Question about the matrix operation
Combining values in one column (or part) when values in another column (or part) match
Can I get UAC prompt for user from batch file? Can I get UAC prompt for user from batch file?  For example I need put some keys to registry under CurrentControlSet from batch file by     reg import path\to\my.reg   PS. runas is not a solution as my customers uses different Windows localisation and I can not guess which name used for Administrator account (this can be Администратор)...  And script don't know administrator password.  And UAC dialog box does not require password entering... Proving that $-a=(-1)\cdot a$ As the title reveals, I want to prove (based on the axioms of field) that $$-a=(-1)\cdot a$$ I've been trying for a while now, but couldn't think of a way to do it and it got me thinking that maybe its does not require a proof, but it doesn't feel right. Any ideas? Array versus List: When to use which? MyClass[] array; List&lt;MyClass&gt; list;   What are the scenarios when one is preferable over the other? And why? This week we rolled out a series of changes to  of the question close workflow.  You can read more about the details of these changes .    For context, the overall effort to improve the question close experience will be optimized for Stack Overflow. Given Stack Overflow’s scale, many of the pain points we hear about with question closing and reopening are unique to Stack Overflow and won’t make sense for other network sites. However some  changes are general improvements that should improve usability and guidance overall. Wherever possible, we plan to roll these changes out network wide as well. Any time we roll out a change network wide, we’ll make sure to cross-post here. This first phase is being rolled out to the network and is why I’m posting today.  Let us know if you run into any issues or have questions regarding the network here. Redirect automatically when selecting an item from a select drop-down list This page does it the way I want it to:   But I want to find a better way using jQuery, can anyone point me to a good script that uses jQuery to accomplish this? Let $E$ be a metric $\mathbb R$-vector space, $I$ be a nonempty set and $(\mu_t)_{t\in I},(\nu_t)_{t\in I}$ be families of nonnegative finite measures on $\mathcal B(E)$.  that if $(\mu_t)_{t\in I}$ and $(\nu_t)_{t\in I}$ are tight$^1$ and bounded in total variation norm, then the family of convolutions $(\mu_t\ast\nu_t)_{t\in I}$ is tight and bounded in total variation norm as well.  Now I would like to show the converse: If $(\mu_t)_{t\in I}$ and $(\mu_t\ast\nu_t)_{t\in I}$ are tight, then $(\nu_t)_{t\in I}$ is tight. (Most probably we need to impose a boundedness assumption on $(\mu_t)_{t\in I}$ and on $(\mu_t\ast\nu_t)_{t\in I}$ or even a priori on $(\nu_t)_{t\in I}$.)  For the moment, I'm only able to prove the claim assuming that the $\mu_t,\nu_t$ are probability measures. Under this assumption, the proof goes as follows: Let $\varepsilon&gt;0$. Since $(\mu_t)_{t\in I}$ and $(\mu_t\ast\nu_t)_{t\in I}$ are tight, there is a compact $K\subseteq E$ with $$\sup\left(\sup_{t\in I}\mu_t(K^c),\sup_{t\in I}(\mu_t\ast\nu_t)(K^c)\right)&lt;\varepsilon\tag1.$$ Now $K-K$ is compact and \begin{equation}\begin{split}1-\varepsilon&lt;(\mu_t\ast\nu_t)(K)&amp;=\underbrace{\int_K\mu_t({\rm d}x)\nu_t(\underbrace{K-x}_{\subseteq\:K-K})}_{\le\:\nu_t(K-K)}+\underbrace{\int_{K^c}\mu_t({\rm d}x)\underbrace{\nu_t(K-x)}_{\le\:1}}_{&lt;\:\varepsilon}\\&amp;&lt;\nu_t(K-K)+\varepsilon\end{split}\tag2\end{equation} for all $t\in I$, which immediately yields $$\nu_t(K-K)&gt;1-2\varepsilon\;\;\;\text{for all }t\in I\tag3.$$  Can we drop the probability measure assumption?  EDIT I'm not able to obtain the claim, even with the help of the answer below. If $\varepsilon&gt;0$, the goal is to show that $$\nu_t(E)-\nu_t(K-K)=\nu_t((K-K)^c)&lt;\varepsilon\tag4.$$ If I'm choosing all the constants as generic as possible, we obtain $$\mu_t(E)\le c_1\tag5$$ $$\mu_t(K^c)\le k_1(\varepsilon)\tag6$$ $$(\mu_t\ast\nu_t)(K)&lt;c_1\nu_t(K-K)+c_2k_1(\varepsilon)\tag6$$ $$\mu_t(E)\ge\alpha_1\tag7$$ $$(\mu_t\ast\nu_t)(E)\le c_3\tag8$$ $$\nu_t(E)\le\frac{c_3}{\alpha_1}=:c_2\tag9$$ $$(\mu_t\ast\nu_t)(E)\ge\alpha_3\tag{10}$$ $$\nu_t(E)\ge\frac{\alpha_3}{c_1}\tag{11}$$ $$(\mu_t\ast\nu_t)(K^c)&lt;k_3(\varepsilon)$$ The assumptions that I'm imposing is that $(\mu_t)$ and $(\mu_t\ast\nu_t)$ are bounded above (by $c_1$ and $c_3$) and below (by $\alpha_1$ and $\alpha_3$) in total variation norm and are tight (so that we can find $K$ for arbitrary $k_1(\varepsilon)$ and $k_3(\varepsilon)$). In order to obtain the claim we need to choose $k_1(\varepsilon)$ and $k_3(\varepsilon)$ such that $(4)$ holds. From everything above, we obtain $$\nu_t(E)-\nu_t(K-K)&lt;\frac{c_3}{\alpha_1}-\frac{\alpha_3}{c_1}+\frac{c_3}{\alpha_1c_1}k_1(\varepsilon)+\frac1{c_1}k_3.