How to make a for cicle changing regex at each iteracion in javascript?
How do you use a variable in a regular expression?
The product of all the elements of a finite abelian group I'm trying to prove the following statements.  Let $G$ be a finite abelian group $G = \{a_{1}, a_{2}, ..., a_{n}\}$.   If there is no element $x \neq e$ in $G$ such that $x = x^{-1}$, then $a_{1}a_{2} \cdot \cdot \cdot a_{n} = e$.   Since the only element in $G$ that is an inverse of itself is the identity element $e$, for every other element $k$, it must have an inverse $a_{k}^{-1} = a_{j}$ where $k \neq j$. Thus $a_{1}a_{1}^{-1}a_{2}a_{2}^{-1} \cdot \cdot \cdot a_{n}a_{n}^{-1} = e$.   If there is exactly one $x \neq e$ in $G$ such that $x = x^{-1}$, then $a_{1}a_{2} \cdot \cdot \cdot a_{n} = x$.   This is stating that $x$ is not the identity element but is its own inverse. Then every other element $p$ must also have an inverse $a_{p}^{-1} = a_{w}$ where $p \neq w$. Similarly to the first question, a rearrangement can be done: $a_{1}a_{1}^{-1}a_{2}a_{2}^{-1} \cdot \cdot \cdot xx^{-1} \cdot \cdot \cdot  a_{n}a_{n}^{-1} = xx^{-1} = e$. And this is where I am stuck since I proved another statement.    Any comments would be appreciated for both problems. Installing debian package through Synaptic I want to install a .deb file. After going through various questions, I came across these three options: dpkg, GDebi and Ubuntu Software Center. However, I want to install the. Deb file via Synaptic Package Manager only. Is there any method by which I can install. Deb file as well as all it's dependencies via Synaptic Package Manager? What is this "answer your own question" jazz? I showed up here to write a perfectly normal rant about misaligned pixels, and there's a big fat checkbox cluttering up the "Ask" page:    WHAT THE EEEEK IS THIS NEW ABOMINATION? Understanding Join Attributes by Location in QGIS? I wonder if there is somewhere an explanation for the parameters that can be set when running the Algorithm "Join Attributes by Location" in QGIS 2.18.  I had a look here:       but there is no explanation. Any hints? Is it better in C++ to pass by value or pass by constant reference?  I am wondering which is better practice.  I realize that pass by constant reference should provide for better performance in the program because you are not making a copy of the variable. Here is a simple table.  I want to merge 4 cells. I want to combine the three "this" cells area in this table. I thought I have to use multirow and multicolum at same time. However, I could not find how to use it.  If possible, could you post the modified LaTeX source code?     My LaTeX code:  \documentclass{article} \usepackage{multirow}% http://ctan.org/pkg/multirow \usepackage{hhline}% http://ctan.org/pkg/hhline \begin{document}  \begin{table}[ph] \begin{center} \begin{tabular}{c|c|c|c|c} \hline \multirow{2}{*}{Raaa (k)} &amp; \multicolumn{4}{c}{C ()} \\ \hhline{~----}  &amp; 3.3 &amp; 2.5 &amp; 1 &amp; 0.5 \\ \hline \multirow{2}{*}{Raaa (k)} &amp; \multirow{2}{*}{this} &amp; this &amp; 0.5 &amp; 0.6\\ \hhline{~~~--}            &amp;                       &amp; this &amp; 0.7 &amp; 1.2 \\ \hline \end{tabular} \caption{R, C ripple size} \label{T:peak} \end{center} \end{table} \end{document} filling area between 2 functions, with shading Creating Text Elements using ArcPy? Is $x^x=y$ solvable for $x$? Given that   $x^x = y$; and  given some value for $y$   is there a way to expressly solve that equation for $x$? Javascript - Change html tag type Coming from a programming background, where should I start to learn web design? I'm a web developer mainly working in front end developing. My main fields are HTML5, CSS3 and Flash ActionScript 3.0.  Here in Iran, teamwork means nothing for most of the people, but I think it's the most important aspect of our work, especially in web design.   I have poor skills in graphic design and UI design. I always have to work with graphic designers for my websites. They are usually good and skilled designers. But they are all print designers and unfortunately they know nothing about the web and designing for it.  For example, one of the designers that I work with most of the time is a great designer and he won a couple awards for his logo and poster designs. However, he knows nothing about the web and most of my time is spent explaining to him how things work on the web, i.e. in what size he should work, using pixels instead of centimeters, and so on... After all he is a print designer, not a web designer. They often think everything is static and constant, not in motion.  