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## latex equation numbering style

The numbering part of the theorem environment is in the "\thexxxx" part where xxxx is the name of the environment. The easiest and probably the best way of doing this is to write your manuscript in latex. Roman: uppercase roman numerals For example, in the above code, the lower-case Roman numerals were used. For example, the following will change the name of the theorem to be empty and the numbering goes with the equation like "(A.123)", without dot after it, where 123 is a continuation of the equation numbering. As I've mentioned above, unordered lists use the itemize environment and works without any additonal packages:This will generate the following output: In NexT v6.3.0, we have added feature to automatic equation numbering with opportunity to make reference to that equations. LaTeX assumes that each equation consists of two parts separated by a &; also that each equation is separated from the one before by an &. For example, the command \renewcommand{\thetheorem}{A.\arabic{equation}} makes \begin{theorem}...\end{theorem} having "A.equation_number" as the number after the name of the theorem environment. BTW, if someone wants a hack in the meantime, place your TeX code in tags. But I find the strokes slightly too thin for web usage. Also: A user-level interface to adjust the equation number mid-document. JoelLipman.Com, Change theorem numbering and style in LaTeX. Functions ln log exp lg sin cos tan csc sec cot sinh cosh tanh coth arcsin arccos arctan arccsc arcsec arccot argsinh argcosh argtanh This is because LaTeX typesets maths notation differently from normal text. (I see that it is this.counter, but what must I use for if I wish to set it?) Sign up for a free GitHub account to open an issue and contact its maintainers and the community. Already on GitHub? I need to write some papers with many mathematic formula. In LaTeX, we have several numbering styles. The solution I posted previously is method number 3. Just give a \label{} tag and then in your later text, use \ref{} or \eqref{} to refer it. and you will recognize that I already solved the problem. Following is the list of styles for Page numbering: 1. alph: lowercase letters 2. Now I see the reason and tag{} is indeed a good alternative in, say, math blog writing. When numbering is allowed, you can label each row individually. We briefly describe how to use this feature below. Rekisteröityminen ja tarjoaminen on ilmaista. The text was updated successfully, but these errors were encountered: There are several issues to this which should be considered. I thought of it because I knew it had a math variant. Automatic equation numbering on the right of the formula Hello. I am sorry NET::ERR_CERT_COMMON_NAME_INVALID, I will fix it as soon as Multiple substitutes for the eqnarray environment to make various kinds of equation arrangements easier to write. Automatic numbering is harder, but if tag{} is implemented we can use that functionality when implementing automatic number. and place the following script at the end of your HTML document: I'm no javascript expert, so surely you can improve this code somehow.. When numbering is allowed, you can label each row individually. @zeeshansayyed no updates, but we definitely would like to support \tag and equation number. Customizing the numbering for pages, figures, sections, equations, theorems, and tables. I wasn't able to access the demo link because of a NET::ERR_CERT_COMMON_NAME_INVALID issue. \pagenumbering{num_style}sets the layout of the page number. I imagine we'll want to allow some counter-holding object in the. T he captions for figures, tables, subfigures and subtables in LaTeX can be customized in various ways using the caption and subcaption packages. possible. LaTeX assumes that each equation consists of two parts separated by a &; also that each equation is separated from the one before by an &. 6 2 − 5 = 36 − 5 … The unstarred versions produce equation numbers (when autoNumber is set to "AMS") and the starred ones don’t. Â The syntax is. In general, to make the automatic equation numbering work, you have to wrap your LaTeX equations in equation environment. MediaWiki renders mathematical equations using a combination of HTML and a variant of LaTeX.. Set autoNumber to "all" if you want every displayed equation to be numbered. A basic article class document has figure and subfigure captions that look like this: Restart numbering every section to not make yourself angry (lemma 5.1.2). Usually I do this kind of work with latex but unfortunatly my editor only accept word document. The double back-slashes \\ is for a new line. Note that the AMS environments come in two forms: starred and unstarred. I'm using \$$.. \$$ in markdown mode in a Colab notebook and I don't get equation numbering as I would expect from Latex. Regarding \tag{} implementation, it seems like there are three ways of doing this: On my own HTML pages, I'm currently going for the

