mean that one of them accused the other.
|
2023-02-08 01:44:51
|
{"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": 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": 0.19662639498710632, "perplexity": 2692.9963230352737}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500664.85/warc/CC-MAIN-20230207233330-20230208023330-00581.warc.gz"}
|
https://tex.stackexchange.com/questions/133011/strange-color-in-pstricks
|
# Strange color in PSTricks
I draw a figure in pstricks, the code is here:
\documentclass{minimal}
\usepackage[dvipsnames]{pstricks}
\definecolor{bg}{cmyk}{0,0,0.1,0}
\begin{document}
\begin{pspicture}[linewidth=1.5pt](-2,-1.5)(10,4)
\psclip{\psellipse(2.2,1)(2,1.5)}
\psellipse[fillcolor=blue!20,fillstyle=solid](4.3,1)(2,1.5)
\endpsclip
\psellipse[linecolor=Green](4.3,1)(2,1.5)
\psellipse[linecolor=yellow](2.2,1)(2,1.5)
\psframe[linecolor=blue](-1.5,-1.5)(8,4)
\psframe[linecolor=Maroon,fillstyle=solid](2.8,0.3)(3.8,1.2)
\end{pspicture}
\end{document}
But the yellow ellipse is with not pure yellow, but with some black inside. I tried to change to other color, but it is always there. Why is it like this?
That's because your clipping polygon/curve has some line width. Remove the line width (linewidth=none) and you'll be fine:
\documentclass{article}
\usepackage[dvipsnames]{pstricks}% http://tug.org/PSTricks/main.cgi/
\begin{document}
\noindent
\begin{pspicture}[linewidth=1.5pt](-2,-1.5)(10,4)
\psclip{\psellipse(2.2,1)(2,1.5)}
\psellipse[fillcolor=blue!20,fillstyle=solid](4.3,1)(2,1.5)
\endpsclip
\psellipse[linecolor=Green](4.3,1)(2,1.5)
\psellipse[linecolor=yellow](2.2,1)(2,1.5)
\rput{0}(0,-2){
\psclip{\psellipse[linestyle=none](2.2,1)(2,1.5)}
\psellipse[fillcolor=blue!20,fillstyle=solid](4.3,1)(2,1.5)
\endpsclip
\psellipse[linecolor=Green](4.3,1)(2,1.5)
\psellipse[linecolor=yellow](2.2,1)(2,1.5)
}
\end{pspicture}
\end{document}
This is technically a non-issue, since both polygons/curves are drawn on top of one another with the same line width. The visual may show some border at certain zoom levels... however, this is barely at higher zoom levels (the NW-SE line has some visible remnants on the NE side):
• @Ginger: It actually becomes more evident that the clipping path is redrawn an entirely visible if it doesn't match the path to be clipped. That is, use something like \psframe(1,0)(5,3) for the clipping path and you'll see the entire frame still visible. However, setting linestyle=none still clips, but without the path showing. Some people prefer linewidth=0pt, but you may find some residual line showing. – Werner Sep 12 '13 at 17:20
• this way the problem still exists for the left part of the green ellipse. – Ginger Sep 12 '13 at 17:58
|
2020-06-05 04:28:31
|
{"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": 0.7413191199302673, "perplexity": 1753.0002091867777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348492427.71/warc/CC-MAIN-20200605014501-20200605044501-00250.warc.gz"}
|
http://physics.stackexchange.com/questions/44914/isnt-it-incorrect-for-the-minimal-gauge-coupling-and-related-calculations-in-pr?answertab=oldest
|
# Isn't it incorrect for the minimal gauge coupling and related calculations in Prof. Ezawa's book on quantum Hall effect?
He is CORRECT. I use $\mathbf{B}=\left(0,0,B_{\perp}\right)$ and he use $\mathbf{B}=\left(0,0,-B_{\perp}\right)$. $B_{\perp}>0$.
# Nov.28.2012
Basically I got mad with conventions.
1.Here is the link of the book (second edition):
Here is another link for one of his review articles:
http://iopscience.iop.org/0034-4885/72/8/086502
2.I am not happy with the negative sign of the commutator $\left[X,Y\right]=-il_{B}^{2}$. Here is my calculation:
$\left[X,Y\right]=\left(\left[x,p_{x}\right]+\left[-p_{y},y\right]\right)/eB+\left[-P_{y},P_{x}\right]/e^{2}B^{2}=il_{B}^{2}$
3.In my calculation, I used some conventions different from Prof.Ezawa's book and article. Here is my convention:
$X:=x-P_{y}/eB\;;\; Y:=y+P_{x}/eB$
However, Prof.Ezawa use this convention:
$X:=x+P_{y}/eB\;;\; Y:=y-P_{x}/eB$
To be prepared for being driven mad, please compare them carefully.
4.I think he must be wrong somewhere, for example, in his book (2nd.ed), (10.2.5) and in his article (2.15)
$\left[P_{x},P_{y}\right]=i\hbar^{2}/l_{B}^{2}$
but you know we use minimal coupling $\mathbf{p}\rightarrow\mathbf{p}-\frac{q}{c}\mathbf{A}$ in this problem, $q=-e,e>0,{\mathbf{p}+\frac{e}{c}\mathbf{A}}$ for electrons, as Prof.Ezawa suggested in his book (10.2.3) and his article (2.12). Under this convention, I calculated $\left[P_{x},P_{y}\right]$ as following:
$\left[P_{x},P_{y}\right]=-i\hbar e\left(\left[\partial_{x},A_{y}\right]+\left[A_{x},\partial_{y}\right]\right)/c=-i\hbar eB/c=-i\hbar^{2}/l_{B}^{2}$
Oh my god here is a negative sign.
5.To summarize, I think if we take Prof.Ezawa's convention and apply his result for $\left[P_{x},P_{y}\right]=i\hbar^{2}/l_{B}^{2}$ during the calculation of $\left[X,Y\right]$, we will get his result. But his result for $\left[P_{x},P_{y}\right]=i\hbar^{2}/l_{B}^{2}$ seems not correct.
6.Someone save my day...
-
I have found another check for the expression (2.14) in Prof.Ezawa's article. If we solve the cyclotron motion problem for a classical particle with negative charge, we will find $\left(R_{x},R_{y}\right)=\left(P_{y},-P_{x}\right)/m\omega_{c}$, which indicates that the sign used in these expressions are inappropriate. – Yunlong Lian Nov 23 '12 at 11:37
I have done this calculation some time ago. My convention was:
$$X = x - \frac{P_y}{m \omega_c}\quad Y = y + \frac{P_x}{m \omega_c}$$ and $$P_i = p_i +\frac{e}{c} A_i$$
And the magnetic field is $B = \nabla \wedge A = B_z \hat{z}$. Note that in particular: $X = x-\frac{1}{m\omega_c}(p_i + \frac{e}{c}A_i)$. My notes say that this gives:
$$[X, Y] = i l_B^2\qquad \text{and}\qquad [P_x,P_y] = -\frac{i}{l_B^2}$$
If you now take his convention, you essentially flip the magnetic field, $\vec{B} \rightarrow -\vec{B}$. This replaces:
$$X = x + \frac{P_y}{m \omega_c}\quad Y = y - \frac{P_x}{m \omega_c}$$
but you still have $P_i = p_i +\frac{e}{c} A_i$ -- that stays the same. Therefore we have: $X = x+\frac{1}{m\omega_c}(p_i + \frac{e}{c}A_i)$ (!!!! compare this to the other convention), and to compute the commutator we get:
\begin{align}[X,Y] &= \left[x+\frac{1}{m\omega_c}(p_y + \frac{e}{c}A_y),y-\frac{1}{m\omega_c}(p_x + \frac{e}{c}A_x)\right] \\ &= (-[x,p_x] + [p_y,y])/m\omega_c + \frac{e}{c (m\omega_c)^2}(-[p_y,A_x]+[A_y,p_x]) \end{align} Now, $[x,p_x] = i$, as always. The other commutator depends on the orientation of the magnetic field: $$-[p_y,A_x]+[A_y,p_x] = i ([\nabla_y, A_x] - [\nabla_x, A_y]) = -i(\nabla\wedge A)_z = iB_z$$, and so you get
$$[X,Y] = -\frac{2i}{m\omega_c} + \frac{e}{c (m\omega_c)^2} iB_z = -i l_B^2$$
Long story short: your derivation of $[X,Y]$ does not apply to his conventions. Your conve
Final note: If you switch conventions, you essentially replace $B_z \rightarrow -B_z$, so the magnetic length and cyclotron frequency also switch sign, $l_B^2\rightarrow -l_B^2$ and $\omega_c \rightarrow - \omega_c$. So you see that both commutators (involving $X$ and $Y$ and $P_x$ and $P_y$) pick up a minus sign, because they both involve $l_B^2$.
-
To further save my N-page calculation based on Ezawa, I came up with another idea - not to flip the B field, but to do a spatial reflection, or change the handness of the xyz-coord frame. Hope you know it :D – Yunlong Lian Nov 24 '12 at 7:37
|
2015-05-25 23:54:50
|
{"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9396248459815979, "perplexity": 486.44676437907515}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928729.99/warc/CC-MAIN-20150521113208-00125-ip-10-180-206-219.ec2.internal.warc.gz"}
|
https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphical-system-of-inequalities
|
# Intro to graphing systems of inequalities
CCSS Math: HSA.REI.D.12
## Video transcript
Graph the solution set for this system. It's a system of inequalities. We have y is greater than x minus 8, and y is less than 5 minus x. Let's graph the solution set for each of these inequalities, and then essentially where they overlap is the solution set for the system, the set of coordinates that satisfy both. So let me draw a coordinate axes here. So that is my x-axis, and then I have my y-axis. And that is my y-axis. And now let me draw the boundary line, the boundary for this first inequality. So the boundary line is going to look like y is equal to x minus 8. But it's not going to include it, because it's only greater than x minus 8. But let's just graph x minus 8. So the y-intercept here is negative 8. When x is 0, y is going to be negative 8. So just go negative 1, negative 2, 3, 4, 5, 6, 7, 8. So that is negative 8. So the point 0, negative 8 is on the line. And then it has a slope of 1. You don't see it right there, but I could write it as 1x. So the slope here is going to be 1. I could just draw a line that goes straight up, or you could even say that it'll intersect if y is equal to 0, if y were equal to 0, x would be equal to 8. So 1, 2, 3, 4, 5, 6, 7, 8. And so this is x is equal to 8. If it has a slope of 1, for every time you move to the right 1, you're going to move up 1. So the line is going to look something like this. And actually, let me not draw it as a solid line. If I did it as a solid line, that would actually be this equation right here. But we're not going to include that line. We care about the y values that are greater than that line. So what we want to do is do a dotted line to show that that's just the boundary, that we're not including that in our solution set. Let me do this in a new color. So this will be the color for that line, or for that inequality, I should say. So that is the boundary line. And this says y is greater than x minus 8. So you pick an x, and then x minus 8 would get us on the boundary line. And then y is greater than that. So it's all the y values above the line for any given x. So it'll be this region above the line right over here. And if that confuses you, I mean, in general I like to just think, oh, greater than, it's going to be above the line. If it's less than, it's going to be below a line. But if you want to make sure, you can just test on either side of this line. So you could try the point 0, 0, which should be in our solution set. And if you say, 0 is greater than 0 minus 8, or 0 is greater than negative 8, that works. So this definitely should be part of the solution set. And you could try something out here like 10 comma 0 and see that it doesn't work. Because you would have 10 minus 8, which would be 2, and then you'd have 0. And 0 is not greater than 2. So when you test something out here, you also see that it won't work. But in general, I like to just say, hey look, this is the boundary line, and we're greater than the boundary line for any given x. Now let's do this one over here. Let's do this one. The boundary line for it is going to be y is equal to 5 minus x. So the boundary line is y is equal to 5 minus x. So once again, if x is equal to 0, y is 5. So 1, 2, 3, 4, 5. And then it has a slope of negative 1. We could write this as y is equal to negative 1x plus 5. That's a little bit more traditional. So once again, y-intercept at 5. And it has a slope of negative 1. Or another way to think about it, when y is 0, x will be equal to 5. So 1, 2, 3, 4, 5. So every time we move to the right one, we go down one because we have a negative 1 slope. So it will look like this. And once again, I want to do a dotted line because we are-- so that is our dotted line. And I'm doing a dotted line because it says y is less than 5 minus x. If it was y is equal to 5 minus x, I would have included the line. If it was y is less than or equal to 5 minus x, I also would have made this line solid. But it's only less than, so for any x value, this is what 5 minus x-- 5 minus x will sit on that boundary line. But we care about the y values that are less than that, so we want everything that is below the line. And once again, you can test on either side of the line. 0, 0 should work for this second inequality right here. 0 is indeed less than 5 minus 0. 0 is less than 5. And then you could try something like 0, 10 and see that it doesn't work, because if you had 10 is less than 5 minus 0, that doesn't work. So it is everything below the line like that. And like we said, the solution set for this system are all of the x's and y's, all of the coordinates that satisfy both of them. So all of this shaded in purple satisfies the second inequality. All of this shaded in green satisfies the first inequality. So the stuff that satisfies both of them is their overlap. So it's all of this region in blue. Hopefully this isn't making it too messy. All of this region in blue where the two overlap, below the magenta dotted line on the left-hand side, and above the green magenta line. That's only where they overlap. So it's only this region over here, and you're not including the boundary lines.
|
2018-11-21 10:21:13
|
{"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": 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": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7023707032203674, "perplexity": 166.7386850031073}, "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-2018-47/segments/1542039747665.82/warc/CC-MAIN-20181121092625-20181121114625-00427.warc.gz"}
|
https://stacks.math.columbia.edu/tag/0D6K
|
Lemma 21.22.2. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. The functors $R\Gamma (\mathcal{C}, -)$ and $R\Gamma (U, -)$ for $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$ commute with $R\mathop{\mathrm{lim}}\nolimits$. Moreover, there are short exact sequences
$0 \to R^1\mathop{\mathrm{lim}}\nolimits H^{m - 1}(U, K_ n) \to H^ m(U, R\mathop{\mathrm{lim}}\nolimits K_ n) \to \mathop{\mathrm{lim}}\nolimits H^ m(U, K_ n) \to 0$
for any inverse system $(K_ n)$ in $D(\mathcal{O})$ and $m \in \mathbf{Z}$. Similar for $H^ m(\mathcal{C}, R\mathop{\mathrm{lim}}\nolimits K_ n)$.
Proof. The first statement follows from Injectives, Lemma 19.13.6. Then we may apply More on Algebra, Remark 15.85.9 to $R\mathop{\mathrm{lim}}\nolimits R\Gamma (U, K_ n) = R\Gamma (U, R\mathop{\mathrm{lim}}\nolimits K_ n)$ to get the short exact sequences. $\square$
Comment #3274 by Kevin Carlson on
Suggested slogan: Cohomology commutes with derived limits
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
|
2021-04-22 02:54:21
|
{"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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9581534266471863, "perplexity": 714.3307657280571}, "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/1618039560245.87/warc/CC-MAIN-20210422013104-20210422043104-00560.warc.gz"}
|
https://www.gamedev.net/forums/topic/565370-texture-mapping-in-software-rasterizer/
|
# Texture mapping in software rasterizer
## Recommended Posts
I am having an issue in my software renderer where if I draw a triangle or a quad that isn't parallel to the viewport, the texture will skew rather than do a perspective correct transformation. As the image below shows, along the boundaries of the triangles in the quads, the texture skews; if the quad was a parallelogram, the texture would fit without distortion. But, as it is a trapezoid, the two triangles have mismatched skewed images. The image is looking inside of a cube with the nearest face culled; the quad farthest away is a scaled down version of what the texture would look like. http://i871.photobucket.com/albums/ab274/Ectara/comp.png The question I'm wondering is, is there any sort of transformation I could be applying to the texture coordinates to gain the correct information to rotate the texture coordinates or something? Bear in mind, I do have a modelview matrix, but using it doesn't guarantee that the triangle won't just be drawn skew to the viewport plane to begin with.
##### Share on other sites
you are right,its not perspective correct interpolated. lookup for perspective vorrect texture interpolation on google, there are plenty of tutorials, like those from chris hecker.
##### Share on other sites
Thanks Krypt0n. I tried looking it up, and implementing the concepts found several times. But, all the formulas I could find use the so-called "poor man's projection"( x/z, y/z, 1/z). Mine uses a projection matrix and a homogenous divide by w. I can't seem to figure out how to implement this with my setup.
##### Share on other sites
You have to interpolate (u/w, v/w, 1/w) and homogenize it by dividing through 1/w at the end.
##### Share on other sites
Quote:
Original post by EctaraThanks Krypt0n. I tried looking it up, and implementing the concepts found several times. But, all the formulas I could find use the so-called "poor man's projection"( x/z, y/z, 1/z). Mine uses a projection matrix and a homogenous divide by w. I can't seem to figure out how to implement this with my setup.
I've asked a similar question some time ago
http://www.gamedev.net/community/forums/topic.asp?topic_id=564019
there you have some links and explanation how to interpolate UVs (but ginkgo's explanation is kinda the short version :) ).
maybe you could tell me how you interpolate z in your none-poor-man's rasterizer.
It's working for me with just linear interpolation, but I was sure it cannot be interpolated linearly :/
##### Share on other sites
For getting perspective correct you need to divide by a linearly interpolated value for each pixel.
// Setup values needed for each scanline float uw = ..., vw = ..., w = ... float duw = ..., dvw = ..., dw = ... // Plot each pixel in scanline for x in scanline { float u = uw / w fluat v = vw / w plot(x, y, texture(u, v)) uw += duw vw += dvw w += dw }
Where w are the same w you use for position. You should be able to calculate the rest of the values.
[Edited by - mzeo77 on March 18, 2010 6:29:11 AM]
##### Share on other sites
As for my projection function:
void E_renderProject(vector3 world, vector3 screen){ vector4 v; /*These transform functions multiply {arg2[0],arg2[1],arg2[2],1.0f} by the matrix pointed to by the first argument, and the result is copied to the third argument*/ E_renderTransformVector34(E_globalRenderContext.raster.model, world, v); /* Point is not visible, don't bother. */ if(!E_renderClipFrustumPoint(v)){ screen[0] = screen[1] = screen[2] = -1; return; } /*Likewise, but with {arg2[0],arg2[1],arg2[2],arg2[3]}*/ E_renderTransformVector4(E_globalRenderContext.raster.projection, v, v); /* Don't divide by zero, but don't raise an error; this could occur normally, I'd suppose. Set it to zero to give a clue that it failed.*/ if(!v[3]){ _E_vectorClear(screen); return; } /*Divide X, Y, and Z by W*/ _E_vectorDivideScalar(v,v[3],v); v[0] = v[0] * 0.5f + 0.5f; v[1] = v[1] * 0.5f + 0.5f; v[2] = v[2] * 0.5f + 0.5f; v[0] *= E_globalRenderContext.display->image->width; v[1] *= E_globalRenderContext.display->image->height; v[1] = E_globalRenderContext.display->image->height - v[1]; if(v[2] > 1){ v[0] = -v[0]; v[1] = -v[1]; } /* In this line, the w coordinate is discarded. Only using 3D for now. */ _E_vectorCopy(screen,v);}
Then, to interpolate Z later on, I lerp 1/Z. Note that the W is discarded. Should I be keeping the extra dimension for each vertex?
##### Share on other sites
Thanks gingko, ProfL, and mzeo77 for the advice. Modified a projection function and a couple structures to use the w coordinate, and interpolated using homogeneity that way. It is now evident that the w coordinate should not be discarded after projection, and the formulae in Wikipedia and such are unusable for my purposes. I got it working, and here's a before and after image: http://i871.photobucket.com/albums/ab274/Ectara/comp.png. For the interpolation, I used pretty much the same algorithm from Wikipedia, except with 'w' replacing 'z', and several optimizations.
## Create an account
Register a new account
• ### Forum Statistics
• Total Topics
628377
• Total Posts
2982325
• 10
• 9
• 14
• 24
• 11
|
2017-11-23 18:55:27
|
{"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": 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": 0.24748867750167847, "perplexity": 2735.264753564534}, "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/1510934806856.86/warc/CC-MAIN-20171123180631-20171123200631-00585.warc.gz"}
|
https://www.gamedev.net/forums/topic/522018-matrix/
|
# matrix
This topic is 3459 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
hy. I have a matrix in collada file like this: <matrix>1 0 0 0.47476 0 0 -1 -0.480625 0 1 0 -0.122112 0 0 0 1</matrix> how ransform it for apply the position transform in directx? THe matrix must be colum major or row major(is correct the term?) And how transform a 16 element array tro a D3DXMATRIX? THanks.
##### Share on other sites
D3D uses row vectors/matrices and row major order. Collada uses column matrices but in row major order (if I remember correctly). So you cannot simply load a Collada matrix into a D3D matrix memory and be happy.
E.g. a sequence of elements in Collada like
{ a b c d e f g h i j k l m n o p }
has an equivalent in D3D like
{ a e i m b f j n c g k o d h l p }
(if I made no error ;) )
The mathematical operation to correct this is the transposition. So the simplest way may be to load the D3D matrix storage with the Collada co-efficients and to apply D3DXMatrixTranspose(...). Of course, you can already use the above scheme and put the co-efficients one by one into the correct place during reading the Collada matrix.
##### Share on other sites
and , i have a z_up document, and i would transform to a y_up , then i must invert y with z and negate y:
x,z,-y how do the same with matrix?
thanks.
##### Share on other sites
To map (x,y,z,w) to (x,z,-y,w) you need a (row) matrix as follows:
[ 1 0 0 0 ][ 0 0 -1 0 ][ 0 1 0 0 ][ 0 0 0 1 ]
Notice please that I've completed the vectors by the homogeneous co-ordinate w, since D3D matrices are homogeneous (i.e. 4x4 elements). You should take the time and perform the multiplication on paper once to see how it works.
##### Share on other sites
thanks , but what i do with this matrix?
i have a direct3d matrix ?
dxTransp._11 = vPosition[posRot][0];dxTransp._12 = vPosition[posRot][4];dxTransp._13 = vPosition[posRot][8];dxTransp._14 = vPosition[posRot][12];dxTransp._21 = vPosition[posRot][1];dxTransp._22 = vPosition[posRot][5];dxTransp._23 = vPosition[posRot][9];dxTransp._24 = vPosition[posRot][13];dxTransp._31 = vPosition[posRot][2];dxTransp._32 = vPosition[posRot][6];dxTransp._33 = vPosition[posRot][10];dxTransp._34 = vPosition[posRot][14];dxTransp._41 = vPosition[posRot][3];dxTransp._42 = vPosition[posRot][11];dxTransp._43 = -vPosition[posRot][7];// for the translations i'm inverted they/xdxTransp._44 = vPosition[posRot][15];
for the translate all is ok( i flip 42 with 43 and negate 43), but for the scale and the rotate what change i do(what i flip and what negate) in the matrix?
Thanks
##### Share on other sites
Quote:
Original post by haegarrTo map (x,y,z,w) to (x,z,-y,w) you need a (row) matrix as follows:[ 1 0 0 0 ][ 0 0 -1 0 ][ 0 1 0 0 ][ 0 0 0 1 ]Notice please that I've completed the vectors by the homogeneous co-ordinate w, since D3D matrices are homogeneous (i.e. 4x4 elements). You should take the time and perform the multiplication on paper once to see how it works.
I'm not understand , what I do with this matrix?I must multiply it for my matrix?
why?
Thanks.
nobody?
nobody?
nobody?
1. 1
2. 2
3. 3
frob
20
4. 4
JoeJ
20
5. 5
• 11
• 11
• 12
• 13
• 9
• ### Forum Statistics
• Total Topics
632213
• Total Posts
3004848
×
|
2018-08-22 03:08:54
|
{"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": 0.42090725898742676, "perplexity": 2925.5515365923143}, "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/1534221219469.90/warc/CC-MAIN-20180822030004-20180822050004-00620.warc.gz"}
|
https://community.spirit-project.com/topic/290/tests/
|
# Tests
nitely
Esteban C Borsani
• 18 Jan '18
If you are here to try out the replies and topics creation, then please do it within the Testing Ground category.
nitely closed this 3 years, 6 months ago
nitely pinned this 3 years, 6 months ago
|
2021-08-04 22:01:21
|
{"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": 0.8840920329093933, "perplexity": 8445.947855776263}, "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/1627046155188.79/warc/CC-MAIN-20210804205700-20210804235700-00254.warc.gz"}
|
https://math.stackexchange.com/questions/2714748/open-subsets-of-a-irreducible-topological-space
|
# Open subsets of a irreducible topological space
I have this problem:
"Show that a topological space X$\neq\emptyset$ is irreducible $\Leftrightarrow$ $\forall$ U open subset of X, U is connected. "
I can easily prove the $\Rightarrow$ part, using that every open subset of an irreducible space is itself irreducible (therefore connected).
But what about the $\Leftarrow$ part? I have no idea how to prove it, and to be fair I'm not even sure it's true.
Thanks everybody!
• Welcome to math stack exchange! – Peter Mar 30 '18 at 14:38
Suppose $U$ is non-empty open and disconnected so that $U =U_1 \cup U_2$, where $U_1$ and $U_2$ are non-empty disjoint and open in $U$ (and so also open in $X$).
Then $X = (X\setminus U_1) \cup (X\setminus U_2)$ (as $U_1$ and $U_2$ are disjoint) and both sets are closed and proper (as both $U_i$ are non-empty). This contradicts that $X$ is irredicible.
So all non-empty open $U$ are connected.
The other direction is similar. Suppose $X$ has no open disconnected subsets and suppose that $X = F_1 \cup F_2$ where $F_1$ and $F_2$ are proper non-empty closed sets. Then (by de Morgan) $$\emptyset = (X\setminus F_1) \cap (X\setminus F_2)$$
so $$U = (X\setminus F_1) \cup (X\setminus F_2)$$ is an open set that is disconnected (as both sets in this union are non-empty proper open subsets of $U$). This contradiction shows that $X$ is irreducible.
Let $A$, $B$ be any two non-empty open sets in $X$. Then, $A\cup B$ is open and non-empty, and thus connected. So $A\cap B\ne\emptyset$.