(\varepsilon)\tag{12}$$ Even if we simplify this by assuming $\alpha_1=\alpha_3$, $c_1=c_3$ and $k_1(\varepsilon)=k_3(\varepsilon)$, the equation $$\frac{c_3}{\alpha_1}-\frac{\alpha_3}{c_1}+\frac{c_3}{\alpha_1c_1}k_1(\varepsilon)+\frac1{c_1}k_3.(\varepsilon)=\varepsilon\tag{13}$$ doesn't seem to admit a solution $(k_1(\varepsilon),k_3(\varepsilon))$ with positive $k_1(\varepsilon)$ and $k_3(\varepsilon)$; unless $\frac{c_3}{\alpha_1}-\frac{\alpha_3}{c_1}\ge0$; which clearly doesn't need to be the case (it is clearly the case for probability measures though ...)  $^1$ Remember that a family $\mathcal F$ of finite signed measures on $\mathcal B(E)$ is called tight if for all $\varepsilon&gt;0$, there is a compact $K\subseteq E$ such that $$\sup_{\mu\in\mathcal F}|\mu|(K^c)&lt;\varepsilon.$$ I have heard several times that some mathematician has given another and more rigorous for an established theorem, but I don't know what does it really mean and what differences makes it to be more 'rigorous'. My understanding of a proof is that a proof is some explanation to convincing others that a statement is true. If some proof is not rigorous, does it mean that while the proof is acceptable for many but it is not for everybody? If so, the proof is not correct since it going to be rejected by some people and it is not a proof at all. Or, does rigorous mean it uses more advanced tools? If so, why not any alternative (but simpler) proof is also acceptable as rigorous (which is more 'valuable' as well since it's simpler!)?   Saying those limited insight of mine, my questions are:   $1-$ What does rigorous proof mean, in general definition?  $2-$ In order to understand your answers, as an example I am re-writing three of the proofs for the compactness of the torus. Which of the following proofs are most rigorous, 'normal' and least rigorous; and why so?    Theorem: The torus $T^2$ is compact.  First proof: The torus is homeomorphic to the product space $S^1 \times S^1$. The circle $S^1$ is compact. Therefore the torus is the product of two compact spaces, and thus it is compact.   Second proof: The torus $T$ is the subspace of $\mathbb{R}^3$ obtained by rotating a circle about the $z$-axis. The torus is closed since given any point in its complement, there is an open ball of sufficiently small radius centered at that point and disjoint from the torus. Also, the torus is bounded since it is contained in the ball of radius $4$ centered at the origin. Since the torus is closed and bounded in $\mathbb{R}^3$, it is compact.   Third proof: The torus is homeomorphic to a space obtained as a quotient  space of the square by identifying opposite edges. The square is a closed and  bounded subset of $\mathbb{R}^3$ and therefore is compact. Furthermore, a quotient map on the square is a continuous function, and the image of a compact space under a continuous function is compact. Therefore the torus is compact.   Thanks a lot for your guidance. How do I move Ubuntu dock to bottom on Ubuntu 17.10 and later? Just upgraded from Ubuntu 17.04 to Ubuntu 17.10.  Please help me to shift the side bar (aka Ubuntu Dock) to bottom.   I tried running the following command which used to work with older Ubuntu releases   gsettings set com.canonical.Unity.Launcher launcher-position Bottom   but it's not working. Answer didn't load temporary Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $ Launchers for installed snap applications (including Ubuntu Software) disappeared after installing GNOME Software Why is ridge regression called "ridge", why is it needed, and what happens when $\lambda$ goes to infinity? Basically, here's my MWE, and I need to include "Chapter" before every section title in the ToC (without changing anything else).      \documentclass[12pt]{article} \usepackage[utf8]{inputenc}  \usepackage[english]{babel} \usepackage[titles]{tocloft} \usepackage{titlesec} \usepackage{titletoc}  \addto\captionsenglish{ \renewcommand*\contentsname{\centerline{TABLE OF CONTENTS}}}  %\renewcommand{\thesection}{CHAPTER} %\renewcommand{\cftsecpresnum}{Chapter \thesection} \titleformat{\section}[display]% {\null\vskip1em\sffamily\bfseries\filcenter}{Chapter \thesection}{0em}{}[] \titlespacing*{\section}{0em}{1em}{1em}  \titlecontents{section} [1.5em] % ie, 1.5em (chapter) + 2.3em {} {\contentslabel{1em}} {\hspace*{-1.5em}} {\titlerule*[0.5pc]{.}\contentspage}  \begin{document} \newpage \tableofcontents \newpage  \section{Section One} \section{Section Two} Content \end{document}   The commented out code is what I've already tried. The first one just changes the number to "CHAPTER" and doesn't move the text in the ToC (so it just overlays on top of the name of the section), and if I include "\thesection" after "CHAPTER" it creates an infinite loop definition error. The second one causes no differences, and the code still compiles.  Thanks! How can I make an InputField with a proper newline/carriage return? Update (March, 2012): This has been rolled out to all sites in the network.    Behind the scenes we've been hard at work making some changes to how we track reputation.  