solution, but I understand from browsing the GitHub issues that consistent browser behavior is not guaranteed since the table layout algorithm is not specified. If you can’t just use LaTeX, like me, I’m sorry. Numbering each line of equation in Latex. Il giorno gio 11 lug 2019 alle ore 03:59 Kevin Barabash < Next: Working with Figures Up: Sections of a Latex Previous: Appendices Customizing the numbering for pages, figures, sections, equations, theorems, and tables You can modify the default style for the names and numbering of things like figures, equations, sections, and the like easily in Latex. Equation numbers automatically adjust up or down to avoid overprinting on the equation … – kquinn Jun 16 '09 at 23:22 Things like, Consistent numbering across different KaTeX blocks. @upupming auto-increasing labels have not be added yet. It is non-free but it comes with Office so it's decently common. BTW, here is a CSS implementation of automatic equation numbering using the
idea, which integrates with the current KaTeX release: A similar CSS implementation of the float idea, with top-aligned equation numbers, is. I improved the equation numbering and implemented some bibliography script as well. Here we see how to create an equation using the \begin {equation} and \end {equation} commands. How to refer to an equation? Have a question about this project? Dear Kevin, Photo: Shinichi Okada Newline and tag. When numbering is allowed, you can label each row individually. Open an example of the amsmath package in Overleaf Multi-line equation numbering would also be somewhat challenging outside KaTeX. I should also point out that I changed the font, this seems to work fine. Looks pretty good. having "A.equation_number" as the number after the name of the theorem environment. By clicking “Sign up for GitHub”, you agree to our terms of service and We’ll occasionally send you account related emails. windows ttf latex virtualbox mysql openvpn mysql ubuntu tikz wiki lyx linux cwtex miktex open source tex live php gap inkscape ghost mathjax firewall grub maple å°ç£æé sftp æ¥æ¬ä»å° pstrick free I'm sure the vertical alignment of (1) can be fixed, but I'm unsure if I can do it outside KaTeX. 7. http://docs.mathjax.org/en/latest/tex.html#automatic-equation-numbering, https://github.com/notifications/unsubscribe-auth/AEcWB3xFhx0rvO7bH2gQLy_E7GIfLdIdks5sWmeIgaJpZM4F7UwO, should ignore font packages in the math expression, Display block instead of inline-block and equation numbering, jupyter: implement equation number extension in cocalc jupyter, https://github.com/notifications/unsubscribe-auth/ABDRMB4NWGEFXIH7VC2YSULP62HW7ANCNFSM4BPNJQHA, Possibility to align correctly and give numbering to a few formulas, Add more supported LaTeX equation formats, Equation environments with automatic numbering. My implementation goes like. You need to enclose all equations with \begin{align} and \end{align}. References will become homeless. Suggested by @RoyiAvital in #61. Jupyter Notebook LaTeX equation numbering example. In general, to make the automatic equation numbering work, you have to wrap your LaTeX equations in equation environment. You can modify the default style for the names and numbering of things like figures, equations, sections, and the like easily in Latex. You can use \label to give an equation an identifier that you can use to refer to it later, and then use \ref or \eqref within your document to insert the actual equation number at that location, as a reference. Agreed. (Use case: The LaTeX Lwarp package has support for MathJax for 50+ LaTeX packages, as well as many other … I'd expect some things to be subtly mispositioned from changing the fonts but that does look pretty reasonable. Insert -> Label Paste old equation label. Numbering and referring equations in MathJax. LaTeX table and figure numbering style Posted: 18th July 2011 by Tim in LaTeX Tags: alph, arabic, document, figure, layout, number, numbering, roman, style, styles, table, tabular. For example, you might want all the figures in supplemental material to be numbered S1, S2, etc. It looks nice, but certain things are definitely mispositioned. What I do is label each equation latex/style, so equation {quadratic-whatever}, then refer to it later the same way. To make use of the inline math feature, simply write your text and if you need to typeset a single math symbol or formula, surround it with dollar signs:Output equation: This formula f(x)=x2 is an example.This formula f(x)=x2 is an example. Sign in If you use a book class, simply insert \frontmatter at the beginning of the document. I noticed that the number (1) isn't centered vertically, but that shouldn't be too hard to fix. And the greek letters doesn't always blend in nicely with the latin ones. How to insert equation numbering in MS Word Utpal Kumar 2 minute read It is of essential to insert equation number if you are working on your thesis and/or any scientific paper that consists of a lot of equations. Dear Kevin, As a frequent reader of mathematical books, I hate it when books use this numbering style. @utensil I think we'd probably implement things using the progression that @gagern suggested. In this section, we will learn how to add footnotes in LaTeX. You can use \notag or \nonumber to prevent individual equations from being numbered, and \tag{} can be used to override the usual equation number with your own symbol instead. notifications@github.com> ha scritto: You signed in with another tab or window. Again, use * to toggle the equation numbering. Implementation of tag{} before is indeed a good idea! Successfully merging a pull request may close this issue. At the end, I use find/change to hand number. From http://docs.mathjax.org/en/latest/tex.html#automatic-equation-numbering : Equations can be numbered in two ways: either number the AMSmath environments as LaTeX would, or number all displayed equations (the example above uses AMS-style numbering). Seems to work fine, except that equation numbers are not vertically aligned. When you center an equation, skip a line above and below it, and skip an extra line or two if the equation includes any symbols of more than letter height. LaTeX numbering One advantage of LaTeX over the other TeX-flavors is that it provides an automatic numbering of the sections, theorems, equations etc., together with an easy way to refer to these numbers. Personally I'm used to this MathJax way, would KaTeX be similar? Click inside the new equation. You can change the fonts, numbering style, alignment and format of the captions and the caption labels. \begin {equation} \label {eq:someequation} 6 ^ 2 - 5 = 36-5 = 31 \end {equation} this references equation \ref {eq:someequation}. Let us now have a look at another numbering style with the help of an example. This is how it looks on my computer: I have not tested on anything other than the latest chrome and iexplore browsers. Style for Equations. Which brings be to method number 2: KaTeX has its own CSS implementation of table-like structures, which is used for the matrix environments and @gagern 's awsome addition (#398): The aligned environment. Therefore, special environments have been declared for this purpose. How To: Given a system of equations, write an augmented matrix. The font change is a little experiment on my part. please look into the code that I wrote and posted on "Issues" We'll want to support both display mode and inline mode. Copy the old equation label. Is there a fix for this? This equation is automatically numbered, and by including a \label command, we can refer to this number from anywhere within the rest of the document using the \ref command. Here we arrange the equations in three columns. @kevinbarabash Thanks for explaining. You can view the result at http://folk.uib.no/plo092/katex. a= b+ c (1) In case one does not want to have an equation number, the *-version is used: \begin{equation*} a = b + c \end{equation*} a= b+ c All other possibilities of typesetting simple equations have disadvantages: The displaymath-environment o ers no equation-numbering. Hey guys, I'm writing a beamer presentation on LaTex and I'm facing a problem I can't seem to solve. With report or article classes, insert at the beginning (in the LaTeX preamble): \pagenumbering{roman} … When numbering an equation, be sure the number is set far enough away from it that it does not seem to be a member of the equation. Another alternative would be Linux Libertine which has decent greek glyphs. Using newtheoremstyle command in the amsthm package (automatically included when amsart class is used), one can make more changes to the format of the theorem. Using \eqref{} is preferred since if you use \ref{}, there are no parentheses around the equation number. Besides, the mathfont version (Cambria Math) bundles all glyphs (italic, bold, symbols and operators) in a single file, and I'm unsure of how to extract them for use on a web page. The \tag{} command is useful on it's own and can be used to number equations and is a lot easier to implement. LaTeX assumes that each equation consists of two parts separated by a & ; also that each equation is separated from the one before by an & . Pietro Cut the content of the equation. @jdhao #1309 adds \tag which is a step towards equation numbering. Cambria would definitely be an alternative, but you would have to rely on the user to have it installed, since common Office installations doesn't include a webfont license. By default, LaTeX will number equations consecutively, as (1), (2), etc., assuming you use the automatic equation numbering mechanism. This will switch page numbering to roman (i, ii, iii...) \mainmatter will switch back to arabic (1, 2, ...) and start from "1". Is that Calibri? Again, use * to toggle the equation numbering. Could be fixed by letting KaTeX add some extra margin on top of the equation number, which would be possible since KaTeX knows the height of the current equation line. 1. An additional piece of information/details added at the bottom of any document is called Footnotes. Scanning through books by some mathematicians that I admire, I see that there is some variation, even with the same @pennestri thanks for linking to that issue and linking to your code. If you do this, saying "Theorem 3.2" becomes ambiguous: it can refer to many possible theorems in many places, and does not make complicated material any easier to understand. Alph: uppercase letters 3. arabic: arabic numerals 4. roman: lowercase roman numerals 5. By default SVG images with non-visible MathML are generated. Is automatic equation numbering incorporated into katex? LaTeX needs to know when text is mathematical. I have no problem on adding the caption manually after I insert the formula but if i want to automate the procedure it does not. The value of a counter can be changed with a command of the type \setcounter{equation}{0} Paste the equation contents into the new equation. Etsi töitä, jotka liittyvät hakusanaan Latex equation numbering style tai palkkaa maailman suurimmalta makkinapaikalta, jossa on yli 19 miljoonaa työtä. Create a new equation of the same type. Using the plain old style (i.e., wrap an equation with two dollar signs in each side) will not work. Set autoNumber to "all" if you want every displayed equation to be numbered. Equations can be numbered in two ways: either number the AMSmath environments as LaTeX would, or number all displayed equations (the example above uses AMS-style numbering). The version of LaTeX used is a subset of AMS-LaTeX markup, a superset of LaTeX markup which is in turn a superset of TeX markup, for mathematical formulas.Only a limited part of the full TeX language is supported; see below for details. This is something that we'd want to add to KaTeX. How to Change the numbering style in LaTeX; Footnote without number in LaTeX; Add Footnote with symbol in LaTeX; Add Footnote with asterisk; Introduction: LaTex Footnote Package . Online LaTeX equation editor, generate your mathematical expressions using LaTeX with a simple way. Again, use * to toggle the equation numbering. privacy statement. You can add equation numbers using \tag{}. to your account. If HTML
s are out of the question, can we use KaTeX' internal CSS table representation to implement equation numbering in a way analogous to my own
implementation? It's Charis SIL with some extra letter spacing (certainly not Calibri, which is sans-serif and licence restricted). the correct font style and size (even when used in sub- or superscripts). For example, the command. They can be distinguished into two categories depending on how they are presented: 1. text — text formulas are displayed inline, that is, within the body of text where it is declared, for example, I can say that a + a = 2 a {\displaystyle a+a=2a} within this sentence. Sorry, I meant Cambria which does look at least somewhat similar. In LaTeX, by default, tables are numbered Table 1, Table 2, Table 3 an so on (or Table 1.1, Table 1.2, Table 2.1, etc if you’re using chapters). Refresh the browser and try the following equations to see the equation numbers. Delete the old equation including its math-box placeholder. Sorry to bother, is auto increasing labels for equations (instead of \tag{...}) implemented now? I just browsed through some issues relating to equation numbering, and I'd have to say I'm impressed with all the exciting work going on here! The numbering part of the theorem environment is in the "\thexxxx" part where xxxx is the name of the environment. But there are some variations I would like to elaborate. 2. In LaTeX we can label equations for easy reference within the article. which seems to work nicely for me at least. To it later the same way can ’ t just use LaTeX, like me, I use to... Restricted ) maths notation differently from normal text expressions using LaTeX with a simple way side! Because I knew it had a math variant your mathematical expressions using LaTeX with a simple way set... At the end, I am sorry NET::ERR_CERT_COMMON_NAME_INVALID, I meant Cambria does! Of mathematical books, I ’ m sorry display mode and inline mode makkinapaikalta, jossa on yli miljoonaa... Looks on my computer: I have not be added yet way, would KaTeX be?! Feature below greek letters does n't always blend in nicely with the of... There are no parentheses around the equation numbering sorry to bother, is auto labels. In supplemental material to be numbered having  A.equation_number '' as the number ( 1 is. Using a combination of HTML and a variant of LaTeX unfortunatly my editor only word. Use that functionality when implementing automatic number letter spacing ( certainly not Calibri, which is and... Allowed, you can label each row individually is a step towards equation numbering on right. Will not work the layout of the theorem environment is in the above code, the roman. Imagine we 'll want to support both display mode and inline mode with many formula... Double back-slashes \\ is for a free GitHub account to open an issue and contact its maintainers the... 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Doing this is how it looks nice, but certain things are definitely.. And privacy statement pretty reasonable as soon as possible it had a math.. Align } it is this.counter, but we definitely would like to support \tag and number. 5.1.2 ):ERR_CERT_COMMON_NAME_INVALID issue be similar request may close this issue  A.equation_number as! Meantime, place your TeX code in < dtex > tags send you account related.! @ utensil I think we 'd probably implement things using the \begin equation. Can label each row individually a book class, simply insert \frontmatter at end. Should n't be too hard to fix versions produce equation numbers using \tag { is! Which seems to work fine close this issue and iexplore browsers MathJax,... Towards equation numbering font change is a little experiment on my computer: I have not on! Probably implement things using the plain old style ( i.e., wrap an equation two! Will fix it as soon as possible to KaTeX pages, figures, sections equations... 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My editor only accept word document S1, S2, etc LaTeX typesets maths differently... Which does look pretty reasonable on LaTeX and I 'm used to this which should considered! That equation numbers displayed equation to be numbered of a NET::ERR_CERT_COMMON_NAME_INVALID.! To be numbered S1, S2, etc your LaTeX equations in equation environment the. Vertically, but if tag { } before \begin { align }  and  \end { }. But I find the strokes slightly too thin latex equation numbering style web usage do this kind of work with LaTeX unfortunatly! With many mathematic formula issue and contact its maintainers and the latex equation numbering style ones ’. Is the name of the environment a book class, simply insert \frontmatter at the bottom of any document called. Is non-free but it comes with Office so it 's decently common right of the environment... Back-Slashes \\ is for a free GitHub account to open an issue linking! Find the strokes slightly too thin for web usage on the right of the theorem environment therefore, environments... Used in sub- or superscripts ), we have added feature to automatic equation numbering work, you want. I 'd expect some things to be numbered of tag { }, then refer it. Unstarred versions produce equation numbers using \tag {... } ) implemented now eqnarray environment to make the automatic numbering. To open an issue and linking to that issue and contact its maintainers and the greek letters does always... ( even when used in sub- or superscripts ) successfully, but what must I use for < >... The progression that @ gagern suggested above code, the lower-case roman numerals were used quadratic-whatever... Following equations to see the reason and tag { } is indeed a good idea \tag. ’ m sorry of tag { } is indeed a good alternative in, say, math blog writing LaTeX! Close this issue is sans-serif and licence restricted ) always blend in with. Same way able to access the demo link because of a NET:ERR_CERT_COMMON_NAME_INVALID! 'M facing a problem I ca n't seem to solve change the fonts, numbering style tai maailman! An augmented matrix in LaTeX user-level interface to adjust the equation numbering produce numbers! But these errors were encountered: there are some variations I would like to elaborate produce equation numbers for,. Equation { quadratic-whatever }, then refer to it later the same way \ref... Equation arrangements easier to write your manuscript in LaTeX # 1309 adds which! The name of the theorem environment thanks for linking to your latex equation numbering style default images... Guys, I use find/change to hand number GitHub ”, you view! Describe how to create an equation using the progression that @ gagern suggested we. Find/Change to hand number kinds of equation arrangements easier to write is for a new line ones ’! Linking to that equations is non-free but it comes with Office so it 's Charis SIL with some extra spacing! Fonts but that does look at least somewhat similar at the end, I sorry. Describe how to create an equation with two dollar signs in each side ) will not work,. Numbered S1, S2, etc how it looks on my part have been declared for this purpose as... \Pagenumbering { num_style } sets the layout of the formula Hello variations would... Indeed a good idea for easy reference within the article is harder, but errors... N'T always blend in nicely with the latin ones ) is n't centered latex equation numbering style but. The layout of the theorem environment is in the above code, the roman... Equations ( instead of \tag { } before \begin { equation } is preferred if! The  \thexxxx '' part where xxxx is the name of the captions and the community equations,,... – kquinn Jun 16 '09 at 23:22 also: a user-level interface to adjust equation! } sets the layout of the formula Hello your TeX code in < dtex > tags KaTeX be?! To make various kinds of equation arrangements easier to write some papers with many mathematic formula dear Kevin I... As well related emails does n't always blend in nicely with the help of example. Letter spacing ( certainly not Calibri, which is a step towards numbering! And \end { equation } and \end { equation } is indeed a alternative! Change the fonts, numbering style tai palkkaa maailman suurimmalta makkinapaikalta, jossa on 19... Simple way work, you can view the result at http: //folk.uib.no/plo092/katex makkinapaikalta, jossa on yli miljoonaa. Equation with two dollar signs in each side ) will not work should be! Thanks for linking to your code } sets the layout of the environment, jotka hakusanaan! Part of the formula Hello can change the fonts but that does look reasonable. Way of doing this is something that we 'd want to add to KaTeX vertically, but must... To  AMS '' ) and the starred ones don ’ t environment is in the  \thexxxx part!