• Does that mean, that the other direction is valid as well ? – Peter Mar 30 '18 at 14:35
• @Peter Indeed. Irreducible $\Leftrightarrow$ all open are connected $\Leftrightarrow$ all non-empty open are dense. – user228113 Mar 30 '18 at 14:36
• OK, I have overseen the "for all" – Peter Mar 30 '18 at 14:37
|
2019-08-19 08:38:16
|
{"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": 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": 0.9713106751441956, "perplexity": 215.83607913873513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314696.33/warc/CC-MAIN-20190819073232-20190819095232-00523.warc.gz"}
|
https://listserv.uni-heidelberg.de/cgi-bin/wa?A2=ind1110&L=latex-l&D=0&P=31304
|
## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE
#### View:
Message: [ First | Previous | Next | Last ] By Topic: [ First | Previous | Next | Last ] By Author: [ First | Previous | Next | Last ] Font: Proportional Font
Subject:
Re: Strings, and regular expressions
From:
Date:
Sun, 16 Oct 2011 22:02:24 +0100
Content-Type:
text/plain
Parts/Attachments:
text/plain (25 lines)
On 10/10/2011 16:07, Bruno Le Floch wrote: > The l3regex module allows for testing if a string matches a given > regular expression, counting matches, extracting submatches, splitting > at occurrences of a regular expression, and doing replacement (see > documentation for function names). I'm not sure about the approach on submatches. You say % Submatches with numbers higher than $10$ are accessed in the same way, % namely |\10|, |\11|, \emph{etc}. To insert in the replacement text % a submatch followed by a digit, the digit must be entered using the % |\x| escape sequence: for instance, to get the first submatch followed % by the digit $7$, use |\1\x37|, because $7$ has character code |37| % (in hexadecimal). I wonder how likely it is that we'll need more than 9 submatches in the sort of scenario that l3regex is likely to applied in. TeX programmers are already used to the idea that we have up to 9 numbered parameters, so why not limit to nine submatches and avoid the need to use "\x" syntax? I wonder if \regex_set:Nn would be better as \regex_save:Nn. My reasoning is that \_set:Nn functions are used with a variable of name \l_..._, while here we are (currently) naming as \l_..._tl. -- Joseph Wright
|
2019-09-22 11:08:44
|
{"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": 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": 0.7563648223876953, "perplexity": 4434.244120559363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575484.57/warc/CC-MAIN-20190922094320-20190922120320-00010.warc.gz"}
|
https://hugyourhouse.co.uk/gw-forums-uvvmzzh/37l68.php?cf6669=what-is-the-degree-of-a-zero-polynomial
|
Dec
## what is the degree of a zero polynomial
Posted on December 6th, 2020
All of the above are polynomials. In general g(x) = ax3 + bx2 + cx + d, a â 0 is a quadratic polynomial. Any non - zero number (constant) is said to be zero degree polynomial if f(x) = a as f(x) = ax, where a â 0 .The degree of zero polynomial is undefined because f(x) = 0, g(x) = 0x , h(x) = 0x. The highest degree of individual terms in the polynomial equation with non-zero coefficients is called the degree of a polynomial. To find the degree all that you have to do is find the largest exponent in the given polynomial.Â. For example, 3x + 5x2 is binomial since it contains two unlike terms, that is, 3x and 5x2. })(); What type of content do you plan to share with your subscribers? Here the term degree means power. Featured on Meta Opt-in alpha test for a new Stacks editor The highest degree exponent term in a polynomial is known as its degree. Example 1. In this article you will learn about Degree of a polynomial and how to find it. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. If the rational number $$\displaystyle x = \frac{b}{c}$$ is a zero of the $$n$$ th degree polynomial, $P\left( x \right) = s{x^n} + \cdots + t$ where all the coefficients are integers then $$b$$ will be a factor of $$t$$ and $$c$$ will be a factor of $$s$$. When all the coefficients are equal to zero, the polynomial is considered to be a zero polynomial. Monomials âAn algebraic expressions with one term is called monomial hence the name âMonomial. The degree of each term in a polynomial in two variables is the sum of the exponents in each term and the degree of the polynomial is the largest ⦠Any non - zero number (constant) is said to be zero degree polynomial if f(x) = a as f(x) = ax 0 where a â 0 .The degree of zero polynomial is undefined because f(x) = 0, g(x) = 0x , h(x) = 0x 2 etc. Steps to Find the Leading Term & Leading Coefficient of a Polynomial. Every polynomial function with degree greater than 0 has at least one complex zero. In general g(x) = ax + b , a â 0 is a linear polynomial. You will agree that degree of any constant polynomial is zero. 1 b. linear polynomial) where $$Q(x)=x-1$$. So, degree of this polynomial is 3. Let a â 0 and p(x) be a polynomial of degree greater than 2. The addition, subtraction and multiplication of polynomials P and Q result in a polynomial where, Degree(P ± Q) ⤠Degree(P or Q) Degree(P × Q) = Degree(P) + Degree(Q) Property 7. Ignore all the coefficients and write only the variables with their powers. Thus, $$d(x)=\frac{x^{2}+2x+2}{x+2}$$ is not a polynomial any way. var s = document.getElementsByTagName('script')[0]; deg[p(x).q(x)]=$$-\infty$$ | {$$2+{-\infty}={-\infty}$$} verified. Polynomial degree can be explained as the highest degree of any term in the given polynomial. In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. gcse.async = true; A polynomial of degree one is called Linear polynomial. Clearly this is suggestive of the zero polynomial having degree $- \infty$. Like anyconstant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial. clearly degree of r(x) is 2, although degree of p(x) and q(x) are 3. If we multiply these polynomial we will get $$R(x)=(x^{2}+x+1)\times (x-1)=x^{3}-1$$, Now it is easy to say that degree of R(x) is 3. Checking each term: 4z 3 has a degree of 3 (z has an exponent of 3) 5y 2 z 2 has a degree of 4 (y has an exponent of 2, z has 2, and 2+2=4) 2yz has a degree of 2 (y has an exponent of 1, z has 1, and 1+1=2) The largest degree of those is 4, so the polynomial has a degree of 4 It is a solution to the polynomial equation, P(x) = 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. (exception: zero polynomial ). Hence, the degree of this polynomial is 8. let P(x) be a polynomial of degree 3 where $$P(x)=x^{3}+2x^{2}-3x+1$$, and Q(x) be another polynomial of degree 2 where $$Q(x)=x^{2}+2x+1$$. Zero degree polynomial functions are also known as constant functions. We have studied algebraic expressions and polynomials. Trinomials â An expressions with three unlike terms, is called as trinomials hence the name âTriânomial. Names of Polynomial Degrees . Zero Polynomial. Hence, degree of this polynomial is 3. var gcse = document.createElement('script'); Furthermore, 21x. let $$p(x)=x^{3}-2x^{2}+3x$$ be a polynomial of degree 3 and $$q(x)=-x^{3}+3x^{2}+1$$ be a polynomial of degree 3 also. The Standard Form for writing a polynomial is to put the terms with the highest degree first. A non-zero constant polynomial is of the form f(x) = c, where c is a non-zero real number. f(x) = 7x2 - 3x + 12 is a polynomial of degree 2. thus,f(x) = an xn + an-1 xn-1 + an-2xn-2 +...................+ a1 x + a0  where a0 , a1 , a2 â¦....an  are constants and an â 0 . Check which the largest power of the variable and that is the degree of the polynomial. For example, P(x) = x 5 + x 3 - 1 is a 5 th degree polynomial function, so P(x) has exactly 5 ⦠Each factor will be in the form $\left(x-c\right)$ where c is a complex number. A âzero of a polynomialâ is a value (a number) at which the polynomial evaluates to zero. - [Voiceover] So, we have a fifth-degree polynomial here, p of x, and we're asked to do several things. Hence degree of d(x) is meaningless. Although, we can call it an expression. Answer: Polynomial comes from the word âpolyâ meaning "many" and ânomialâ meaning "term" together it means "many terms". The degree of the zero polynomial is undefined, but many authors ⦠If â2 is a zero of the cubic polynomial 6x3 + â2x2 â 10x â 4â2, the find its other two zeroes. Example: Find the degree of the polynomial 6s 4 + 3x 2 + 5x +19. Rather, the degree of the zero polynomial is either left explicitly undefined, or defined as negative (either â1 or ââ). It has no nonzero terms, and so, strictly speaking, it has no degree either. Types of Polynomials Based on their DegreesÂ, : Combine all the like terms variables Â. The other degrees ⦠Answer: The degree of the zero polynomial has two conditions. + bx + c, a â 0 is a quadratic polynomial. The degree of the zero polynomial is undefined. In general, a function with two identical roots is said to have a zero of multiplicity two. My book says-The degree of the zero polynomial is defined to be zero. d. not defined 3) The value of k for which x-1 is a factor of the polynomial x 3 -kx 2 +11x-6 is I have already discussed difference between polynomials and expressions in earlier article. To answer this question, I have to remember that the polynomial's degree gives me the ceiling on the number of bumps. Wikipedia says-The degree of the zero polynomial is $-\infty$. Zero of polynomials | A complete guide from basic level to advance level, difference between polynomials and expressions, Polynomial math definition |Difference between expressions and Polynomials, Zero of polynomials | A complete guide from basic level to advance level, Zero of polynomials | A complete guide from basic level to advance level – MATH BACKUP, Matrix as a Sum of Symmetric & Skew-Symmetric Matrices, Solution of 10 mcq Questions appeared in WBCHSE 2016(Math), Part B of WBCHSE MATHEMATICS PAPER 2017(IN-DEPTH SOLUTION), HS MATHEMATICS 2018 PART B IN-DEPTH SOLUTION (WBCHSE), Different Types Of Problems on Inverse Trigonometric Functions, $$x^{3}-2x+3,\; x^{2}y+xy+y,\;y^{3}+xy+4$$, $$x^{4}+x^{2}-2x+3,\; x^{3}y+x^{2}y^{2}+xy+y,\;y^{4}+xy+4$$, $$x^{5}+x^{3}-4x+3,\; x^{4}y+x^{2}y^{2}+xy+y,\;y^{5}+x^{3}y+4$$, $$x^{6}+x^{3}+3,\; x^{5}y+x^{2}y^{2}+y+9,\;y^{6}+x^{3}y+4$$, $$x^{7}+x^{5}+2,\; x^{5}y^{2}+x^{2}y^{2}+y+9,\;y^{7}+x^{3}y+4$$, $$x^{8}+x^{4}+2,\; x^{5}y^{3}+x^{2}y^{4}+y^{3}+9,\;y^{8}+x^{3}y^{3}+4$$, $$x^{9}+x^{6}+2,\; x^{6}y^{3}+x^{2}y^{4}+y^{2}+9,\;y^{9}+x^{2}y^{3}+4$$, $$x^{10}+x^{5}+1,\; x^{6}y^{4}+x^{4}y^{4}+y^{2}+9,\;y^{10}+3x^{2}y^{3}+4$$. Example #1: 4x 2 + 6x + 5 This polynomial has three terms. A polynomial having its highest degree 3 is known as a Cubic polynomial. In general g(x) = ax2 + bx + c, a â 0 is a quadratic polynomial. Discovering which polynomial degree each function represents will help mathematicians determine which type of function he or she is dealing with as each degree name results in a different form when graphed, starting with the special case of the polynomial with zero degrees. Polynomial functions of degrees 0â5. A polynomial has a zero at , a double zero at , and a zero at . 63.2k 4 4 gold ⦠In this case, the degree is 6, so the highest number of bumps the graph could have would be 6 â 1 = 5.But the graph, depending on the multiplicities of the zeroes, might have only 3 bumps or perhaps only 1 bump. Constant (non-zero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, This is because the function value never changes from a, or is constant.These always graph as horizontal lines, so their slopes are zero, meaning that there is no vertical change throughout the function. Definition: The degree is the term with the greatest exponent. Recall that for y 2, y is the base and 2 is the exponent. The constant polynomial. A question is often arises how many terms can a polynomial have? + dx + e, a â 0 is a bi-quadratic polynomial. Let us get familiar with the different types of polynomials. The zero polynomial is the additive identity of the additive group of polynomials. Classify these polynomials by their degree. First, find the real roots. (function() { The function P(x) = x2 + 4 has two complex zeros (or roots)--x = = 2i and x = - = - 2i. So root is the same thing as a zero, and they're the x-values that make the polynomial equal to zero. Required fields are marked *.            x5 + x3 + x2 + x + x0. asked Feb 9, 2018 in Class X Maths by priya12 ( -12,629 points) polynomials If the polynomial is not identically zero, then among the terms with non-zero coefficients (it is assumed that similar terms have been reduced) there is at least one of highest degree: this highest degree is called the degree of the polynomial. lets go to the third example. A polynomial all of whose terms have the same exponent is said to be a homogeneous polynomial, or a form. 0 c. any natural no. There are no higher terms (like x 3 or abc 5). 1.7x 3 +5 2 +1 2.6y 5 +9y 2-3y+8 3.8x-4 4.9x 2 y+3 ⦠The corresponding polynomial function is theconstant function with value 0, also called thezero map. Now the question is what is degree of R(x)? Discovering which polynomial degree each function represents will help mathematicians determine which type of function he or she is dealing with as each degree name results in a different form when graphed, starting with the special case of the polynomial with zero degrees. 2x 2, a 2, xyz 2). Binomials â An algebraic expressions with two unlike terms, is called binomial hence the name âBiânomial. As P(x) is divisible by Q(x), therefore $$D(x)=\frac{x^{2}+6x+5}{x+5}=\frac{(x+5)(x+1)}{(x+5)}=x+1$$. A polynomial having its highest degree 4 is known as a Bi-quadratic polynomial. This is because the function value never changes from a, or is constant.These always graph as horizontal lines, so their slopes are zero, meaning that there is no vertical change throughout the function. y, 8pq etc are monomials because each of these expressions contains only one term. 7/(x+5) is not, because dividing by a variable is not allowed, ây is not, because the exponent is "½" .Â. For example, f (x) = 10x4 + 5x3 + 2x2 - 3x + 15, g(y) = 3y4 + 7y + 9 are quadratic polynomials. it is constant and never zero. Names of polynomials according to their degree: Your email address will not be published. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial. Thus, it is not a polynomial. then, deg[p(x)+q(x)]=1 | max{$$1,{-\infty}=1$$} verified. Yes, "7" is also polynomial, one term is allowed, and it can be just a constant. see this, Your email address will not be published. For example, f(x) = x- 12, g(x) = 12 x , h(x) = -7x + 8 are linear polynomials. In this article let us study various degrees of polynomials. ⇒ let p(x) be a polynomial of degree ‘n’, and q(x) be a polynomial of degree ‘m’. In that case degree of d(x) will be ‘n-m’. For example, $$x^{5}y^{3}+x^{3}y+y^{2}+2x+3$$ is a polynomial that consists five terms such as $$x^{5}y^{3}, \;x^{3}y, \;y^{2},\;2x\; and \;3$$. It is that value of x that makes the polynomial equal to 0. For example, f (x) = 2x2 - 3x + 15, g(y) = 3/2 y2 - 4y + 11 are quadratic polynomials. The individual terms are also known as monomial. Explain Different Types of Polynomials. Second degree polynomials have at least one second degree term in the expression (e.g. A polynomial having its highest degree 2 is known as a quadratic polynomial. Zero degree polynomial functions are also known as constant functions. Checking each term: 4z 3 has a degree of 3 (z has an exponent of 3) Example: what is the degree of this polynomial: 4z 3 + 5y 2 z 2 + 2yz. If r(x) = p(x)+q(x), then $$r(x)=x^{2}+3x+1$$. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial. is not, because the exponent is "-2" which is a negative number. On the other hand, p(x) is not divisible by q(x). A Constant polynomial is a polynomial of degree zero. The function P(x⦠Step 4: Check which the largest power of the variable and that is the degree of the polynomial, 1. But it contains a term where a fractional number appears as an exponent of x . It is due to the presence of three, unlike terms, namely, 3x, 6x2 and 2x3. The constant polynomial whose coefficients are all equal to 0. Degree of Zero Polynomial. The degree of the zero polynomial is either left undefined, or is defined to be negative (usually â1 or ââ). It is due to the presence of three, unlike terms, namely, 3x, 6x, Order and Degree of Differential Equations, List of medical degrees you can pursue after Class 12 via NEET, Vedantu The degree of the zero polynomial is undefined, but many authors conventionally set it equal to or . which is clearly a polynomial of degree 1. Question 4: Explain the degree of zero polynomial? We ‘ll also look for the degree of polynomials under addition, subtraction, multiplication and division of two polynomials. The constant polynomial whose coefficients are all equal to 0. A trinomial is an algebraic expression with three, unlike terms. You can think of the constant term as being attached to a variable to the degree of 0, which is really 1. The degree of the equation is 3 .i.e. To check whether 'k' is a zero of the polynomial f(x), we have to substitute the value 'k' for 'x' in f(x). Definition: A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.. A constant polynomial (P(x) = c) has no variables. Enter your email address to stay updated. Share. So this is a Quadratic polynomial (A quadratic polynomial is a polynomial whose degree is 2). The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. also let $$D(x)=\frac{P(x)}{Q(x)}\;and,\; d(x)=\frac{p(x)}{q(x)}$$. Allowing for multiplicities, a polynomial function will have the same number of factors as its degree. Repeaters, Vedantu let P(x) be a polynomial of degree 2 where $$P(x)=x^{2}+6x+5$$, and Q(x) be a linear polynomial where $$Q(x)=x+5$$. Terms of a Polynomial. The first one is 4x 2, the second is 6x, and the third is 5. Based on the degree of the polynomial the polynomial are names and expressed as follows: There are simple steps to find the degree of a polynomial they are as follows: Example: Consider the polynomial 4x5+ 8x3+ 3x5 + 3x2 + 4 + 2x + 3, Step 1: Combine all the like terms variables Â. Highest degree of its individual term is 8 and its coefficient is 1 which is non zero. For example, the polynomial function P(x) = 4ix 2 + 3x - 2 has at least one complex zero. Main & Advanced Repeaters, Vedantu i.e. Follow answered Jun 21 '20 at 16:36. Solution: The degree of the polynomial is 4. Polynomials in two variables are algebraic expressions consisting of terms in the form $$a{x^n}{y^m}$$. Now the question arises what is the degree of R(x)? e is an irrational number which is a constant. Polynomial simply means âmany termsâ and is technically defined as an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.. Itâs ⦠Although there are others too. In general g(x) = ax4 + bx2 + cx2 + dx + e, a â 0 is a bi-quadratic polynomial. For example $$2x^{3}$$,$$-3x^{2}$$, 3x and 2. Example: Put this in Standard Form: 3 x 2 â 7 + 4 x 3 + x 6 The highest degree is 6, so that goes first, then 3, 2 and then the constant last: Since 5 is a double root, it is said to have multiplicity two. A real number k is a zero of a polynomial p(x), if p(k) = 0. In the first example $$x^{3}+2x^{2}-3x+2$$, highest exponent of variable x is 3 with coefficient 1 which is non zero. How To: Given a polynomial function $f$, use synthetic division to find its zeros. So we consider it as a constant polynomial, and the degree of this constant polynomial is 0(as, $$e=e.x^{0}$$). The degree of a polynomial is nothing but the highest degree of its individual terms with non-zero coefficient,which is also known as leading coefficient. The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7. In the last example $$\sqrt{2}x^{2}+3x+5$$, degree of the highest term is 2 with non zero coefficient. It has no variables, only constants. For example: In a polynomial 6x^4+3x+2, the degree is four, as 4 is the highest degree or highest power of the polynomial. i.e., the polynomial with all the like terms needs to be ⦠For example, f (x) = 8x3 + 2x2 - 3x + 15, g(y) = y3 - 4y + 11 are cubic polynomials. Browse other questions tagged ag.algebraic-geometry ac.commutative-algebra polynomials algebraic-curves quadratic-forms or ask your own question. The terms of polynomials are the parts of the equation which are generally separated by â+â or â-â signs. For example, 3x + 5x, is binomial since it contains two unlike terms, that is, 3x and 5x, Trinomials â An expressions with three unlike terms, is called as trinomials hence the name âTriânomial. To find zeroes of a polynomial, we have to equate the polynomial to zero and solve for the variable. Thus, in order to find zeros of the polynomial, we simply equate polynomial to zero and find the possible values of variables. I am totally confused and want to know which one is true or are all true? To find the degree of a term we ‘ll add the exponent of several variables, that are present in the particular term. Well, if a polynomial is of degree n, it can have at-most n+1 terms. Step 3: Arrange the variable in descending order of their powers if their not in proper order. If the remainder is 0, the candidate is a zero. And let's sort of remind ourselves what roots are. Binomials â An algebraic expressions with two unlike terms, is called binomial hence the name âBiânomial. Sorry!, This page is not available for now to bookmark. Similar to any constant value, one can consider the value 0 as a (constant) polynomial, called the zero polynomial. In this case, the degree is 6, so the highest number of bumps the graph could have would be 6 â 1 = 5.But the graph, depending on the multiplicities of the zeroes, might have only 3 bumps or perhaps only 1 ⦠Degree of a zero polynomial is not defined. Let p(x) be a polynomial of degree ‘n’, and q(x) be a polynomial of degree ‘m’. A mathematics blog, designed to help students…. P(x) = 0.Now, this becomes a polynomial ⦠Note that in order for this theorem to work then the zero must be reduced to ⦠The zero polynomial is the additive identity of the additive group of polynomials. Let P(x) = 5x 3 â 4x 2 + 7x â 8. Degree of a multivariate polynomial is the highest degree of individual terms with non zero coefficient. 3xy-2 is not, because the exponent is "-2" which is a negative number. 2+5= 7 so this is a 7 th degree monomial. What could be the degree of the polynomial? Example: what is the degree of this polynomial: 4z 3 + 5y 2 z 2 + 2yz. A polynomial having its highest degree zero is called a constant polynomial. let R(x) = P(x)+Q(x). Pro Lite, NEET Any non - zero number (constant) is said to be zero degree polynomial if f(x) = a as f(x) = ax0 where a â 0 .The degree of zero polynomial is undefined because f(x) = 0, g(x) = 0x , h(x) = 0x2 etc. I ‘ll also explain one of the most controversial topic — what is the degree of zero polynomial? Example: f(x) = 6 = 6x0 Notice that the degree of this polynomial is zero. The function P(x) = x2 + 3x + 2 has two real zeros (or roots)--x = - 1 and x = - 2. Likewise, 11pq + 4x2 â10 is a trinomial. To check whether 'k' is a zero of the polynomial f(x), we have to substitute the value 'k' for 'x' in f(x). Here are the few steps that you should follow to calculate the leading term & coefficient of a polynomial: Zero Polynomial. Pro Subscription, JEE + cx + d, a â 0 is a quadratic polynomial. What is the Degree of the Following Polynomial. A polynomial of degree three is called cubic polynomial. In the above example I have already shown how to find the degree of uni-variate polynomial. Let me explain what do I mean by individual terms. For example a quadratic polynomial can have at-most three terms, a cubic polynomial can have at-most four terms etc. The exponent of the first term is 2. Here is the twist. A monomial is a polynomial having one term. So technically, 5 could be written as 5x 0. The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.To find the degree all that you have to do is find the largest exponent in the polynomial.Note: Ignore coefficients-- coefficients have nothing to do with the degree of a polynomial. And its coefficient is 1 which is non zero 0 as a ( ). Is only a constant, such as 15 or 55, then the degree a... Is that value of x, f ( x ) = x3 + +! As follows: monomials âAn algebraic expressions with three identical roots is said to be the of... R ( x ) polynomial 0, then the degree an exponent of several variables, that is degree... Degree by 1 ( unless its degree by 1 ( unless its.. Irrational number which is non zero cx2 + dx + e, a â 0 is a linear.! S take some example to understand that degree of any of the zero polynomial is nothing but the exponent... Has no nonzero terms, degree of zero polynomial is either left explicitly undefined, but many conventionally... For a univariate polynomial, 1 this properly, this is a th. If the degree of any constant polynomial said to be the degree of this polynomial: 4z +! Is degree of a polynomial having its highest degree of individual terms that for all possible Rational of... We ‘ ll also explain one of the zero polynomial is \$ -\infty.... The most controversial topic — what is the degree of zero polynomial either. For example- 3x + 5x2 is binomial since it contains a term where a fractional number appears as exponent. ( unless its degree by 1 ( unless its degree is 2 ) what do i mean by terms... Values of variables z 2 + 3x - 2 has at least one degree! Many authors conventionally set it equal to 0 = ax2 + bx + c, a â is... Their powers constant value, one term value, the candidate into the polynomial f ( x?. Monomial hence the name âTriânomial largest number of zeros it has no variables exponent in. Bx + c, a double root, it is that value of x, f ( )... X-Values that make the polynomial equation with non-zero coefficient is undefined ( ). Of the equation which are generally separated by â+â or â-â signs solution: the degree a. As a zero polynomial is nothing but the highest degree one is called quadratic polynomial can at-most... Meta Opt-in alpha test for a univariate polynomial, we have following names for highest!, 3x and 2 degree 3 is known as constant functions } -3x^ { }... Is 4x 2 + 2yz find zeros of the zero polynomial: Arrange the variable in descending of. ÂLl add the exponent is -2 '' which is a zero of zero... Will have the same thing as a ( constant ) polynomial, we must add their exponents together determine... P of x, f ( x ) = ax3 + bx2 cx. Separated by â+â or â-â signs \left ( x-c\right ) [ /latex,... Of that polynomial is n ; the largest exponent in the expression ( e.g it. Each part of the polynomial P ( x ) = ax4 + bx2 + cx + d a... And they 're the x-values that make the polynomial equal to 0 of this expression is 3 with coefficient which! ÂLl add the like terms variables  except for few cases 0 votes a given possible by... Polynomial is not zero stay at 0 ) th degree monomial that you have to equate the polynomial is ;. Abc 5 ) ( -3x^ { 2 } +3x+1\ ) is not divisible q! Better way convenient that degree of a polynomial having its highest degree among these four terms etc also! Familiar with the different types of polynomials, so i am not getting into this..... Thing as a bi-quadratic polynomial the terms ; in this case, it is 7 P of.... Already shown how to find it of degree two is called monomial hence the degree of zero. Its coefficient is 1 which is non zero constant polynomial is undefined irrational number which is non.. T find any nonzero coefficient in the polynomial equation with non-zero coefficients is called monomial hence name... At least one complex zero + bx2 + cx2 + dx + e, â..., one can consider the value 0 as a cubic polynomial be explained as the highest power of equation! In proper order as an exponent of x negative infinity ( \ ( x^ 3. Way, it is due to the presence of three, unlike terms, degree of R ( x.... Same number of zeros it has no variables of non zero way that is 3x. Count of like terms it results in 15x 3 and also its is! Zeros it has is also polynomial, called the degree all that you have to the. Trinomial is an example of a polynomial, the polynomial is known as a polynomial... K.X^ { -\infty } \ ), \ ( q ( x ) will m n! Of different types of polynomials angles of a term we âll add the what is the degree of a zero polynomial is to. Called binomial hence the name âBiânomial polynomial 0, also called the zero polynomial ) )! Of factors as its degree by 1 ) +Q ( x ) a..., unlike terms, is called the degree of the polynomial equal to 0 means.: find the degree of polynomial addition and multiplication ( like x 3 or abc 5 ) learn about of! Candidate is a zero degree polynomial functions are also known as a zero degree polynomial functions are also as! What roots are the x-values that make the polynomial, i.e the base and 2 ) whose... Be ‘ n-m ’ is often arises how many terms can a polynomial we need the highest 4... Polynomial what is the degree of a zero polynomial ( x ) is 2, the polynomial f ( ). The given polynomial, the degree of a polynomial and how to: given polynomial! Or are all true + c is an expression that contains any count of like it. Speaking, it is 7 where k is a zero x that makes the polynomial is either undefined or as. Unlike terms, is called the zero polynomial is 3. is an algebraic expressions two! Polynomial whose coefficients are all equal to zero and solve for the degree zero! Same exponent is -2 '' which is non zero real number k is a polynomial! Of more than one variables x is equal to zero several variables, that are present in the polynomial,! Ax3 + bx2 + cx + d, a â 0 and P x! At-Most three terms where c is a trinomial = ax4 + bx2 + cx2 + dx + e a... So on present in the given polynomial degree is 0, also called the polynomial. Function f ( x ) = 0, which is non zero coefficient, (... Let P ( x ) × q ( x ) =x-1\ ) be... 3Xy-2 is not available for now to bookmark this properly, this page is not 0 is 1 is! -1 or â ) their DegreesÂ,: Combine all the like terms, is a polynomial. Fractional number appears as an exponent of several variables, that are present the! Types of polynomials according to their degree question Next question â Related questions 0 votes polynomials Based on their,! Want to know the different types of polynomials your email address will not be.! In an equation is a zero polynomial is 3. is an expression that contains any count of terms! It has no degree either highest exponent of x, f ( x =... 2 ) contains any count of like terms, is called constant polynomial P ( x ), \ -3x^. A â 0 is a similar like addition of polynomials according to their degree your. Your polynomial is the base and 2 and let 's sort of remind what... Is really zero ( a { x^n } { y^m } \ ).... Or â ) { -\infty } \ ), 3x + 6x2 â 2x3 is trinomial! =0 whose coefficients are all equal to zero, unlike terms situations coefficient Leading! We simply equate polynomial to zero of view degree of the following statements must be true says-The... Fractional number appears as an exponent of several variables, that are present what is the degree of a zero polynomial expression... With three identical roots is said to have multiplicity two polynomial of one variable only the name.! Two, unlike terms, that are present in the above example i have already discussed difference between polynomials expressions. A univariate polynomial, we have following names for the degree of what is the degree of a zero polynomial.. Above example i have already discussed difference between polynomials and expressions in earlier article term Leading! Authors conventionally set it equal to 0 book says-The degree of a polynomial are zero we get a zero,!, is called quadratic polynomial exponent is said to have a zero, the is. The remainder is 0, which of the polynomial, one term 6 = 6x0 Notice that the degree a. The exponent of several variables, that are present in the particular term is to. ( e.g often arises how many terms can a polynomial, called degree! You will also get to know the different names of polynomials negative infinity ( \ a! C is what is the degree of a zero polynomial negative number to find the degree of a polynomial of degree three is called a,! ( x^ { 3 } \ ) polynomial and how to find the largest number of factors as degree...
Back to News
|
2022-01-17 20:12:13
|
{"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": 3, "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": 0.7678943276405334, "perplexity": 468.8364058842177}, "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-20220117182124-20220117212124-00629.warc.gz"}
|
https://tecza.org/tumbleweed-meme-ojboga/ch4-%2B-h2o-redox-70e7cd
|
Herein, what type of reaction is ch4 2o2 → co2 2h2o? If the effective oxidation number of any particular atom changes during the reaction then a redox reaction has occurred. Fe^2+ +2OH^- =Fe(OH)2 I chose number 3, is this correct? in a particular redox reaction, MnO2 is oxidized to MnO4â and fe3+ is reduced to fe2+. C. Stationary solid ions are produced. To enter charge species, just type them as they are, for example Hg2+, Hg22+, or Hg2^2+ Chemistry How do i figure out if 2NO2 -> N2O4 is a redox reaction, asked by Cabby on March 18, 2016 Academic writers all over the world at Tutorsonspot round the clock. Use oxidation numbers to identify which of these reactions are REDOX reactions. 3 Ca(s) + 2 Al^3+(aq) -> 3 Ca^2+(aq) + 2 Al(s) 2. The loss of hydrogen What is the possible ionic equation of TrisEDTA solution? How do you write redox reactions. Even Urgent within 1 hour! Balance atoms other than H & O 3. asked by Emily on April 3, 2013 Zn+CuCl2 -> ZnCl2+Cu HCl+NaOH -> H2O+NaCl 2CO+O2 -> 2CO2 SO3+H2O -> H2SO4. We only accept PayPal as our payment method. The reaction CH4 (g) + 2 O2 (g) ? Chemistry The use of water and hydrogen ions to balance redox reactions is an accepted technique even if it is unlikely that H+ exists in the reaction mechanism. 2PbSO4 + 2H2O PbO2 + 2H2SO4. Balance the following redox reaction. Input Equation Balanced Equation; N2+H2=NH3: N2 + 3H2 = 2NH3: NO2+H2O=HNO3+H2O: 0NO2 + H2O = 0HNO3 + H2O: NO2+H2O=HNO3+NO: 3NO2 + H2O = 2HNO3 + NO: NaBr + CaF2 = NaF + CaBr2 Từ Điển Phương Trình đã xây dựng một công cụ tìm kiếm mở rộng kết hợp với Google Vietnam Click vào đây để tìm kiếm thông tin mở rộng Báo lỗi cân bằng. Phases are optional. b) Calculate the enthalpy of reaction? Z2 and Z5 only 3. C) an exothermic reaction. CH 4 is a reducing agent, O 2 is an oxidizing agent. chem “However, the Ag^+ + I^- reacted to give AgI (but that is not a redox reaction) and if they reacted why didn’t Br^- and Ag^+?” Hi Dr.Bob, I am also given additional information for reaction #1 Cu(s) I-(aq) Ag(s) Br- (aq), asked by Joseph on April 15, 2008 How do you know if a reaction is redox or non redoxâ¦.how do you know what would be reduced? Scan our work with all plagiarism checking tools, Result will always be 0%. -REDOX, Al metal is being reduced or -REDOX, Al metal is being oxidized. Classify each of the following as a redox reaction or a non-redox reaction. and TOS management takes strict action against those writers. chemistry Also whether each reaction is a redox or non redox reaction. The oxidation number of a simple ion is the charge of the ion. I got 1 mols for. Fe(OH)2 + O2 + H2O —> Fe(OH)3 This is in my chemistry teacher’s homework, and it comes up with an answer, but I don’t see how to use the half reaction method when there is. Let us help you simplify your studying. Complete and balance the equation for this reaction in basic solution. Given a redox reaction below: Zn(s) + Pb2+(aq) –> Zn2+(aq) + Pb(s) Pb2+(aq) + 2 e—>Pb(s)Eº = -0.13V Zn2+(aq) + 2 e—>Zn(s)Eº = -0.76V Calculate the E.M.F. What does a negative E cell indicate about a redox reaction? asked by Summer on April 5, 2018 CHEMISTRY Hello, I am trying to balance this redox reaction WITHOUT using the half-reaction method. [Examples : 1) Cr2O7^2- + H^+ + e^- = Cr^3+ + H2O, 2) S^2- + I2 = I^- + S ] Redox Reaction is a chemical reaction in which oxidation and reduction occurs simultaneously and the substance which gains electrons is termed as oxidizing agent. If you are thinking, can Chem I redox reaction: Hydrogen peroxide is added to an acidified solution of potassium permanganate. We perform a detailed research when writing your paper. The volume of water in the calorimeter decreased by 0.18 mL during the reaction a) Write the equation for the reaction which occurs. Chemistry help pls chemistry Answer: D. Learn More : Share this Share on Facebook Tweet on Twitter Plus on Google+ « Prev Question. What are two half reactions to show how many electrons are gained or lost by each species? asked by lori on November 21, 2014 Check the equation to make sure it is balanced (including charges) Some of the most common mistakes made when balancing redox reactions are as follows: Forgetting to add the hydroxides if the reaction is basic; Copying down numbers wrong and forgetting to check final equation Redox Chemistry The chemogenesis analysis identifies five distinct types of electronic reaction mechanism, here, and one of these is redox chemistry.This page explores the different types of oxidation and reduction reaction behaviour that lie behind the easily memorised (but over simplistic): OIL RIG, Oxidation Is [electron] Loss and Reduction Is [electron] Gain. Complete and balance the equation for this reaction in acidic solution. Which substance functions as a reducing agent in the following redox reaction? In a particular redox reaction, MnO2 is oxidized to MnO4â and Ag is reduced to Ag. Our videos prepare you to succeed in your college classes. i’m having trouble balancing the redox reaction for the iodine clock lab. ap And to balance the redox equation, we simply eliminate the electrons.... (i)+ 2× (ii): CH 4(g) +2O2(g) → CO2(g) +2H 2O(l) Of course, when we balance hydrocarbon combustions we forget all this pfaff, and simply balance the carbons as carbon dioxide, then the hydrogens as water, and then balance the oxygens. asked by Jake UCD 11/15/11 on November 15, 2011 Complete and balance the, asked by Mia on March 22, 2014 asked by Natalea on November 15, 2010 N2 + 4 H2O + Cr2O3 as one or more of the following: Z1) combination Z4) metathesis Z2) decomposition Z5) displacement Z3) redox 1. Phases are optional. Furthermore, if you have any questions, just reach What are the units used for the ideal gas law? a) Mg(s)+H2O(g)->Mg(OH)2(s)+H2 b) Cr(NO3)(aq)+Al(s)->Al(NO3)(aq)+Cr(s) c) PF3(g)+F2(g)->PF5(g), asked by Cassaundra on October 10, 2011 â¦, I am an admired writer in all fields of writing with over 5 years of â¦, We have over 1500 academic writers ready and waiting to help you achieve academic success. B. Phases are optional. The reaction of quicklime (CaO) with sulfur dioxide (SO2) is an important reaction for reducing SO2 emissions from coal-fired power plants: CaO(s) + SO2(g) â CaSO3(s) This reaction is an example of: A. a precipitation reaction B. an electrolysis reaction, asked by M on March 29, 2012 How do you calculate the ideal gas law constant? How would one balance the following redox reaction using the half reaction method? D. Ions are, asked by Sadie on June 24, 2010 Custom writing help for your homework, Academic Paper and Assignments from Then, Could someone balance this redox reaction for me? Science Here is the unbalanced equation: MnO4 -(aq) + Zn(s)–> Mn 2+(aq) + Zn 2+(aq) It looks as if both elements are being oxidized. I know an oxidation reaction loses, asked by Anonymous on October 4, 2008 Do all electrochemical cells involve redox reactions? HCI+H2O=H3O^+ +CI^- 2. Cr + Cu2+ = CrO42- + Cu+, asked by Anonymous on February 24, 2012 SO2(g)+H2O(l)-> H2SO3(aq) NH3(aq)+HS(-)(aq)-> NH4(+)(aq)+S(2-) Na2O2(l)->, asked by sara on April 5, 2011 science Is this a redox reaction? Can someone check my answers for me thank you. It is 100% secure. Calculate delta G rxn for a redox reaction with n = 2 that has an equilibrium constant of K = 4.4Ã10â2. O3SOOSO3^(2â) + Cr^(3+)+ -> HSO4^(1-) + Cr2O7^(2-). , it is a redox reaction. for Drbob222 Methane, CH4, burns in oxygen gas to form water and carbon dioxide. Chemistry what substance is being reduced in the following redox reaction? Complete and balance the equation for this reaction in basic solution. CH4(g) + 2 O2(g) {eq}\rightarrow {/eq} CO2(g) + 2 H2O (g) Redox Reaction: In a redox reaction two or more atoms present undergo changes in oxidation state, due to a transfer of electrons between them. asked by will on January 12, 2016 chemistry Whenever there is removal of H we term it as reduction .Also, O2 is being attached with the C which inturn is termed as oxidation.So, since oxidation and reduction both are taking place in this rxn. Chemistry balance the redox reaction NO2^- + Ag^+ = NO3^- + Ag, asked by LOLA on February 14, 2015 Oxidation= loss of electrons. Which reaction is a redox reaction? asked by moe on November 22, 2010 PreChem Ok one more! AP Chemistry Identify the atom whose oxidation number increases in the following redox reaction. Thanks. asked by Maria on September 15, 2016 Chemistry The typical battery used in a standard flashlight produced approximately 1.5 V. If the value for ÎG° of the reaction were â289,500 J, what would you calculate as the moles of electrons exchanged in the balanced redox reaction? Pay using paypal though verified gateway for maximum safety, No risk. What occurs in the process of ionization? Choose all of the chemical reactions which correctly show that chemical reactions must obey the Law of Conservation of Matter. what does H2SO4 + Sugar turn into? The figure below shows a fairly typical voltaic cell. a. Compare our price. AP Chemistry underneath 2Pb(NO3)2 => 2PbO + 4NO2 + O2 +2 -1 +2-2 +4-2 0 I got all the o.s. AgNO3+NaCL=AgCL+NaNO3 is not a redox reaction but Cu+2AgNO3=2Ag+Cu(NO3)2 is a redox reaction.explain. Regardless of the difficulty, we deliver an unparalleled solution without any delay. the help from any of your homework. Zn + Cr3+ –> Zn2+ + Cr Write the half-reaction for the reduction that occurs. Chemistry Methane + Dioxygen = Carbon Dioxide + Water . Reaction 1: I2(aq)Cu^+2(aq) Ag^+(aq)Br2(aq) Column 1—Column 2—Column 3—Column 4—Column 5 I-(aq)—X—X—T—T Cu(s)—T—X—T—T Ag(s)—X—X—X—T Br-(aq)—X—X—X—X Reaction of metals and solution of ions Reaction 2: asked by Joseph on April 14, 2008 Complete and balance the equation for this reaction in basic solution: NO + Cu^2+ –> NO3^- + Cu^+ help. I’m having a hard time with Redox and how to figure out which is redox Select all of the reactions that are redox reactions. Balance the following redox reaction using the half reaction method: NaIO3+KI==> I2+H20+Na(+1)+K(+1). Consider the reaction Cu2+ (aq) + Zn(s) ⎯→ Cu(s) + Zn2+(aq). 2VO3- (aq) + Zn (s) + 8H+ (aq) â 2VO2+ (aq) + Zn2+ (aq) + 4H2O (l) d. Zn(NO) (aq) + 2NaOH (aq) â Zn(OH) (s) + 2NaNO (aq) part 2 For the redox. asked by mohit on June 30, 2016 asked by Ted on January 26, 2013 asked by Adam R on August 13, 2009 I) Ca + 2H2O ï® Ca(OH)2 + H2 II) CaO + H2O ï® Ca(OH)2 III) Ca(OH)2 + H3PO4 ï® Ca3(PO4)2 + H2O IV) Cl2 + 2 KBr ï® Br2 + 2 KCl I, asked by Mark on March 18, 2010 Bi3+(aq) + Co(s)Bi(s) + Co2+(aq), asked by Shahzaib on November 20, 2015 To Fe2⦠donât take and store any Credit/Debit card information reactions are redox reactions the. Deliver an unparalleled solution WITHOUT any delay or false? increases in the process of?! And do great on your exams, which atom is reduced ) ch4 b ) O2 )... What is the correct balanced Chemical equation for this reaction in basic solution hydrogen sulfite ion and iodate in... You always could choose go nuts or keep calm with us or WITHOUT,! Chem true or false? the oxidation number of a reaction ; it a! Of any particular atom changes during the reaction a ) a redox reaction below ) + Zn2+ ( aq +! 29, 2020 | 0 comments OK at Tutorsonspot round the clock, they allowed... Of potassium permanganate scan our work with all plagiarism checking tools, Result will be. Three definitions you can depend on us to help you out CO2 ( g ) �� 2so2 g! Your homework, and oxide ions, O^2-, to make CO2 is even more of a 0.744 M of. By Sara on October 7, 2013 Chemistry Write the equation for this reaction as their only negative ions Academic... +2O2 →CO2 +2H2O a ) Write the half-reaction method all information is and. > Zn2+ + Cr Write the reduction half reaction method, give the complete half. ) b cah2 mgh2 nah 0 h2 +1 ch4 HCl H2O nh3 any questions just., i.e 26, 2013 Chemistry use oxidation numbers, explain why it not! Peroxide is added to an acidified solution of KClO h2 +1 ch4 HCl H2O.. Into 1/2 rxns ( reduction & oxidation ) 2 I chose number 3, is ch4 2o2 CO2 a... The calorimeter decreased by 0.18 mL during the reaction of Al metal is being or. Zn2+ + Cr Write the reduction half reaction has been balanced except the! The atom whose oxidation number for hydrogen in most compounds is -2 H2O. Simple ion is the possible ionic equation of TrisEDTA solution units used for reaction... That is written specifically for them burns in oxygen gas to form water and carbon dioxide on your.... Fairly typical voltaic cell balanced except for the electrons be included 2xxstackrel ( -III ) C-Cstackrel ( )!, explain why this reaction is redox reactions CO2 d ) H2O cheri on October 4, 2008 Chemistry the! In your paper 2 O2 ( g ) + 2 H2O ( )! → CO 2 + 2 O, 2010 Chemistry can anyone give me a brief about! - > H2O+NaCl 2CO+O2 - > H2SO4 HCl H2O nh3 is private and confidential it... What would be reduced about redox we donât ask Client name and give user name his/her! Chemistry Hello, I am a qualified and experienced Writer, Researcher, Tutor, analyst Consultant... Here charge for their efforts not for Copy/Paste work and TOS management takes strict action against those writers →CO2 a! > HCI + H2SO4 true or false? May 3, 2010 Chemistry someone! Zncl2 + H2O - Chemical equation for this reaction in acidic solution about the rate )... Out of 5 / number of oxygen in most compounds is +1 na s. Forms Al2O3 attached with C in ch4 is getting separated more of a reaction is not shared any! Functions as a liquefied compressed gas can use for oxidation: 1 charge! Writers working here are recruited and chosen after taking strict Evaluation of information: 5.0 out of 5 number! Equations and assign oxidation numbers to identify reaction is a redox reaction has occurred )... An unparalleled solution WITHOUT any delay parts of the above E ) none of the following redox reaction voltaic.. Our terms and conditions related to it am still confused as to whether or not this makes it a reaction..., they were O at … which substance functions as a liquefied compressed gas clientâs all information private... Confused as to whether or not this makes it a redox reactions, the reactants can actually be in. Reaction of Al metal ch4 + h2o redox being oxidized H3O+ ( aq ) b content. #, i.e by Rebekah on May 3, is ch4 2o2 CO2 H2O a redox reaction gas! Understanding any of it these two reactions involving iron 2011 Chemistry for the ideal gas law constant the.. Does not have plagiarism in your paper, 2014 Chemistry how do you calculate the gas... Note: Normal constituent of air ( about 300 ppm ) ] someone help me with my research paper policy! Reduction half reaction has been balanced except for the following redox reaction will help you.... Explanation about redox as providing quality homework solution is our first priority temp ] = ch4 2! Will know that you can get of votes: 1 is the correct balanced Chemical for! Team that is written specifically for them more of a simple ion the. Of hydrogen ions Statistics, we gots # H_3stackrel ( -III ) C-Cstackrel ( +I ) #. Of hydrogen ions hydroxide ions, as their only negative ions 1/2 rxns ( &... Oxidation numbers to identify which of the above E ) none of the.... Chemical equation for this reaction in acidic solution OH ) 2 I chose number,! That you have any questions, just reach out to our customer service team that is written for. Me what happens when zinc and copper sulfate react on Google+ « Prev Question a typical. Table which gives you oxidation numbers to identify if this reaction in an acidified solution on your exams NO3^- Cu^+. Just contact us and get the best services that you have taken for... Reaction Cu2+ ( aq ) + 2 O2 ( g ) -2 -2 change! 16, 2016 Chem I OK one more take and store any Credit/Debit card information,... And reduction parts of the reactions track of spectator ions in the following half reaction method of redox! Were O at … which substance functions as a redox or non redox reaction CHCl3 + MnO4- CL2. Of votes: 1 ( s ) + CO32- ( aq ) b customers with customized that... H_3 #, i.e and experienced Writer, Researcher, Tutor, analyst and Consultant which substance functions as liquefied... Researcher, Tutor, analyst and Consultant Daphne on March 16, 2013 Science Part which. Brief explanation about redox Al ) with oxygen ( O2 ) forms Al2O3 how electrons! To an acidified solution of KClO ch4 + h2o redox CL2 +SO2 -- > HCI +.. To all atoms in these two reactions involving iron ) forms Al2O3 > NO3^- + Cu^+ help and! This Share on Facebook Tweet on Twitter Plus on Google+ « Prev.. Comments | Nov 29, 2020 | 0 comments OK you calculate the ideal gas law for! To an acidified solution by | Nov 29, 2020 | 0 comments | Nov,... =Fe ( OH ) 2 conditions related to ch4 + h2o redox to carbon dioxide oxygen is reduced to Fe2⦠April,. + Al+3 ( aq ) Na+1 ( aq ) â 2NH4+ ( )... 8, 2013 Chemistry use oxidation numbers when writing your paper will you... … which substance functions as a liquefied compressed gas your Academic paper from.... Got your back flow between them information including personal details are safe with us.We have strict policy. No change – not redox 2018 Chemistry Hello, I am trying to balance this redox.! Is high enough to stain sinks and turn drinking water light brown for. Hcl H2O nh3 2013 Science Part 1 which of the difficulty, we gots # H_3stackrel ( )! Fe3+ to Fe2+ and then titrating with MnO4- in acidic solution the balanced! Me a brief explanation about redox ) ] the H attached with C in ch4 getting. Specifically for them Compound Acts as the Oxidizing agent Chemistry balanced equations.. done back. Questions, just reach out to our customer service team that is available the! Except for the redox reaction using the half-reaction method, check our and. Chemistry using oxidation numbers to identify if this reaction is a redox reaction: hydrogen peroxide is added to acidified! Assignment experts from all over the world for all subjects = ch4 + +2. / number of oxygen in most compounds is -2 original content that does not have in... Nah 0 h2 +1 ch4 HCl H2O nh3 OH ) 2 = > +. H_3Stackrel ( -III ) C+6xxstackrel ( +I ) H # specifically for them 2010. Ki = I2 + 1, 2012 Chemistry here is a redox reaction.. types of redox reaction zn... Shared with any other party 3ch3oh + H2O 2 ) balance this redox reaction.. types of redox reaction 4! L ) a combustion process, and do great on your exams in your paper and a reaction. Organic, Physics, Calculus, or Statistics, we gots # H_3stackrel ( -III ) C-Cstackrel ( )... Your solution understand this guarantee, check our terms and conditions related to it reduced! +I ) H # E ) none of the reaction ch4 ( g ) -2 -2 change... Half reactions to show how many electrons are gained or lost by each species actually be in! Gas to form water and carbon dioxide particular redox reaction help me with my research?! 2Cr3+ + 3CH2O + 8OH-10 use for oxidation: 1 is occurring writers and we promise 0 % (. + 3CH2O + 8OH-10 Al ( s ) + 2 H2O the oxidation number increases in the decreased.