Here are some of the issues we're aiming to address with these changes:   Reputation Skew (your actual reputation doesn't match what's shown) Up/Down votes oddities (mostly with the daily rep cap, the magical +2) Historical Deletes (not impacting rep immediately, contributing to skew) Unaccepts (display issues in the profile) User Deletion (magically missing rep, another skew contributor)   To be clear: reputation values are not changing, every action in the system is still worth the same amount.   Here’s what will be different:   Your reputation will be correct at all times Deletions will have a much more immediate effect on reputation, not waiting on a recalc  (but reputation sync takes up to 5 minutes on a delete/undelete action; as to not block the user's response thread, it's offloaded to a background queue) Recalcs will no longer be necessary Up/Down vote reversals will restore the correct reputation amount Up/Down vote reversals will correctly adjust to the reputation cap The reputation history in your profile will be more detailed and accurate (e.g. when a post is deleted, you'll see that in the reputation tab of your profile)   This means your reputation will go up and down more than it has previously, but it will be in sync.  To think of it more easily: imagine that a recalc will be done after every action in the system.  Probably the biggest impact many will be concerned with is that you may see your reputation drop in cases where it didn't seem like it did before  This was effectively happening before, but the results of that change were not applied immediately, but on the next rep recalc.  Post deletion is the biggest factor here, previously it didn't (immediately) account for the reputation impact...that will no longer be the case.  Reputation changes from the deletion will now be applied within the hour, and most other changes will be instant.  Now the part that will make everyone throw vegetables our way:  this will require a global recalc to get everything in sync.  We'll be rolling it out first here on meta, then the rest of the network...the enabling of the detailed rep view and global recalc on each individual site will coincide.  During the rollout you will see empty reputation tabs on profiles as we transition to the new storage behind the scenes, they'll be restored as the recalc rolls though each user.  We’ll put up a blog post on  before the network-wide rollout.  If you have any questions about this change or details I may have left out, please do so in answers below so that we can clear up as much as possible before this rolls out. How to use Noto Color Emoji with lualatex? I want to use Noto Color Emoji with lualatex (package fonts-noto-color-emoji on my box). However, this fails as follows. How to use Noto Color Emoji with lualatex?  \documentclass{article} \usepackage{fontspec} \setmainfont{Noto Color Emoji} \begin{document} 😺 👅  \end{document}   Error:  $ lualatex emoji.tex  This is LuaTeX, Version 1.07.0 (TeX Live 2019/dev/Debian)   restricted system commands enabled. (./emoji.tex LaTeX2e &lt;2018-12-01&gt;  luaotfload | main : initialization completed in 2.224 seconds (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2018/09/03 v1.4i Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo)) (/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec.sty (/usr/share/texlive/texmf-dist/tex/latex/l3packages/xparse/xparse.sty (/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3.sty (/usr/share/texlive/texmf-dist/tex/latex/l3kernel/expl3-code.tex) (/usr/share/texlive/texmf-dist/tex/latex/l3kernel/l3pdfmode.def))) (/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec-luatex.sty (/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty (/usr/share/texlive/texmf-dist/tex/latex/base/tuenc.def)) (/usr/share/texlive/texmf-dist/tex/latex/fontspec/fontspec.cfg))) (./emoji.aux) [1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] (./emoji.aux))  409 words of node memory still in use:    3 hlist, 1 vlist, 1 rule, 2 glue, 3 kern, 1 glyph, 5 attribute, 48 glue_spec , 5 attribute_list, 1 write nodes    avail lists: 2:15,3:4,4:1,5:21,6:1,7:13,8:1,9:6 &lt;/usr/share/fonts/truetype/noto/NotoColorEmoji.ttf ! error:  (file /usr/share/fonts/truetype/noto/NotoColorEmoji.ttf) (ttf): sfnt  table not found !  ==&gt; Fatal error occurred, no output PDF file produced! Using exec and tee to redirect logs to stdout and a log file in the same time In a bash script, how can I redirect all standard outputs to a log file and tee the output on the screen using exec ?  log_file="$HOME/logs/install.txt-`date +'%Y-%m-%d_%H-%M-%S'`" [ -f "$log_file" ] || touch "$log_file" exec 1&gt;&gt; $log_file 2&gt;&amp;1   This code redirect all the log to the log file but not to the screen . The difference between try/catch/throw and try/catch(e)/throw e Can't resolve issue: iptables: No chain/target/match by that name How do I log into my Linux laptop if I have forgotten both the username and password?