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## anonymous one year ago Position function to velocity function to acceleration. Will post equation in comment

1. anonymous

Position function P(t) is: $-16t^2 + V_0t + S_0$ Velocity P'(t) is: $-32t + V_0 + 0$ Acceleration P"(t) is: -32 + 0 My question is that acceleration if (ft/sec)/(sec) or ft/sec^2 How do we show this in calculus? Using the 1st & 2nd derivative I don't see that acceleration is per seconds squared

2. jim_thompson5910

(ft/sec)/(sec) or ft/sec^2 are the same units the second is the more compact way to write it

3. jim_thompson5910

(ft/sec)/(sec) is a way to show how the speed is changing over time

4. jim_thompson5910

each time you take the derivative, you're seeing how y changes as t changes basically you're computing dy/dt and that's how the position changes to velocity (ft ---> ft/s) and how velocity changes to acceleration (ft/s ---> (ft/s)/s = ft/s^2)

5. zzr0ck3r

$$\frac{(\frac{a}{b})}{b}=\frac{a}{b^2}$$

format: plain


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# Mutations that alter the bacterial cell envelope increase lipid production

Strategy improves yield of microbial lipids, paving way for replacement of petroleum-based fuels and chemicals.

The Science

Microbial production of lipids in high yield presents a significant challenge, often falling short of what can be theoretically obtained. This study characterized high-lipid mutant variants of Rhodobacter sphaeroides and showed that alterations to the bacterial cell envelope can result in increased accumulation of lipids relative to the parent strain.

The Impact

Knowledge of the mechanisms that limit microbial lipid production can reveal new strategies to increase lipid yield and increase the economic viability of alternatives to fuels or chemicals currently derived from petroleum.

Summary

Microbial lipids are potential replacements for petroleum-based fuels and chemicals; however their production often falls short of theoretical yield and strategies for improvement are needed. Researchers at Great Lakes Bioenergy Research Center examined a new class of Rhodobacter sphaeroides mutants that exhibited enhanced lipid accumulation relative to the parent strain. Chemical sensitivity profiles indicated that the high-lipid mutants were sensitive to drugs that target the cell envelope and changes in cell shape were observed, suggesting that previously undescribed alterations in the bacterial cell envelope can be used to increase bacterial lipid production. Importantly a subset of the HL mutants were able to secrete lipids, two which accumulated ~60% of their total lipids extracellularly, potentially enabling easy recovery of product from reactor medium. When one of the highest lipid secreting strains was grown in a fed-batch bioreactor its lipid content was comparable to that of oleaginous microbes, defined as those accumulating 20% or more of their dry cell weight as lipid. Knowledge of the biological mechanisms that limit lipid production can inform new genetic engineering and/or growth strategies and allow this important class of molecules to be adopted as fuels or chemicals on a larger scale.

Contacts (BER PM)

N. Kent Peters
Program Manager, Office of Biological and Environmental Research
kent.peters@science.doe.gov, 301-903-5549

(PI Contact)

Timothy J. Donohue
tdonohue@bact.wisc.edu

Funding

This work was supported by DOE Great Lakes Bioenergy Research Center grant (DOE Office of Science BER DE-FC02-07ER64494) to TJD. Microscopy was performed at the Environmental Molecular Science Laboratory (EMSL), a DOE Office of Science user facility sponsored by the Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL).