|
2021-03-03 13:58:54
|
{"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": 0.40420880913734436, "perplexity": 5734.018744488853}, "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/1614178366969.45/warc/CC-MAIN-20210303134756-20210303164756-00270.warc.gz"}
|
https://gmatclub.com/forum/what-is-the-value-of-x-1-x-3-6x-x-2-2-14x-x-3-5x-254290.html
|
It is currently 17 Jan 2018, 06:55
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2
Author Message
TAGS:
### Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 43307
Kudos [?]: 139278 [1], given: 12782
What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
26 Nov 2017, 22:39
1
KUDOS
Expert's post
00:00
Difficulty:
45% (medium)
Question Stats:
57% (04:06) correct 43% (00:53) wrong based on 54 sessions
### HideShow timer Statistics
What is the value of x ?
(1) $$x^3 = 6x − x^2$$
(2) $$14x = x^3 + 5x^2$$
[Reveal] Spoiler: OA
_________________
Kudos [?]: 139278 [1], given: 12782
Director
Joined: 18 Aug 2016
Posts: 627
Kudos [?]: 208 [0], given: 166
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
26 Nov 2017, 22:45
Bunuel wrote:
What is the value of x ?
(1) $$x^3 = 6x − x^2$$
(2) $$14x = x^3 + 5x^2$$
(1)
x^3 = 6x − x^2
x (x^2 + x - 6) = 0
x (x+3) (x-2) = 0..multiple answers not sufficient
(2)
14x = x^3 + 5x^2
x(x^2 + 5x -14) = 0
x(x+7)(x-2) = 0....multiple answers not sufficient
on combining x=0 or 2
Not Sufficient
E
_________________
We must try to achieve the best within us
Thanks
Luckisnoexcuse
Last edited by Luckisnoexcuse on 26 Nov 2017, 22:52, edited 1 time in total.
Kudos [?]: 208 [0], given: 166
Manager
Joined: 31 Jul 2017
Posts: 142
Kudos [?]: 22 [0], given: 491
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
26 Nov 2017, 22:49
Bunuel wrote:
What is the value of x ?
(1) $$x^3 = 6x − x^2$$
(2) $$14x = x^3 + 5x^2$$
From Stmnt 1: x(x+3)(X-2) = 0
From Stmnt 2: x(x+7)(x-2) = 0
Combined x= 2,0
Should be E
Kudos [?]: 22 [0], given: 491
Intern
Joined: 24 Aug 2017
Posts: 8
Kudos [?]: 1 [0], given: 355
Re: What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
11 Dec 2017, 16:53
I got 2 or -3 for (1) and -7 or 2 for (2) so I picked C because x can be 2 in both (1) and (2). Why is that wrong?
Posted from my mobile device
Kudos [?]: 1 [0], given: 355
Manager
Joined: 27 Oct 2017
Posts: 88
Kudos [?]: 37 [1], given: 33
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
11 Dec 2017, 17:01
1
KUDOS
1
This post was
BOOKMARKED
Hi
You have missed the case when x can be zero.
Hence by using both the statements, x can be 0 or 2.
Hence insufficient.
[the quote="najsh2"]I got 2 or -3 for (1) and -7 or 2 for (2) so I picked C because x can be 2 in both (1) and (2). Why is that wrong?
Posted from my mobile device[/quote]
Posted from my mobile device
_________________
If you like my post, encourage me by providing Kudos...
Happy Learning...
Kudos [?]: 37 [1], given: 33
Intern
Joined: 24 Aug 2017
Posts: 8
Kudos [?]: 1 [0], given: 355
Re: What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
11 Dec 2017, 17:02
gmatbusters wrote:
Hi
You have missed the case when x can be zero.
Hence by using both the statements, x can be 0 or 2.
Hence insufficient.
[the quote="najsh2"]I got 2 or -3 for (1) and -7 or 2 for (2) so I picked C because x can be 2 in both (1) and (2). Why is that wrong?
Posted from my mobile device
Posted from my mobile device[/quote]
Thats what i was missing. Its very clear. Thank you!
Sent from my iPhone using GMAT Club Forum mobile app
Kudos [?]: 1 [0], given: 355
Manager
Joined: 27 Oct 2017
Posts: 88
Kudos [?]: 37 [1], given: 33
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink]
### Show Tags
12 Dec 2017, 03:46
1
KUDOS
Hi najsh2
If u really like my explanation, please provide me Kudos... ?
najsh2 wrote:
gmatbusters wrote:
Hi
You have missed the case when x can be zero.
Hence by using both the statements, x can be 0 or 2.
Hence insufficient.
[the quote="najsh2"]I got 2 or -3 for (1) and -7 or 2 for (2) so I picked C because x can be 2 in both (1) and (2). Why is that wrong?
Posted from my mobile device
Posted from my mobile device
Thats what i was missing. Its very clear. Thank you!
Sent from my iPhone using GMAT Club Forum mobile app[/quote]
Posted from my mobile device
_________________
If you like my post, encourage me by providing Kudos...
Happy Learning...
Kudos [?]: 37 [1], given: 33
Re: What is the value of x ? (1) x^3 = 6x − x^2 (2) 14x = x^3 + 5x^2 [#permalink] 12 Dec 2017, 03:46
Display posts from previous: Sort by
|
2018-01-17 14:55:21
|
{"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": 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": 0.5885187387466431, "perplexity": 6870.671653365302}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886946.21/warc/CC-MAIN-20180117142113-20180117162113-00251.warc.gz"}
|
https://kops.uni-konstanz.de/handle/123456789/920
|
The optimal choice of the doping levels in an inline selective emitter design for screen printed multicrystalline silicon solar cells
2009
Authors
Haverkamp, Helge
Bleidiessel, Robert
Fleuster, Martin
Publication type
Contribution to a conference collection
Published in
Proceedings of the 24th European PV SEC, Hamburg, 21 - 25 September 2009. - München : WIP, 2009. - pp. 1795-1797. - ISBN 3-936338-25-6
Abstract
A selective emitter from a single diffusion process has been applied to screen printed multicrystalline silicon solar cells. The influence of different dopant concentrations in the highly doped regions intended for metallisation and alignment tolerances has been investigated. It was found that the gain reached by increasing the dopant concentration and thereby lowering the specific contact resistance of the emitter electrode can be outweighed by the loss in the short circuit current density (JSC) caused by an increased recombination at the front surface and in the emitter. Therefore the process parameters have to be chosen carefully. The open circuit voltage (VOC) was found to be nearly independent of the initial doping level.
530 Physics
Keywords
Selective Emitter,Doping,Manufacturing and Processing
Conference
24th European Photovoltaic Solar Energy Conference, Sep 21, 2009 - Sep 25, 2009, Hamburg
Cite This
ISO 690LAUERMANN, Thomas, Felix BOOK, Amir DASTGHEIB-SHIRAZI, Giso HAHN, Helge HAVERKAMP, Robert BLEIDIESSEL, Martin FLEUSTER, 2009. The optimal choice of the doping levels in an inline selective emitter design for screen printed multicrystalline silicon solar cells. 24th European Photovoltaic Solar Energy Conference. Hamburg, Sep 21, 2009 - Sep 25, 2009. In: Proceedings of the 24th European PV SEC, Hamburg, 21 - 25 September 2009. München:WIP, pp. 1795-1797. ISBN 3-936338-25-6. Available under: doi: 10.4229/24thEUPVSEC2009-2CV.5.24
BibTex
@inproceedings{Lauermann2009optim-920,
year={2009},
doi={10.4229/24thEUPVSEC2009-2CV.5.24},
title={The optimal choice of the doping levels in an inline selective emitter design for screen printed multicrystalline silicon solar cells},
isbn={3-936338-25-6},
publisher={WIP},
booktitle={Proceedings of the 24th European PV SEC, Hamburg, 21 - 25 September 2009},
pages={1795--1797},
author={Lauermann, Thomas and Book, Felix and Dastgheib-Shirazi, Amir and Hahn, Giso and Haverkamp, Helge and Bleidiessel, Robert and Fleuster, Martin}
}
RDF
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bibo="http://purl.org/ontology/bibo/"
xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
xmlns:foaf="http://xmlns.com/foaf/0.1/"
xmlns:void="http://rdfs.org/ns/void#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#" >
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/920/1/Lauermann_opus-103946.pdf"/>
<dc:contributor>Bleidiessel, Robert</dc:contributor>
<dcterms:issued>2009</dcterms:issued>
<dc:creator>Haverkamp, Helge</dc:creator>
<dc:creator>Bleidiessel, Robert</dc:creator>
<dcterms:abstract xml:lang="eng">A selective emitter from a single diffusion process has been applied to screen printed multicrystalline silicon solar cells. The influence of different dopant concentrations in the highly doped regions intended for metallisation and alignment tolerances has been investigated. It was found that the gain reached by increasing the dopant concentration and thereby lowering the specific contact resistance of the emitter electrode can be outweighed by the loss in the short circuit current density (JSC) caused by an increased recombination at the front surface and in the emitter. Therefore the process parameters have to be chosen carefully. The open circuit voltage (VOC) was found to be nearly independent of the initial doping level.</dcterms:abstract>
<dc:contributor>Book, Felix</dc:contributor>
<dc:creator>Dastgheib-Shirazi, Amir</dc:creator>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/920/1/Lauermann_opus-103946.pdf"/>
<dc:creator>Hahn, Giso</dc:creator>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:52:03Z</dcterms:available>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dcterms:title>The optimal choice of the doping levels in an inline selective emitter design for screen printed multicrystalline silicon solar cells</dcterms:title>
<dc:language>eng</dc:language>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/>
<dc:creator>Book, Felix</dc:creator>
<dc:contributor>Haverkamp, Helge</dc:contributor>
<dc:contributor>Dastgheib-Shirazi, Amir</dc:contributor>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:52:03Z</dc:date>
<dc:contributor>Hahn, Giso</dc:contributor>
<dc:creator>Fleuster, Martin</dc:creator>
<dc:rights>terms-of-use</dc:rights>
<dcterms:bibliographicCitation>Publ. in: Proceedings of the 24th European PV SEC, Hamburg, 21-25 September 2009</dcterms:bibliographicCitation>
<dc:contributor>Lauermann, Thomas</dc:contributor>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/920"/>
<dc:creator>Lauermann, Thomas</dc:creator>
<dc:contributor>Fleuster, Martin</dc:contributor>
</rdf:Description>
</rdf:RDF>
Yes
|
2023-03-21 10:47:48
|
{"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": 0.4915907084941864, "perplexity": 6404.880609692208}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943695.23/warc/CC-MAIN-20230321095704-20230321125704-00044.warc.gz"}
|
http://paperity.org/journal/51767/journal-of-high-energy-physics/5
|
# Journal of High Energy Physics
## List of Papers (Total 10,583)
#### Supersymmetric Janus solutions of dyonic ISO(7)-gauged $\mathcal{N}$ = 8 supergravity
Abstract We study supersymmetric Janus solutions of dyonic ISO(7)-gauged $\mathcal{N}$ = 8 supergravity. We mostly find Janus solutions flowing to 3d $\mathcal{N}$ = 8 SYM phase which is the worldvolume theory on D2-branes and non-conformal. There are also solutions flowing from the critical points which are dual to 3d SCFTs from deformations of the D2-brane theory.
#### On holographic Rényi entropy in some modified theories of gravity
Abstract We perform a detailed analysis of holographic entanglement Rényi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the Rényi entropy as well as the scaling dimension of the twist...
#### Future DUNE constraints on EFT
Abstract In the near future, fundamental interactions at high-energy scales may be most efficiently studied via precision measurements at low energies. A universal language to assemble and interpret precision measurements is the so-called SMEFT, which is an effective field theory (EFT) where the Standard Model (SM) Lagrangian is extended by higher-dimensional operators. In this...
#### Thermoelectric DC conductivities in hyperscaling violating Lifshitz theories
AbstractWe analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent z and hyperscaling violating parameter θ. We show that the heat current in the dual Lifshitz theory...
#### On geometric classification of 5d SCFTs
Abstract We formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose an exhaustive classification of local 3-folds engineering rank 2...
#### Worldline quantization of field theory, effective actions and L∞ structure
AbstractWe formulate the worldline quantization (a.k.a. deformation quantization) of a massive fermion model coupled to external higher spin sources. We use the relations obtained in this way to show that its regularized effective action is endowed with an L∞ symmetry. The same result holds also for a massive scalar model.
#### Supersymmetric flaxion
AbstractRecently, a new minimal extension of the Standard Model has been proposed, where a spontaneously broken, flavor-dependent global U(1) symmetry is introduced. It not only explains the hierarchical flavor structure in the quark and lepton sector, but also solves the strong CP problem by identifying the Nambu-Goldstone boson as the QCD axion, which we call flaxion. In this...
#### To gauge or not to gauge?
AbstractThe D0 brane, or BFSS, matrix model is a quantum mechanical theory with an interesting gravity dual. We consider a variant of this model where we treat the SU(N) symmetry as a global symmetry, rather than as a gauge symmetry. This variant contains new non-singlet states. We consider the impact of these new states on its gravity dual. We argue that the gravity dual is...
#### Dark matter “transporting” mechanism explaining positron excesses
Abstract We propose a novel mechanism to explain the positron excesses, which are observed by satellite-based telescopes including PAMELA and AMS-02, in dark matter (DM) scenarios. The novelty behind the proposal is that it makes direct use of DM around the Galactic Center where DM populates most densely, allowing us to avoid tensions from cosmological and astrophysical...
#### Helicity amplitudes for QCD with massive quarks
AbstractThe novel massive spinor-helicity formalism of Arkani-Hamed, Huang and Huang provides an elegant way to calculate scattering amplitudes in quantum chromodynamics for arbitrary quark spin projections. In this note we compute two families of tree-level QCD amplitudes with one massive quark pair and n − 2 gluons. The two cases include all gluons with identical helicity and...
#### Heterotic line bundle models on elliptically fibered Calabi-Yau three-folds
Abstract We analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus on elliptically fibered three-folds with a second section and a freely-acting involution. Specifically, we consider toric weak Fano surfaces as base manifolds and identify six such...
#### Improved positivity bounds and massive gravity
Abstract Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the...
#### Brane SUSY breaking and the gravitino mass
AbstractSupergravity models with spontaneously broken supersymmetry have been widely investigated over the years, together with some notable non-linear limits. Although in these models the gravitino becomes naturally massive absorbing the degrees of freedom of a Nambu-Goldstone fermion, there are cases in which the naive counting of degrees of freedom does not apply, in...
#### Segmented strings coupled to a B-field
Abstract In this paper we study segmented strings in AdS3 coupled to a background two-form whose field strength is proportional to the volume form. By changing the coupling, the theory interpolates between the Nambu-Goto string and the SL(2, ℝ) Wess-Zumino-Witten model. In terms of the kink momentum vectors, the action is independent of the coupling and the classical theory...
#### Two-loop integrals for CP-even heavy quarkonium production and decays: elliptic sectors
AbstractBy employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even\ heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and...
#### The AdS3 propagator and the fate of locality
AbstractWe recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field ϕ in AdS3. In this paper we study the propagator 〈ϕϕ〉. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results...
#### Pulsating strings with mixed three-form flux
AbstractCircular strings pulsating in AdS3 × S3 × T 4 with mixed R-R and NS-NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in...
#### Exact results for the O(N ) model with quenched disorder
Abstract We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O(N )-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending...
|
2018-08-16 07:45:39
|
{"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": 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": 0.6540013551712036, "perplexity": 1271.699950717725}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210559.6/warc/CC-MAIN-20180816074040-20180816094040-00068.warc.gz"}
|
https://blog.richpollock.com/2014/07/replicating-excels-logarithmic-curve-fitting-in-r/
|
# Replicating Excel’s logarithmic curve fitting in R
For a new work project, we’ve just been provided with a Kaplan-Meier curve showing kidney graft survival over 12 months in two groups of patients. As the data is newly generated, we don’t yet have access to the raw data and there are too many patients in the samples to see any discrete steps on the K-M curve, meaning that we can’t extract data on time to individual events. Since we wanted to get a rough idea of how our budget impact analysis (the main focus of the project) might look with these data in place, we traced the data from the K-M curve using WebPlotDigitizer by Ankit Rohatgi.
Looking at the shape of the data we had and knowing that longer-term kidney graft survival (from donors after brain death) typically looks like that in Figure 1, we opted for a simple logarithmic model of the data:
$$S(t) = \beta ln(t) + c$$
It’s very easy to generate a logarithmic fit in Excel by selecting the “Add Trendline…” option for a selected series in a chart, selecting the “Logarithmic” option and checking the “Display equation on chart” and “Display R-squared value on chart”. The latter options display the coefficient and intercept values, and the R-squared value (using the Pearson product-moment correlation coefficient), respectively.
However, since we’re ultimately going to be using R for the analysis (when the raw K-M data become available and we use the R survival package to fit a Weibull model, or similar, to the data), I thought it would make sense to also use R to give us our rough logarithmic fit of the data. As one might expect, it’s very straightforward to replicate the results that are produced in Excel using just a few lines of R:
t <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
survival <- c(1, 0.97909, 0.97171, 0.96186, 0.95694, 0.95387, 0.95264, 0.9520, 0.94956, 0.94526, 0.94279, 0.94033, 0.94033)
s_t <- data.frame(t, survival)
log_estimate <- lm(survival~log(t), data=s_t)
summary(log_estimate)
Running this gives the following output, which tallies exactly with the intercept, log(t) parameters and R squared values reported in Excel for the same data:
Residuals:
Min 1Q Median 3Q Max
-0.0033502 -0.0016374 0.0000542 0.0014951 0.0037662
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.996234 0.001636 609.13 < 2e-16 ***
log(t) -0.022377 0.000868 -25.78 3.46e-11 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.002302 on 11 degrees of freedom
Multiple R-squared: 0.9837, Adjusted R-squared: 0.9822
F-statistic: 664.6 on 1 and 11 DF, p-value: 3.458e-11
And if we overlay the resulting curve over the NHSBT data in Figure 1, we can see that the simple logarithmic fit matches the clinical reality pretty well when projected over a five-year time horizon:
We can then use this approximation of the K-M curve to derive a survival function that we’ll use in the model until we have access to the full data set. A nice, quick approach that certainly couldn’t be accused of overfitting.
|
2021-10-25 03:18:20
|
{"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": 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": 0.5281859040260315, "perplexity": 1098.6417342682894}, "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-2021-43/segments/1634323587623.1/warc/CC-MAIN-20211025030510-20211025060510-00471.warc.gz"}
|
http://tatome.de/zettelkasten/zettelkasten.php?standalone&reference=gori-et-al-2008
|
# Show Reference: "Young Children Do Not Integrate Visual and Haptic Form Information"
Young Children Do Not Integrate Visual and Haptic Form Information Current Biology, Vol. 18, No. 9. (6 May 2008), pp. 694-698, doi:10.1016/j.cub.2008.04.036 by Monica Gori, Michela Del Viva, Giulio Sandini, David C. Burr
@article{gori-et-al-2008,
abstract = {Summary Several studies have shown that adults integrate visual and haptic information (and information from other modalities) in a statistically optimal fashion, weighting each sense according to its reliability [1] and [2]. When does this capacity for crossmodal integration develop? Here, we show that prior to 8 years of age, integration of visual and haptic spatial information is far from optimal, with either vision or touch dominating totally, even in conditions in which the dominant sense is far less precise than the other (assessed by discrimination thresholds). For size discrimination, haptic information dominates in determining both perceived size and discrimination thresholds, whereas for orientation discrimination, vision dominates. By 8-10 years, the integration becomes statistically optimal, like adults. We suggest that during development, perceptual systems require constant recalibration, for which cross-sensory comparison is important. Using one sense to calibrate the other precludes useful combination of the two sources.},
author = {Gori, Monica and Del Viva, Michela and Sandini, Giulio and Burr, David C.},
day = {6},
doi = {10.1016/j.cub.2008.04.036},
journal = {Current Biology},
keywords = {alignment, biology, learning, multi-modality},
month = may,
number = {9},
pages = {694--698},
pmid = {18450446},
posted-at = {2011-12-14 10:54:26},
priority = {2},
title = {Young Children Do Not Integrate Visual and Haptic Form Information},
url = {http://dx.doi.org/10.1016/j.cub.2008.04.036},
volume = {18},
year = {2008}
}
|
2018-11-16 22:06:03
|
{"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": 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": 0.7113000750541687, "perplexity": 10637.997426698572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743216.58/warc/CC-MAIN-20181116214920-20181117000920-00092.warc.gz"}
|
https://forum.math.toronto.edu/index.php?PHPSESSID=ra15jhi630lqj81oh6lhef6703&action=printpage;topic=944.0
|
# Toronto Math Forum
## MAT244-2018S => MAT244--Tests => Quiz-1 => Topic started by: Yingqi Wang on January 26, 2018, 12:43:48 AM
Title: Q1-T0401
Post by: Yingqi Wang on January 26, 2018, 12:43:48 AM
My solution is in the attachment.
Title: Re: Q1-T0401
Post by: Meng Wu on January 26, 2018, 09:19:01 AM
$$\cases{ t^3y'+4t^2y=e^{-t}, & t<0\cr y(-1)=0}$$
First, we divide both sides of given equation by $t^3$, we get:
$$y'+{4\over t}y={e^{-t}\over t^3}$$
Since given differential equation has the form
$$y'+p(t)y=g(t)$$
Hence $p(t)={4\over t}$ and $g(t)={e^{-t}\over t^3}$$\\ First, we find the integrating factor \mu(t) \\ As we know. \mu(t)=\exp^{\int{p(t)dt}} \\ Thus, \mu(t)=\exp^{\int{{4\over t}dt}}=e^{4ln|t|}=t^4$$\\$
Then mutiply $\mu(t)$ to both sides of the equation, we get:
$$t^4y'+4t^3y=te^{-t}$$
and $$(t^4y)'=te^{-t}$$
Integrating both sides:
$$\int{(t^4y)'}=\int{te^{-t}}$$
Thus, $$t^4y=\int{te^{-t}}$$
For $\int{te^{-t}}$, we use Integration By Parts:$\\$
Let $u=t, dv=e^{-t}$.$\\$
Then $du=dt, v=-e^{-t}$$\\ Hence,$$\int{te^{-t}}=uv-\int{vdu}\int{te^{-t}}=-te^{-t}-\int{-e^{-t}dt}\int{te^{-t}}=-te^{-t}-e^{-t}+c$$Thus$$t^4y=-te^{-t}-e^{-t}+c$$where c is arbitrary constant.\\ Now we divide both sides by t^4, we get the general solution:$$y=(-te^{-t}-e^{-t}+c)/t^4$$To satisfy the initial condition, we set t=-1 and y=0$$\\$
Hence, $$0={-(-1)e^{-(-1)}-e^{-(-1)}+c\over (-1)^4}$$
$$0=e-e+c$$
so $$c=0$$
Therefore, the solution of the initial problem is
$$y=(-te^{-t}-e^{-t})/t^4, \space t<0$$
|
2021-10-25 20:46:35
|
{"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": 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": 0.9999769926071167, "perplexity": 3612.6292934469056}, "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-2021-43/segments/1634323587767.18/warc/CC-MAIN-20211025185311-20211025215311-00184.warc.gz"}
|
https://web2.0calc.com/questions/help_2552
|
+0
# help
0
71
1
The perimeter of a rhombus is 48 and the sum of the lengths of its diagonals is 26.
What is the area of the rhombus?
Jun 21, 2020
#1
+9789
+1
The perimeter of a rhombus is 48 and the sum of the lengths of its diagonals is 26.
What is the area of the rhombus?
Hello Guest!
A diagonal is x.
$$(\frac{x}{2})^2+(\frac{26-x}{2}^2)=(\frac{48}{4})^2$$
$$\frac{x^2}{4}+\frac{676-52x+x^2}{4}=\frac{2304}{16}=\frac{576}{4}\\\ x^2+676-52x+x^2=576\\ 2x^2-52x+100=0\\x^2-26x+50=0$$
$$x=13\pm\sqrt{169-50}\\ x=13\pm\sqrt{119}$$
$$x_1=23.91\\x_2=2.091$$
$$A=4\times (\frac{x}{2}\cdot\frac{26-x}{2})/2\\ A=4\times \frac{2.901\cdot (26-2.901)}{2\cdot 2\cdot2}$$
$$A=25$$
$$A=4\times \frac{x(26-x)}{2\cdot 2\cdot 2}\\ A=4\times \frac{23.91\cdot (26-23.91)}{2\cdot 2\cdot 2}$$
$$A=25$$
!
Jun 21, 2020
edited by asinus Jun 21, 2020
edited by asinus Jun 21, 2020
edited by asinus Jun 21, 2020
edited by asinus Jun 21, 2020
|
2020-08-14 05:10:42
|
{"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": 0.9928267002105713, "perplexity": 3263.9941641480646}, "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/1596439739177.25/warc/CC-MAIN-20200814040920-20200814070920-00197.warc.gz"}
|
http://clay6.com/qa/40907/if-a-b-c-and-d-find-iii-a-cap-d
|
Want to ask us a question? Click here
Browse Questions
Ad
Home >> CBSE XI >> Math >> Sets
0 votes
# If A={x : x is a natural number},B={x : x is an even natural number},C={x : x is an odd natural number } and D={x : x is a prime number },Find (iii) $A\cap D$
$\begin{array}{1 1}(A)\;\{1,2,3,4,5....\}&(B)\;\{1,3,5,7.......\}\\(C)\;\{2,3,5,7,11.....\}&(D)\;\{2,4,6,8.....\}\end{array}$
Can you answer this question?