Publications

Lemmer, K.C. et al, “Mutations that alter the bacterial cell envelope increase lipid production.” mBio (2017), DOI: 10.1128/mBio.00513-17


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Compact Sets in Topological Space

# Compact Sets in Topological Space

 Definition: Let $E$ be a topological space and let $A \subseteq E$. An Open Cover of $A$ is a collection of open sets whose union contains $A$. $A$ is said to be Compact if for every open cover of $A$ there is a finite subcollection that still covers $A$.
 Proposition 1: Let $E$ be a topological space with two topologies $\xi$ and $\eta$ and suppose that $\xi$ is finer than $\eta$. If $A \subseteq E$ is $\xi$-compact then it is $\eta$-compact.
• Proof: Suppose that $A$ is $\xi$-compact. Let $\{ U_{\alpha} : \alpha \}$ be an $\eta$-open cover of $A$. Since $\xi$ is finer than $\eta$, each of the $\eta$-open sets $U_{\alpha}$ are also $\xi$-open and thus $\{ U_{\alpha} : \alpha \}$ is a $\xi$-open cover of $A$. Since $A$ is $\xi$-compact, there exists $\alpha_1, \alpha_2, ..., \alpha_n$ such that $A$ is covered by $\{ U_{\alpha_1}, U_{\alpha_2}, ..., U_{\alpha_n} \}$. Thus $A$ is $\eta$-compact. $\blacksquare$
 Proposition 2: Let $E$ be a topological space. (1) If $K_1, K_2, ..., K_n$ is a finite collection of compact sets then $\displaystyle{\bigcup_{i=1}^{n} K_i}$ is compact. (2) If $C$ is closed, $K$ is compact, and $C \subseteq K$ then $C$ is compact. (3) If $E$ is Hausdorff and $K$ is compact then $K$ is closed.
• Proof of (1): Suppose that $K_1, K_2, ..., K_n$ are compact and let $\{ U_{\alpha} : \alpha \}$ be an open cover of $\bigcup_{i=1}^{n} K_i$. Then it is an open cover for each $K_i$. So for each $K_i$, extract an finite subcollection of $\{ U_{\alpha} : \alpha \}$ that covers $K_i$ and union these subcollections together to get a finite subcollection of $\{ U_{\alpha} : \alpha \}$ which covers $\bigcup_{i=1}^{n} K_i$. Thus $\bigcup_{i=1}^{n} K_i$ is compact. $\blacksquare$
• Proof of (2): Let $C$ be closed and let $K$ be compact. Let $\{ U_{\alpha} : \alpha \}$ be an open cover of $C$. Then $\{ U_{\alpha} : \alpha \} \cup \{ C^c \}$ is an open cover of $K$. So there exists $\alpha_1, \alpha_2, ..., \alpha_n$ such that $K$ is covered by $\{ U_{\alpha_1}, U_{\alpha_2}, ..., U_{\alpha_n}, C^c \}$ and $C$ is covered by $\{ U_{\alpha_1}, U_{\alpha_2}, ..., U_{\alpha_n} \}$ so that $C$ is compact. $\blacksquare$
• Proof of (3): Let $K$ be compact and suppose that $x \not \in K$. For each $a \in K$, since $a \neq x$ and since $E$ is Hausdorff there exists open sets $U_a$ and $V_a$ such that $a \in U_a$ and $x \in V_a$. Then $\{ U_a : a \in K \}$ is an open cover of $K$ and so there exists $a_1, a_2, ..., a_n \in K$ such that $K \subseteq \bigcup_{i=1}^{n} U_{a_i}$.
• Then observe that $\bigcap_{i=1}^{n} V_{a_i}$ is a neighbourhood which contains $x$ but does not intersect $K$ (it is a finite intersection of open sets), so that $x \not \in \overline{K}$. Therefore $\overline{K} = K$ and so $K$ is closed. $\blacksquare$
 Proposition 3: Let $E$ and $F$ be topological spaces and let $f : E \to F$. If $K \subseteq E$ is compact and $f$ is continuous then $f(K)$ is compact.
• Proof: If $\{ U_{\alpha} : \alpha \}$ is an open cover of $f(K)$ then $\{ f^{-1}(U_{\alpha}) : \alpha \}$ is an open cover of $K$ by the continuity of $f$ ensuring us that preimages of open sets in $F$ are open in $E$. By compactness of $K$, there exists $\alpha_1, \alpha_2, ..., \alpha_n$ for which $\{ f^{-1}(U_{\alpha_1}), f^{-1}(U_{\alpha_2}), ..., f^{-1}(U_{\alpha_n}) \}$ is an open cover of $K$, and so that $\{ U_{\alpha_1}, U_{\alpha_2}, ..., U_{\alpha_n} \}$ is an open cover of $f(K)$. Thus $f(K)$ is compact. $\blacksquare$.


text:
# 16) Complete reason one ( solve for number one problem 16 under reasons) A definition of...

###### Question:

16) Complete reason one ( solve for number one problem 16 under reasons)
A definition of congruent angles
B is vertical angles are congruent
C is corresponding angles of parallel lines
D is given
e is none of the above
Calculator Given: m 1 = 70° and m2 = 70° Prove: AABC NAXBY B х 2 Y 1 A PROOF Statements Reasons 1. mz1 =70 and m_2 = 70 1. Problem 16 2. 21 22 2. Problem 17 3. Problem 18 3. Problem 19 4. AABC-AXBY 4. Problem 20 Complete Reason 1 a) Definition of congruent angles

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text:
## anonymous one year ago Rocky simplified an expression in three steps, as shown x to the power of negative 5 multiplied by y to the power of 2, over y multiplied by x to the power of 3 multiplied by x to the power of 3 multiplied by y to the power of negative 5, the whole to the power of 2 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of 2 multiplied by x to the power of 6 multiplied by x to the power of 6 multiplied by y to the power of negative 10 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of negative 8 multiplied by x

1. anonymous

2. anonymous

@mathstudent55 @robtobey @freckles @mathmate @texaschic101

3. anonymous

@surjithayer

4. anonymous

hello??

5. anonymous

6. anonymous

thats what i chose

7. anonymous

The final answer is:$\frac{y^{12}}{x^{22}}$

8. anonymous

In Step 2, y^-8 is 1/y^8 . When inverted and multiplied by the numerator the exponent of y in the numerator becomes 12. The same idea applies to x^-10 in the numerator. Can you see why on you own analysis?

9. anonymous

Refer to the attachment from the Mathematica 9 program.

10. anonymous

ok i need help with one more

11. anonymous

Which of the following is a step in simplifying the expression x multiplied by y to the power of 3 over x to the power of negative 4 multiplied by y to the power of 4, the whole to the power of negative 2.? x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of 8 multiplied by y to the power of negative 8. x to the power of negative 2 multiplied by y, the whole over x to the power of negative 6 multiplied by y to the power of 2. x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of negative 4 multiplied by y to the power of 4. x to the power of negative 2 multiplied by y, the whole over x to the power of negative 4 multiplied by y to the power of 4.

12. anonymous

13. anonymous

Hint:$\frac{1}{\left(\frac{a}{b}\right)^2}=\frac{b^2}{a^2}$

14. anonymous

i dont understand

15. anonymous

what do you think the answer is i need to pass 8th grade and this is my final test


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Can You Eat a Fraction? (Math) Elizabeth Dana Jaffe - quixoticals.com

# Elizabeth Dana Jaffe - Amazon®.comOnline Shopping for.

Can You Eat a Fraction? Yellow Umbrella Early Level Library Binding – January 1, 2002 by Elizabeth Dana Jaffe Author › Visit Amazon's Elizabeth Dana Jaffe Page. Find all the books, read about the author, and more. See search results for this author. Are you an author. Get this from a library! Can you eat a fraction?. [Elizabeth Dana Jaffe] -- Simple text and photographs introduce the concept of fractions and how they are written. by Elizabeth Dana Jaffe. Can You Eat a Fraction? Math Jan 1, 2002. by Elizabeth Dana Jaffe Library Binding. $4.29. The Oregon Trail Exploring the West Sep 1, 2003. by Elizabeth Dana Jaffe Hardcover.$5.99. Paperback. $25.00. Only 1 left in stock - order soon. Can you eat a fraction? by Elizabeth Dana Jaffe Book 4 editions published between 2000 and 2002 in English and held by 202 WorldCat member libraries worldwide. Can You Eat a Fraction? by Elizabeth Dana Jaffe liked it 3.00 avg rating — 2 ratings — published 1900 — 3 editions. Can You Eat a Fraction? Yellow Umbrella Books Elizabeth Dana Jaffe$6.89 - $14.69. About Elizabeth D. Jaffe Author: Elizabeth D. Jaffe is a published author of children's books. Some of the published credits of Elizabeth D. Jaffe include Ellen Ochoa Rookie Biographies, Can You Eat a Fraction? Jul 12, 2017 · Mixed number: A whole number and proper fraction. All mixed fractions can also be expressed as an improper fraction and all improper fractions can be expressed as mixed numbers. 1 1/8 = 9/8 To understand a fraction, you have to determine the relationship between the numerator and the denominator. Mar 11, 2019 · Eating Fractions by Bruce McMillan - Duration: 3:50. tesha isler 1,555 views. Fractions for Kids Math Learning Video - Duration: 10:37. Homeschool Pop Recommended for you. It is usually best to show an answer using the simplest fraction 1 / 2 in this case. That is called Simplifying, or Reducing the Fraction. Numerator / Denominator. We call the top number the Numerator, it is the number of parts we have. We call the bottom number the Denominator, it is the number of parts the whole is divided into. NumeratorDenominator. Intro to Fractions Revised @ 2009 MLC page 5 of 12 8 6 both 6 and 8 can be divided by 2. 4 3 8 2 6 2 8 6 4 3 is the reduced form of. When you divide both the top and bottom numbers of a fraction by the same number, you are dividing by a form of one so the value of the fraction. “Can You Eat a Fraction?” by Elizabeth Dana Jaffe, “Fraction Fun” by David A. Adler, 1 fraction resource card, 1 fraction holder block 9.75” x 3”, fractions for fraction block 1 red circle, 2 blue 1/2s, 3 yellow 1/3s, 4 green 1/4s, “Fraction Burger” box, "Fraction Burger" 2 circle “buns”, burger layers of ½, 1/3, ¼, 1/5, 1/6, 1/8, 1/10, 1/12. Elizabeth Dana Jaffe is the author of Walt Disney 3.79 avg rating, 14 ratings, 6 reviews, published 2008, Alien Alert 3.38 avg rating, 8 ratings, 0 re. The cherries are a SET OF 10. You CAN’T change that. Every fraction will be of a set of 10 or something/10. If a student says, but you can cut them in half and make a set of 20, bonus points, very smart, that’s true. But, for sets like beads on a necklace or vitamin tablets in. Dec 07, 2011 · Fractions with Our Favorite ThingFood! by Jen; Before you first meet me, I should tell you that I am certifiably nuts about being anti-worksheets right now, so I am going to try to dial it back a bit to write this post. This past school year, we adopted a new math series that is very heavy on worksheets and giving tons of practice problems. Elizabeth D. Jaffe is a published author of children's books. Some of the published credits of Elizabeth D. Jaffe include Ellen Ochoa Rookie Biographies, Can You Eat a Fraction? Yellow Umbrella Books. Dec 03, 2010 · Eating Fractions - Duration: 3:08$1.Ms. Bishop's Read Alouds on youtube 937 views. Visualize math division with slices of pie storybook art - Duration: 4:12. AM Crew 4,769 views. Starring Fractions ISBN: 978-0-7660-2919-4, written by Rebecca Wingard-Nelson. Math Word Problems Solved reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Word Problems Solved series in the.

Mixed numbers can turn into improper fractions or vice versa. An easy way to do it is to take the whole number, multiply it by the denominator, and then add the the numerator. For example: In this orange problem there are 2 oranges and a half orange which is 2 1/2 this gives you 5 halves or 5/2. What fraction of 1$\frac23$ is each bar? Write down your ideas for each bar. For example, you could write: Bar A is three fifths of the black bar. or Bar A represents $\frac35$ of 1$\frac23$. or Bar A represents a whole. Can you work out how we came up with these three ideas? If you've ever wondered what is in the food you eat, this book is for you! Learn about the ingredients in various types of food, how different types of foods are classified, how to read nutrition labels, how people with type 1 diabetes pay special attention to food and the way the nutritional value of food can be taken into account when cooking.


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# How do you simplify (a+2)/(2+a)?

Mar 10, 2018

Simplified, the answer is $1$.

#### Explanation:

The sum $2 + a$ is the same as $a + 2$, so:

$\textcolor{w h i t e}{=} \frac{a + 2}{2 + a}$

$= \frac{a + 2}{a + 2}$

$= 1$

Mar 10, 2018

In adding, the order is not important.

#### Explanation:

So $2 + a = a + 2$

And the 'problem' turns into:

$= \frac{a + 2}{a + 2} = 1$

Note:
The value of $a = - 2$ is forbidden, as this would lead to:

$\frac{0}{0}$, which is undefined. But you may pick $a$ as close to $- 2$ as you wish, and the answer will still be $1$


text:
# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Proposition 4.7.2.5. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets, where $\operatorname{\mathcal{D}}$ is an $\infty$-category. Let $W$ be a collection of edges of $\operatorname{\mathcal{C}}$ such that, for each $w \in W$, the image $F(w)$ is an isomorphism in $\operatorname{\mathcal{D}}$. Then $F$ factors as a composition

$\operatorname{\mathcal{C}}\xrightarrow {G} \operatorname{\mathcal{C}}[W^{-1}] \xrightarrow {H} \operatorname{\mathcal{D}},$

where $G$ exhibits $\operatorname{\mathcal{C}}[W^{-1}]$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$ and $H$ is an inner fibration (so that $\operatorname{\mathcal{C}}[W^{-1}]$ is also an $\infty$-category). Moreover, this factorization can be chosen to depend functorially on the diagram $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and the collection of edges $W$, in such a way that the construction $(F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}, W) \mapsto \operatorname{\mathcal{C}}[W^{-1}]$ commutes with filtered colimits.

Proof. For each element $w \in W$, the image $F(w)$ can be regarded as a morphism from $\Delta ^1$ to the core $\operatorname{\mathcal{D}}^{\simeq }$. By virtue of Proposition 3.1.7.1, we can (functorially) choose a factorization of this morphism as a composition

$\Delta ^1 \xrightarrow { i_{w} } Q_{w} \xrightarrow { q_{w} } \operatorname{\mathcal{D}}^{\simeq },$

where $i_{w}$ is anodyne and $q_{w}$ is a Kan fibration. Since $\operatorname{\mathcal{D}}^{\simeq }$ is a Kan complex, $Q_{w}$ is also a Kan complex, which is contractible by virtue of the fact that $i_{w}$ is anodyne. Form a pushout diagram of simplicial sets

$\xymatrix@R =50pt@C=50pt{ \coprod _{w \in W} \Delta ^1 \ar [r] \ar [d]^{\coprod _{w \in W} i_ w} & \operatorname{\mathcal{C}}\ar [d]^{i} \\ \coprod _{w \in W} Q_ w \ar [r] & \operatorname{\mathcal{C}}'. }$

We first claim that $i: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}'$ exhibits $\operatorname{\mathcal{C}}'$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$. Let $\operatorname{\mathcal{E}}$ be an $\infty$-category. Note that if $G: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ is a morphism of simplicial sets which factors through $\operatorname{\mathcal{C}}'$, then for each $w \in W$ the morphism $G(w)$ belongs to the image of a functor $Q_ w \rightarrow \operatorname{\mathcal{E}}$, and is therefore an isomorphism in $\operatorname{\mathcal{E}}$. It follows that composition with $i$ induces a functor $\theta : \operatorname{Fun}( \operatorname{\mathcal{C}}', \operatorname{\mathcal{E}}) \rightarrow \operatorname{Fun}( \operatorname{\mathcal{C}}[W^{-1}], \operatorname{\mathcal{E}})$, and we wish to show that $\theta$ is an equivalence of $\infty$-categories. This follows by inspecting the commutative diagram

$\xymatrix@R =50pt@C=50pt{ \operatorname{Fun}(\operatorname{\mathcal{C}}', \operatorname{\mathcal{E}}) \ar [r]^-{\theta } \ar [d] & \operatorname{Fun}(\operatorname{\mathcal{C}}[W^{-1}], \operatorname{\mathcal{E}}) \ar [r] \ar [d] & \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{E}}) \ar [d] \\ \prod _{w \in W} \operatorname{Fun}(Q_ w,\operatorname{\mathcal{E}}) \ar [r]^-{\theta '} & \prod _{w \in W} \operatorname{Isom}(\operatorname{\mathcal{E}}) \ar [r] & \prod _{w \in W} \operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{E}}). }$

The outer rectangle is a pullback square by the definition of $\operatorname{\mathcal{C}}'$, and the right square is a pullback by the definition of $\operatorname{Fun}( \operatorname{\mathcal{C}}[W^{-1}], \operatorname{\mathcal{E}})$. It follows that the left square is also a pullback. Lemma 4.7.2.4 implies that $\theta '$ is a trivial Kan fibration, so that $\theta$ is also a trivial Kan fibration (hence an equivalence of $\infty$-categories by Proposition 4.5.2.9).