## 1 Answer
0 votes
$A=\{1,2,3,4,5...\}$
$D=\{2,3,5,7,11...\}$
$A\cap D=\{1,2,3,4,5...\}\cap \{2,3,5,7,11.....\}$
$\Rightarrow \{2,3,5,7,11....\}$
Here all prime numbers are common elements in both A & D
Hence (C) is the correct answer.
answered May 27, 2014
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
|
2016-10-26 23:11:34
|
{"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": 0.6284719705581665, "perplexity": 7147.571104110373}, "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-2016-44/segments/1476988721008.78/warc/CC-MAIN-20161020183841-00210-ip-10-171-6-4.ec2.internal.warc.gz"}
|
https://acm.ecnu.edu.cn/problem/2425/
|
# 2425. Sub Version Network System
In 20XX, a epoch-making telecommunication system is invented. In this system, once this system is operated, it is possible to communicate permanently without cost, it does not depend on the distance nor amount of data. However, in this system, there are three different versions (1.0, 2.0 and 3.0) and a special conversion device is required in order to communicate between systems of different version. When the difference of the version is x , this device costs c * x2 to communicate between them. That is, communicating between version 1.0 and version 3.0 costs 4.0 * c, and communicating between version 2.0 and version 3.0 costs c.
ICPC (International Company of Portable Communications) is a global company and its branch offices are all over the world. ICPC decides to buy the telecommunication system and to set up in all branch offices to construct inter-office communication network. Now, ICPC should determine a version to set up at a branch office because different selection may lead different cost. The price for the system is different because of its version and country. Moreover, the system cannot transport another country.
Your job is to write a program to calculate the minimum cost of the entire system from given cost information and given information about communication between pairs of branch offices.
### 输入格式
Input consists of multiple test cases. The first line of each test case contains two positive integers n ( n <= 50 ), c (c <= 100,000) separated by single space character. The integer n indicates the number of countries with branch office of ICPC, and the integer c indicates initial cost for starting communication. Each branch offices are numbered from 1 to n. The following n lines contain 2 positive integers b1 and b2 ( b1 , b2 <= n , b1 != b2 ) separated by single space. These integers indicate information about a branch office b1 communicates to b2. Input is terminated by a case of n = c = 0, and it should not be processed.
You can assume that the total cost does not exceeds 10,000,000.
### 输出格式
For each test case, you should output the minimum cost.
### 样例
Input
1 1
1 2 3
0
4 1
10 20 30
10 20 30
10 20 30
10 20 30
3
1 2
2 3
2 4
4 100
0 99999 99999
99999 0 99999
99999 99999 0
0 99999 99999
3
1 2
2 3
2 4
0 0
Output
1
40
300
0 人解决，1 人已尝试。
0 份提交通过，共有 4 份提交。
9.9 EMB 奖励。
|
2021-09-17 19:19:16
|
{"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": 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": 0.20059163868427277, "perplexity": 1043.9019709017687}, "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/1631780055775.1/warc/CC-MAIN-20210917181500-20210917211500-00084.warc.gz"}
|
https://www.physicsforums.com/threads/tension-force.44854/
|
# Tension Force
BlackMamba
Hello again,
I'm stuck on a new problem. Again, I thought I had the correct equation but apparently not as my answer is not correct.
Here's the problem: A steel I-beam has a weight of 9.10 N and is being lifted at a constant velocity. What is the tension in each cable attached to its ends?
Here is what the picture looks like: http://www.webassign.net/CJ/4-50.gif
This is the equation I came up with to solve for this problem but apparently it isn't the correct one.
F = (2mg)cos70.0 degrees
But like I said, when solving for the above equation my answer is not correct.
Any help or direction given would be greatly appreciated.
$$\sum_{i=1}^{n} \vec{F}_{i} = 0 \rightarrow \vec{V} = constant$$
|
2022-10-07 22:47:00
|
{"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": 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": 0.6891676187515259, "perplexity": 393.51319073835907}, "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/1664030338280.51/warc/CC-MAIN-20221007210452-20221008000452-00358.warc.gz"}
|
https://www.researchgate.net/topic/Inequality
|
Science topics: Social PolicyInequality
Science topic
# Inequality - Science topic
Explore the latest questions and answers in Inequality, and find Inequality experts.
Questions related to Inequality
• asked a question related to Inequality
Question
Tax cuts to the rich is the prefer idea on how to promote and expand economic growth in supply side economics despite knowing it does not work as expected. Yet, this policy is usually the first choice in supply side run democracies like in the USA or now the UK when supply side promoters are in power.
Any policy that worsens inequality should be expected in practice to negatively affect economic growth as under extreme inequality or worsening inequality the traditional trickle down should be expected to be mute or not to work as intended. And this raises the question, tax cuts to the rich and the embudo effect, is that why the trickled down effect does not work as intended?
What do you think?
Stephen, good day.
I asked the question because I see the policy has been implemented in the UK and it is backfiring from the mainstream point of view, but what the critics of the tax cut policy appear not to realize that for exism movements/populism with a mask movements like Brexism or Trumpism or Brazilianism and so on implementing the policy is a win as they have the interest of the movement/the minority in mind, not of the interest of the country.... I guess a tax cut to the rich is in the works in Italy right now and it will materialize soon....
Hence, what looks like a failure of reaganomics it is a successful tool for Trumpconomics, but most people appear not to realize that even facing the majority backlash they would do it again if they can as the decision is based on ideology not on science.
Thank you for commenting!
Lucio
• asked a question related to Inequality
Question
If for example the position of an electron in a one-dimensional box is measured at A (give and take the uncertainty), then the probability of detecting the particle at any position B at a classical distance from A becomes zero instantaneously.
In other words, the "probability information" appears to be communicated from A to B faster than light.
The underlying argument would be virtually the same as in EPR. The question might be generalized as follows: as the probability of detecting a particle within an arbitrarily small interval is not arbitrarily small, this means that quantum mechanics must be incomplete.
Yet another formulation: are the collapse of the wave function and quantum entanglement two manifestations of the same principle?
It should be relatively easy to devise a Bell-like theorem and experiment to verify "spooky action" in the collapse of the wave function across a given classical interval.
• asked a question related to Inequality
Question
Hi my dynamic model is
Gender Inequality Index(GII) = a+GIIt-1+bFDI+ (ControlV)+U
My control variables are 7. I have used all the control variables and my main explanatory variable as the strictly exogenous ivstyle instruments. Is this correct. I have read somewhere that we can treat all the regressors in ivstyle but i still don't understand why?
xtabond2 GII lag_GII log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2 Fertilityrate Y*, gmm(GII, lag (0 5) collapse) iv( log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2 Fertilityrate Y*, equation(level)) nodiffsargan two
> step robust orthogonal small
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: countrycode Number of obs = 239
Time variable : Year Number of groups = 49
Number of instruments = 24 Obs per group: min = 1
F(17, 48) = 22.88 avg = 4.88
Prob > F = 0.000 max = 9
----------------------------------------------------------------------------------------------
| Corrected
GII | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
lag_GII | .4063319 .1660706 2.45 0.018 .0724247 .7402392
log_FDIinflowreal | .0052016 .004571 1.14 0.261 -.0039891 .0143923
NaturalresourceRent | .0001336 .0007056 0.19 0.851 -.0012852 .0015523
Generalgovernmentexpenditure | -.0011517 .0027406 -0.42 0.676 -.0066621 .0043588
GDPGrowth | .0000538 .0011326 0.05 0.962 -.0022235 .0023311
Schoolsecondaryfemale | -.0015661 .0005599 -2.80 0.007 -.0026918 -.0004405
UrbanPopulationControl | .0002386 .000501 0.48 0.636 -.0007687 .0012459
polity2 | .0029176 .00107 2.73 0.009 .0007662 .005069
Fertilityrate | .0172748 .0121555 1.42 0.162 -.0071655 .0417151
Year | -.0002603 .0066672 -0.04 0.969 -.0136656 .013145
Yeardummy1 | .1047832 .1552767 0.67 0.503 -.2074215 .4169879
Yeardummy17 | -.006658 .0432925 -0.15 0.878 -.0937034 .0803874
Yeardummy18 | -.0006796 .0359611 -0.02 0.985 -.0729842 .071625
Yeardummy19 | -.0071339 .0330241 -0.22 0.830 -.0735332 .0592655
Yeardummy20 | -.0066488 .0261336 -0.25 0.800 -.0591938 .0458963
Yeardummy21 | .0021421 .0180578 0.12 0.906 -.0341655 .0384498
Yeardummy22 | .0005937 .0097345 0.06 0.952 -.0189789 .0201663
_cons | .8149224 13.41294 0.06 0.952 -26.15361 27.78345
----------------------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(0/5).GII collapsed
Instruments for levels equation
Standard
log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure
GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2
Fertilityrate Year Yeardummy1 Yeardummy2 Yeardummy3 Yeardummy4 Yeardummy5
Yeardummy6 Yeardummy7 Yeardummy8 Yeardummy9 Yeardummy10 Yeardummy11
Yeardummy12 Yeardummy13 Yeardummy14 Yeardummy15 Yeardummy16 Yeardummy17
Yeardummy18 Yeardummy19 Yeardummy20 Yeardummy21 Yeardummy22 Yeardummy23
Yeardummy24
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.GII collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.70 Pr > z = 0.090
Arellano-Bond test for AR(2) in first differences: z = 0.43 Pr > z = 0.669
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(6) = 18.25 Prob > chi2 = 0.006
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(6) = 5.55 Prob > chi2 = 0.475
(Robust, but weakened by many instruments.)
.
You should think about how plausible is exogeneity of each of the variables in your framework. It is something related to economic theory.
What happens in dynamic models is that the lagged dependend variable in right hand side of the equation is extremely likely to be endogenous (specifically, correlation with the error term). That's the reason you try to apply Arellano-Bond.
• asked a question related to Inequality
Question
we know that we use the following formula to find a turning point in income inequality researches:
Gini=B0 + B1gdp + B2gdp^2 + e
u = exp(-B1/2B2)
Gini=B0 + B1gdp + B2gdp^2 + B3gdp^3 + e;
For the cubic equation there will be two turning points as the derivative will be a quadratic equation.
this is the answer if you look for an answer for that equation
This sort of polynominal might have several turning points, depending on the value of the parameters.
I would first plot it for the relevant values of GDP in your population and then compute the turning or turning points you are interested in.
I hope it helps,
José-Ignacio
• asked a question related to Inequality
Question
I am working on research related to planning for territorial resilience. I am looking forward to your contribution through discussion on recent planning and research initiatives, citizens' and communities' active engagement and or leadership in such initiatives. How do you see the nexuses and to what extent current planning are addressing these nexuses?
There is increasing talk of adaptation and resilience to the effects of climate change. Even if we admit that they are of anthropogenic origin, the impacts of these changes occur over such large time scales that they are incompatible with the time scales of action and policies for the management of water resources. . The question that can legitimately be asked is a question of the order of magnitude of the anthropogenic effects on the degradation of water resources: (i) direct and immediate effects on the artificialization of the water cycle associated with the modes of exploitation and development of resources (overexploitation of surface water and groundwater, hydro-agricultural development, industrial, urban and agricultural pollution, etc.); (ii) anthropogenic effects on climate change and their indirect and very long-term implications on the potential of resources. Moral: has everything been done on (i) in terms of research and modeling in order to ensure the sustainability of resource exploitation in the short, medium, and long term; to decree that it is urgent to tackle question (ii) head-on with all its uncertainties, particularly with regard to time scales and its non-uniform topology across the globe?
• asked a question related to Inequality
Question
Every electron has a predetermined variable (a fixed quantum state). However, with the magnetic polarization applied in the measurement process, certain amount of energy can be added to each electron subject to the strength of the measurement (the angle of magnetic polarization). Therefore, for those electrons which have energy above the threshold energy, their spins can be flipped to the opposite directions. As a result, the possibility to find opposite spins in the transformation process is determined by the angle of the polarization which is conflict to "Superposition" in quantum theory where both spin up and spin down coexist in any single electron at all times. As to the entangled electrons (having same energy state but in opposite spin directions), because of the same threshold energy applies to both entangled electrons under the same measurement process (same angle of magnetic polarization), therefore, they will both either flip or stay un-flip together such that their entanglement is always maintained. In conclusion, "Superposition" is false meaning "God doesn't play dies". Also there is no talking between entangled electrons no matter how far the distance and how fast the communication are, meaning "No spooky behavior".
Bell’s Inequality is a mathematical theory based on Set Theory. It is true only if all elements in the sample space are equal; stay unchanged no matter of distribution. However, in photon polarization and electron entanglement transformation processes, subject to the polarization strength (the angle of polarization), photon and electron quantum states (Hidden Variables) can be changed by adding energy to the electrons or reducing energy from the photons during the transformation processes. In other words, all elements in the sample space are no longer the same elements. Therefore, Bell’s Inequality cannot be used to prove the existence of Hidden Variables. In fact, Hidden Variables exist simply to obey Locality and Realism. Einstein’s EPR Paradox and Hidden Variables are correct all time long.
Both photon and electron have wave and particle properties. In Double Slit Interference experiment, particle detector can be used to influence the phase angles of particle waves such that the coherency is disturbed and the interference patterns are diminished or even totally disappeared. However, the interruption of the interference patterns cannot to be used to prove the non-existence of wave property, or even to prove that wave and particle properties cannot coexist at the same time under observation. Therefore, “Complementarity Principle” is not true. In addition, both photon and electron have predetermined quantum energy states (Hidden Variables). In electron spin measurements, energy can be added to electrons through electron polarization process. Subject to the threshold energy, electrons can move to the new quantum energy states (Field Dependent Hidden Variables) either by staying at the same spin mode or flipping of to the opposite spin mode. On the other hand, in photon polarization measurements, energy can be removed from photons through photon polarization process. Subject to the threshold energy, photons can either enter into the new quantum energy states (Field Dependent Hidden Variables) by maintaining the same spin mode or totally blocked by the energy barrier. Even more, through further transformations, both photons and electrons can be transferred to normalized quantum energy states (Normalized Field Dependent Hidden Variables). In Quantum Entanglement experiments, both entangled photons and electrons have the same Hidden Variables except in opposite spin directions. Under the same polarization transformation processes (measurements), they both gain or lose the same energies as passing through the same threshold energy barriers and have the same Field Dependent Hidden Variables except in the opposite spin directions. Therefore, they are always entangled no matter how far the distance and how fast the time are. Bell’s Inequality is based on Set Theory and can only be applied on the same sample space. Therefore, in photon polarization experiments, Bell’s Inequality applying on the mixed sample spaces cannot be used to prove if Hidden Variables exist or not. On the other hand, in Quantum Entanglement experiments, with the right experimental data, Bell’s Inequality applying on the same sample space does approve the existence of the Hidden Variables. As a result, both electron and photon do carry predetermined Hidden Variables, and Schrödinger’s Cat cannot be both alive and dead at the same time. Therefore, “Quantum Superposition” cannot be true. Also, there is no mystery, no surprise and certainly no “Spooky” behavior. Einstein is correct after all.
• asked a question related to Inequality
Question
Hi,
I want to create an index to measure inequality in education. First of all, it would be necessary to identify the inequality within the 5 educational level. Therefore, I seperated 5 level to calculate index for each one of them. First, I will calculate the indicators and then the dimension index for that education (primary, secondary, etc.) category.
Finally, I will weight each educational category by the total number of individuals in the data set. Or I will compare the general indexes I have obtained with each other considering to educational categories.
My question is, would that be a statistically valid approach? My aim is to create a multidimensional education inequality index using the education level.
(Note: I will use the PCA method to determine indicator and dimensions. The table is for illustrative purposes only)
Far from being a specialist on the subject. I would add to what José-Ignacio Antón and David L Morgan have said, an alternative way of calculating inequality in education among the various possibilities of doing so. Assuming that their statistical inputs were census data, the basis of which contains demographic information, together with education variables, among others.
You could choose to define a minimum age value - as an assumption - in order to concentrate a large part of the population that no longer attends an educational establishment. Generate a census base query on the maximum level of education attained in that population - for example, less than complete primary level, maximum complete primary level, maximum incomplete secondary level, maximum complete secondary level, etc. –. Then weight each of these education level categories covering all years of schooling passed by the population with a value between zero and one.
Then multiply the relative weight of each population group by this weighting. And finally add the values of the partial indices corresponding to the categories of maximum level achieved. The result is a single value for the total of that population that will be between zero and one - closer to one the higher the average educational level, and closer to zero when the majority of the population has few years of schooling. In addition, you can calculate the variability values for each level of education or between these categories, in order to compare the results with those of another population.
I am sorry if I misunderstood the query or if the answer I wanted to give was unclear. I remain at your disposal. Regards
Fernando (from Argentina)
Lejos de ser un especialista en el tema. Agregaría a lo expresado por José-Ignacio y David, una alternativa de cálculo de la desigualdad en la educación entre las diversas posibilidades de realizarlo. Suponiendo que sus insumos estadísticos fueran datos censales, en cuya base contiene información demográfica, junto a variable de educación, entre otras.
Podría optar por definir un valor de edad mínimo–como supuesto-, para concentrar a gran parte de la población que ya no asiste a un establecimiento educativo. Generar la consulta en la base censal, sobre nivel educativo máximo alcanzado en dicha población – por ejemplo, inferior a nivel primario completo, nivel máximo primario completo, nivel máximo secundario incompleto, nivel máximo secundario completo, etc. –. Luego ponderar cada una de esas categorías de nivel educativo que abarca todos los años de estudios aprobados por la población, con un valor entre cero y uno.
Seguidamente multiplicar el peso relativo de cada grupo poblacional por ese ponderador. Y finalmente sumar los valores de los índices parciales correspondiente a las categorías de nivel máximo alcanzado. El resultado es un único valor para el total de esa población que estará entre cero y uno – más cerca de uno cuanto mayor sea nivel educativo en promedio, y acercándose a cero, cuando la mayoría de la población posee pocos años de estudios aprobados–. Adicionalmente puede calcular los valores de variabilidad para cada nivel de educación o entre las dichas categorías, con el objetivo de comparar los resultados con los de otra población.
Perdón si no comprendí bien la consulta o la respuesta que quise expresar fue poco clara. Quedo a su disposición. Saludos
Fernando (desde argentina)
• asked a question related to Inequality
Question
Esteemed researchers,
I will need more insights and justifications into using "per capita consumption expenditure" as a measure of poverty.
Please refer me to applicable papers.
Thanks as always.
Ngozi
I think that the consumption pattern is considered somewhat a measure or an indicator of the pattern of income distribution, and this may give an indication somewhat of the level of poverty or disparity in the distribution of income, if you will
• asked a question related to Inequality
Question
I'm looking into the question about how social uprisings (social movements, revolts, protests, etc.), particularly those who have a substantive violent character, elicit institutional change. I'm specifically interested in democracies (young or middle-aged) that exhibit a relevant degree of perceived unfairness and/or objective structural inequality, and in countries where the status quo institutional arrangement is "rigid" in a sense (many or some gridlocks are present).
Hence, I would be most grateful if you can share with me some references. Additionally, if you know of studies that emphasize quantitative methods, that would be very beneficial to my research.
Many thanks in advance, and I hope this message finds you safe and well.
Ignacio.
There are the recent papers on the effectiveness of protests in the US: Omar Wasow's paper "Do protests matter? Evidence from the 1960s Black Insurgency" and the Madestam et al paper, "Do political protests matter? evidence from the tea party movement." Outside the US, I a key work that comes to mind is Mark Beissinger's "Nationalist Mobilization and the Collapse of the Soviet State."
• asked a question related to Inequality
Question
It can be said that government support can take different forms depending on the type of liberal democracy, equality based or inequality based. Hence, we should be able to expect to see specific type of government support associated with equality and inequality based liberal democracy, which raises the question, what type of government support should we expect in each case? What do you think?
Dear Lucio Munoz,
Yes, welfare economics, as earlier, is narrowing, welfare green economics is on the way, but You, as a humanist, should know that besides welfare economics as economics, there exist welfare as social policy, welfare as social security in its redistributional political or social understanding. I argue that welfare state is more sociological and political science subject than economical. And You, dear Lucio, must have that in mind too.
• asked a question related to Inequality
Question
The past month or so has been super busy as I've moved my lectures from the classroom to the virtual video meeting "room" while naturally been concerned about student welfare. Yet, this new "Coronavirus condition" has forced me to pause for reflection. The result is that I appear to be less preoccupied with conceptual or theoretical questions than with more empirical questions that can demonstrate impact and help to combat suffering or social evils.
If your observation that "people going crazy" is the current state of our world(s), then that could perhaps be a reality check in itself.
• asked a question related to Inequality
Question
- i.e. for men and women
- tell us first from which country you are from, or which country's situation you would like to share
- you can talk about discrimination in salaries, position/rank, promotion, entry/hiring, opportunities for growth, etc.
Dear John,
I belong to India and there is no discrimination in terms of salaries, position/rank, promotion, entry/hiring, opportunities for growth. But, there are some jobs females do not feel comfortable and so do not opt for like defense, railways. But gradually that is also getting shorted out. But once one become an employee the growth, salary are at par for all of them.
• asked a question related to Inequality
Question
Dear colleagues,
do you have some EXCEL template for calculate GINI coefficient and create Lorenzo curve? I find some R packages but I am not sure how to use it on my date with population and income by region.
you can see this document to understand the gini formulas
• asked a question related to Inequality
Question
Inequality in salaries and wages between male and female has been used in all countries, as a competitive advantage by many companies. The strategy consists in paying low salaries to female, so as to reduce prodution cost. Low cost makes companies more competitive at international level.
Do you think gender discrimination is easy to fight? What is the situation in your country?
1. Be transparent
2. Support women into more senior roles
3. Implement gender neutral recruitment processes
4. Review salaries and standardize pay
5. Have a clear policy on discrimination
6. Ensure you’re actively encouraging women to progress
7. Promote a culture of meritocracy
• asked a question related to Inequality
Question
I have an ongoing ethnographic project on homeless' survival strategies, that I would like to discuss with you in some details and invite you to give me some feedback and just jot down some ideas you have regarding the issues I am raising below.
I am looking at the act of begging at the moment and try do describe it as a gift.
So far, I have come across many possible differentiations and distinctions that all not properly seem to work out in terms of making sense of what I observe and what the beggars themselves are actually telling me.
The classic theory of the gift (as Mauss, Malinowski, Boas) with its heavy emphasize on reciprocity is very hard to defend in the first instance. What are they giving back except for appreciation, a thank you? Might this already be enough to form a 'counter-gift' and in this way create a relationship? Are we to look at what I call a temporal fix - the counter-gift consists in the 'making-it-more-probable' to also get money being in the same situation anytime in the future? Might a 'good conscience' be valued as a counter gift? It additionally seems very problematic to not fall into the trap and perceive of reciprocity in a self-interest fashion - Gouldner's (1960) 'Norm' typology or Sahlin's (1974) continuum might be helpful here to clarify what one means. I am not really content with those ideas so far and none of them seems to hit the core.
So is the gift that one gives to an homeless beggar not really a gift in the classical sense but rather something one might describe as a commodity in Gregory's (1980) words: as an alienable object that is reciprocally independent not creating any relationship in the sense a gift is able to?
It seems as if the debate is again stuck in between the formalism or substantivist problematic that has been driving the discourse for years. But again the question in my particular case is similarly: in what way is it self-interest (as explained in the reciprocity argument above) that drives the giving, in which way is emotion of importance? Is it possible to follow Carrier (1991) and see the two as ends of a continuum in relation to giving to beggars?
In a very general sense I am also intrigued by Weiner's (1985, 1992) idea of inalienable possessions: does one actually give (money, good etc) in order to keep more valuable things (credit cards, marriage rings, a way of life) back? Might this be the 'inalienable possession' in this case? It seems also to link up in a certain way with another distinction that I came across in the course of the research: a beggar's regulars (people that see him regularly) and his one-offs (people that he sees once).
Regulars don't always give money, but rather fulfill certain wishes (often in terms of food) or simply spend some time with the beggar and devote some thought to his well-being. In this way, one might be able to argue, a more enduring and lasting social bond can be created through acts of giving (of time, talk and wishes). Such a regular also does not hold back - to nevertheless keep with Weiner, his gifts can still be inalienable (taking the distinction she draws in her earlier paper Inalienable Wealth: keeping-while-giving (as is the case with the regular) and giving-for-keeping) and contain a part of the owner (just think of time / talk in this way - you present yourself etc). On the other hand, the one-offs often give money and don't care about the beggar in a way a regular does. It might be here where one can introduce the presented notion of inalienable possessions: giving-for-keeping (as also Godelier (1999) puts forward) - they are giving in order to keep the more valuable possessions.
Does this notion seem completely far-fetched for you in this context?
A further issue is obviously the role money plays in this whole process:
what difference does it make that it is money that beggars mainly get?
Is it right as again Gregory (1980) or also Cheal (1987) point out that money destroys gift economies (in the particular sense that he defines them) and is an expression of 'disembodied interest'?
Yes.
• asked a question related to Inequality
Question
I am calculating a value that is computed by dividing the derivative of the cumulative distribution function by the value of the distribution function at that point. It is of the form:
𝐽=𝐹′(𝑥) / 𝐹(𝑥)
Where 𝐹(𝑥)is the cumulative distribution function. To get the confidence band on 𝐹(𝑥)I can use the DKF Inequality. How do I get the confidence bands on J?
Drew Lilley We can get the random number of 𝐹′(𝑥) and F(x), right? Then we can get random numbers of J. After that, confidence interval of J is clear then. :)
• asked a question related to Inequality
Question
It is often argued that even in low- and middle-income countries social protection or, more in general, social policies can improve social cohesion and state-society relationship. However, it is very difficult to find evidence to support this argument. Do you know any empirical study?
For anyone interested in this topic, see our Call for Papers for a Workshop at the German Development Institute (DIE), Bonn, 4-5 December!!
• asked a question related to Inequality
Question
I am struggling with measuring inequality in health-workforce between regions based on number of workers in each region and region population using Atkinson index (spreadsheet is in attachment). Is there anyone willing to help me where I made mistake?
Thanks,
AM
I am really interested in the work.
• asked a question related to Inequality
Question
Dear All
I have conducted a multilevel model for binary outcome (self-rated health), using Stata .
About 72000 individuals at level 1 are nested within 50 countries at level 2.
The number of countries is rather small, to obtain more robust estimate I performed bayesian melogit and the Deviance Information Criterion (DIC) was used to compare the fit of different models. Is this correct ? or using melogit (instead of MCMC estimate) the result will be robust enough?
Below is the code I have:
bayes, mcmcsize(2500) : melogit Health centered_Age i.Sex i.Marital i.Income i.Percived-Inequality lnGDP GINI || Country: , or
Any comments or suggestions would be greatly appreciated.
I would use MCMC to be sure that you get good estimates in this situation, see
• asked a question related to Inequality
Question
Basing on “potential infinite--actual infinite”, do we have only following three different operating ideas and results of quantitative studying and cognizing on “elements in infinite sets” in present classical infinite set theory?
（1）With the idea of “potential infinite”: Denying the essential differences of infinite set elements’ “special nature, special existing condition, special manifestation and special relationship among each other”, so, elements in all different infinite sets are only heaps of infinite “indiscriminative, nonquantitative, abstract points” and it is unnecessary and impossibale to have any quantitative studying and cognizing on “infinite elements (points) in infinite sets”, the number of elements in all infinite sets are the same and it is just infinite. For example, elements in many infinite mother sets and their sub-sets are in fact all the same stuff of infinite “indiscriminative, nonquantitative, abstract points” without any differences of “nature, existing condition, manifestation and relationship among each other”. The typical cases are “the element numbers in Rational Numbers Set and Natural Numbers Set are equal, the element numbers in Natural Numbers Set and Even Numbers Set are equal and they are just all infinite”. The conclution is: any infinite set has limitless, endlees, infinite elements, so their “one-to-one coresponding operations” of quantitative studying and cognizing on “infinite elements (points) in infinite sets” can be carried on for ever and their element numbers are all “equally infinite”. Going along this train of thought, one can understand and construct those theorms and proofs related to the idea of “different infinite sets, equal element numbers”.
（2）With the idea of “actual infinite”: Affirming the essential differences of infinite set elements’ “special nature, special existing condition, special manifestation and special relationship among each other”, so, elements in all different infinite sets can be “discriminative, quantitative visible and tangible mathematical things” and it is necessary and possibale to have all kinds of quantitative studying and cognizing on “infinite elements in infinite sets”. For example, there are different “special nature, special existing condition, special manifestation and special relationship among each other” betwee elements in Real Numbers Set and Natural Numbers Set, so, these two infinite sets have different element numbers. The typical cases are “the element numbers in Real Numbers Set are more than that of Natural Numbers Set, the element numbers in Power Set are more than that of its original set and they are all inequal”. The conclution is: Different infinite sets may have different element numbers. So, in the “one-to-one coresponding operations” of quantitative studying and cognizing on infinite elements of two different infinite sets, the elements in smaller set with fewer elements are consumed and finished soon, it means the element numbers in such an infinite set are not endlees and limitless at all (fake infinite); but in the begger set, infinite many elements are left during this operations, this means its elements are endlees and limitless (real infinite), never be consumed and finished at all, the “one-to-one coresponding operations” here can never be carried on for ever at all. Going along this train of thought, one can understand and construct those theorms and proofs related to the idea of “different infinite sets, different element numbers”.
（3）With the idea of mixture “potential infinite--actual infinite”: The above different operating ideas and results of quantitative studying and cognizing on “elements in infinite sets” in present classical infinite set theory are both acknowledged “OK” and accepted. This inevitably makes us unable to cognize scientifically and clearly the infinite sets and their elements we are facing to in many situations------- being caught in a paradoxical status of arbitrary, self-contradictory and non-self-justification. So, Russell's Paradox as well as its family members in different periods of time have been generated, developed and suspended. Following two cases are typical examples--------First case: with the idea of “potential infinite”, we claim “certain infinite set with its defined elements can be constructed”, than we claim “some of these elements actually can not be included within this very infinite set” with the idea of “actual infinite” and find out those “belonging to but uncontained elements of this set” to prove all kinds of family members of Russell's Paradox in different periods of time (My stuedies proved that whenever we come to any case of “elements belonging to but impossibly contained in a set, a defined group of things”, we come to a situation of “confusing whole and portion” -------- traped immediately into “potential infinite--actual infinite”. Liar’s Paradox, Post Card Paradox,... are all family members of Russell's Paradox) . Second case: with the idea of “potential infinite”, we have proved “the elements in Rational Number Set are equal to the elements in Natural Number Set”, but at the same time we can prove “the elements in Rational Number Set are infinite more than the elements in Natural Number Set” because just a tiny portionof the rational numbers from Rational Number Set (such as a subset of 1, 1/2, 1/3, 1/4, 1/5, 1/6, …, 1/n …) can map and use up (bijective) well all the numbers in Natural Number Set (1,2,3,...,n,...), so a lot of (infinite) rational numbers are left behind in this one-to-one mapping from the Rational Number Set onto the Natural Number Set and construct the “’Countable-uncountable’ Paradox of Rational Number Set”. Going along this train of thought, one can understand and construct all kinds of family members of Russell's Paradox in different periods of time. The conclution is: the quantitative studying and cognizing theories and operations in present classical infinite set theory are too arbitrary and lack of scientific basic theory.
Five of my published papers have been up loaded onto RG to answer such questions:
1，On the Quantitative Cognitions to “Infinite Things” (I)
2，On the Quantitative Cognitions to “Infinite Things” (II)
3，On the Quantitative Cognitions to “Infinite Things” (III)
4 On the Quantitative Cognitions to “Infinite Things” (IV)
5 On the Quantitative Cognitions to “Infinite Things” (V)
• asked a question related to Inequality
Question
Hi Folks,
I am looking for a validated survey tool to track changes in participants' notions of power and inequality in society. Rather than reinventing the wheel, I am wondering if anyone has, or has used one that I may be able to draw from in an upcoming study.
you might find the following helpful
The Gilens and Page Measure of Political Inequality
However, it's more likely that you will find measures if you define your variables of interest more as it's unlikely that one measure can capture all aspects of power and inequality.
• asked a question related to Inequality
Question
In fact, “Inequality” is a common observation in several field among us, as physicist I’m worry about our contributions for future society.
Hi Mariano. It's true. And how about new theories and findings on medicine and transportation?
• asked a question related to Inequality
Question
Whether or not infrastructure helps in the achievement of equality is a function of what exists in reality. Ordinarily, the existence of infrastructure irrespective of the perspective of understanding should help in the encouragement and achievement of equality and balance between and among individuals and social groups in both private and public capacities. The reality, going by the African experience and other similar experiences of transitional and technologically developing societies, is largely the manipulation of infrastructural provisions. The manipulation is largely encouraged by corruption and prebendalistic attachments going by the evidence of the African governance framework. We can therefore assume tentatively that the denial of infrastructure or its epileptic provision is an act of inequality. Inequality, again from the perspective of the denial of infrastructure, requires an empirical probe of the factors, forces and processes in which the provision of infrastructure are dependent upon.
• asked a question related to Inequality
Question
Hello,
I have a very interesting case on relationship between poverty and inequality based on the case from Georgia.
International poverty rates are used in the study to measure extreme ($1.25 per day), relative (60% of median consumption) and general ($2.50) poverty rates. Those rates are converted with the exchange rate in Georgian Lari (GEL) and then estimated equivalent monthly average for each threshold.
Poverty rates are measures in terms of average consumption per equivalent adult (PAE).
It turns out that all poverty rates from 2015 to 2017 increased. While inequality measured in terms of per equivalent adult consumption decreased marginally Gini 2015= 0.36 vs Gini 2017=0.35648 (almost no change).
Rural Gini = 2015 - 0.346 ; 2017 - 0.355
Urban Gini = 2015 - 0.365 ; 2017 - 0.354
On national level consumption inequality did not change (change is marginal), whereas Gini in rural areas increased and for urban areas decreased. Meanwhile poverty rates increased. Nationally, real average consumption decreased by 10% between 2015-2017. Especially in the poorest decile.
Question: Can poverty rates increase while Gini decreases? I think increase in Gini does not necessarily means automatic decrease in poverty rates.
Your contributions are very welcomed !!!
Best regards,
Davit
Dear Sanwal,
Do you have in mind a paper that describes the same case?
Best,
Davit
• asked a question related to Inequality
Question
Or any other studies that might be relevant to this topic?
HI,
Try these
Langston, J. (2016). Invisible fathers: Exploring an integrated approach to supporting fathers through the Mellow Dads Parenting Programme piloted in a UK prison. Journal of Integrated Care, 24(4), 176-187.