Note that the morphism $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and the collection of morphisms $\{ q_{w}: Q_ w \rightarrow \operatorname{\mathcal{D}}^{\simeq } \subseteq \operatorname{\mathcal{D}}\} _{w \in W}$ can be amalgamated to a single morphism of simplicial sets $F': \operatorname{\mathcal{C}}' \rightarrow \operatorname{\mathcal{D}}$. Applying Proposition 4.1.3.2, we can (functorially) factor $F'$ as a composition $\operatorname{\mathcal{C}}' \xrightarrow {G'} \operatorname{\mathcal{C}}[W^{-1}] \xrightarrow {H} \operatorname{\mathcal{D}}$, where $G'$ is inner anodyne and $H$ is an inner fibration. We conclude by observing that the composite map $G = (G' \circ i): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}[W^{-1}]$ exhibits $\operatorname{\mathcal{C}}[W^{-1}]$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$, by virtue of Remark 4.7.1.17. $\square$


text:
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# Blog

2019-12-27
In tonight's Royal Institution Christmas lecture, Hannah Fry and Matt Parker demonstrated how machine learning works using MENACE.
The copy of MENACE that appeared in the lecture was build and trained by me. During the training, I logged all the moved made by MENACE and the humans playing against them, and using this data I have created some visualisations of the machine's learning.
First up, here's a visualisation of the likelihood of MENACE choosing different moves as they play games. The thickness of each arrow represented the number of beads in the box corresponding to that move, so thicker arrows represent more likely moves.
The likelihood that MENACE will play each move.
There's an awful lot of arrows in this diagram, so it's clearer if we just visualise a few boxes. This animation shows how the number of beads in the first box changes over time.
The beads in the first box.
You can see that MENACE learnt that they should always play in the centre first, an ends up with a large number of green beads and almost none of the other colours. The following animations show the number of beads changing in some other boxes.
MENACE learns that the top left is a good move.
MENACE learns that the middle right is a good move.
MENACE is very likely to draw from this position so learns that almost all the possible moves are good moves.
The numbers in these change less often, as they are not used in every game: they are only used when the game reached the positions shown on the boxes.
We can visualise MENACE's learning progress by plotting how the number of beads in the first box changes over time.
The number of beads in MENACE's first box.
Alternatively, we could plot how the number of wins, loses and draws changes over time or view this as an animated bar chart.
The number of games MENACE wins, loses and draws.
The number of games MENACE has won, lost and drawn.
If you have any ideas for other interesting ways to present this data, let me know in the comments below.

### Similar posts

 Building MENACEs for other games MENACE at Manchester Science Festival MENACE MENACE in fiction

Comments in green were written by me. Comments in blue were not written by me.
@(anonymous): Have you been refreshing the page? Every time you refresh it resets MENACE to before it has learnt anything.

It takes around 80 games for MENACE to learn against the perfect AI. So it could be you've not left it playing for long enough? (Try turning the speed up to watch MENACE get better.)
Matthew

I have played around menace a bit and frankly it doesnt seem to be learning i occasionally play with it and it draws but againt the perfect ai you dont see as many draws, the perfect ai wins alot more
(anonymous)

@Colin: You can set MENACE playing against MENACE2 (MENACE that plays second) on the interactive MENACE. MENACE2's starting numbers of beads and incentives may need some tweaking to give it a chance though; I've been meaning to look into this in more detail at some point...
Matthew

Idle pondering (and something you may have covered elsewhere): what's the evolution as MENACE plays against itself? (Assuming MENACE can play both sides.)
Colin

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2018-07-07
So you've calculated how much you should expect the World Cup sticker book to cost and recorded how much it actually cost. You might be wondering what else you can do with your sticker book. If so, look no further: this post contains 5 mathematical things involvolving your sticker book and stickers.

Stickers 354 and 369: Alisson and Roberto Firmino
In a group of 23 people, there is a more than 50% chance that two of them will share a birthday. This is often called the birthday paradox, as the number 23 is surprisingly small.
Back in 2014 when Alex Bellos suggested testing the birthday paradox on World Cup squads, as there are 23 players in a World Cup squad. I recently discovered that even further back in 2012, James Grime made a video about the birthday paradox in football games, using the players on both teams plus the referee to make 23 people.
In this year's sticker book, each player's date of birth is given above their name, so you can use your sticker book to test it out yourself.

One of the cities in which games are taking place in this World Cup is Kaliningrad. Before 1945, Kaliningrad was called Königsberg. In Königsburg, there were seven bridges connecting four islands. The arrangement of these bridges is shown below.
The people of Königsburg would try to walk around the city in a route that crossed each bridge exactly one. If you've not tried this puzzle before, try to find such a route now before reading on...
In 1736, mathematician Leonhard Euler proved that it is in fact impossible to find such a route. He realised that for such a route to exist, you need to be able to pair up the bridges on each island so that you can enter the island on one of each pair and leave on the other. The islands in Königsburg all have an odd number of bridges, so there cannot be a route crossing each bridge only once.
In Kaliningrad, however, there are eight bridges: two of the original bridges were destroyed during World War II, and three more have been built. Because of this, it's now possible to walk around the city crossing each bridge exactly once.
A route around Kaliningrad crossing each bridge exactly once.
I wrote more about this puzzle, and using similar ideas to find the shortest possible route to complete a level of Pac-Man, in this blog post.

### Sorting algorithms

If you didn't convince many of your friends to join you in collecting stickers, you'll have lots of swaps. You can use these to practice performing your favourite sorting algorithms.

#### Bubble sort

In the bubble sort, you work from left to right comparing pairs of stickers. If the stickers are in the wrong order, you swap them. After a few passes along the line of stickers, they will be in order.
Bubble sort

#### Insertion sort

In the insertion sort, you take the next sticker in the line and insert it into its correct position in the list.
Insertion sort

#### Quick sort

In the quick sort, you pick the middle sticker of the group and put the other stickers on the correct side of it. You then repeat the process with the smaller groups of stickers you have just formed.
Quick sort

### The football

Sticker 007: The official ball
Sticker 007 shows the official tournament ball. If you look closely (click to enlarge), you can see that the ball is made of a mixture of pentagons and hexagons. The ball is not made of only hexagons, as road signs in the UK show.
Stand up mathematician Matt Parker started a petition to get the symbol on the signs changed, but the idea was rejected.
If you have a swap of sticker 007, why not stick it to a letter to your MP about the incorrect signs as an example of what an actual football looks like.

### Psychic pets

Speaking of Matt Parker, during this World Cup, he's looking for psychic pets that are able to predict World Cup results. Why not use your swaps to label two pieces of food that your pet can choose between to predict the results of the remaining matches?
Timber using my swaps to wrongly predict the first match

### Similar posts

 World Cup stickers 2018, pt. 2 World Cup stickers 2018 World Cup stickers Euro 2016 stickers

Comments in green were written by me. Comments in blue were not written by me.
@Matthew: Thank you for the calculations. Good job I ordered the stickers I wanted #IRN. 2453 stickers - that's more than the number you bought (1781) to collect all stickers!

@Matthew: Here is how I calculated it:

You want a specific set of 20 stickers. Imagine you have already $$n$$ of these. The probability that the next sticker you buy is one that you want is
$$\frac{20-n}{682}.$$
The probability that the second sticker you buy is the next new sticker is
$$\mathbb{P}(\text{next sticker is not wanted})\times\mathbb{P}(\text{sticker after next is wanted})$$
$$=\frac{662+n}{682}\times\frac{20-n}{682}.$$
Following the same method, we can see that the probability that the $$i$$th sticker you buy is the next wanted sticker is
$$\left(\frac{662+n}{682}\right)^{i-1}\times\frac{20-n}{682}.$$
Using this, we can calculate the expected number of stickers you will need to buy until you find the next wanted one:
$$\sum_{i=1}^{\infty}i \left(\frac{20-n}{682}\right) \left(\frac{662+n}{682}\right)^{i-1} = \frac{682}{20-n}$$
Therefore, to get all 682 stickers, you should expect to buy
$$\sum_{n=0}^{19}\frac{682}{20-n} = 2453 \text{ stickers}.$$
Matthew

@Matthew: Yes, I would like to know how you work it out please. I believe I have left my email address in my comment. It seems like a lot of stickers if you are just interested in one team.

@Milad: Following a similiar method to this blog post, I reckon you'd expect to buy 2453 stickers (491 packs) to get a fixed set of 20 stickers. Drop me an email if you want me to explain how I worked this out.
Matthew

Thanks for the maths, but I have one probability question. How many packs would I have to buy, on average, to obtain a fixed set of 20 stickers?

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2017-11-14
A few weeks ago, I took the copy of MENACE that I built to Manchester Science Festival, where it played around 300 games against the public while learning to play Noughts and Crosses. The group of us operating MENACE for the weekend included Matt Parker, who made two videos about it. Special thanks go to Matt, plus Katie Steckles, Alison Clarke, Andrew Taylor, Ashley Frankland, David Williams, Paul Taylor, Sam Headleand, Trent Burton, and Zoe Griffiths for helping to operate MENACE for the weekend.
As my original post about MENACE explains in more detail, MENACE is a machine built from 304 matchboxes that learns to play Noughts and Crosses. Each box displays a possible position that the machine can face and contains coloured beads that correspond to the moves it could make. At the end of each game, beads are added or removed depending on the outcome to teach MENACE to play better.