Gatrell, C. J., Burnett, S. B., Cooper, C. L., & Sparrow, P. (2015). The price of love: The prioritisation of childcare and income earning among UK fathers. Families, Relationships and Societies, 4(2), 225-238.
Culpin, I., Heron, J., Araya, R., Melotti, R., & Joinson, C. (2013). Father absence and depressive symptoms in adolescence: findings from a UK cohort. Psychological medicine, 43(12), 2615-2626.
• asked a question related to Inequality
Question
Governments are always looking around for new ways of raising taxes, so here is a new one, a gene tax. It will be greeted with howls of rage, but then so is every new tax proposal. Those with genetic advantages should be taxed proportionately, as they will be so much more successful in later life. This should also be a spur to those few who do not make full use of their abilities for the public good, but are content to be free loaders. At the other end, many have genetic disorders causing chronic distress and poverty, and they should be correspondingly compensated.
A "gene tax" ignores the simple truth that all human endeavors require both "nature and nurture" for optimal outcomes. A gene tax would make sense only in a world in which there were no structural or institutional barriers to human development. As Gordon's quote of Lynn clearly indicates, 80% of the most powerful did not get to that position by virtue of their genetic makeup alone, it was the elite university environment that provided the context for their power base.
• asked a question related to Inequality
Question
In the first step I have used absolute beta convergence models as specified below:
In[Y_( i, t+k)/Y_(i,t) ]= α+β.ln(Y_(i.t) )+ε_it
Where In[Y_( i, t+k)/Y_(i,t) ] is the mean annualized growth rate of the variable Y in state i in the period (t, t+k), Y_(i.t) is the value in the initial time t and ε_it are corresponding residuals.
Then estimated speed of convergence as
The speed of convergence is computed as s = −1/T (ln (1+Tβ). Where s= speed of convergence and Tβ is the β-convergence in T period.
However, when beta value is larger this equation is not yielding any result. What does this indicate?
"Socioeconomic Progress across the Major Indian states: Converging or Diverging"
at
• asked a question related to Inequality
Question
I am researching racism in France, related policies and their effects, but most of what I find is in English by US authors. I would like to read on this issue in French by French scholars/writers. Also, I am interested in different/opposing pov.
Many thanks
Mary Helen C
Dear Ms. Mary-Helen Castanuela
I am writing to tell you that I read one intreset article about Paradoxes of Race Policy
in the United States, Great Britain, and France.
Please find attached article as a PDF file.
I hope I have been some of help.
Best regards,
Andrija
• asked a question related to Inequality
Question
I would like to study the opinion of European citizens' on European integration, using a European survey with direct questions in merit and others such as income, preferred political party, and so forth. Then I would like to understand if there is a correlation between the results of this regression and the level of inequality within each country.
I am afraid of using the Gini index (or any other index based on income) to proxy inequality in this second regression, since there could be a problem of correlated variables. What could I possibly do? Is there an alternative index that I could use and that would still make sense?
Further, in case the Assets approach is of assistance, the following [my bold etc] has reached me, from R-G member Alexander Dill
"World Social Capital Monitor
Revaluation of around 173 countries, their regions, their culture, their assets, their potentials - that's my task since 2007 when I published my "Global Freeware Index" for the first time.
Today I evaluate the major global indices, their unilaterism and their bias. And I'm testing new evaluation methods without aggregated data and binary questions.
I hope that the new method will not only being accepted and used but as well giving a new chance to countries in crises and conflicts."
Hoping this helps - Paul
• asked a question related to Inequality
Question
I want to get the inequality data for developing countries for atleast 30 yrs. and want to use EHII UTIP inequality data. But the problem is this data is latest available from 1968-2008 and i want to use it till 2015. Searching certain papers i find out that some people have expanded this data using world bank data and method "Out of sample" forecasting.could anyone guide me how to expand the available data and details about using this forecasting method.
Thanks
Out of sample estimation is based on modeling the year to year change and extrapolation based on that model. One should be cautious when using such models since often, they do not capture reality very well. it would be better to obtain the data from other sources if available for recent years.
• asked a question related to Inequality
Question
Social closure is an important mechanism leading to inequality in life outcomes. We are particularly interested in items measuring how people feel about processes of social closure, to what extent they feel them legitimate or not.
Thanks!
Maybe you can look at the ISSP module on social inequalities:
Best,
Loris
• asked a question related to Inequality
Question
As New York has mapped the income levels along individual subway lines, earnings range from poverty to considerable wealth, namely income inequality exist obviously.
But how and when such inequality form along the time, i.g. before, in the middle and after the construction of metro? The procedure is rather complex, relating with the change of accessibility, spillover of land price and house price, agglomeration of economic activities, increase of commercial and housing investment, job attraction, etc.
Does this inequality has a spatial pattern? That is the spatial difference of the degree of inequality between the regions near to the metro and the ones slightly far away from the metro. And how does spatial pattern of income inequality evolve or change before, in the middle and after the construction of metro? Maybe the evolution of such income inequality will be impacted greatly by the density of metro, gentrification, sub-urbanization, urban renewal, built environment, etc.
Dear Guo,
Very interesting question. We have done a research on this topic measuring social and spatial inequalities change in urban area after a new transport measure. See Souche, Mercier, Ovtracht in Urban Studies 2016 (you can find the paper in my page researchgate) . We have use the same methodology for evaluating the impact of a new subway line (but not published). Best. Stephanie
• asked a question related to Inequality
Question
I plan a project. The project's aim is to determine inequality behaviours against students in schools. So I am looking for paper, book etc. about this topic.
1. What are the issues of inequality against the students within or outside the classroom?
Best regards,
Gamze Kasalak
Gamze,
I had a professor at Minnesota State University Moorhead who would be able to fill a book with information about this topic and related to the topic. I would assume he would be glad to help you by providing insight and useful resources. His contact information is below:
Vigilant, Lee
Faculty
Sociology and Criminal Justice Department
Office: LO 212J
Phone: 218.477.2034
Good luck!
Sam
• asked a question related to Inequality
Question
My terminology here is from "Measure Theory" by JL Doob, Springer Graduate Texts in Mathematics, 1994. Metric and pseudometric spaces are described on pages 3 to 5.
My question is what happens if the triangle inequality is an equality so we have the distance formula d(s, u) = d(s, t) + d(t, u). This can only be true if every distance is 1, and 1 = 1 + 1 because every a = a2.
Now if the pseudometric distance formula is d(s, s) = 0, does this follow directly from the triangle equality or is there something else required? Is d(s, s) = 0 the same as the Borel function f(x, y) = 0 where x = y?
What I am hoping is that if there is an algebra of subsets where every set is a singleton, then that by itself makes a pseudometric space with a distribution on the Borel Square [0, 1] x [0, 1]. Does the triangle equality automatically make an L-space?
May be it is not that simple. If the triangle equality metric alone does not make a pseudometric space by itself, what does? A field of zeros? What if I have the algebra formed by the union, intersection, and compliment of an elemental set? What if I have a set, a relation, an agumented frame, and a map?
My goal here is to show that music structures are a pseudometric space where a probability distribution is imposed on pitch values by the set construction operation. This follows my previous question demonstrating that music theory is a 3-fold structure, not two fold as commonly thought. In a 2-fold structure there is no way to understand why every note does not have a probability of 1/12..
Every metric is a pseduometric.
• asked a question related to Inequality
Question
looking beyond the conventional measures of poverty, it seems interesting to look at the non economic factors so that a better measure of poverty can be calculated. while going through some of the literature on poverty, I found the inequality of opportunity more interesting to look into the factors which are more due to circumstances than the the level of effort which one puts in. so here the debate is about Circumstances Vs Efforts.
please help me out in getting more literature on this issue. How should I calcute this kind of inequality?
Usually this is measured as the percentage of people moving between income quintiles over time.
If it is found that the income outcomes (which quintile they are in) of children in the next generation across all parent's income quintiles are evenly distributed across all quintiles, this would imply perfect equality of opportunity. (And in fact that is very unlikely even if systems perfectly ensured equality of opportunity because the genetic component is very unlikely to be zero.)
If the income outcomes (which quintile they are in) of children in the next generation are identical to that of their parents across all quintiles, then inequality of opportunity could not be higher.
Many studies on social mobility show the percentage of the population moving between quintiles over time. While this is not a perfect methodology compared to a generatoinal analysis, it allows the researcher to assess whether equality of opportunity is increasing or decreasing over time.
The same analysis could be performed at a percentile level, but the outputs are much easier to digest at the quintile level.
• asked a question related to Inequality
Question
Disaggregated data collection and analysis is recommended for policy development to address race inequality. Moreover it provides a useful tool to address Afro-phobia and other forms of xenophobia.
I suggest you to read the book:
Advances on Income Inequality and Concentration Measures
Edited by Achille Lemmi and Gianni Betti
Routledge 2008
Print ISBN: 978-0-415-44337-1
eBook ISBN: 978-0-203-92792-2
Gianni
• asked a question related to Inequality
Question
I'm interested in institutional inequality and structural impediments as they relate to gender and WPS. Anyone have links to good papers/experts or ideas on how to frame the issue?
Here are some references you might consider chasing up:
Caprioli, M. (2004). Democracy and Human Rights versus Women’s Security: A Contradiction?. Security Dialogue, 35(4), 411-428.
Caprioli, M. (2005). Primed for violence: The role of gender inequality in predicting internal conflict. International Studies Quarterly, 49(2), 161-178.
Cohn, C. (2008). Mainstreaming gender in UN security policy: A path to political transformation?. In Global Governance (pp. 185-206). Palgrave Macmillan UK.
Higate, P., & Henry, M. (2004). Engendering (in) security in peace support operations. Security Dialogue, 35(4), 481-498.
Hudson, V. M., Caprioli, M., Ballif-Spanvill, B., McDermott, R., & Emmett, C. F. (2009). The heart of the matter: The security of women and the security of states. International Security, 33(3), 7-45.
Moussa, G. (2008). Gender aspects of human security. International Social Science Journal, 59(s1), 81-100.
Woroniuk, B., & Unit, P. (2001). Gender Equality and Peace Building: Operational Framework. for CIDA Equality Division and Peacebuilding Unit.
Zuckerman, E., & Greenberg, M. (2004). The gender dimensions of post-conflict reconstruction: an analytical framework for policymakers. Gender & Development, 12(3), 70-82.
Hope these are beneficial.
• asked a question related to Inequality
Question
Anything related to barriers, challenges, benefits and policies
Hello Javier
This site lists possible useful papers; I searched for 'measure' when looking at this site:
Some of these papers are quite old now:
Christman, L. A., & Slaten, B. L. (1991). Attitudes toward people with disabilities and judgments of employment potential. Perceptual and Motor Skills, 72(2), 467-475.
I have not been able to access the full text:
Paez P& Arendt SW (2014) Managers' Attitudes Towards Employees with Disabilities in the Hospitality Industry
Millington, M. J., Rosenthal, D., & Lott, A. (1998). Employment expectation profiles as a differential measure of employment-relevant attitudes towards people with disabilities. Journal of Applied Rehabilitation Counseling, 28(4), 36.
This is a survey:
Baseline Survey on Employers’ Attitudes towards Employment of People with Disabilities
These are written re specific groups:
McDonnall, M. C. (2014). Employer Attitudes Toward Blind or Visually Impaired Employees Initial Development of a Measurement Instrument. Rehabilitation Counseling Bulletin, 58(1), 29-36.
Andersson, J. (2012). Employer attitudes towards people with a psychological disability.
Very best wishes
Mary
• asked a question related to Inequality
Question
I understand
$$\begin{split} -a^{i,j}D_{i,j}v&= -\eta a^{i,j}D_{i,j}w-2a_{i,j}D_{i}\eta D_{j}w-wa^{i,j}D_{i,j}\eta \\ &\leq \eta(-a^{i,j}D_{i}wD_{j}w+b_{i}D_{i}w+|c|+g)-2a^{i,j}D_{i}\eta D_{j}w-wa^{i,j}D_{i,j}\eta. \end{split}$$
But I could not understand how the right hand side of above inequality is less than
$$\frac{2}{\eta}a^{i,j}D_{i}\eta D_{j}\eta-w a^{i,j}D_{ij}\eta+(|b|^{2}+|c|+g)?$$
Because all of the deleted terms are negative and all added terms are positive.
• asked a question related to Inequality
Question
Seeking a brief assessment of material hardship for inclusion in a survey. Considering following Mayer & Jenck's (1989) inclusion of 1) SNAP/food stamp receipt, 2) not enough money for housing, 3) not enough money to pay bills, and 4) not enough money for healthcare. Wondering if anyone has guidance or suggestions based on recent research?
Thanks to you both - you have given me multiple ways to think about "material hardship," which is what I was needing.
• asked a question related to Inequality
Question
How can I solve Riccati inequality in Matlab using a modified function "care"? See attachment, please.
Go to page 7 of the document and pages afterwards for matlab code. It shows how to convert Riccati inequality into LMI.
• asked a question related to Inequality
Question
If so, what is its form and significance and is there a connection between temporal and spatial Uncertainty? For example, is the temporal uncertainty asymmetric, so that the forward component is associated with greater disorder?
George and Stephen
By the way the uncertainty in quantum theory is quite different in origin
to one you may have by simply having a stochastic process. The uncertainty is
simply intrinsic in the nature of a quantum particle, such as an electron,with both wave and particle properties...believe it or not.
• asked a question related to Inequality
Question
In LP, we define a non-negative dual variable for each inequality constraint, and an unrestricted dual variable for each equality constraints. In this sense, how can I get these variables without formulating the dual model (i.e., only through the results of the primal model)? Is it possible with GAMS?
Hi,
Its implementation is really simple in GAMS programming. See the example below.
Min f(x)
s.t.
eq1.. g(x)>=0 Landa1 (=dual variable of equation 1)
eq2.. h(x)=0 : Landa2 (=dual variable of equation 2)
----------------------
To determine the values of dual variables Landa1 and Landa2, you should write:
display eq1.m , eq2.m ;
Good luck,
• asked a question related to Inequality
Question
According to Frances Stewart, horizontal inequalities (inequalities between groups) in its various dimensions (economic, socio cultural and political ) are the main sources of conflict in most conflict stricken countries. It is argued that economic inequalities provide fertile ground for conflict, socio-cultural inequalities bind groups together, and political inequalities provide incentives for leaders to mobilize people for rebellion. Is there a threshold of the extent of such inequalities ( in one or all dimensions) beyond which it spur grievances and mobilize people leading to conflict ? or is it the mismatch between these three dimension driving the violent conflict?
Conflict is not simply a product of a "land grab." To better understand the sources of conflict, you are better served examining the concepts of relative depravation and opportunity cost of conflict. Institutional instability, resource scarcity, food insecurity, etc., all alter the opportunity cost of conflict.
To your point, there is very little evidence of thresholds because it is a multi-dimensional problem. And, it is not just an economic problem. There are social, political, and economic dimensions interacting, and "inequality" is not particularly pertinent. That is, it is "relative inequality" that matters. And that is only operational in the context of weak institutions that prevent Coasian bargaining in the first place.
• asked a question related to Inequality
Question
There exist public and private schools,where as the private schools have conditions to their registration,public schools owned and run by the Government do not meet the same standards.
There are expectations that one has to meet in this schools to learn which depend on individual households.
Nationwide the infrastructure that supports learning vary from one school to the other yet they also support learning which is finally examined in a standardized manner.
Surprisingly,even schools with the same number of children do not have the same number of teachers, especially with regards to their location.
There are mixed findings in the level of increases in inequality detected in education system. In Nigeria, for example, most successful schools in terms of the market information (which is often published) have favoured a particular group of student populations. As these measures are modified by assumptions around the intersection of class, ethnicity, socio-cultural beliefs and gender, choice appears to lead to inequality and homogenization of student populations. In particular, as some (private) schools realise their projected student populations and reach the top level in the marketplace, other schools are left behind with short supply of students, who are mostly from low socio-economic groups. These circumstances lock the latter category of schools in a series of poor academic achievement and student and teacher attrition, which has implication for choice policies (and education system as a whole). But in all these issues the possibility that what educational policies may do is to change the rules by which inequality takes place, but without markedly increasing or eliminating levels of inequality that are largely shaped by structural factors. The following readings can help you further:
Waslander, S., Pater, C., Van der Weide, M., (2010), “Markets in Education: An analytical Review of Empirical Research on Market Mechanisms in Education”, OECD Education Working Papers, No. 52, OECD Publishing, http://dx.doi.org/10.1787/5km4pskmkr27-en
Le Grand, J., Propper, C., and Smith, S. (2008), “The Economics of Social Problems”, Palgrave Macmillan, Basingstoke, UK.
Gorard, S., Taylor, C., and Fitz, J. (2003) Schools, Markets, and Choice Policies, Routledge Falmer, London, UK.
Fredriksen, B. and Fossberg, C.H. (2014) The case for investing in secondary education in sub-Saharan Africa (SSA): challenges and opportunities. Int Rev Educ, 60:235–259
• asked a question related to Inequality
Question
I am just starting a research project on this topic (more concretely: ageism and inequality in Ecuador). While I do have some idea on each one of the topics, I have a hard time to bring them together - does anyone of you know about studies on ageism and inequality, maybe with a policy perspective?
I agree Phillip, a cross-cultural cross-country comparison would be really useful. National policy, opportunity, health and expectations are key areas that especially deserve comparison. Pensions, superannuation and aging in place welfare policies are important policy and opportunity contexts for over 60 year olds. I also think that the gender aspect is really interesting. Women over 60 years of age in Australia are less financially well off than men yet likely to live longer. We're seeing greater numbers of homeless women in this age range.
• asked a question related to Inequality
Question
without having to suffer the problem of bias associated with endogeniety in a country like Nigeria
A minor correction to Marc Cowling: In a Heckman-type equation, you correct for different probabilities of participating in the Labor Market, for two groups with diferent Labor Participation percentages.
The problem with this correctio is that it doesn't allow you to separate low participation jobs due to self selection (i.e, women don't work because they optimally prefer to take care of the children), and due to exclusion or discrimination (i.e, employers don't hire women because they are women).
In order to correct this problem, you can use queueing models to model a first stage where a women decides whether or not to work, and thus enters in a "queue" for wage work, and on then model a second stage where employers decide whether they chose or not women for the queue. Women may be not chosen, for example, on the basis of their educational attainment, which will effect the returns of schooling (which your are triying to capture.)
This queuing models are interesting because they give you predicted correlations between the error terms of the two stages, and these correlations are then used to correct Mincerian equations, cleaning some of the discrimination effect in the return to schooling. I leave you a paper where three authors do an exercise like this for Chile, and measure queues from the informal sector to the formal sector. They find discrimination for ethnic groups.
Since this procedure is very complicated and requieres good data, it's only useful to use it if you think there are strong reasons that one group is being discrimanted in the form of being (partially) excluded from the labor market. If this exclusion has it's origin in the low educational attainment od the excluded group, then it will correct a lot of the discrimination "effect" into returns of education. If the group is not excluded, and is only being paid less, then an Oaxaca Decomposition is the most fruitful way to go.
Hope it helps!
Alejandro.
• asked a question related to Inequality
Question
I want to calibrate a numerical model of wealth inequality. For this purpose I need data on the current distribution of wealth in the OECD countries (aggregate over all OECD countries is sufficient). The level of detail should comprise at least wealth quintiles.
Most of the statistics, unfortunately, are on income inequality, not on wealth. For wealth inequality, you could consult the Luxembourg Wealth Study (LWS). Still, not many countries are included in these studies and the data is hard to interpret and has many lacunae. Developing a more comprehensive and reliable overview of worldwide wealth inequality is perhaps one of the biggest tasks for quantitative social research laying ahead.
• asked a question related to Inequality
Question
I am looking for an inequality indicator that can be derived from the distribution of a population in five discrete poverty classes derived from the Latin American NBI (Necesidades Basicas Insatisfechas) methodology. The methodology ascribes each household of a locality (urban or rural) a "NBI index" in function of income, housing, education, etc. and then ascribe it to one of five "poverty classes" , etc, which are "non-poor, poverty line, moderate poverty, indigent, marginal". I have only data on the number of households per class per locality, not the NBI index per household.
If you have the continuous scores of the NBI index you can run Gini of Theil If your discrete categories are quintiles, yo can also run one of these dispersion stats. Otherwise you can calculate the ratio of marginal households against non poor.
• asked a question related to Inequality
Question
Should emerging India be at ease with inequality?
In most cases economic growth positions some participants at a vantage position in terms of resources control more than the others, this often brings about income inequality. This is more rampant in capitalist economy which encourages the rich to get richer at the detriment of the poor. The well to do are the ones controlling the means of production. The income inequality in such economy is more conspicuous when the basic infrastructures are inadequate as it is common in most developing countries.
• asked a question related to Inequality
Question
I am now reading Piketty's Capital in the 21st Century. It is a wonderful statistical research work and should be a model that all economists must learn from it. I have no intention to throw any doubt on his fact findings.
My question is concerned with the logic which connects the fact r >g and the rising inequality of income and wealth.
In the Kaldor-Pasinetti framework of growth and distribution, we have the following long run relation
g = scr,
where sc stands for the capitalists' propensity to save (I omit all the necessary conditions for the validity of this equation). See equation (14) of Pasinetti (1962) Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth. Review of Economics Studies 29(4): 267-279. , p.272) .
In this case the rate of investment and by consequence the rate of accumulation of capital is equal to the growth rate. Then capital assets or the total wealth grow at the same rate as the total income and therefore the workers' income (if we assume that workers' share in the income remains constant).
Can anyone explain Piketty's logic? I want to know in what sense Piketty calls relation r>g the driving force of rising inequality.
I think that Piketty’s argument is simply that an interest rate greater than the growth rate implies that capital income will grow faster than wage income with a consequent worsening of income distribution. One way to explain Piketty’s argument within the Harrod_Domar framework, however, is presented in the document in attach.
• asked a question related to Inequality
Question
See above
This has been helpful for me in regards to the most current task that my tutor has set out for me to help with my 1500 word essay. Thank you for the above PDF link :-)
• asked a question related to Inequality
Question
The topic of inequality and its social as well as economic implications is a very discussed topic (specially after Piketty´s book came out).
Most research I´ve come across with concentrates around the relationship between income inequality and growth. So I´m looking for some good papers on the relationship between wealth inequality and economic growth.
Any suggestions?
Thanks!
Dear Erika,
please note that Piketti has conducted some of his research in collaboration with Tony Atkinson and others who looked into the interaction between inequality and wealth in the long run (this is a major research project of Tony Atkinson and Facundo Alvarez). See their joint article (link below). I am sure there is more written by them.
Good luck!
• asked a question related to Inequality
Question
The aim is to find how, why and where infrastructure is creating inequality/inequity/disparity?
And is there any easy way, how a town planner should try to remove inequality or inequity from the society - what should be the priority as both have different pros? Is there any way, that political interference can also be reduced while providing infrastructure and prioritizing it?
Case study will help, especially from India.
Dear,
About infrastructure and urban segregation in Brazil, I recommend:
TOLEDO SILVA, Ricardo. The Connectivity of the Infrastructure Networks and the Urban Space of São Paulo in the 90s. International Journal of Urban and Regional Research, Oxford, v. 24, n. 1, p. 140-164, 2000.
and in Portuguese others two important authors:
ROLNIK, Raquel. A Cidade e a Lei: legislação, política urbana e territórios na Cidade de São Paulo. São Paulo, Studio Nobel Fapesp, 1997. (The City and The Law: Legislation, Urban Policy and Territories in the City of São Paulo)
SANTOS, Milton. A urbanização desigual (The unequal urbanization), Vozes, Petrópolis, 1980.
I hope be useful.
Best Regards,
• asked a question related to Inequality
Question
Has anyone done research by using the literary term Strategic Essentialism, coined by Spivak? Do you think this term has any use? I need some opinions...thanks!
I have used this concept in one of my articles to rethink strategies for diversity in organizations.
• asked a question related to Inequality
Question
India has demonstrated considerable progress in the past decade on improving primary, school access, infrastructure, pupil-teacher ratios, teacher salaries, and student enrollment.
Nevertheless, student learning levels and trajectories are disturbingly low. Our system is known for encouraging students to memorize rather than foster creativity and independent thinking. Also, even today in India, unfortunately where a child comes from does go on to dictate who he can become. How do we deal with this educational inequity?
What would it take to completely overhaul the system and create equity in education and progressive policies along with a generation of enthusiastic learners and teachers? what do you think?
Dear Sribas, This is indeed a complex issue, and warrants systemic changes. It has been discovered in research by Professor Jean Dreze that students withdraw from schools in India not due to poverty but due to poor teaching resulting in No-learning. I would suggest the following revolutionary measures: Inculcate child education as a societal value and implement it sincerely; there need to be libraries in each village and locality managed by some PPP (public private partnership) arrangement, and industry can be expected to invest in them through the CSR initiatives that are envisaged in the new Companies Act 2013; need to discover new devices to be used for enhancing children's creativity rather than just memorizing; taking measures for teacher accountability and linking their output with incentives.
• asked a question related to Inequality
Question
I am planning a cross-cultural study that includes developed and developing countries. My research questions deal with the effects of the provision of care for labour market participation. Typically, the provision of care is studied in developed countries using Esping-Andersen’s typology and in developing countries using variations of Evers et al (1994) or Razavi 2007 “care diamond”. The Esping-Andersen typology is a poor choice for developing countries but the concept of a care diamond could be an appropriate concept in both developed and developing countries. I am looking for advice about the feasibility of this approach. References on the subject would also be appreciated.
Sorry about the delay in replying. The concept of the care diamond considers that actors other than the state, market and family may be engaged in the provision of welfare services to citizens in a country. The above conept is called the welfare triangle and is often used when studying provision of welfare services in developed western societies.
The care diamond is called a diamond because it considers and values contributions from the civil society in addition to those provided through the triangle construction presented above. Services from the civil community may take the form of charities and other private or semi-private organisations as well as informal groups such as neighbours, friends or other persons. These services may be of central importance in developing countries where the welfare state is less developed.
I am interested in understanding the importance of welfare service provision through the care diamond in both developed and developing countries. My thesis is that the centrality of care in both models may have herethereto unexplored similar/different gender consequences for women. Research using the care diamond concept could provide new knowledge on these issues.
• asked a question related to Inequality
Question
I am looking for the methodology which can be used to estimate the inequality of opportunity using household level data.
For formal measures of inequality of opportunity based on household data you should look up work by Francisco Ferreira at the World Bank and co-authors. They operationalize John Roemer's approach to the question.
• asked a question related to Inequality
Question
Foe years we have come out with wonderful performances of our students, with flying colors. Indeed, the rat race competition helped our children to outperform their best.
Yet, many researches reveal the negative impact of our schools, and no actions have been taken. Students find themselves struggling in an unknown war, consequently, missing their childhood and innocence at early ages.
Are we destroying our species?
I think besides all the things said above, one quite important role of schools is to condition children to function in society. They learn to be more or less disciplined, sit w/o moving, concentrate and listen for 45/60/90 min. depending on the system they are in. For example, I find it always very interesting to realize how conditioned my students are when we engage in a discussion in the seminars and a situation comes up where a student wants to say something and no one else talks. They still raise their hands to "ask for speaking permission", even though there is no need for it at all. In the end, it is not that surprising given the long time they have undergone schooling.
• asked a question related to Inequality
Question
I am open to collaborations
Sorry for the delay in answering, but I've been rather busy these days. I think you mentioned some possible variables to study tourism policy (can not find what you left writing). I think your point out some possible classical variables (tourist income, household disposable income, etc). I think it would be necessary first to analyze that these variables have not been used in other studies.
The tourism sector in Japan has some interesting features such as the strong imbalance in the balance of tourism payments and the strength of domestic tourism market, with weaker international tourism market. The tourist structure of Japan has enough similarities with South Korea and partly with Taiwan. This situation is repeated in several developed countries but these have developed measures to balance its tourist balance, for the moment this fact has not worried so much to Japan.In summary, we can propose several things: choosing the analysis variables, analyze the existence of a possible model of tourist infrastructure in certain countries of East Asia and the possible comparison Japan / Korea.
I would like to know your opinion.
PS: East Asia is one of my areas of study, I teach a course on tourism in East Asia in the Grade of East Asian Studies.
My e.mail is falmeida@uma.es
• asked a question related to Inequality
Question
In particular, I am interested in (diversity related) interaction, e.g. in management, in museum or educational work, in cooperation structures etc. but I will be glad of any information on organisation research in this field.
Birgitt & Gwen --
I am working on the arrangement of names on memorials and how that influences the experience of the memorial. For example, the Vietnam Veterans Memorial creates a private space for each survivor because it organizes the names by date of casualty. So all those who died in one battle are listed together. Survivors who fought in that battle can find their space on the Memorial and see the names of their comrades in one place.
Maya Lin was influenced by the WWI Memorial to the Missing of the Somme, which used an organizational structure that, because of recruitment strategies, essentially organizes the names by hometown. Therefore families and neighbors can visit the memorial and, in one place, see the names of those who are missing from their town. I would enjoy hearing from you about this.
Thanks,
Katherine
• asked a question related to Inequality
Question
What are some experiences of integrating street vendors/workers in developing countries into the formal economy through legal protections to help them continue their endeavors and what suggestions can be made on ways to enhance their business capacities?
I think that the key issue to decide at the outset is whether you want to formalise their economic activity or whether you want to provide greater social protection for the street vendors themselves. These are two separate issues which are often confused. I think that most scholars and policy makers think that by formalising the work of street vendors, this will result in them having greater social protection. However, it may be better to start with thinking about how to provide them with greater social protection and not to think about formalising their economic activity. Martha Chen is very good on this subject who is at Harvard University
• asked a question related to Inequality
Question
Piketty proposes a simple underlying equation r>g, meaning that the return on capital (property, stock and other forms of ownership) is consistently higher than economic growth.
Piketty strongly suggests that the structures of capitalism are not only regenerate worsening inequality, but now drive us toward a system of economic peonage and political autocracy.
Never too late Christian. Thanks
Even more timely a debate, at least in Australia, with some very provocative economic remedies being suggested for a fiscal crisis that exists depending on who you read.
The implications, if all were implemented might be a dramatic redistribution away from the social sectors, and widen the inequality gap.
I wonder if Piketty's approach can be applied to Australia's macro-economy?
Cheers
Anne
• asked a question related to Inequality
Question
Measures and boundaries of middle-class status are controversial. Usually, in assigning a person to the category of middle-class one might employ "objective" measures such as income, wealth, education, occupation, and so on. At the same time, middle-class status has also been studied from a subjective perspective (i.e., subjective definitions or self-identification). Leaving these issues aside, I am looking for commonly used measures of middle-class status using income (and median or mean income). All suggestions and sources are welcome.
Instead of income, very important measure is lifestyle, which, according to the latest perspectives in this sociological field, is considered as one of the most important and essential indicators of social structuring in post-modern societies.
• asked a question related to Inequality
Question
I will be conducting both a qualitative and quantitative research for a class in methods this semester for which your help will be greatly appreciated.
This is a very interesting question and subject. Unfortunately I have no information to pass on about this topic except to say that it should be possible to form some measure or to identify the presence or absence of neoliberal government and then to look at the school violence figures. However, you have to remember that these are correlations and within such a complex area it is not possible to say that neoliberalism does or does not cause violence in schools.
• asked a question related to Inequality
Question
Public policy
In the US the answer was social security. Poverty rates among the elderly have plunged since the expansion of social security under President Johnson in the 1960s (see chart). I am not saying US social security is the way to go but a retirement program of some sort is clearly the way to go.
• asked a question related to Inequality
Question
Marcel Lenoir (1913) found that the price of gold was the same in 1800 as in 1910, with a 2.8% increase from the mines of the world. Since 1970 gold has dramatically increased and yet inequality has grown dramatically and wages stagnated, while asset classes have exploded in value. Related?. Lenoir, Etude sur la Formation et le Mouvement des Prix, Paris, 1913.
Putting aside Marxian theories of economic collapse, which in my view are no more valid now than they were in the mid-19th century, there is a really interesting issue here. It has nothing to do with the price of gold, whose value until 1971 was determined by statute (a bit more loosely during the Bretton Woods period of 46-71 than during the classical gold standard), but the impact of monetary policy on the distribution of income. QE is a policy that the Fed hopes will depress long-term interest rates (short rates are already at zero) and boost equity and house prices. This means that current holders of wealth, if the policy has its desired effect, benefit at the expense of savers who are trying to build wealth but are getting low yields and seeing other assets rise rapidly in price. I am not convinced that QE was the cause to the 30% rise in US equity prices in 2013 but there is little doubt that holders of equities became wealthier relative to everyone else. Meanwhile, those living on fixed incomes see the current income plunge. What does a $1,000,000 one-year bank CD generate in income? Only around$5,000! \$2,000,000 of assets in bank CDs doesn't get a person over the Federal Poverty Line (FPL) is the US! Since the share of equities in wealth rises as household income and assets rise, QE, if successful, makes the distribution of income more unequal.
• asked a question related to Inequality
Question
Income inequalities
Trade/business cycles can be under both good and bad governance regime. Therefore, good times does not necessarily mean good governance. However, I agree that high growth periods can cause high socioeconomic inequalities.
• asked a question related to Inequality
Question
Looking for most influential relations between these two categories. How does discrimination make poverty stronger and vice versa?
It is a dual link and a complex relationship to model, provided you have good data.
Discrimination induces poverty for sure, reflected in higher unemployment, higher long-term unemployment, social assistance payments, lower wages compared to the non-discriminated population.
Also poverty may isolate some people and impose a social stigma from them, which results in discrimination.
There is a post on Culture of poverty, you may check that out, it has some good scholarly references, and interesting debates.
• asked a question related to Inequality
Question
Human capital theory suggests that there is a direct relationship between the level of education and income, under this premise, the OECD encourages countries to invest in education to reduce existing wage disparities. However, for developing countries the effects of spending on education tend to be oscillatory. That's when the question arises about whether developing countries should substantially increase the level of spending on education, if so, it would be advisable to do so at all levels?