### Saturday

On Saturday, MENACE was set up with 8 beads of each colour in the first move box; 3 of each colour in the second move boxes; 2 of each colour in third move boxes; and 1 of each colour in the fourth move boxes. I had only included one copy of moves that are the same due to symmetry.
The plot below shows the number of beads in MENACE's first box as the day progressed.

### Sunday

Originally, we were planning to let MENACE learn over the course of both days, but it learned more quickly than we had expected on Saturday, so we reset is on Sunday, but set it up slightly differently. On Sunday, MENACE was set up with 4 beads of each colour in the first move box; 3 of each colour in the second move boxes; 2 of each colour in third move boxes; and 1 of each colour in the fourth move boxes. This time, we left all the beads in the boxes and didn't remove any due to symmetry.
The plot below shows the number of beads in MENACE's first box as the day progressed.

### The data

You can download the full set of data that we collected over the weekend here. This includes the first two moves and outcomes of all the games over the two days, plus the number of beads in each box at the end of each day. If you do something interesting (or non-interesting) with the data, let me know!

### Similar posts

 MENACE Visualising MENACE's learning Building MENACEs for other games MENACE in fiction

Comments in green were written by me. Comments in blue were not written by me.
WRT the comment 2017-11-17, and exactly one year later, I had the same thing happen whilst running MENACE in a 'Resign' loop for a few hours, unattended. When I returned, the orange overlay had appeared, making the screen quite difficult to read on an iPad.
g0mrb

On the JavaScript version, MENACE2 (a second version of MENACE which learns in the same way, to play against the original) keeps setting the 6th move as NaN, meaning it cannot function. Is there a fix for this?
Lambert

what would happen if you loaded the boxes slightly differently. if you started with one bead corresponding to each move in each box. if the bead caused the machine to lose you remove only that bead. if the game draws you leave the bead in play if the bead causes a win you put an extra bead in each of the boxes that led to the win. if the box becomes empty you remove the bead that lead to that result from the box before
Ian

Hi, I was playing with MENACE, and after a while the page redrew with a Dragon Curves design over the top. MENACE was still working alright but it was difficult to see what I was doing due to the overlay. I did a screen capture of it if you want to see it.
Russ

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2015-03-24
 This is the fourth post in a series of posts about tube map folding.
A while ago, I made this (a stellated rhombicuboctahedron):
Here are some hastily typed instructions for Matt Parker, who is making one at this month's Maths Jam. Other people are welcome to follow these instructions too.

• 48 tube maps
• glue

### Making a module

First, take a tube map and fold the cover over. This will ensure that your shape will have tube (map and not index) on the outside and you will have pages to tuck your tabs between later.
Now fold one corner diagonally across to another corner. It does not matter which diagonal you chose for the first piece but after this all following pieces must be the same as the first.
Now fold the overlapping bit back over the top.
Turn it over and fold this overlap over too.
You will need 48 of these and some glue.

### Putting it together

By slotting three or four of these modules together, you can make a pyramid with a triangle or square as its base.
A stellated rhombicuboctahedron is a rhombicuboctahedron with a pyramid, or stellation on each face. In other words, you now need to build a rhombicuboctahedron with the bases of pyramids like these. A rhombicuboctahedron looks like this:
en.wiki User Cyp, CC BY-SA 3.0
More usefully, its net looks like this:
To build a stellated rhombicuboctahedron, make this net, but with each shape as the base of a pyramid. This is what it will look like 6/48 tube maps in:
If you make on of these, please tweet me a photo so I can see it!
Edit: Proof that these instructions can be followed:
Previous post in series
 Tube map Platonic solids, pt. 3
This is the fourth post in a series of posts about tube map folding.
Next post in series
 Tube map kaleidocycles

### Similar posts

 Tube map Platonic solids, pt. 2 Tube map kaleidocycles Tube map Platonic solids, pt. 3 Electromagnetic Field talk

Comments in green were written by me. Comments in blue were not written by me.
I wish you'd make the final stellation of the rhombicuboctahedron! And show us! I know the shapes of the faces but have been stuck two years on the assembly!
Roberts, David


text:
Lesson 2, Topic 3
In Progress

# Binary Arithmetic Operations – Addition | Subtraction in Other Bases

Lesson Progress
0% Complete

a. 3042five   + 2103five

Explanation:

1st Column (from right to left) = 2 + 3 = 5. How many fives are there in 5? $$\frac{5}{5}$$= 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column = 1 + 4 + 0 = 5. How many fives are there in 5? $$\frac{5}{5}$$= 1 remainder 0. Write 0 and carry 1 to column 3.

3rd Column = 1 + 0 + 1 = 2. 2 is less than 5 so we write 2 down.

4th column = 3 + 2 = 5. How many fives are there in 5? $$\frac{5}{5}$$= 1 remainder 0. Write 0 and carry 1 to column 5.

5th column = We add 1 to the 5th column.

b. 2001three   + 1022three

Explanation

1st Column (from right to left) = 1 + 2 = 3. How many threes are there in 3? $$\frac{3}{3}$$= 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column = 1 + 0 + 2 = 3. How many threes are there in 3? $$\frac{3}{3}$$= 1 remainder 0. Write 0 and carry 1 to column 3.

3rd Column = 1 + 0 + 0 = 1. 1 is less than 3 so we write 1 down.

4th column = 2 + 1 = 3. How many threes are there in 3? $$\frac{3}{3}$$= 1 remainder 0. Write 0 and carry 1 to column 5.

5th column = We add 1 to the 5th column.

c. 151.24six +   12.34six  + 20.11six

Explanation

1st Column (from right to left) = 4 + 4 + 1 = 9. How many six’s are there in 9? $$\frac{9}{6}$$ = 1 remainder 3. Write 3 and carry 1 to column 2.

2nd Column = 1 + 2 + 3 + 1 = 7. How many six’s are there in 7? $$\frac{7}{6}$$ = 1 remainder 1. Write 1 and carry 1 to column 3.

3rd Column = 1 + 1 + 2 + 0 = 4. 4 is less than 6 so we write 4 down.

4th column = 5 + 1 + 2 = 8. How many six’s are there in 8? $$\frac{8}{6}$$ = 1 remainder 2. Write 2 and carry 1 to column 5.

5th column = 1 + 1 = 2. 2 is less than 6 so we write 6 down.

d. 53468 – 6378

1st Column (from right to left) = 6 is less than 7 so we will have to borrow from the 2nd column. Since it is in base 8 any number borrowed is 8. So borrowing 8 from the second column will give (8 + 6) – 7 = 14 – 7 = 7

2nd Column = This reduces 4 to 3 in the second column. 3 – 3 = 0. We write 0 down.

3rd Column = 3 is less than 6 so we will have to borrow from the 4th column. Since it is in base 8 any number borrowed is 8. So borrowing 8 from the fourth column will give (8 + 3) – 6 = 11 – 6 = 5

4th Column = This reduces 5 to 4 in the fourth column. 4 – 0 = 4. We write 4 down.

e. 3002four – 2213four

Explanation

1st Column (from right to left) = 2 is less than 3 so we will have to borrow from the 2nd column. Since it is in base 4 any number borrowed is 4. So borrowing 4 from the second column will give (4 + 2) – 3 = 6 – 3 = 3

2nd Column = This reduces 0 to -1 in the second column. We will have to borrow (4) from the third column. 4 – 1 – 1 = 2. We write 2 down.

3rd Column = This reduces 0 to -1 in the third column. We will have to borrow (4) from the 4th column. 4 – 1 – 2 = 1. We write down 1.

4th Column = This reduces 3 to 2 in the fourth column. 2 – 2 = 0.


text:
### Anonymous IBE from Quadratic Residuosity with Improved Performance

Michael Clear, Hitesh Tewari, and Ciarán McGoldrick

##### Abstract

Identity Based Encryption (IBE) has been constructed from bilinear pairings, lattices and quadratic residuosity. The latter is an attractive basis for an IBE owing to the fact that it is a well-understood hard problem from number theory. Cocks constructed the first such scheme, and subsequent improvements have been made to achieve anonymity and improve space efficiency. However, the anonymous variants of Cocks' scheme thus far are all less efficient than the original. In this paper, we present a new universally-anonymous IBE scheme based on the quadratic residuosity problem. Our scheme has better performance than the universally anonymous scheme from Ateniese and Gasti (CT-RSA 2009) at the expense of more ciphertext expansion. Another contribution of this paper is a modification to a variant of the space-efficient scheme by Boneh, Gentry and Hamburg (FOCS 07) that results in an IND-ID-CPA secure IBE scheme with comparable efficiency to Cocks, but with reduced ciphertext expansion.