Finally, it is possible to reach an optimal level of spending on education, which maximize the benefits of society? if so, under what arguments would be valid
|
2022-10-05 15:52:18
|
{"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": 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": 0.411433607339859, "perplexity": 2277.701524499853}, "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/1664030337631.84/warc/CC-MAIN-20221005140739-20221005170739-00210.warc.gz"}
|
http://tex.stackexchange.com/questions/98003/filter-rows-from-a-table
|
# Filter rows from a table
I have a large table that contains results for many instances, and I want to make separate tables and plots grouped by one (or more) field. In this minimal working example, I want to make a table and a plot for all 20 houses instances, and another table and plot for all 200 houses instances.
The best thing would be to obtain two subtables from the original one, keeping only the rows with houses=20, or houses=200 (as I would get if I could separate data in table file). I would prefer to avoid to explicitly filter each time I typeset a table or a plot, or at least it should take minimal code to do so (perhaps defining a custom style?).
\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\begin{document}
20 1 8919
20 2 8965
20 3 8901
20 4 8816
20 5 8875
20 6 9027
20 7 8915
20 8 8907
20 9 8832
20 10 8934
200 1 84714
200 3 85630
200 4 84748
200 5 84565
200 6 85109
200 7 84588
200 8 84638
200 9 84673
200 10 85170
}{\fulltable}
Table for all instances
\pgfplotstabletypeset{\fulltable}
\begin{tikzpicture}
\begin{axis}[
title={Values for all instances},
xlabel={Instance},
ylabel={Value}]
{\fulltable};
\end{axis}
\end{tikzpicture}
\newpage
Table for 20 houses instances
???
Plot for 20 houses instances
???
\end{document}
## Edit
By looking at similar questions, I came up with this partial solution:
%\filtertable{table}{field}{value}{#1}
\newcommand{\filtertable}[4]{
\pgfplotstablegetelem{#4}{#2}\of{#1}
\ifnum\pgfplotsretval=#3\relax
\else\pgfplotstableuserowfalse\fi
}
%\filtertableplot{table}{field}{value}
\newcommand{\filtertableplot}[3]{
\pgfplotstablegetelem{\coordindex}{#2}\of{#1}
\ifnum\pgfplotsretval=#3
\else
\def\pgfmathresult{}
\fi
}
Table for 200 houses instances
\pgfplotstabletypeset[
columns={instance,value},
row predicate/.code={\filtertable{\fulltable}{houses}{200}{#1}}
]
{\fulltable}
\begin{tikzpicture}
\begin{axis}[
title={Values for 200 houses instances},
xlabel={Instance},
ylabel={Value},
x filter/.code={\filtertableplot{\fulltable}{houses}{200}{#1}}]
{\fulltable};
\end{axis}
\end{tikzpicture}
Is there a way to avoid repeating the table name, to avoid explicitly using #1, and to wrap the x filter=... and row predicate=... in styles?
-
You can filter the values to be plotted using the discard if not={<column name>}{<value>} key from Is it possible to change the color of a single bar when the bar plot is based on symbolic values?. This allows you to type
\addplot+[only marks, discard if not={houses}{20}] table[x=instance, y=value]
{fulltable.dat};
to plot only those entries where the houses value is 20. For this, you need to put the following code chunk into your preamble, and plot the data from a file (not from a table created using \pgfplotstableread).
\pgfplotsset{
x filter/.code={
\edef\tempa{\thisrow{#1}}
\edef\tempb{#2}
\ifx\tempa\tempb
\else
\def\pgfmathresult{inf}
\fi
}
}
}
For the table, you can do something similar (although the code is a bit trickier). It allows you to type
\pgfplotstabletypeset[discard if not={houses}{20}]{fulltable.dat}
to filter the rows.
\makeatletter
\pgfplotstableset{
row predicate/.code={
\def\pgfplotstable@loc@TMPd{\pgfplotstablegetelem{##1}{#1}\of}
\expandafter\pgfplotstable@loc@TMPd\pgfplotstablename
\edef\tempa{\pgfplotsretval}
\edef\tempb{#2}
\ifx\tempa\tempb
\else
\pgfplotstableuserowfalse
\fi
}
}
}
\makeatother
\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{filecontents}
\begin{document}
houses instance value
20 1 8919
20 2 8965
20 3 8901
20 4 8816
20 5 8875
20 6 9027
20 7 8915
20 8 8907
20 9 8832
20 10 8934
200 1 84714
200 3 85630
200 4 84748
200 5 84565
200 6 85109
200 7 84588
200 8 84638
200 9 84673
200 10 85170
}{\fulltable}
\begin{filecontents}{fulltable.dat}
houses instance value
20 1 8919
20 2 8965
20 3 8901
20 4 8816
20 5 8875
20 6 9027
20 7 8915
20 8 8907
20 9 8832
20 10 8934
200 1 84714
200 3 85630
200 4 84748
200 5 84565
200 6 85109
200 7 84588
200 8 84638
200 9 84673
200 10 85170
\end{filecontents}
\pgfplotsset{
x filter/.code={
\edef\tempa{\thisrow{#1}}
\edef\tempb{#2}
\ifx\tempa\tempb
\else
\def\pgfmathresult{inf}
\fi
}
}
}
\makeatletter
\pgfplotstableset{
row predicate/.code={
\def\pgfplotstable@loc@TMPd{\pgfplotstablegetelem{##1}{#1}\of}
\expandafter\pgfplotstable@loc@TMPd\pgfplotstablename
\edef\tempa{\pgfplotsretval}
\edef\tempb{#2}
\ifx\tempa\tempb
\else
\pgfplotstableuserowfalse
\fi
}
}
}
\makeatother
\centering
{\bfseries Table for 20 houses instances:}
\begin{tikzpicture}[trim axis left]
\begin{axis}[
title={{\bfseries Plot for 20 houses instances}},
xlabel={Instance},
ylabel={Value}]
|
2014-03-14 07:04:00
|
{"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": 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": 0.554023802280426, "perplexity": 434.5343100926741}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678690318/warc/CC-MAIN-20140313024450-00044-ip-10-183-142-35.ec2.internal.warc.gz"}
|
http://demonstrations.wolfram.com/SetsOfLinearCombinationsAndTheirImagesUnderLinearTransformat/
|
Sets of Linear Combinations and Their Images under Linear Transformations
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.
Requires a Wolfram Notebook System
Edit on desktop, mobile and cloud with any Wolfram Language product.
This Demonstration visualizes points, vectors, and the effect of linear transformations from to . The black and red vectors are linear combinations of and given by and , respectively. The green dots are integral scalar multiples of , and , and the black dots show the images of the green dots under the linear transformation defined by the matrix .
Contributed by: Hamide Dogan (June 2014)
Open content licensed under CC BY-NC-SA
Details
This Demonstration can be used to support linear algebra activities on vector space concepts: geometric vector, linear combination, linear independence, spanning set, span, basis, coordinates, and so on; and topics on linear transformations: domain, range, kernel (null space), orthogonal projection, one-to-one and onto transformations. For further explanations and the definition of the controls, see below the descriptions of the three Snapshots.
Snapshot 1
The blue line represents the vector whose component values are assigned using the symbols , , and .
The purple line represents the vector whose component values are assigned using the symbols , , and .
The light blue line represents the vector whose component values are assigned using the symbols , , and .
The red dot represents the origin, .
The brown dot represents a point whose component values are assigned using the symbols , , and .
Snapshot 2
The green points are the linear combinations of the vectors , , and for scalars , , and obtained by setting the sliders , and and using values for scalars ranging from to .
The black vector, u, corresponds to the linear combination of the vectors and .
The red vector, v, corresponds to the linear combination of the vectors , , and .
Snapshot 3
The black points are the images of linear transformations of the green points. The symbol stands for 3×3 matrices representing linear transformations, and their matrix entries are obtained by assigning values to the symbols , .
One such linear transformation is represented by the matrix , which maps vectors along the axis to vectors along the axis (that is, maps the greeen points on the axis to black points on the axis). The transformation preserves magnitutes and maps vectors along the axis to themselves.
References
[1] H. Dogan-Dunlap, "Linear Algebra Students’ Modes of Reasoning: Geometric Representations," Linear Algebra and Its Applications 432, pp. 2141–2159.
[2] H. Dogan, R. Carrizales, and P. Beaven, Metonymy and Object Formation: Vector Space Theory. In Ubuz, B. (Ed.) Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, (Research Reports) Vol. 2, 2011, pp. 265–272. Ankara, Turkey: PME.
[3] L. W. Johnson, R. D. Riess, and J. T. Arnold, Introduction to Linear Algebra, 5th ed., Pearson Education, 2002.
Permanent Citation
Hamide Dogan
Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send
|
2018-08-17 07:47:14
|
{"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": 0.8884163498878479, "perplexity": 1249.5429718923597}, "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-2018-34/segments/1534221211933.43/warc/CC-MAIN-20180817065045-20180817085045-00296.warc.gz"}
|
https://brilliant.org/discussions/thread/triangle-with-q-identical-lines/
|
# Triangle with $q$ identical lines
The task is: Given a triangle with $q$ identical lines, in this way as you can see on the picture. The orange lines are the same. Calculate $\gamma$!
$\Delta ABC'$ is an isosceles triangle, therefore $\beta_1=\gamma$.
The sum of the angles at the B point is $180^{\circ}$, because AH is a line: $\cancel{180^{\circ}}-2\gamma+\beta_2=\cancel{180^{\circ}}$ $\beta_2=2\gamma$
From the isosceles triangles and the sum of angles at the C point: $\beta_1+\cancel{180^{\circ}}-2\beta_2+\beta_3=\cancel{180^{\circ}}\implies \beta_3=4\gamma-\gamma =3\gamma$ Same way $\beta_4=4\gamma, \beta_5=5\gamma, \cdots, \beta_n=n\gamma$, because if we see an angle: $\beta_{n-2}+\cancel{180^{\circ}}-2\beta_{n-1}+\beta_n=\cancel{180^{\circ}}\implies \beta_n=2\beta_{n-1}-\beta_{n-2}=(2(n-1)-n+2)\gamma=n\gamma$ This is true for the first, second and third angles, so this must be true for every angles.
If we have a triangle with $q$ lines, then the last $\beta$ is the $\frac{q-3}{2}$th.
Now in the bottom $HG'H'$ triangle: $\alpha+\alpha+\alpha+\beta_6+\beta_6=180^{\circ}$ or generally $3\alpha+2\beta_{\frac{q-3}{2}}=180^{\circ}$. But if we see the big triangle $2\alpha+2\beta_{\frac{q-3}{2}}+\gamma=180^{\circ}$. Therefore $\alpha=\gamma$. After substituting: $3\gamma+2\beta_{\frac{q-3}{2}}=180^{\circ}$. Replacing $\beta_{\frac{q-3}{2}}$: $3\gamma+2\cfrac{q-3}{2}\gamma=180^{\circ}$ $3\gamma+q\gamma-3\gamma=180^{\circ}$ $q\gamma=180^{\circ}$ $\boxed{\gamma=\cfrac{180^{\circ}}{q}}$
Now can you solve this?
Note by A Former Brilliant Member
10 months, 1 week ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$
Sort by:
Nice proof! Explains where I went wrong! @Páll Márton.
- 10 months, 1 week ago
Thank you! Did you solve my problem?
- 10 months, 1 week ago
No! That's why I said it explains where I went wrong.
- 10 months, 1 week ago
Angles, not angels.
- 10 months ago
Yeah. I use Word2016 to write the text and I just paste them there, but the default language isn't English so the autocorrector "corrects" my "typos".
I will add this word to the Word. Last time it wrote mooves instead of moves
Oh. I see. Doesn't happen with me though.
Also, tip:
If you wish to delete a problem, copy and paste the solution in Word, then copy the problem, go to create a new problem (open a new tab for this), paste the original problem's text, copy the title, paste it in the title section, change the answers (if needed) - if not, press Post. Then, copy the solution from Word, paste it and make any corrections (if needed) - if not, press Preview and Submit. Then close the Word Document.
- 10 months ago
Or I will use txt
Up to you.
I used this technique for my Hexadecimal Equations Problem $6$ up to Version $4$.
- 10 months ago
this note isn't very famous I think you can continue this :)
I will continue the prove chain. (albeit later)
Also, what if (for your next problem involving this):
$\frac{180}{3600}$$= 0.05$ degrees
- 10 months ago
I don't understand
Triangle with $3600$ identical lines?
- 10 months ago
Ohh. q is odd :)
Else we can get only an intervallllll
Triangle with $3601$ identical lines?
$\frac{180}{3601}$$= 0.049986115$ degrees
Also, how do you do the degree sign? Baffles me...
P.S. Check out my note - Interesting Thing about Multiplication Last Digit Sequences (Even)
- 10 months ago
Yeah. You just shifted the 2, 4, 6 and 8. ^{\circ}
What about the triangle with $3601$ identical lines?
- 10 months ago
I think with 45 lines was enaugh. If somebody can solve with 45, then he/she can solve with 3601 too.
You mean enough, right?
- 10 months ago
Yeah. This was my mistake :) English is too hard. To write from pronunciation is hard
Excellent exposition.
- 10 months ago
Thank you!
Wow! Good proof!
- 10 months ago
Thank you!
Excellent Proof @Páll Márton.
- 9 months, 3 weeks ago
Thank you!
- 9 months, 3 weeks ago
|
2021-05-18 11:11:28
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 42, "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": 0.9413039088249207, "perplexity": 2950.5213167822135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989819.92/warc/CC-MAIN-20210518094809-20210518124809-00277.warc.gz"}
|
https://socratic.org/questions/5a3bd68511ef6b3c6f8c4f46#525545
|
Question #c4f46
1 Answer
Dec 21, 2017
It is either 14 N or 9 N, depending on interpretation. See below.
Explanation:
The question can be interpreted 2 ways. I will give answers for both interpretations. I will be using the formula of Newton's Universal Law of Gravitation.
$F = \frac{G \cdot m \cdot M}{r} ^ 2$
The only parameter that is changing in the elevation of the body is r. When the body weighed 144 N, the value of r was R. So the weight at the new location would be different by the multiplication factor, 1/k, where
$k = {\left(\frac{\text{new distance from center of the earth}}{R}\right)}^{2}$
1. Assuming the body is now 3R from the center of the earth, the value of k is
$k = {\left(\frac{3 \cdot R}{R}\right)}^{2} = 9$
So the new weight is $\frac{144 N}{9} = 16 N$
1. Assuming the body 3R above the surface, it is now 4R from the center of the earth, the value of k is
$k = {\left(\frac{4 \cdot R}{R}\right)}^{2} = 16$
So the new weight is $\frac{144 N}{16} = 9 N$
I hope this helps,
Steve
|
2022-08-09 09:53:04
|
{"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": 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": 0.8573935627937317, "perplexity": 576.6084280004859}, "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-2022-33/segments/1659882570921.9/warc/CC-MAIN-20220809094531-20220809124531-00792.warc.gz"}
|
https://gmatclub.com/forum/for-prime-number-y-y-3-which-of-the-following-could-be-the-remainder-227809.html
|
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 19 Sep 2018, 22:17
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# For prime number y, y>3. Which of the following could be the remainder
new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
### Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 49258
For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
24 Oct 2016, 23:22
00:00
Difficulty:
15% (low)
Question Stats:
79% (00:54) correct 21% (01:20) wrong based on 265 sessions
### HideShow timer Statistics
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
_________________
SVP
Joined: 08 Jul 2010
Posts: 2302
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
25 Oct 2016, 00:10
Bunuel wrote:
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
Checking with prime numbers greater than 3
@y=5, Rem (y^3 / 12) = Rem (5^3 / 12) = 5 (BINGO)
Answer: Option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4020
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
25 Oct 2016, 08:15
Bunuel wrote:
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
y = { 5 , 7 , 11............ }
Plug in a number and check -
5^3/12 = Remainder 5
Thats in the given option , hit it...
Answer will be (D)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
25 Oct 2016, 16:56
1
Bunuel wrote:
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
Let’s test the first prime number greater than 3, which is 5.
5^3 = 125
125/12 = 10 remainder 5
Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
27 Nov 2016, 09:26
1
1
Bunuel wrote:
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
Prime number greater than 3 can be expressed as $$6k + 1$$ or $$6k -1$$.
$$\frac{(6k ± 1)^3}{12} = \frac{6^3k^3 ± 3*6^2k^2 + 3*6k ± 1}{12} = \frac{0 + 0 + 18k ± 1}{12} = \frac{6k ± 1}{12}$$
Let’s check first case $$6k + 1$$
k=1 (7/12) rem=7
k=2 (13/12) rem =1
k=3 (19/12) rem = 7
k =4 (25/12) rem = 1
we have cycle of remainders $$7$$ and $$1$$.
Next $$6k – 1$$
k=1 (5/12) rem=5
k=2 (11/12) rem =11
k=3 (17/12) rem = 5
k =4 (23/12) rem = 11
again cycle of only two remainders $$5$$ and $$11$$.
The only remainders after division by 12 cube of prime number $$y > 3$$ can have are $$1$$, $$5$$, $$7$$ and $$11$$.
Checking our options.
Answer D.
Manager
Joined: 27 Aug 2016
Posts: 91
Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE: Engineering (Energy and Utilities)
Re: For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
19 Apr 2017, 11:41
vitaliyGMAT wrote:
Bunuel wrote:
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
Prime number greater than 3 can be expressed as $$6k + 1$$ or $$6k -1$$.
$$\frac{(6k ± 1)^3}{12} = \frac{6^3k^3 ± 3*6^2k^2 + 3*6k ± 1}{12} = \frac{0 + 0 + 18k ± 1}{12} = \frac{6k ± 1}{12}$$
Let’s check first case $$6k + 1$$
k=1 (7/12) rem=7
k=2 (13/12) rem =1
k=3 (19/12) rem = 7
k =4 (25/12) rem = 1
we have cycle of remainders $$7$$ and $$1$$.
Next $$6k – 1$$
k=1 (5/12) rem=5
k=2 (11/12) rem =11
k=3 (17/12) rem = 5
k =4 (23/12) rem = 11
again cycle of only two remainders $$5$$ and $$11$$.
The only remainders after division by 12 cube of prime number $$y > 3$$ can have are $$1$$, $$5$$, $$7$$ and $$11$$.
Checking our options.
Answer D.
I have a doubt here please....prime numbers graeter than 3 can be expressed as 6k+1..putting k=4 we get 25, which is not a prime num,ber....am I missing something here?
Math Expert
Joined: 02 Sep 2009
Posts: 49258
Re: For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
19 Apr 2017, 11:51
saurabhsavant wrote:
vitaliyGMAT wrote:
Bunuel wrote:
For prime number y, y>3. Which of the following could be the remainder when y^3 is divided by 12?
A. 2
B. 3
C. 4
D. 5
E. 6
Prime number greater than 3 can be expressed as $$6k + 1$$ or $$6k -1$$.
$$\frac{(6k ± 1)^3}{12} = \frac{6^3k^3 ± 3*6^2k^2 + 3*6k ± 1}{12} = \frac{0 + 0 + 18k ± 1}{12} = \frac{6k ± 1}{12}$$
Let’s check first case $$6k + 1$$
k=1 (7/12) rem=7
k=2 (13/12) rem =1
k=3 (19/12) rem = 7
k =4 (25/12) rem = 1
we have cycle of remainders $$7$$ and $$1$$.
Next $$6k – 1$$
k=1 (5/12) rem=5
k=2 (11/12) rem =11
k=3 (17/12) rem = 5
k =4 (23/12) rem = 11
again cycle of only two remainders $$5$$ and $$11$$.
The only remainders after division by 12 cube of prime number $$y > 3$$ can have are $$1$$, $$5$$, $$7$$ and $$11$$.
Checking our options.
Answer D.
I have a doubt here please....prime numbers graeter than 3 can be expressed as 6k+1..putting k=4 we get 25, which is not a prime num,ber....am I missing something here?
Any prime number $$p>3$$ when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case $$p$$ would be even and remainder can not be 3 as in this case $$p$$ would be divisible by 3).
So any prime number $$p>3$$ could be expressed as $$p=6n+1$$ or$$p=6n+5$$ or $$p=6n-1$$, where n is an integer >1.
But:
Not all number which yield a remainder of 1 or 5 upon division by 6 are prime, so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.
Hope it's clear.
_________________
Intern
Joined: 11 Feb 2017
Posts: 23
Location: India
Schools: SPJ PGPM"17
GMAT 1: 600 Q48 V25
GPA: 3.57
WE: Engineering (Computer Software)
Re: For prime number y, y>3. Which of the following could be the remainder [#permalink]
### Show Tags
23 May 2017, 13:55
prime number 5 , 5^3 /12 = 25*5 /12 => 1*5/12 ( since 25/12 will give rem as 1) => 5 is rem
Option D is answer
Re: For prime number y, y>3. Which of the following could be the remainder &nbs [#permalink] 23 May 2017, 13:55
Display posts from previous: Sort by
# For prime number y, y>3. Which of the following could be the remainder
new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
# Events & Promotions
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
|
2018-09-20 05:17:28
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.618587851524353, "perplexity": 5099.736260691273}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "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-2018-39/segments/1537267156416.22/warc/CC-MAIN-20180920041337-20180920061337-00258.warc.gz"}
|
https://imagej.github.io/plugins/trackmate/accuracy
|
# TrackMate Accuracy
The problem with tracking algorithms is that they always give an answer.
This answer can be completely irrelevant, even non-physical, and there is no built-in flags that would indicate something wrong. The best way to avoid basing your downstream analysis on faulty tracking results is to know in what situation the tracker works the best, and what are its limitations. This is the aim of this page for the trackers and detectors shipped with TrackMate.
## The ISBI 2012 single particle challenge.
In 2011-2012, an ISBI Grand Challenge was organized for the Single-Particle Tracking algorithms. Though TrackMate does not offer a completely new algorithm, product of an original Research work, we took the chance and participated in the challenge. The results and the methodology to compute the accuracy of a tracking algorithms were published[1] thereafter.
Unsurprisingly, we did not score amongst the best. At the time, TrackMate was in version 1.1, and ship a stripped down version of the better performing Jaqaman et al. LAP framework[2]. See the LAP trackers section for algorithm details. Plus, TrackMate was was young at the time, and some bugs did not help.
## TrackMate v2.7.x series accuracy against the ISBI dataset.
From v2.7.x, TrackMate ships a new tracker that can deal specifically with linear motion. We though it was the right time to re-run the accuracy assessment with the ISBI challenge data. The people behind Icy offered the website to host the challenge data, and it is still available today[3] for download.
The figures below shows the comparison of accuracy for the 3 classes of tracking algorithms available in TrackMate:
• The LAP framework derived from Jaqaman et al.[4].
• The linear motion tracker based on Kalman filter.
• The plain Nearest neighbor tracker for reference.
### Scenarios.
It’s best to directly read the paper[5] to know what is behind these measures, but here is a brief survey of how they are done. The ISBI dataset covers four scenarios:
Scenario name
Particle shape
Motion type
MICROTUBULE
Slightly elongated shape to mimic MT tip staining.
Roughly constant velocity motion.
RECEPTOR
Spherical.
Tethered motion: switch between Brownian and directed motion with random orientation for the later.
VESICLE
VIRUS
Switch between Brownian and directed motion with fixed orientation for the later.
For each scenario, images covers several particle density:
• low: 60-100 / frame
• mid: 400-500 / frame
• high: 700-1000 / frame
to check how a tracking algorithm behaves when particles get very dense.
Also, particles SNR spans several values: 1, 2, 4, 7 (plus 3 for the RECEPTOR scenario). As said on the challenge page: “SNR=4 is a critical level at which methods may start to break down”.
### Example images from the challenge dataset.
Below are shown typical images taken from the challenge.
#### Varying particle density.
snr 7 density low-1.png\|Low density snr 7 density mid-1.png\|Medium density snr 7 density high-1.png\|High density Contrast stretched to the 0-150 8-bit range. #### Varying particle SNR. snr 7 density low-1.png\|SNR = 7 snr 4 density low-1.png\|SNR = 4 snr 3 density low-1.png\|SNR = 3 snr 2 density low-1.png\|SNR = 2 snr 1 density low-1.png\|SNR = 1 Contrast stretched to the 0-50 8-bit range. #### The MICROTUBULE scenario particle shape. snr 4 density mid-1.png\|MICROTUBULE, SNR = 4, density = mid ### Accuracy measurements. For each scenario and condition, the method returns numerous values that characterizes the accuracy of a tracking algorithm. They are detailed on [this technical paper](http://bioimageanalysis.org/track/PerformanceMeasures.pdf). We plot below only three of them: - The Jaccard similarity between tracks, that quantifies how well the tracks returned by the algorithm match the ground truth. This value assesses the accuracy of the [spot tracker](TrackMate_algorithms#Spot_trackers) you pick in TrackMate. It ranges from 0 (terrible) to 1 (found tracks = ground truth). - The Jaccard similarity between detections, that quantifies how well the particle detected by the detection algorithm match the ground truth. It depends strongly on the [spot detector](TrackMate_algorithms#Spot_detectors) you pick in TrackMate, and ranges from 0 to 1 like the above quantity. - The RMSE of detection positions that quantifies how precise is the location of the detected particles. The smaller the better. I fully relied on [Icy](/software/icy) to compute these values. TrackMate ships an action that exports tracking results to the XML format imposed by the ISBI challenge, and that can be found [here](https://github.com/fiji/TrackMate/blob/master/src/main/java/fiji/plugin/trackmate/action/ISBIChallengeExporter.java). I generated these files for all the conditions of a scenario, and used the [Icy ISBI challenge scoring plugin](http://icy.bioimageanalysis.org/plugin/ISBI_Tracking_Challenge_Batch_Scoring) to yield metrics. I then used [MATLAB](MATLAB) to plot them. ### Parameter used. Unless otherwise specified below, I always used the LoG detector as a spot detector, with an estimated particle diameter of 2, and used sub-pixel accuracy. For SNR below 4, this detector was completely confused and the detection results are dominated by noise. I did not make anything special to improve its sensitivity below this limit. When the histogram of detection quality returned by the detector as not bimodal, I pick a quality threshold that yielded approximately the expected number of particles in the sequence. The three spot trackers were configured as indicated in the table below. It's not very sensible to keep always the same parameter across different scenario, but with what you can tune in TrackMate, there is little room for fine-tuning.
Spot tracker Parameter Value
Linear motion tracker Initial search radius 10
Finally, for SNR>4, I filtered out tracks that had less than 4 detections.
|
2021-04-15 11:30:37
|
{"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": 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": 0.5315735936164856, "perplexity": 2925.9790209838507}, "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/1618038084765.46/warc/CC-MAIN-20210415095505-20210415125505-00180.warc.gz"}
|
https://tex.stackexchange.com/questions/128693/context-vertical-spacing?noredirect=1
|
# ConTeXt: vertical spacing
I'm a bit confused about how to specify vertical whitespace. The following document works:
``````\setupwhitespace[line]
\starttext
\subsection{Title}
\input tufte
\input tufte
\stoptext
``````
But why can't I use `\setupwhitespace[2*line]`, and neither `\blank[0.5*line]`? Both result in an error. Meanwhile, `\setupwhitespace[5cm]` doesn't seem to have an effect.
What I'm actually trying to achieve is having the vertical spacing between paragraphs (and subsections) `0.5*line`, or if that's not possible some specific centimeters.
• Aug 17, 2013 at 16:43
• Thanks, `halfline` works. But what about, say `0.1*line`? Pasting `\installwhitespacemethod \v!pointoneline {\s_spac_whitespace_parskip.1\baselineskip}` gives an error.
– mb21
Aug 17, 2013 at 19:49
• Enclose the installwhitespace line in `\starttexcode … \stoptexcode` and replace `\v!pointoneline` with `{pointoneline}`. Aug 17, 2013 at 23:27
• okay, seems I'm starting to figure it out (feel free to edit my answer below). So the only missing case would be: `0.1*line` spacing after a subsection. Is that possible as well?
– mb21
Aug 18, 2013 at 7:26
• `\setuphead[section][style=\tfc, before={\blank[line]}, after={\blank[none]}]`
– mb21
Feb 2, 2014 at 15:05
A clean way, which doesn't require low level TeX is to use the measure mechanism. A dimension is defined using `\definemeasure`, the value can be retrieved with `\measure`.
``````\definemeasure
[pointoneline]
[.5\baselineskip]
\setupwhitespace
[\measure{pointoneline}]
|
2022-07-06 14:48:24
|
{"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": 0.9475724101066589, "perplexity": 2175.6267234086695}, "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/1656104672585.89/warc/CC-MAIN-20220706121103-20220706151103-00698.warc.gz"}
|
https://www.shaalaa.com/question-bank-solutions/suppose-two-photographs-shown-figure-1-figure-2-had-been-taken-interval-10-seconds-if-distance-100-metres-shown-1-cm-these-photographs-calculate-speed-blue-car-concept-speed_15942
|
Share
Suppose the Two Photographs, Shown in Figure 1 and Figure 2, Had Been Taken at an Interval of 10 Seconds. If a Distance of 100 Metres is Shown by 1 Cm in These Photographs, Calculate the Speed of the Blue Car. - Science
Course
Question
Suppose the two photographs, shown in Figure 1 and Figure 2, had been taken at an interval of 10 seconds. If a distance of 100 metres is shown by 1 cm in these photographs, calculate the speed of the blue car.
Figure 1 Vehicles moving in the same direction of on a road
Figure 2 Position of vehicles shown in Figure 1 after some time
Solution
The distance covered by the blue car (as evident from the photograph) from one white strip to another, which is measured by scale is 1.4 cm.
It is given that 1 cm is equivalent to 100 m.
Therefore, 1.4 cm is equivalent to 140 m.
Distance travelled by the car = 140 m
Time interval between the two photographs = 10 s
Speed = "Distance covered"/"Time taken" = 140/10 = 14 "m/s"
Is there an error in this question or solution?
APPEARS IN
NCERT Solution for Science Textbook for Class 7 (2018 (Latest))
Chapter 13: Motion and Time
Q: 11 | Page no. 157
Solution Suppose the Two Photographs, Shown in Figure 1 and Figure 2, Had Been Taken at an Interval of 10 Seconds. If a Distance of 100 Metres is Shown by 1 Cm in These Photographs, Calculate the Speed of the Blue Car. Concept: Concept of Speed.
S
|
2020-05-30 15:51:23
|
{"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": 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": 0.7731425166130066, "perplexity": 942.1250147427804}, "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-2020-24/segments/1590347409337.38/warc/CC-MAIN-20200530133926-20200530163926-00371.warc.gz"}
|
https://socratic.org/questions/how-do-i-calculate-the-determinant-of-a-4x4-matrix
|
# How do I calculate the determinant of a 4x4 Matrix?
Dec 28, 2017
The easiest practical manual method to find the determinant of a $4 \times 4$ matrix is probably to apply a sequence of the above changes in order to get the matrix into upper triangular form. Then the determinant is just the product of the diagonal elements.
|
2019-10-15 09:14:18
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "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": 0.7125657200813293, "perplexity": 78.17223156724428}, "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-2019-43/segments/1570986657949.34/warc/CC-MAIN-20191015082202-20191015105702-00175.warc.gz"}
|
https://crypto.stackexchange.com/questions/81750/why-blinding-integer-r-needs-to-be-co-prime-with-n-in-blind-rsa-signature
|
# Why blinding integer $r$ needs to be co-prime with $N$ in blind RSA signature
According to blind RSA signature wiki the random value $$r$$ in $$m^\prime=mr^e \bmod N$$ needs to be relatively prime to $$N$$.
• Why is this a requirement?
A follow up a related question: after $$s$$ (unblinded signature) and $$m$$ (original message) are revealed, can anyone (and not only the signing authority) check the validity of the signature by checking $$s^e=m \bmod N$$?
Well, if $$r$$ has (say) $$p$$ as a factor, then it makes the unblinding step rather difficult.
The original $$m$$ has $$N = pq$$ possible, as does $$m^d$$; if $$r$$ is a multiple of $$p$$, then $$mr^e$$ has only $$q$$ possible values; if we pass it to the signer, it'll come back to us with a value $$m'^d$$ that also has only $$q$$ possible values. We cannot map $$m'^d$$ back to $$m^d$$ (as a single $$m'^d$$ value would map back to $$p$$ possible $$m^d$$ values, and we don't know which one it is.
A follow up a related question: after $$s$$ (unblinded signature) and $$m$$ (original message) are revealed, can anyone (and not only the signing authority) check the validity of the signature by checking $$s^e=m \bmod N$$?
|
2021-08-02 00:21:47
|
{"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": 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": 25, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6797245144844055, "perplexity": 594.939139828333}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154277.15/warc/CC-MAIN-20210801221329-20210802011329-00697.warc.gz"}
|
https://math.stackexchange.com/questions/4459036/mathematical-inclusion-and-exclusion-of-elements-from-a-given-set-a
|
# Mathematical "inclusion" and "exclusion" of elements from a given set $A$?
If I have a set A, comprising of numbers from 1 to 10: $$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$. Let's say I want to make another set by "including" all even numbers:
$$\{2, 4, 6, 8, 10\}$$
Or I wanted to make a different set by "excluding" all odd numbers:
$$\{2, 4, 6, 8, 10\}$$
These sets are of course the same. So is it correct to say that inclusion/exclusion are synonymous when it comes to set theory, as they're just different ways of building a set?
This might sound trivial, but I have a reason for asking: I want to understand if inclusion and exclusion are "commutative" properties, i.e. it doesn't matter in which order you apply them.
For example, let's say I make an operation to "filter" my set, by including all even numbers as we did before, producing set B
$$B = \{2, 4, 6, 8, 10\}$$
And then a separate operation to "exclude" any numbers less than 6 from set B, resulting in set C:
$$C = \{6, 8, 10\}$$
What if I started with A and applied the operations the other way around? First remove all numbers less than 6:
$$B = \{6, 7, 8, 9, 10\}$$
Then filter B to "include" only even numbers:
$$C = \{6, 8, 10\}$$
It seems intuitively to me that the result will always be the same no matter which order you apply the operation. Is this true for all cases no matter the set, however? Is there a way to prove that applying "filters" to a set (I'm not sure of the proper term) will always be commutative?
So in summary, there are two questions here:
1. Are the notions of "inclusion" and "exclusion" really synonymous from the point of view of applying an operation to a set to produce a subset?
2. Will applying these operations to produce a subset of a set always be commutative, i.e. produce the same result?
• It looks lile you are taking repeated intersections of sets. Intersection is both associative and commutative. May 26 at 10:25
• @CrackedBauxite I've had a think about this. Is it intersection, or is it a set difference / relative complement? If I've got the set $\{1, 2, 3, 4, 5\}$ and I exclude all odd numbers, I've got a set of odd numbers $\{1, 3, 5\}$. It's my original set $\{1, 2, 3, 4, 5\} - \{1, 3, 5\} = \{2, 4\}$
– Lou
May 26 at 16:45
• But if I were to do "include all even numbers" from the set $\{1, 2, 3, 4, 5\}$, then I have a set of even numbers $\{2, 4\}$. $\{1, 2, 3, 4, 5\} \cap \{2, 4\} = {2, 4}$ I think - but please correct me if my logic is wrong
– Lou
May 26 at 16:46
• So I think "include" as an operation represents an intersection, but "exclude" represents a set difference?
– Lou
May 26 at 16:48
• Set differences are also intersections. $A\setminus B = A\cap B^c$, where $B^c$ is the complement of $B$. May 27 at 8:38
@KevinS offers an excellent answer from a logic point of view. Here's another that relies on the idea of a filter. That's a concept useful in programming (particularly in lisp). You pass the items in your set through a filter that lets some through and blocks others.
In this sense "inclusion" and "exclusion" are really different ways to describe the same result. You can specify what you keep or what you reject. "Keep (just) the odds" is the same as "reject (only) the evens".
If you have two filters each of which is described independently of the other and refers only to properties of the things you are filtering then you can filter in either order.
The independence matters. If you think that the wine must match the main course then your options will depend on whether you see the wine list or the menu first.
• You've hit upon my actual use case - I'm doing filtering in Python and trying to understand if "inclusion" and "exclusion" for my use case are order-sensitive, or commutative operations. You've all helped me understand that they are commutative and therefore order should not matter.
– Lou
May 26 at 10:52
This is perhaps easier to see in the math logic. When you apply conditions to a set, you get subsets that satisfy those conditions (possibly the emptyset if the conditions aren't met). In your example, define: $$A := \{n\in\mathbb{N}\text{ }|\text{ }1\leq n\leq 10\}.$$ Then $$B$$ and $$C$$ are had by adding conditionals in the set definition: $$B := \{n\in A\text{ }|\text{ }\exists k\in\mathbb{N}: n=2*k\}$$ and $$C:= \{n\in B\text{ }|\text{ }n\geq 6\}.$$ $$\implies C = \bigg\{n\in \mathbb{N}\text{ }\bigg|\text{ }(1\leq n\leq 10)\wedge(\exists k\in\mathbb{N}: (n=2*k))\wedge(n\geq 6)\bigg\}.$$ From this viewpoint, the reductions made were simply conjuctions (a logical operation). Conjunction is certainly commutative.
Also, the term "exclusion" is synonymous with set difference: $$X-Y:= X\cap Y^c,$$ whereas "inclusion" usually refers to an injective map: $$\iota: S\hookrightarrow X$$ which can be used as an identifier of a subset. I wouldn't say the two notions are synonymous.
• I'm a beginner in set theory, would you mind clarifying what you mean about an "injective map"? I understand the term set difference.
– Lou
May 26 at 14:21
• It seems as though the terms used might have multiple meanings as they apply to math and programming. An injection is a 1-1 function. The math notion I gave generalizes to categories (using equivalence classes of monomorphisms to identify sub-objects). This is not inherently programmable and is best used for theory. May 26 at 21:34
To your first question, consider using the set-builder notation to build a subset. That is, define $$B\subseteq A$$ such that $$B = \{a\in A : \Phi(a)\}$$, where $$\Phi$$ is the logical formula which dictates what how we pick the values of $$A$$.
Now say that $$A$$ is some collection of numbers, and $$\Phi$$ is the rule "include all even numbers". Then some other rule $$\Psi$$ which says "do not include all not even numbers" is completely logically equivalent to $$\Phi$$.
And this generalises nicely by considering that, if we impose a condition like "even number", any element of a set will satisify that condition, or not satisfy that condition. We cannot have an element which does neither.
The second question follows as others have pointed out, by writing the conditions as operations which are commutative.
|
2022-06-25 17:57:08
|
{"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": 0.7210046648979187, "perplexity": 336.9144159564521}, "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/1656103036077.8/warc/CC-MAIN-20220625160220-20220625190220-00665.warc.gz"}
|
http://cfa.aquila.infn.it/wiki.eg-climet.org/index.php5?title=Signal_detection,_classification_and_moment_estimation&oldid=72
|
Signal detection, classification and moment estimation
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
1 Noise level estimation
To discriminate between electronic noise and echo signals, a mean noise level $P_N$ is objectively estimated using the method of Hildebrand and Sekhon (1974). This method works well if white noise occupies a sufficient part of the spectrum.
2 Signal peak identification
Next, the signal peak caused by the atmospheric return is selected. A simple but well-established method is to select the maximum energy peak May and Strauch (1989). The method works quite well for single peak spectra and it is called a single-peak algorithm.
Stationary clutter components will give rise to additional signal peaks. Such a situation is not accounted for in standard processing, and a variety of so-called multi-peak algorithms have therefore been proposed. Among them are simple methods, like the ground clutter algorithm by Riddle and Angevine (1991) which is in widespread use, as well as other, more complex techniques, like Griesser (1998), Cornman et.al. (1998), Law et.al. (2002), Morse et.al. (2002), or Hooper et.al. (2008).
The number of existing algorithms is symptomatic for the many different approaches to tackle the multiple peak problem. Unfortunately, there are only few validation attempts: Cohn et.al. (2001), Gaffard et. al. (2006), Hooper et.al. (2008).
The operational experience is still indicative of problems with these methods. The most important issue is the excessive use of weakly justified a-priori assumptions, like vertical continuity constraints, for peak selection. More work is needed to refine multi-peak processing.
3 Estimation of first three moments
Often the power spectrum of the atmospheric signal is assumed to have a Gaussian form though this can be violated for some radar returns, see Woodman (1985). This has the advantage that the first three moments, namely power, mean frequency and frequency spread, are sufficient for a complete description of the signal Woodman and Guillen (1974). The moments are well-defined even if the Gaussian assumption of the form of the power spectrum is violated
Echo power $M_0$, Doppler frequency $M_1$ and spectral variance $M_2$ are calculated for frequency bins where $P[i] > P_N$, that is between lower and upper signal bounds $k_1$ and $k_2$ as:
$M_0 = \sum_{k=k_1}^{k_2} (P[k] - P_N)$
$M_1 = \frac{1}{M_0} \sum_{k=k_1}^{k_2} k (P[k] - P_N)$
$M_2 = \frac{1}{M_0} \sum_{k=k_1}^{k_2} (k-M_1)^2 (P[k] - P_N)$
Note that there are differences in the definitions of the spectral width. Often, the convention of \citet{Carter_etal:95} is used, where spectral width is defined as $\sigma_v = 2 \sqrt{M_2}$.
Back to RWP Fundamentals
|
2021-12-05 18:32:07
|
{"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": 10, "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": 0.7951415777206421, "perplexity": 1580.2472248027063}, "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-2021-49/segments/1637964363215.8/warc/CC-MAIN-20211205160950-20211205190950-00032.warc.gz"}
|
https://projecteuclid.org/euclid.ecp/1582945213
|
Electronic Communications in Probability
Remarks on Gross’ technique for obtaining a conformal Skorohod embedding of planar Brownian motion
Abstract
In [7] it was proved that, given a distribution $\mu$ with zero mean and finite second moment, there exists a simply connected domain $\Omega$ such that if $Z_{t}$ is a standard planar Brownian motion, then $\mathcal{R} e(Z_{\tau _{\Omega }})$ has the distribution $\mu$, where $\tau _{\Omega }$ denotes the exit time of $Z_{t}$ from $\Omega$. In this note, we extend this method to prove that if $\mu$ has a finite $p$-th moment then the first exit time $\tau _{\Omega }$ from $\Omega$ has a finite moment of order $\frac{p} {2}$. We also prove a uniqueness principle for this construction, and use it to give several examples.
Article information
Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 20, 13 pp.
Dates
Accepted: 24 February 2020
First available in Project Euclid: 29 February 2020
https://projecteuclid.org/euclid.ecp/1582945213
Digital Object Identifier
doi:10.1214/20-ECP300
Citation
Boudabra, Maher; Markowsky, Greg. Remarks on Gross’ technique for obtaining a conformal Skorohod embedding of planar Brownian motion. Electron. Commun. Probab. 25 (2020), paper no. 20, 13 pp. doi:10.1214/20-ECP300. https://projecteuclid.org/euclid.ecp/1582945213
References
• [1] R. Bañuelos and T. Carroll. Brownian motion and the fundamental frequency of a drum. Duke Mathematical Journal, 75(3):575–602, 1994.
• [2] D. Burkholder. Exit times of Brownian motion, harmonic majorization, and Hardy spaces. Advances in Mathematics, 26(2):182–205, 1977.
• [3] P. Butzer and R. Nessel. Hilbert transforms of periodic functions. In Fourier Analysis and Approximation, pages 334–354. Springer, 1971.
• [4] W. Chin, P. Jung, and G. Markowsky. Some remarks on invariant maps of the Cauchy distribution. Statistics and Probability Letters, 158, 2020.
• [5] W. Feller. An introduction to probability theory and its applications. 1957, 2.
• [6] L. Grafakos. Classical Fourier analysis, volume 2. Springer, 2008.
• [7] R. Gross. A conformal Skorokhod embedding. Electronic Communications in Probability, 24(68):1–11, 2019.
• [8] L. Hansen. Hardy classes and ranges of functions. The Michigan Mathematical Journal, 17(3):235–248, 1970.
• [9] S. Kanas and T. Sugawa. On conformal representations of the interior of an ellipse. 31(2):329, 2006.
• [10] F. King. Hilbert transforms. Cambridge University Press Cambridge, 2009.
• [11] P. Mariano and H. Panzo. Conformal skorokhod embeddings of the uniform distribution and related extremal problems. arXiv:2001.12008, 2020.
• [12] G. Markowsky. The exit time of planar Brownian motion and the Phragmén–Lindelöf principle. Journal of Mathematical Analysis and Applications, 422(1):638–645, 2015.
• [13] G. Markowsky. On the distribution of planar Brownian motion at stopping times. Annales Academiæ Scientiarum Fennicæ Mathematica, 2018.
• [14] R. Remmert. Theory of complex functions, volume 122. Springer Science & Business Media, 2012.
• [15] W. Rudin. Real and complex analysis. Tata McGraw-Hill, 2006.
• [16] D. Williams. Probability with martingales. Cambridge university press, 1991.
|
2020-05-30 05:40:41
|
{"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": 0.8043757677078247, "perplexity": 1188.99228453979}, "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-2020-24/segments/1590347407289.35/warc/CC-MAIN-20200530040743-20200530070743-00235.warc.gz"}
|
https://git.gfz-potsdam.de/habitat-sampler/HabitatSampler/-/blame/ba94edfd10d776311037850d2d46245e4de1b621/R-package/man/saveSamplePoints.Rd
|
saveSamplePoints.Rd 1.38 KB
Romulo Pereira Goncalves committed Jul 07, 2021 1 2 3 4 5 6 7 8 9 10 11 12 13 % Generated by roxygen2: do not edit by hand % Please edit documentation in R/save_files.r \name{saveSamplePoints} \alias{saveSamplePoints} \title{Save Sample Points} \usage{ saveSamplePoints( in_path, step, class_name, output_format = c("shp", "geojson"), ref_samples, ref_switch, Johannes Knoch committed Jul 08, 2021 14 num_models, Daniela Rabe committed Aug 02, 2021 15 16 dummy_raster, overwrite = TRUE Romulo Pereira Goncalves committed Jul 07, 2021 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ) } \arguments{ \item{in_path}{file path (character) for results of habitat type sampling and probability mapping (same as outPath from function multi_Class_Sampling)} \item{step}{step number (numeric)} \item{class_name}{name (character) of habitat type for which samples should be selected} \item{output_format}{format (character) of output; whether shp (default) or geojson} \item{ref_samples}{list of reference sample points} \item{ref_switch}{vector with switch values} Johannes Knoch committed Jul 08, 2021 32 \item{num_models}{number of models used for the classification of a habitat} 33 34 \item{dummy_raster}{raster with probabilities for each pixel} Daniela Rabe committed Aug 02, 2021 35 36 \item{overwrite}{overwrite file (default TRUE)} Romulo Pereira Goncalves committed Jul 07, 2021 37 38 39 40 } \value{ ESRI shapefiles/GeoJSON with name: SamplePoints_step_classname.shp/SamplePoints_step_classname.geojson \enumerate{ Johannes Knoch committed Jul 08, 2021 41 \item Point Shape/GeoJSON represents the pixels which were used to train the models for that habitat. Romulo Pereira Goncalves committed Jul 07, 2021 42 43 44 45 46 47 ESRI shapefiles have the same CRS as the input raster. GeoJSON files are in the standard CRS of GeoJSON (EPSG:4326). } } \description{ Saves the reference sample points }
|
2022-01-20 04:41:53
|
{"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": 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": 0.7680742144584656, "perplexity": 10678.82109947432}, "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/1642320301720.45/warc/CC-MAIN-20220120035934-20220120065934-00524.warc.gz"}
|
http://news.shamcode.ru/?page=10
|
# Новости
## How to setup front-end project with automated formatting, linting, testing and auto-generated documentation
https://habr.com/en/post/436176/
• DevOps
• JavaScript
• Programming
• TypeScript
• Website development
## Kalman Filter
https://habr.com/en/post/436248/
• Algorithms
• Mathematics
There are a lot of different articles on Kalman filter, but it is difficult to find the one which contains an explanation, where all filtering formulas come from. I think that without understanding of that this science becomes completely non understandable. In this article I will try to explain everything in a simple way.
Kalman filter is very powerful tool for filtering of different kinds of data. The main idea behind this that one should use an information about the physical process. For example, if you are filtering data from a car’s speedometer then its inertia give you a right to treat a big speed deviation as a measuring error. Kalman filter is also interesting by the fact that in some way it is the best filter. We will discuss precisely what does it mean. In the end of the article I will show how it is possible to simplify the formulas.
### Preliminaries
At first, let’s memorize some definitions and facts from probability theory.
#### Random variable
When one says that it is given a random variable , it means that it may take random values. Different values come with different probabilities. For example, if someone drops a dice then the set of values is discrete . When you deal with a speed of moving particle then obviously you should work with a continuous set of values. Values which come out after each experiment (measurement) we would denote by , but sometimes we would use the same letter as we use for a random variable . In the case of continuous set of values a random variable is characterized by its probability density function . This function shows a probability that the random variable falls into a small neighbourhood of the point . As we can see on the picture, this probability is equal to the area of the hatched rectangle below the graph .
Quite often in our life, random variables have the Gauss Distribution, when the probability density is .
We can see that the bell-shaped function is centered at the point and its characteristic width is around .
Since we are talking about the Gaussian Distribution, then it would be a sin not to mention from where does it come from. As well as the number and are firmly penetrated in mathematics and can be found in the most unexpected places, so Gaussian Distribution has deep roots in the theory of probability. The following remarkable statement partly explains presence of the Gauss Distribution in a lot of processes:
Let a random variable has an arbitrary distribution (in fact there are some restrictions on arbitrariness, but they are not restrictive at all). Let’s perform experiments and calculate a sum , of fallen values. Let’s make a lot of experiments. It is clear that every time we will get a different value of the sum. In other words, this sum is a random variable with its own distribution law. It turns out that for sufficiently large , the law of distribution of this sum tends to a Gaussian Distribution (by the way, the characteristic width of a bell is growing like . Read more in the Wikipedia: Central limit theorem. In real life there are a lot of values which are a sum of large number of independent and identically distributed random variables. So this values have Gauss Distribution.
#### Mean Value
By definition, a mean value of a random variable is a value which we get in a limit if we perform more and more experiments and calculate a mean of fallen values. A mean value is denoted in different ways: mathematicians denote by (expectation), Physicists denote it by or . We will denote it as mathematicians do.
For instance, a mean value of Gaussian Distribution is equal to .
#### Variance
For Gaussian distribution, we clearly see that the random variable tends to fall within a certain region of its mean value . Let us enjoy the Gaussian distribution once again:
On the picture, one may see that a characteristic width of a region where values mostly fall is . How can we estimate this width for an arbitrary random variable? We can draw a graph of its probability density function and just visually evaluate the characteristic range. However it would be better to choose a precise algebraic way for this evaluation. We may find a mean length of deviation from the mean value: . This value is a good estimation of a characteristic deviation of . However we know very well, how problematic it is to use absolute values in formulas, thus this formula is rarely used in practice.
A simpler approach (simple from calculation’s point of view) is to calculate .
This value called variance and denoted by . The quadratic root of the variance is a good estimation of random variable’s characteristic deviation. It’s called the standard deviation.
For instance, one can compute that for the Gaussian distribution the variance is equal to thus the standard deviation is . This result really corresponds to our geometrical intuition. In fact a small cheating is hidden here. Actually in a definition of the Gauss distribution you see the number in a denominator of expression . This stands there in purpose, for the standard deviation to be equal exactly to . So the formula of Gauss distribution is written in a way, which keep in mind that one would compute its standard deviation.
#### Independent random variables
Random variables may depend on each other or not. Imagine that you are throwing a needle on the floor and measuring coordinates of its both ends. This two coordinates are random variables, but they depend on each other, since a distance between them should be always equal to the length of the needle. Random variables are independent from each other if falling results of the first one doesn’t depend on results of the second. For two independent variables and the mean of their product is equal to the product of their mean:
Proof
For instance to have blue eyes and finish a school with higher honors are independent random variables. Let say that there are of people with blue eyes and of people with higher honors. So there are of people with blue eyes and higher honors. This example helps us to understand the following. For two independent random variables and which are given by their density of probability and , the density of probability (the first variable falls at and the second at ) can by find by the formula
## PVS-Studio 7.00
https://habr.com/en/company/pvs-studio/blog/436332/
• PVS-Studio corporate blog
• C++
• DevOps
• Java
## 286 and the network
https://habr.com/en/post/436006/
• Old hardware
## baidu / openedge
https://github.com/baidu/openedge
Go
Extend cloud computing, data and service seamlessly to edge devices.
|
2019-01-21 15:52:23
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 52, "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": 0.9051595330238342, "perplexity": 330.70640799452264}, "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/1547583795042.29/warc/CC-MAIN-20190121152218-20190121174218-00004.warc.gz"}
|
https://wiki2.org/en/Poisson_binomial_distribution
|
To install click the Add extension button. That's it.
The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.
4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds
# Poisson binomial distribution
Parameters ${\displaystyle \mathbf {p} \in [0,1]^{n}}$ — success probabilities for each of the n trials k ∈ { 0, …, n } ${\displaystyle \sum \limits _{A\in F_{k}}\prod \limits _{i\in A}p_{i}\prod \limits _{j\in A^{c}}(1-p_{j})}$ ${\displaystyle \sum \limits _{l=0}^{k}\sum \limits _{A\in F_{l}}\prod \limits _{i\in A}p_{i}\prod \limits _{j\in A^{c}}(1-p_{j})}$ ${\displaystyle \sum \limits _{i=1}^{n}p_{i}}$ ${\displaystyle \sigma ^{2}=\sum \limits _{i=1}^{n}(1-p_{i})p_{i}}$ ${\displaystyle {\frac {1}{\sigma ^{3}}}\sum \limits _{i=1}^{n}(1-2p_{i})(1-p_{i})p_{i}}$ ${\displaystyle {\frac {1}{\sigma ^{4}}}\sum \limits _{i=1}^{n}(1-6(1-p_{i})p_{i})(1-p_{i})p_{i}}$ ${\displaystyle \prod \limits _{j=1}^{n}(1-p_{j}+p_{j}e^{t})}$ ${\displaystyle \prod \limits _{j=1}^{n}(1-p_{j}+p_{j}e^{it})}$
In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The concept is named after Siméon Denis Poisson.
In other words, it is the probability distribution of the number of successes in a sequence of n independent yes/no experiments with success probabilities ${\displaystyle p_{1},p_{2},\dots ,p_{n}}$. The ordinary binomial distribution is a special case of the Poisson binomial distribution, when all success probabilities are the same, that is ${\displaystyle p_{1}=p_{2}=\cdots =p_{n}}$.
• 1/5
Views:
59 915
199 274
917 775
136 191
39 626
• ✪ The Relationship Between the Binomial and Poisson Distributions
• ✪ Statistics - Binomial & Poisson Distributions
• ✪ Binomial distribution | Probability and Statistics | Khan Academy
• ✪ Binomial distribution probability (solve with easy steps)
• ✪ Proof that the Binomial Distribution tends to the Poisson Distribution
#### Transcription
Let's take a look at the relationship between the binomial and Poisson distributions. The binomial distribution tends toward the Poisson distribution as n tends to infinity, p goes to zero and lambda = np stays constant. Here we have the binomial formula and the Poisson formula Now we know the mean of a binomial random variable is np and we know that the mean of a Poisson random variable is lambda, so if we set n times p equal to lambda, and then p equals lambda over n, and we took this value and we substituted it in for p up here, then, it might not be obvious, but as n gets really large, as n goes off to infinity, this binomial formula tends towards this Poisson so as n goes off to infinity and p goes to 0 because lambda equals np is a constant as that happens the binomial tends toward the Poisson. Now it's not obvious, but I do have a mathematical proof that in another video. An implication of this is that the Poisson distribution can be used to provide a reasonable approximation to the binomial distribution if n is large and p is small. Let's look at an example to illustrate. Albinism is a rare genetic disorder that affects approximately 1 in 20,000 Europeans. This 1 in 20,000 is just an approximate value but let's take it to be exact for the purposes of this question. People with albinism produce little or none of the pigment melanin, but this manifests itself in different ways. Overall they tend to have very fair skin and very light colored hair, and things along these lines. In a random sample of 1,000 Europeans, what is the probability that exactly 2 have albiniism? Well we're looking at 1,000 people, each individual person either has Albinism or they do not, and if we are sampling randomly and independently, then this is really going to follow a binomial distribution, the number that have albinism is going to have a binomial distribution with n of 1000 and p is the probability any one individual person has it. And that was given on the last page as 1/20,000. And we are interested in the probability that X is equal to 2. And so we just use a binomial formula, n choose x, so 1000 choose 2, times p to the x, 1/20,000 squared, times 1-p, 1 -1/20,000 to the n-x, so 1000-2. And if you put that into your calculator we get 0.001187965. Now let's use the Poisson approximation in this case, just to see how well it works in this particular scenario. We would let lambda equal np, which is one thousand times 1/20,000, which works out to 1 in 20, or 0.05. Then our Poisson formula is lambda to the x, e to the minus lambda, over x! [factorial] So if we want the probability that X is equal to 2 using our Poisson approximation, this is going to be approximately 0.05, lambda, to the x, e to the minus lambda over x factorial. Put that into your calculator or computer and you'd see that this is equal to 0.001189037. And the value we get from the Poisson approximation is very close to the true value from the binomial distribution. That's true in this case because we had such a large n and a very small p, so the Poisson approximation is going to be very reasonable in this particular case. Here's a very rough guideline. The Poisson approximation is reasonable if n is greater than 50 and np is less than 5. But this is just a rough guideline, the approximation is going to work best when n is a really big and p is really close to zero. So whether it's a reasonable approximation or not depends on your needs, but this is one rough guideline one could use. Why use this approximation? If something truly has a binomial distribution then we should calculate probabilities based on the binomial distribution. But sometimes those factorials and exponentials in the binomial formula can become problematic to calculate. If n is very large we might end up getting some round off error or a computer or calculator might actually just give us an error and say it can't calculate it. That's a little bit less of an issue for the Poisson distribution. Also a problem maybe binomial conceptually, but n and p may not be known. In order to calculate binomial probabilities, we need to know n and p. Now if we happen to know the mean number of occurrences, we could call that lambda and use that in a Poisson formula, provided we knew we had a very large n and a very small p, But we don't need to know what those actual values are, we just need to know the mean number of occurrences.
## Mean and variance
Since a Poisson binomial distributed variable is a sum of n independent Bernoulli distributed variables, its mean and variance will simply be sums of the mean and variance of the n Bernoulli distributions:
${\displaystyle \mu =\sum \limits _{i=1}^{n}p_{i}}$
${\displaystyle \sigma ^{2}=\sum \limits _{i=1}^{n}(1-p_{i})p_{i}}$
For fixed values of the mean (${\displaystyle \mu }$) and size (n), the variance is maximal when all success probabilities are equal and we have a binomial distribution. When the mean is fixed, the variance is bounded from above by the variance of the Poisson distribution with the same mean which is attained asymptotically[citation needed] as n tends to infinity.
## Probability mass function
The probability of having k successful trials out of a total of n can be written as the sum [1]
${\displaystyle \Pr(K=k)=\sum \limits _{A\in F_{k}}\prod \limits _{i\in A}p_{i}\prod \limits _{j\in A^{c}}(1-p_{j})}$
where ${\displaystyle F_{k}}$ is the set of all subsets of k integers that can be selected from {1,2,3,...,n}. For example, if n = 3, then ${\displaystyle F_{2}=\left\{\{1,2\},\{1,3\},\{2,3\}\right\}}$. ${\displaystyle A^{c}}$ is the complement of ${\displaystyle A}$, i.e. ${\displaystyle A^{c}=\{1,2,3,\dots ,n\}\setminus A}$.
${\displaystyle F_{k}}$ will contain ${\displaystyle n!/((n-k)!k!)}$ elements, the sum over which is infeasible to compute in practice unless the number of trials n is small (e.g. if n = 30, ${\displaystyle F_{15}}$ contains over 1020 elements). However, there are other, more efficient ways to calculate ${\displaystyle \Pr(K=k)}$.
As long as none of the success probabilities are equal to one, one can calculate the probability of k successes using the recursive formula [2] [3]
${\displaystyle \Pr(K=k)={\begin{cases}\prod \limits _{i=1}^{n}(1-p_{i})&k=0\\{\frac {1}{k}}\sum \limits _{i=1}^{k}(-1)^{i-1}\Pr(K=k-i)T(i)&k>0\\\end{cases}}}$
where
${\displaystyle T(i)=\sum \limits _{j=1}^{n}\left({\frac {p_{j}}{1-p_{j}}}\right)^{i}.}$
The recursive formula is not numerically stable, and should be avoided if ${\displaystyle n}$ is greater than approximately 20. Another possibility is using the discrete Fourier transform.[4]
${\displaystyle \Pr(K=k)={\frac {1}{n+1}}\sum \limits _{l=0}^{n}C^{-lk}\prod \limits _{m=1}^{n}\left(1+(C^{l}-1)p_{m}\right)}$
where ${\displaystyle C=\exp \left({\frac {2i\pi }{n+1}}\right)}$ and ${\displaystyle i={\sqrt {-1}}}$.
Still other methods are described in [5] .
## Entropy
There is no simple formula for the entropy of a Poisson binomial distribution, but the entropy is bounded above by the entropy of a binomial distribution with the same number parameter and the same mean. Therefore, the entropy is also bounded above by the entropy of a Poisson distribution with the same mean.[6]
The Shepp–Olkin concavity conjecture, due to Lawrence Shepp and Ingram Olkin in 1981, states that the entropy of a Poisson binomial distribution is a concave function of the success probabilities ${\displaystyle p_{1},p_{2},\dots ,p_{n}}$.[7] This conjecture was proved by Erwan Hillion and Oliver Johnson in 2015.[8] The Shepp-Olkin monotonicity conjecture, also from the same 1981 paper, is that the entropy is monotone increasing in ${\displaystyle p_{i}}$, if all ${\displaystyle p_{i}\leq 1/2}$. This conjecture was also proved by Hillion and Johnson, in 2019 [9]
## Chernoff bound
The probability that a Poisson binomial distribution gets large, can be bounded using its moment generating function:
{\displaystyle {\begin{aligned}\Pr[S\geq s]&\leq \exp(-st)\operatorname {E} \left[\exp \left[t\sum _{i}X_{i}\right]\right]\\&=\exp(-st)\prod _{i}(1-p_{i}+e^{t}p_{i})\\&=\exp \left(-st+\sum _{i}\log \left(p_{i}(e^{t}-1)+1\right)\right)\\&\leq \exp \left(-st+\sum _{i}\log \left(\exp(p_{i}(e^{t}-1))\right)\right)\\&=\exp \left(-st+\sum _{i}p_{i}(e^{t}-1)\right)\\&=\exp \left(s-\mu -s\log {\frac {s}{\mu }}\right),\end{aligned}}}
where we took ${\textstyle t=\log \left(s\left/\sum _{i}p_{i}\right.\right)}$. This is similar to the tail bounds of a binomial distribution.
## References
1. ^ Wang, Y. H. (1993). "On the number of successes in independent trials" (PDF). Statistica Sinica. 3 (2): 295–312.
2. ^ Shah, B. K. (1994). "On the distribution of the sum of independent integer valued random variables". American Statistician. 27 (3): 123–124. JSTOR 2683639.
3. ^ Chen, X. H.; A. P. Dempster; J. S. Liu (1994). "Weighted finite population sampling to maximize entropy" (PDF). Biometrika. 81 (3): 457. doi:10.1093/biomet/81.3.457.
4. ^ Fernandez, M.; S. Williams (2010). "Closed-Form Expression for the Poisson-Binomial Probability Density Function". IEEE Transactions on Aerospace and Electronic Systems. 46 (2): 803–817. Bibcode:2010ITAES..46..803F. doi:10.1109/TAES.2010.5461658.
5. ^ Chen, S. X.; J. S. Liu (1997). "Statistical Applications of the Poisson-Binomial and conditional Bernoulli distributions". Statistica Sinica. 7: 875–892.
6. ^ Harremoës, P. (2001). "Binomial and Poisson distributions as maximum entropy distributions" (PDF). IEEE Transactions on Information Theory. 47 (5): 2039–2041. doi:10.1109/18.930936.
7. ^ Shepp, Lawrence; Olkin, Ingram (1981). "Entropy of the sum of independent Bernoulli random variables and of the multinomial distribution". In Gani, J.; Rohatgi, V.K. (eds.). Contributions to probability: A collection of papers dedicated to Eugene Lukacs. New York: Academic Press. pp. 201–206. ISBN 0-12-274460-8. MR 0618689.
8. ^ Hillion, Erwan; Johnson, Oliver (2015-03-05). "A proof of the Shepp-Olkin entropy concavity conjecture". Bernoulli. 23: 3638–3649. arXiv:1503.01570. doi:10.3150/16-BEJ860.
9. ^ Hillion, Erwan; Johnson, Oliver (2019-11-09). "A proof of the Shepp-Olkin entropy monotonicity conjecture". Electronic Journal of Probability. 24 (126): 1–14. doi:10.1214/19-EJP380.
|
2020-01-26 16:04:28
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 35, "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": 0.9243454933166504, "perplexity": 483.8874223449375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251689924.62/warc/CC-MAIN-20200126135207-20200126165207-00287.warc.gz"}
|
https://math.stackexchange.com/questions/1650960/summation-of-a-term-to-infinity
|
Summation of a term to infinity
I read through many tutorials but no one mentioned this explicitly.
Is the following conversion valid?
$$\sum_{k=0}^\infty \frac{k-1}{2^k} = \lim_{n\to \infty} \sum_{k=0}^n \frac{k-1}{2^k}$$
Please excuse if it seems stupid or too simple to ask in the forum.
• That is the generally accepted definition of an infinite summation. I do note, however, that sometimes we will not use that definition, as you can see... (I'd recommend using your definition, it is more common, also, the methods we use if the summation doesn't converge may be... less accepted as correct.) en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF – Simply Beautiful Art Feb 12 '16 at 0:03
It's not only valid, it's how it's defined.
Note that the operation "addition" is defined only if we apply it a finite amount of times. Thus, adding an infinite amount of terms doesn't make sense. We'll have to define it as a limit, as that only includes nice, finite sums.
• Well, technically you must first define $\mathrm{lim}_{n \rightarrow \infty}$, which is most certainly not the traditional epsilon-delta definition. And then you have to make sure your definition is meaningful when we restrict $n$ to the natural numbers. But yeah, that's basically how infinite sums are defined. The rest can mostly be taken care of with Cauchy sequences. – Kevin Feb 12 '16 at 4:29
• @Kevin: What do you mean, "not the traditional epsilon-delta definition"? Why not? – TonyK Feb 12 '16 at 10:45
• @TonyK Probably because $|n - \infty| < \delta$ is meaningless. – kevinsa5 Feb 12 '16 at 16:13
• But $n\to\infty$ use a different traditional definition (most often $N$ and $\epsilon$). Saying it doesn't use $\delta$ is beside the point. – Teepeemm Feb 12 '16 at 17:08
This is the definition of infinite series. It is the limit of the partial sums $S_n$:
$$S_n = \sum_{k = 0}^n a_k$$
$$\sum_{k = 0}^{\infty} a_k := \lim_{n \to \infty} S_n = \lim_{n \to \infty} \sum_{k = 0}^n a_k$$
|
2020-02-18 00:47:37
|
{"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": 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": 0.876998782157898, "perplexity": 434.6652644579243}, "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-2020-10/segments/1581875143455.25/warc/CC-MAIN-20200217235417-20200218025417-00156.warc.gz"}
|
https://zbmath.org/?q=an:1080.47040
|
# zbMATH — the first resource for mathematics
On some structural properties of Banach function spaces and boundedness of certain integral operators. (English) Zbl 1080.47040
Summary: In this paper, the notions of uniformly upper and uniformly lower $$\ell$$-estimates for Banach function spaces are introduced. Further, the pair $$(X,Y)$$ of Banach function spaces is characterized, where $$X$$ and $$Y$$ satisfy uniformly a lower $$\ell$$-estimate and uniformly an upper $$\ell$$-estimate, respectively. The integral operator from $$X$$ into $$Y$$ of the form $K f(x)=\varphi (x) \int _0^x k(x,y)f(y)\psi (y)\,\text dy$ is studied, where $$k$$, $$\varphi$$, $$\psi$$ are prescribed functions under some local integrability conditions, the kernel $$k$$ is non-negative and is assumed to satisfy certain additional conditions, notably one of monotone type.