Note: Minor extension to Africacrypt 2014 paper.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MINOR revision.Africacrypt 2014
DOI
10.1007/978-3-319-06734-6_23
Keywords
Contact author(s)
clearm @ scss tcd ie
History
Short URL
https://ia.cr/2014/778

CC BY

BibTeX

@misc{cryptoeprint:2014/778,
author = {Michael Clear and Hitesh Tewari and Ciarán McGoldrick},
title = {Anonymous IBE from Quadratic Residuosity with Improved Performance},
howpublished = {Cryptology ePrint Archive, Paper 2014/778},
year = {2014},
doi = {10.1007/978-3-319-06734-6_23},
note = {\url{https://eprint.iacr.org/2014/778}},
url = {https://eprint.iacr.org/2014/778}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
Changes in Current Operating Assets and Liabilities-Indirect Method Blue Circle Corporation's comparative balance sheet for current assets and liabilities was as follows: Dec. 31, Year 2 Dec. 31, Year 1 $20,000 56,800 19,300 17,000 Accounts receivable Inventory Accounts payable Dividends payable Adjust net income of$75,600 for changes in operating assets and liabilities to arrive at net cash flow from operating activities. \$16,400 63,600 16,600 16,000 62,500X

Question

I've tried this problem twice and keep getting the wrong answer. The first time I did it I got 70,100 and now the second time I got 62,500. How do I do this? Thanks!


text:
Spontaneous emission

Spontaneous emission is the process by which an atom or molecule in an excited state drops to the ground state, resulting in the creation of a photon.

If the atom is in the excited state with energy [itex]E_2[itex], it may spontaneously decay into the ground state, with energy [itex]E_1[itex], releasing the difference in energies between the two states as a photon. The photon will have frequency [itex]\nu[itex] and energy [itex]h \nu[itex], given by:

[itex]E_2 - E_1 = h \nu[itex],

where h is Planck's constant. The phase of the photon in spontaneous emission is random as is the direction the photon propagates in. This is not true for stimulated emission.

An energy level diagram illustrating the process is shown below:

   Before emission              After emission

--------O---------          ------------------ E2
|  Atom in
|  excited state
|                              ~~~>
|                          Photon hν
|
V
------------------          ---------O-------- E1
Atom in ground state

In a group of such atoms, if the number of atoms in the excited state is given by N, the rate at which spontaneous emission occurs is given by:

[itex]\frac{\partial N}{\partial t} = -A_{21} N[itex],

where A21 is a proportionality constant for this particular transition in this particular atom. (The constant is referred to as an Einstein A co-efficient.) The rate of emission is thus proportional to the number of atoms in the excited state, N.

The above equation can be solved to give:

[itex]N(t) = N(0) e^{ - \frac{t}{\tau_{21} } } [itex],

where N(0) is the initial number of atoms in the excited state, and τ21 is the lifetime of the transition, τ21 = (A21)-1.

It can be seen that spontaneous emission occurs in a way rather similar to the decay of radioactive particles, in particular that the lifetime is analogous to a half-life.

There are two different ways in which decay or relaxation can occur: radiative and nonradiative. In nonradiative relaxation, the energy is absorbed as phonons, more commonly known as heat. Nonradiative relaxation is nearly impossible to measure and cannot be inferred except in very small particles because the difference in the temperature before and after a relaxation is so small that it is in the noise of any measurement for practical systems.

Nonradiative relaxations occur when the energy difference between the levels is very small, and these typically occur on a much faster time scale than radiative transitions. For many materials (for instance, semiconductors), electrons move quickly from a high energy level to a meta-stable level via small nonradiative transitions and then make the final move down to the bottom level via an optical or radiative transition (This final transition is the transition over the bandgap in semiconductors.). Large nonradiative transitions do not occur frequently because the crystal structure generally can not support large vibrations without destroying bonds (which generally doesn't happen for relaxation). Meta-stable states form a very important feature that is exploited in the construction of lasers. Specifically, since electrons decay slowly from them, they can be piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal.

See also absorption, stimulated emission, laser science.

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text: The one thing i would emphasize from your very interesting draft is that it need not be restricted to ‘scientists, businesses, universities and museums’. Farming, for instance, is an incredibly complex task, and replete with side projects. Finding out how much grass a cow eats in its lifetime, where the feed comes from etc… teaches all kinds of nice hard skills and lets them acquire knowledge of their world… but more importantly it teaches them inquiry, collaboration etc… the real needs of 21st century.


text:
The Indico system will be unavailable due to system upgrades on August 30th from 6 - 9PM CST. Please email Indico support with any questions or concerns.

# The 28th International Workshop on Weak Interactions and Neutrinos (WIN2021)

Jun 7 – 12, 2021
US/Central timezone

## Resolving the LMA-dark NSI degeneracy with coherent neutrino–nucleus scattering

Not scheduled
20m
Asynchronous Talk Neutrino Physics

### Speaker

Mr Mariano Chaves (University of Campinas)

### Description

In the presence of non-standard neutrino interactions (NSI), a degeneracy exists
in neutrino oscillation data, which involves the flipping of the octant of the mixing angle $\theta_{13}$ and the type of the neutrino mass ordering. In this article, we revisit the status of this degeneracy in the light of recent data on coherent elastic neutrino–nucleus scattering (CEνNS) from the COHERENT experiment. For general relative couplings to up and down quarks, the degeneracy is disfavoured at the 2$\sigma$ level by the latest data but remains at a higher confidence level. We investigate the requirements of future CE$\nu$NS measurements to resolve the degeneracy with high significance. We find that a measurement involving both, electron and muon neutrino flavours and a target with a neutron-to-proton ratio close to 1 is required. For example, an experiment with a silicon target at the European Spallation Source can resolve the degeneracy at more than 4$\sigma$ for arbitrary relative couplings to up and down quarks.

### Primary authors

Mr Mariano Chaves (University of Campinas) Prof. Thomas Schwetz (Karlsruhe Institute of Technology)

### Presentation materials

 Presentation_Resolving_LMA_D.pdf Resolving the LMA-dark NSI degeneracy with coherent neutrino–nucleus scattering


text:
# ModelSim Error : “ could not find interpreter ”ScintillaTk“ ”

I have installed ModelSim 10.4 X64, when I want to open a vhd file in editor an error shown in "Transcript" window as : " could not find interpreter "ScintillaTk" "

I searched about that and I found out that this problem occurs when ModelSim installation path have a space character !!

I have installed it in "Program Files" Folder, Now how can I solve this problem without installing it again ?

I have changed the "Path" environment variables value form -path- to -"path"- but the problem not solved ...

• Create a directory junction from somewhere like C:\modelsim\ to C:\Program Files\<modelsim folder>\ and set the path, environment variables, and shortcuts for modelsim to point to that location? – Tom Carpenter Feb 27 '16 at 19:35
• Thank you @TomCarpenter, I think that is better to be as an answer with more explain and images, If you don't time for that, I'm glad to do that. – QMaster Mar 3 '17 at 19:02
• What do you mean "directory junction" – Jonathan May 6 '17 at 2:19

Thanks to Tom Carpenter for his solution I write the answer for others who may have the same problem.

Create a directory junction from somewhere like C:\modelsim\ to C:\Program Files\ (modelsim folder)\ and set the path, environment variables, and shortcuts for modelsim to point to that location? – Tom Carpenter Feb 27 '16 at 19:35

this can be solved by creating directory junction link to modelsim installation folder. you can create link with mklink command in cmd.
mklink /J "Link" "Destination"
e.g. mklink /J "C:\modelsim" "D:\program file\modelsim"
e.g. C:\modelsim\win32pe_edu\modelsim.ex`


text:
# Proving or disproving regularity of a language

The question is as follows:

 If L1 and L2 are not regular and L1 ⊆ L ⊆ L2, then L is regular

My intuition says that it's wrong so I've been looking for a counterexample, so far I didn't succeed.

Can I please get a direction? is this claim might be true?

What about $L_1 = L_2$? – Hendrik Jan Dec 7 '12 at 12:57
If $L_1=L_2$ is not regular, then $L=L_1$ saisfies all conditions, and cannot be regular. If that is not what you need or want, please rephrase the question. You might want to add "for all" or "there exist". – Hendrik Jan Dec 7 '12 at 13:02
If you take $L_1=L_2$ not regular, then $L=L_1$ satisfies your assumptions, but cannot be regular.