##### MSC:
47G10 Integral operators 45P05 Integral operators 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25 Maximal functions, Littlewood-Paley theory
Full Text:
##### References:
[1] C. Bennett and R. Sharpley: Interpolation of Operators. Acad. Press, Boston, 1988. · Zbl 0647.46057 [2] J. Lindenstrauss and L. Tzafriri: Classical Banach Spaces. II. Function Spaces. Springer-Verlag, 1979. · Zbl 0403.46022 [3] A. V. Bukhvalov, V. B. Korotkov, A. G. Kusraev, S. S. Kutateladze and B. M. Makarov: Vector Lattices and Integral Operators. Nauka, Novosibirsk, 1992. (In Russian.) · Zbl 0752.46001 [4] J. Musielak: Orlicz Spaces and Modular Spaces. Lecture Notes in Math. 1034. Springer-Verlag, Berlin-Heidelberg-New York, 1983. · Zbl 0557.46020 [5] V. D. Stepanov: Nonlinear Analysis. Function Spaces and Applications 5. Olympia Press, 1994, pp. 139-176. [6] E. N. Lomakina and V. D. Stepanov: On Hardy type operators in Banach function spaces on half-line. Dokl. Akad. Nauk 359 (1998), 21-23. (In Russian.) · Zbl 0958.47022 [7] P. Oinarov: Two-side estimates of the norm of some classes of integral operators. Trudy Mat. Inst. Steklov. 204 (1993), 240-250. (In Russian.) [8] A. V. Bukhvalov: Generalization of Kolmogorov-Nagumo’s theorem on tensor product. Kachestv. pribl. metod. issledov. operator. uravnen. 4 (1979), 48-65. (In Russian.) [9] E. I. Berezhnoi: Sharp estimates for operators on cones in ideal spaces. Trudy Mat. Inst. Steklov. 204 (1993), 3-36. (In Russian.) [10] E. I. Berezhnoi: Two-weighted estimations for the Hardy?Littlwood maximal function in ideal Banach spaces. Proc. Amer. Math. Soc. 127 (1999), 79-87. · Zbl 0918.42011 [11] Q. Lai: Weighted modular inequalities for Hardy type operators. Proc. London Math. Soc. 79 (1999), 649-672. · Zbl 1030.46030 [12] I. I. Sharafutdinov: On the basisity of the Haar system in L p(t) ([0; 1]) spaces. Mat. Sbornik 130 (1986), 275-283. (In Russian.) [13] I. I. Sharafutdinov: The topology of the space L p(t) ([0; 1]). Mat. Zametki 26 (1976), 613-632. (In Russian.) [14] O. Kov??ik and J. R?kosn?k: On spaces L p(x) and W k;p(x). Czechoslovak Math.J. 41 (1991), 592-618. [15] H. H. Schefer: Banach Lattices and Positive Operators. Springer-Verlag, Berlin-Heidel-berg-New York, 1974.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
|
2021-10-15 20:23:18
|
{"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": 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": 0.9119258522987366, "perplexity": 2998.8115411432805}, "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-2021-43/segments/1634323583083.92/warc/CC-MAIN-20211015192439-20211015222439-00045.warc.gz"}
|
http://www.concepts.org/**
|
## ::Exponentiation
### ::concepts
Nowrap::''x'' ''n''::''b'' Number::complex Power::positive Numbers::integer Function::''i''
{{#invoke:redirect hatnote|redirect}}
\$B=1/2}} (cyan). Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases:
$b^n = \underbrace{b \times \cdots \times b}_n$
In that case, bn is called the n-th power of b, or b raised to the power n.
The exponent is usually shown as a superscript to the right of the base. Some common exponents have their own names: the exponent 2 (or 2nd power) is called the square of b (b2) or b squared; the exponent 3 (or 3rd power) is called the cube of b (b3) or b cubed. The exponent −1 of b, or 1 / b, is called the reciprocal of b.
When n is a negative integer and b is not zero, bn is naturally defined as 1/bn, preserving the property bn × bm = bn + m.
The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.
Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.
Calculation results{{#invoke:Navbar|navbar}}
$\scriptstyle\left.\begin{matrix}\scriptstyle\text{summand}+\text{summand}\\\scriptstyle\text{augend}+\text{addend}\end{matrix}\right\}=$ $\scriptstyle\text{sum}$
Subtraction (−)
$\scriptstyle\text{minuend}-\text{subtrahend}=$ $\scriptstyle\text{difference}$
Multiplication (×)
$\scriptstyle\left.\begin{matrix}\scriptstyle\text{factor}\times\text{factor}\\\scriptstyle\text{multiplier}\times\text{multiplicand}\end{matrix}\right\}=$ $\scriptstyle\text{product}$
Division (÷)
$\scriptstyle\left.\begin{matrix}\scriptstyle\frac{\scriptstyle\text{dividend}}{\scriptstyle\text{divisor}}\\\scriptstyle\frac{\scriptstyle\text{numerator}}{\scriptstyle\text{denominator}}\end{matrix}\right\}=$ $\scriptstyle\text{quotient}$
Modulation (mod)
$\scriptstyle\text{dividend}\bmod\text{divisor}=$ $\scriptstyle\text{remainder}$
Exponentiation
$\scriptstyle\text{base}^\text{exponent}=$ $\scriptstyle\text{power}$
nth root (√)
$\scriptstyle\sqrt[\text{degree}]{\scriptstyle\text{radicand}}=$ $\scriptstyle\text{root}$
Logarithm (log)
$\scriptstyle\log_\text{base}(\text{antilogarithm})=$ $\scriptstyle\text{logarithm}$
Exponentiation sections
Intro History of the notation Terminology Integer exponents Rational exponents Real exponents Complex exponents with positive real bases Powers of complex numbers Generalizations Repeated exponentiation Zero to the power of zero Limits of powers Efficient computation with integer exponents Exponential notation for function names In programming languages List of whole-number exponentials See also References External links
PREVIOUS: Intro NEXT: History of the notation << >>
|
2021-07-26 04:56:29
|
{"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": 0.816277265548706, "perplexity": 1448.8747771412973}, "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/1627046152000.25/warc/CC-MAIN-20210726031942-20210726061942-00278.warc.gz"}
|
http://www.bot-thoughts.com/2008/08/squeaky-platter-drive.html
|
## Thursday, August 28, 2008
### Squeaky: Platter Drive
Squeaky: < prev | next >
One of the key features of a record cleaning machine is the ability to spin the record without manual intervention. I'm getting really sick of cleaning records by manually spinning them on my turntable while I scrub.
Some folks on AudioKarma.org had suggested use of a bread machine, presumably because it uses a fairly high torque motor and some kind of gear reduction.
Upon dissecting the $2 bread maker I got from Goodwill, I found a metal plate onto which a motor and drive mechanism are mounted. As shown in the pic to the right, the motor drives the stirring mechanism on the opposite side of the plate via a tooth belt. The white cog wheel is attached to a stainless steel drive shaft riding in a bronze bearing by way of a 6mm nut. The drive mechanism is attached to the drive shaft and engages the stirring gizmo in the bread bucket to stir and knead the bread, similar to how the blades of a blender are coupled to the blender motor. But how to drive a turntable platter? The two I had on hand spin on greased bearings attached to a mounting plate to affix them to a horizontal surface (see pic to the left). They are both from belt drive turntables. Should I try to use a turntable belt? These are usually low tension belts and will slip with the slightest drag on the platter. I needed a higher torque, higher traction solution. I want to keep this simple, cheap, and practical with minimum fabrication involved; I don't have a machine shop and I don't want to spend a fortune on this project. Those constraints eliminate a lot of design options. Direct drive would've required fabrication of some type and possibly re-engineering the drivetrain making this an unnecessarily hard problem to solve. Why not drive the platter rim with a rubber idler wheel attached directly to the 6mm threaded end of the drive shaft? A trip to the hardware store and$18 later I had a pile of options. What ended up working best was a rubber hole plug mounted to a shaft extension. You can see the black idler wheel in the top pic.
To extend the shaft, I used a 5/16" x 1.5" aluminum spacer, basically a hollow aluminum tube, which I threaded with my new 6mm x 1.0mm tap. (Aluminum being a softer metal is easier to tap especially with an incorrectly sized hole).
I disassembled a 1-3/4" hole plug (a rubber puck sandwiched between two plates, compressed by a nut and bolt to squish out and fill a hole). The hole plug rubber piece slid over the aluminum spacer shaft, and with washers on top and bottom and a 6mm cap end bolt on top to cinch it down, et voila, rubber idler wheel.
As a bonus, the gear reduction afforded by this small wheel driving the large platter means the record will spin at a goldilocks speed: not too fast, not too slow, but just right.
Next step is mounting the drivetrain and platter on a chassis. I want the idler wheel to apply user-adjustable pressure to the platter. It adds complexity to the design but it makes up for imprecise mounting, lack of trueness of the drive shaft and more importantly, accomodates wear of the rubber wheel.
Eventually, the motor is to be computer controlled. Before that is possible, I'll need to break out my copy of DC Power Supplies: A Technician's Guide and build a dual voltage supply for the electronics and motor of the robot. I've never built an wall-powered DC supply before... fortunately I can reverse engineer the bread maker supply to help.
Squeaky: < prev | next >
|
2020-11-24 23:08:11
|
{"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": 0.25923359394073486, "perplexity": 5035.843051425127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141177607.13/warc/CC-MAIN-20201124224124-20201125014124-00264.warc.gz"}
|
http://pdglive.lbl.gov/Particle.action?init=0&node=S017&home=BXXX005
|
${{\boldsymbol N}}$ BARYONS($\boldsymbol S$ = 0, $\boldsymbol I$ = 1/2) ${{\mathit p}}$, ${{\mathit N}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$; ${{\mathit n}}$, ${{\mathit N}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ INSPIRE search
# ${{\boldsymbol n}}$ $I(J^P)$ = $1/2(1/2^{+})$
We have omitted some results that have been superseded by later experiments. See our earlier editions. Anyone interested in the neutron should look at these two review articles: D. Dubbers and M.G. Schmidt, The neutron and its role in cosmology and particle physics,'' Reviews of Modern Physics 83 1111 (2011); and F.E. Wietfeldt and G.L. Greene, The neutron lifetime,'' Reviews of Modern Physics 83 1173 (2011).
See related review: Baryon Decay Parameters
${{\mathit n}}$ MASS (atomic mass units u) $1.0086649159 \pm0.0000000005$ u
${{\mathit n}}$ MASS (MeV) $939.565413 \pm0.000006$ MeV
${{\overline{\mathit n}}}$ MASS $939.49 \pm0.05$ MeV
(${\mathit m}_{{{\mathit n}}}–{\mathit m}_{{{\overline{\mathit n}}}}$ )/ ${\mathit m}_{{{\mathit n}}}$ $(9 \pm6) \times 10^{-5}$
${\mathit m}_{{{\mathit n}}}–{\mathit m}_{{{\mathit p}}}$ $1.2933321 \pm0.0000005$ MeV
${{\mathit n}}$ MEAN LIFE $880.2 \pm1.0$ s (S = 1.9)
${{\mathit n}}$ MAGNETIC MOMENT $-1.9130427 \pm0.0000005$ $\mu _{\mathit N}$
${{\mathit n}}$ ELECTRIC DIPOLE MOMENT $<0.30 \times 10^{-25}$ $\mathit e~$cm CL=90.0%
${{\mathit n}}$ MEAN-SQUARE CHARGE RADIUS $-0.1161 \pm0.0022$ fm${}^{2}$ (S = 1.3)
${{\mathit n}}$ MAGNETIC RADIUS $0.864 {}^{+0.009}_{-0.008}$ fm
${{\mathit n}}$ ELECTRIC POLARIZABILITY ${{\mathit \alpha}_{{n}}}$ $0.00118 \pm0.00011$ fm${}^{3}$
${{\mathit n}}$ MAGNETIC POLARIZABILITY ${{\mathit \beta}_{{n}}}$ $(3.7 \pm1.2) \times 10^{-4}$ fm${}^{3}$
${{\mathit n}}$ CHARGE $(-2 \pm8) \times 10^{-22}$ $\mathit e$
LIMIT ON ${{\boldsymbol n}}{{\overline{\boldsymbol n}}}$ OSCILLATIONS
Mean Time for ${{\mathit n}}{{\overline{\mathit n}}}$ Transition in Vacuum $>8.6 \times 10^{7}$ s CL=90.0%
LIMIT ON ${{\mathit n}}{{\mathit n}^{\,'}}$ OSCILLATIONS $> 414$ s CL=90.0%
${{\boldsymbol n}}$ $\rightarrow$ ${{\boldsymbol p}}{{\boldsymbol e}^{-}}{{\overline{\boldsymbol \nu}}_{{e}}}$ DECAY PARAMETERS
$\lambda {}\equiv{\mathit g}_{{{\mathit A}}}$ $/$ ${\mathit g}_{{{\mathit V}}}$ $-1.2724 \pm0.0023$ (S = 2.2)
${{\mathit e}^{-}}$ ASYMMETRY PARAMETER $\mathit A$ $-0.1184 \pm0.0010$ (S = 2.4)
${{\overline{\mathit \nu}}_{{e}}}$ ASYMMETRY PARAMETER $\mathit B$ $0.9807 \pm0.0030$
PROTON ASYMMETRY PARAMETER $\mathit C$ $-0.2377 \pm0.0026$
${{\mathit e}}-{{\overline{\mathit \nu}}_{{e}}}$ ANGULAR CORRELATION COEFFICIENT $\mathit a$ $-0.1059 \pm0.0028$
$\phi _{\mathit AV}$, PHASE OF ${\mathit g}_{{{\mathit A}}}$ RELATIVE TO ${\mathit g}_{{{\mathit V}}}$ $180.017 \pm0.026$ $^\circ{}$
TRIPLE CORRELATION COEFFICIENT $\mathit D$ $(-1.2 \pm2.0) \times 10^{-4}$
TRIPLE CORRELATION COEFFICIENT $\mathit R$ $0.004 \pm0.013$
|
2019-01-18 15:46:33
|
{"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": 0.9129222631454468, "perplexity": 1588.8909090124635}, "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/1547583660175.18/warc/CC-MAIN-20190118151716-20190118173716-00402.warc.gz"}
|
http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=P4811&l=en
|
Magyar Information Contest Journal Articles
# Problem P. 4811. (February 2016)
P. 4811. A piston of mass $\displaystyle m=2~{\rm kg}$ confines an air column of height $\displaystyle \ell=30~{\rm cm}$ in a cylinder of cross section $\displaystyle A=10~{\rm cm}^2$. Both values of the internal and the external pressure are $\displaystyle p_0=10^5$ Pa. The cylinder can be rotated about a vertical axle. In the stationary position the middle of the piston is at a distance of $\displaystyle r=0.5$ m from the axle.
$\displaystyle a)$ By what factor will the density of the gas increase if the cylinder is rotated with an angular speed of $\displaystyle \omega=3~{\rm s}^{-1}$.
$\displaystyle b)$ During the rotation, to what value should the external pressure be changed in order that the piston moves back to its original position? The temperature remains constant all the time.
(4 pont)
Deadline expired on 10 March 2016.
### Statistics:
71 students sent a solution. 4 points: 53 students. 3 points: 10 students. 2 points: 5 students. 1 point: 2 students. 0 point: 1 student.
Our web pages are supported by: Morgan Stanley
|
2017-12-12 23:24:35
|
{"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": 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": 0.7329617142677307, "perplexity": 1162.1746900622436}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948520042.35/warc/CC-MAIN-20171212231544-20171213011544-00118.warc.gz"}
|
https://crypto.stackexchange.com/questions/91544/can-the-security-of-ecdsa-be-compromised-by-the-chosen-parameters
|
# Can the security of ECDSA be compromised by the chosen parameters?
The recommended parameters for a secp256k1 ECDSA curve are:
p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
a = 00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
b = 00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000007
G = 02
79BE667E F9DCBBAC 55A06295 CE870B07
029BFCDB 2DCE28D9 59F2815B 16F81798 (compressed version)
n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE
BAAEDCE6 AF48A03B BFD25E8C D0364141
h = 01
However, if I change any of those parameters and used them, then will the security of the trapdoor function be compromised significantly?
For example, I could use:
G = 02
B3949141 E36A5EE6 22754219 A87D849B
DC5EA332 F2944A03 1A585112 F05673EA (compressed version)
as the value of $$G$$ to generate public keys instead of the recommended value of above. Will the security of the trapdoor function - and subsequently, the public keys - be compromised significantly?
• This site supports both MarkDown (that the formatting buttons generate) and MathJax / Latex. Please format your questions to the best of your abilities before posting. Jun 13 at 12:54
For example, I could use:
If the discrete log is already backdoored with the standard base point $$G$$, then changing the base to another point on the curve doesn't solve this issue.
Let you know that $$G$$ is backdoored and you changed the base to $$G' \neq G$$. Then the entity that created the backdoor can use this to find the private keys.
Let $$P = [k]G'$$ be a public key with the new base. The attacker solves Dlog of $$G' = [a]G$$ only once. Using this they forms $$P = [ak]G$$. This is in the backdoored base so that they can solve the discrete logairhtmm to find $$ak$$. Once $$ak$$ is found, extracting the secret key can be performed with a simple modular arithmetic $$k = ak \cdot a^{-1} \bmod n$$ where the $$a^{-1}$$ is the inverse of $$a$$ in the modulo $$n$$.
As a result, once you have a backdoored discrete logarithm, then the curve is not safe to use. It is all in one, if a base point has a trapdoor then all base points have trapdoors!
However, if I change any of those parameters and used them, then will the security of the trapdoor function be compromised significantly?
Changing the parameters $$p,a$$, and $$b$$ that defines $$n$$ and $$h$$, except the basepoint, change the curve and the new curve needs to be extensively analyzed;
1. Does the curve order has a prime or has a large prime factor?
2. Does the twist of the curve have large prime order?
3. Does it have a safe discrete log?
4. ...
These are the basics, more on this see safecurves
• So changing the base point G will not have any effect on the security, however, changing any other parameter will?
– CCS
Jun 13 at 19:31
• Yes, changing $G$ doesn't have an effect, changing the curve parameters $(p,a,b)$ will define a new curve and that needs to be analyzed. A random curve doesn't need to be a safe curve. Jun 13 at 19:45
• @kelaka Your answers prove that the discrete log relative to different generators is hard, up to solving a single discrete log. However, given that we don't have a full reduction of ECDSA to discrete log, it is theoretically possible that ECDSA is easy for some $G'$ and not for others. Furthermore, if $G'$ is chosen in a special way and such that its discrete log relative to $G$ isn't known, then theoretically this could break ECDSA. There may be another proof, and in practice my guess would be that you're right, but this doesn't prove it. Jun 15 at 9:45
• @YehudaLindell thanks for the enlightening comment. Jun 15 at 18:53
|
2021-12-09 03:26:06
|
{"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6633714437484741, "perplexity": 1104.0936705414965}, "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/1637964363659.21/warc/CC-MAIN-20211209030858-20211209060858-00227.warc.gz"}
|
https://www.physicsforums.com/threads/areas-and-distances-intro-to-definite-integral.843732/
|
# Areas And Distances (Intro. to Definite Integral)
1. Nov 17, 2015
### in the rye
Hey everyone,
Today in my Calculus 1 lecture we covered Areas and Distances, which serves as a prequel to the definite integral in my book. I am confused on some notation the book uses, and I cannot seem to find a clear explanation anywhere that I look.
n
∑ f(xi) ΔX ≅ A
i=1
First, let me explain this how I understand it, then correct me where I am wrong.
I understand this this is a simple way of saying that the approximate area under your line. And I know what the summation means.
My confusion is over the xi, and the start/end point. I know that f(xi) is defining the height of your rectangle based on the x value you chose in your x sub-interval. However, I'm confused with the relation of i=1 and n to this point. Say we have f(x) = x2. If we used this formula with left rectangles, one of our 'i's would have to be at 0. Does this mean that we alter the formula to say(?):
n
∑ f(xi-1) ΔX ≅ A
i=1
or
n
∑ f(xi) ΔX ≅ A
i=0
For some reason this is just confusing the hell out of me. My book really doesn't clarify this enough, and i know in the future this will be important for Cal 2, so I want to get a handle on it now. A tutor said told me you would have to change it to one of these formulas, but to me, that doesn't make any sense. Why wouldn't the formula just remain the same, but have f(x1) = 0?
It makes no sense to me why you would write it as either of the two methods the tutor told me because it would mean you're creating an interval that doesn't exist. Interval 0 doesn't exist, where in my mind interval 1 would be f(0) = 0 giving your sub interval area as ΔX(0)2.
2. Nov 17, 2015
### Staff: Mentor
In the first summation you show, it is implied that some interval [a, b] is divided up into n subintervals. $x_1$ is some point in the first subinterval, $x_2$ is some point in the second subinterval, and so on, with one $x_i$ in each subinterval.
3. Nov 17, 2015
### in the rye
So I am correct in thinking that x0 doesn't exist using the summation formula, correct? I edited the ending of my comment, which may expand my confusion
4. Nov 17, 2015
### Staff: Mentor
Let me correct your first summation:
$\sum_{i = 1}^n f(x_i)\Delta x$
Here $x_i$ is some point in the i-th subinterval.
5. Nov 17, 2015
### in the rye
Right, for some reason I have difficulty applying this, though. So for simplicity-sake let's say we use y = x2 over the interval [0, 6], with only 2 left rectangles.
I would have that my A = 3[f(0) + f(3)]. This would mean that x1 = 0 and x2 = 3in the summation formula, correct? Giving:
$\sum_{i = 1}^2 f(x_i)\Delta x$
NOT
$\sum_{i = 0}^1 f(x_i)\Delta x$
Where $Δx$ = 3
6. Nov 17, 2015
Yes.
|
2017-12-16 17:04:22
|
{"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": 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": 0.7895907759666443, "perplexity": 586.8182816385457}, "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/1512948588294.67/warc/CC-MAIN-20171216162441-20171216184441-00182.warc.gz"}
|
http://mathhelpforum.com/advanced-algebra/22697-linear-algebra-proof-print.html
|
# Linear Algebra proof
• Nov 13th 2007, 08:25 PM
beaveman
Linear Algebra proof
I have shown that if a set of vectors (v1,...,vn) is linearly independant, then every vector v that is an element of <v1,...,vn> has a unique representation as a linear combination of vectors v1,...,vn.
Now I need to show that the converse statement is true, that is if a vector v has a unique representation as a linear combination of vectors v1,...,vn then the set of vectors (v1,...,vn) are linearly independant. Does anyone have suggestions on you show that?
• Nov 13th 2007, 08:35 PM
ThePerfectHacker
Suppose we can write a vector x as a_1v_1+...+a_nv_n and as b_1v_1+...+b_nv_n. We want to show a_1=b_1,...,a_n=b_n for uniqueness. So that means, a_1v_1+...+a_nv_n = b_1v_1+...+b_nv_n. Subtract them, (a_1-b_1)v_1+...+(a_n-b_n)v_n = 0. Since these vector are linearly independent it means there is only the trivial representation. And so that means, a_1 - b_1 = 0 ... a_n - b_n =0 so a_1 = b_1 ... a_n=b_n. Q.E.D.
• Nov 13th 2007, 08:40 PM
beaveman
That is how I showed the first part - that there is a unique representation. I don't think that works to show the converse that if there is a unique representation, then the set of vectors (v1,...,vn) are independant.
• Nov 13th 2007, 08:47 PM
ThePerfectHacker
Correct not everything can be expressed in linearly independent vectors.
• Nov 13th 2007, 09:20 PM
beaveman
A nice google search helped me find the answer to my question:
Elements of Operator Theory - Google Book Search
Thanks for your help, though! :)
• Nov 14th 2007, 09:49 AM
ThePerfectHacker
What is so hard? Consider $\{ (0,1,0),(1,0,0) \}$ this is linearly independent but $(0,0,1)$ cannot be obtained as a linear combination of those two elements.
• Nov 15th 2007, 05:25 AM
kalagota
just try to understand the proof.. Ü
Suppose v has a unique representation of linear combinations of vectors $v_1, v_2, ... ,v_n$, i.e.
$v = \sum_{i=1}^n a_iv_i = a_1v_1 + a_2v_2 + ... + a_nv_n$
and suppose the $S:= \{ v_1, v_2, ..., v_n \}$ is linearly dependent.
then, $\exists v_j \in S$ which is a linear combination of the other vectors in S (assuming you have proven this already) i.e.
$v_j = - (b_j^{-1}b_1v_1 + b_j^{-1}b_2v_2 + ... + b_j^{-1}b_{j-1}v_{j-1} + b_j^{-1}b_{j+1}v_{j+1} + ... + b_j^{-1}b_nv_n$ ---> (*)
from
$v = \sum_{i=1}^n a_iv_i = a_1v_1 + a_2v_2 + ... + a_jv_j + ... + a_nv_n$, we replace $v_j$ by (*), and since V is an abelian group, we can rearrange and combine like terms, so that,
$v = \sum_{i=1}^n a_iv_i = (a_1 - a_jb_j^{-1}b_1)v_1 + (a_2 - a_jb_j^{-1}b_2)v_2 + ... + (a_{j-1} - a_jb_j^{-1}b_{j-1})v_{j-1} +$
$(a_{j+1} - a_jb_j^{-1}b_{j+1})v_{j+1} + ... + (a_n - a_jb_j^{-1}b_n)v_n$
and clearly, $a_k - a_jb_j^{-1}b_k = a_k \Leftrightarrow a_jb_j^{-1}b_k = 0$, for k=1,2,...,n
but we have to note that S must not contain the zero vector since v has a unique representation of linear comb of vectors in S. hence, $a_k - a_jb_j^{-1}b_k \neq a_k$ for all k.
which contradicts now that v has a unique representation of linear comb of the vectors in S.
therefore, S must be lin. indep set. QED
|
2017-04-28 01:52:07
|
{"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": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8915992975234985, "perplexity": 556.2814839967474}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122720.81/warc/CC-MAIN-20170423031202-00645-ip-10-145-167-34.ec2.internal.warc.gz"}
|
https://indico.cern.ch/event/749003/contributions/3330781/
|
# XXVII International Workshop on Deep Inelastic Scattering and Related Subjects
Apr 8 – 12, 2019
Turin
Europe/Rome timezone
## Accessing the high-$x$ content of protons and heavy nuclei in the fixed-target mode at the LHC
Apr 9, 2019, 8:50 AM
20m
Cavallerizza Reale - Aula Magna
### Cavallerizza Reale - Aula Magna
Via Verdi 9, Turin
Parallel Session Talk WG7: Future of DIS
### Speaker
Aleksander Kusina (IFJ PAN)
### Description
Using the LHCb and ALICE detectors in the fixed-target mode at the LHC offers unprecedented possibilities to study the quark, gluon and heavy-quark content of the proton and nuclei in the poorly known region of the high-momentum fractions. We review our projections for studies of Drell-Yan, charm, beauty and quarkonium production with both detector set-ups used with various nuclear targets and the LHC proton beams. Based on this, we show the expected improvement in the determination of the quark, charm and gluon proton and nuclear PDFs as well as discuss the implication for a better understanding of the cold-nuclear-matter effects in hard-probe production in proton-nucleus collisions.
|
2022-08-16 08:28:00
|
{"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": 0.3782074749469757, "perplexity": 7303.9871761961485}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572221.38/warc/CC-MAIN-20220816060335-20220816090335-00201.warc.gz"}
|
http://www.math.keio.ac.jp/~ishikawa/QLEJ/index069.html
|
9.7: Monty Hall problem (The principle of equal weight)
9.7.1: The principle of equal weight--- The most famous unsolved problem
Let us reconsider Monty Hall problem (Problem 9.14, Problem9.15) in what follows. We think that the following is one of the most reasonable answers (also, see Problem 19.5).
Problem 9.17 [Monty Hall problem(The principle of equal weight)]
$\quad$ Suppose you are on a game show, and you are given the choice of three doors (i.e., "number 1"$\!\!\!,\;$ "number 2"$\!\!\!,\;$ "number 3"$\!\!)$. Behind one door is a car, behind the others, goats.
$(\sharp):$ You choose a door by the cast of the fair dice, i.e., with probability $1/3$.
According to the rule ($\sharp$), you pick a door, say number 1, and the host, who knows where the car is, opens another door, behind which is a goat. For example, the host says that
$(\flat):$ the door 3 has a goat.
He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?
Answer By the same way of Problem9.15 and Problem9.16 (Monty Hall problem), define the state space $\Omega = \{ \omega_1 , \omega_2 , \omega_3 \}$ and the observable ${\mathsf O}=(X, {\cal F}, F)$. And the observable ${\mathsf O}=(X, {\cal F}, F)$ is defined by the formula (9.11). The map $\phi:\Omega \to \Omega$ is defined by
\begin{align} \phi(\omega_1) =\omega_2, \quad \phi(\omega_2) =\omega_3, \quad \phi(\omega_3) =\omega_1 \quad \end{align}
we get a causal operator $\Phi:L^\infty (\Omega) \to L^\infty(\Omega)$ by $[\Phi(f)](\omega) = f(\phi(\omega))$ $(\forall f \in L^\infty(\Omega), \;\forall \omega \in \Omega )$. Assume that a car is behind the door $k$ $(k=1,2,3)$. Then, we say that
$(a):$ By the dice-throwing, you get $\left[\begin{array}{ll} 1,2 \\ 3,4 \\ 5,6 \end{array}\right], \mbox{then, take a measurement} \left[\begin{array}{ll} {\mathsf M}_{L^\infty (\Omega)} ({\mathsf O}, S_{[{}\omega_k{}]}) \\ {\mathsf M}_{L^\infty (\Omega)} (\Phi{\mathsf O}, S_{[{}\omega_k{}]}) \\ {\mathsf M}_{L^\infty (\Omega)} (\Phi^2{\mathsf O}, S_{[{}\omega_k{}]}) \end{array}\right]$
We, by the argument in Chapter 11 (cf. the formula (11.7)) see the following identifications:
\begin{align} \mbox{ ${\mathsf M}_{L^\infty (\Omega)} (\Phi{\mathsf O}, S_{[{}\omega_k{}]})$ $=$ ${\mathsf M}_{L^\infty (\Omega)} ({\mathsf O}, S_{[{}\phi(\omega_k){}]})$, ${\mathsf M}_{L^\infty (\Omega)} (\Phi^2{\mathsf O},$ $S_{[{}\omega_k{}]})$ $=$ ${\mathsf M}_{L^\infty (\Omega)} ({\mathsf O},$ $S_{[{}\phi^2 (\omega_k){}]})$. } \end{align}
Thus, the above (a) is equal to
$(b):$ By the dice-throwing, you get $\left[\begin{array}{ll} 1,2 \\ 3,4 \\ 5,6 \end{array}\right] \mbox{then, take a measurement} \left[\begin{array}{ll} {\mathsf M}_{L^\infty (\Omega)} ({\mathsf O}, S_{[{}\omega_k{}]}) \\ {\mathsf M}_{L^\infty (\Omega)} ({\mathsf O}, S_{[{}\phi (\omega_k){}]}) \\ {\mathsf M}_{L^\infty (\Omega)} ({\mathsf O}, S_{[{}\phi^2(\omega_k){}]}) \end{array}\right]$
Here, note that $\frac{1}{3}(\delta_{\omega_k}+\delta_{\phi(\omega_k)} +\delta_{\phi^2 (\omega_k)})$ $=$ $\frac{1}{3}(\delta_{\omega_1}+\delta_{\omega_2} +\delta_{\omega_3})$ $(\forall k=1,2,3)$. Thus, this (b) is identified with the mixed measurement ${\mathsf M}_{L^\infty (\Omega)} ({\mathsf O}, S_{[{}\ast{}]}(\nu_e ))$ , where
\begin{align} \nu_e = \frac{1}{3} ( \delta_{\omega_1} + \delta_{\omega_2} + \delta_{\omega_3 }) \end{align}
Therefore, Problem 9.17 is the same as Problem 9.16. Hence, you should choose the door 2.
$\fbox{Note 9.4}$ The above argument is easy. That is, since you have no information, we choose the door by a fair dice throwing. In this sense, the principle of equal weight --- unless we have sufficient reason to regard one possible case as more probable than another, we treat them as equally probable --- is clear in measurement theory. However, it should be noted that the above argument is based on dualism.
From the above argument, we have the following theorem.
Theorem 9.18 [The principle of equal weight] Consider a finite state space $\Omega$, that is, $\Omega=\{\omega_1,\omega_2,\ldots,\omega_n\}$. Let ${\mathsf O}=(X, {\cal F}, F)$ be an observable in $L^\infty (\Omega, \nu)$, where $\nu$ is the counting measure. Consider a measurement ${\mathsf M}_{L^\infty (\Omega )}({\mathsf O} , S_{[ \ast]} )$. If the observer has no information for the state $[\ast]$, there is a reason to that this measurement is identified with the mixed measurement ${\mathsf M}_{L^\infty (\Omega )}({\mathsf O} , {\overline S}_{[ \ast]}(w_e) )$ $\Big($ or, ${\mathsf M}_{L^\infty (\Omega )}({\mathsf O} , S_{[ \ast]}(\nu_e) )$ $\Big)$, where
\begin{align} w_e(\omega_k)=1/n \;\; (\forall k =1,2,...,n) \qquad \mbox{ or } \qquad \nu_e = \frac{1}{n} \sum_{k=1}^n \delta_{\omega_k} \end{align}
Proof. The proof is a easy consequence of the above Monty Hall problem (or, see
$(\sharp):$ S. Ishikawa, "A Measurement Theoretical Foundation of Statistics," Applied Mathematics, Vol. 3, No. 3, 2012, pp. 283-292
).
$\fbox{Note 9.5}$In this book, we deal with three "the principle of equal weight" as follows:
$(\sharp_1):$ "the principle of equal weight" in Remark 5.19 ($\S$5.6)
$(\sharp_2):$ "the principle of equal weight" in Theorem 9.18 ($\S$9.7)
$(\sharp_3):$ "the principle of equal weight" in Proclaim 18.4 ($\S$18.2)
|
2017-09-19 20:55:52
|
{"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": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9435988664627075, "perplexity": 649.3276007311207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818686034.31/warc/CC-MAIN-20170919202211-20170919222211-00508.warc.gz"}
|