So the best way to work around this is to improve my skills in graphical designing. I just want to be able to design good layouts, make good color selections, and etc for my websites. I do not want to design illustrations and do heavy graphical works. Just design websites with no Photoshop illustrations like posters and etc.  What do you do for your graphic works, and if you do them yourself, which books or references do you suggest I read? Where should I start? I'm practicing proofs and given the following statement:  Let $\Sigma$ be an alphabet, $\epsilon$ the empty word and $\sigma:\Sigma^{*}\rightarrow\Sigma^{*}$ an operation which for $a\in\Sigma$ and $w\in\Sigma^{*}$ is defined as $$\sigma(\epsilon)=\epsilon,\\\sigma(wa)=a\sigma(w).$$  I would like to prove through induction that $\sigma$ is equal to the word reversal operation $rev$ meaning that $\sigma(w)=rev(w)=w_{n}...w_{1}$ for every $w=w_{1}...w_{n}\in\Sigma^{*}$.  My suggestion is as follows:  For $w=\epsilon$ we have $$\sigma(w)=\sigma(\epsilon)=\epsilon=rev(\epsilon)=rev(w).$$  Let $w=xa$ with $x\in\Sigma^{*}$ and $a\in\Sigma$, then $$\sigma(x)=x_{n}...x_{1}=rev(x).$$  Thus we also have $$\sigma(w)=\sigma(xa)=\sigma(x_{1}...x_{n}a)=a\sigma(x_{1}...x_{n})=ax_{n}\sigma(x_{1}...x_{n-1})=...=ax_n...x_{1}=rev(x_{1}...x_{n}a)=rev(xa)=rev(w).$$  Does that constitute a correct and sufficient proof? If not, I would very much appreciate your feedback. Seriously, it was fun and all, but I can't and I don't want to stay married to the same woman for the rest of my life - one real life marriage is enough..  Is there a lawyer or process of some kind in the world of Skyrim, and if not, who could help me divorce her?  If all else should fail, (sigh), do I have to take her to the backyard, thwack her head with the shovel and dig a shallow grave? Expandably change letter case and use inside \csname, without a package I want to change the letter-case of a single character argument, and use that changed letter inside a \csname.  And I want to do it without an additional package.  For example, I want to pass a macro the letter {S}, and have it execute the macro \csname macros\endcsname, or pass it the letter {T}, and have it execute the macro \csname macrot\endcsname.    In my MWE, I show three approaches:   I didn't expect \lowercase to work, since I recall reading that it is not truly expanded until the last possible moment.  Surprisingly, it goes into an \edef okay, but it must not be truly expanded, because it breaks the \csname. I also formulated an approach where I used \numexpr to add 32 to the ASCII code of the argument and perform a \char upon that result.  Like \lowercase, it gives the appearance of being expandable, but it also fails inside the \csname. I finally achieve success with the stringstrings package.  Having written the package, I know the conversion was not pretty... essentially, it is an exhaustive 26-fold check of the form \if #1Aa\else\if #1Bb\else\if #1Cc\else...\fi\fi\fi, which has the virtue that it can be expandably placed into an \edef, and so it works.   There has to be a better way.  The MWE works only because I use the inefficiently calculated \tmp from METHOD 3 inside the \csname.  If I use \tmp from either of the two earlier methods, it breaks.  \documentclass{article} \usepackage{stringstrings} \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t} \newcommand\convert[1]{%   %MAKE THE ARGUMENT LOWER CASE   1) LOWERCASE\\   \edef\tmp{\lowercase{#1}}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   2) ASCII CONVERSION\\   \edef\tmp{\expandafter\char\numexpr`#1+32\relax}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   3) STRINGSTRINGS PACKAGE\\   \caselower[q]{#1}\def\tmp{\thestring}% WORKS BUT USES A PACKAGE   Here is the ``expanded'' conversion: \tmp\\   %   Now use it in a csname: \csname macro\tmp\endcsname% } \begin{document} \convert{S}\par \convert{T} \end{document}       SUMMARY OF ANSWERS:  I have added egreg's code snippets into this MWE to produce a document (and not just terminal output), showing the methods put forth to this point:  \documentclass{article}  %%%%%%%%%%%%%%%%%%%%%%%%%%%% L3 APPROACH  \usepackage{expl3}  \ExplSyntaxOn \cs_set_eq:NN \Xexplower \tl_expandable_lowercase:n \ExplSyntaxOff  %%%%%%%%%%%%%%%%%%%%%%%%%%%% EGREG'S LESS HACKY SOLUTION  \def\explowerchar#1{%   \ifcase\numexpr`#1-`A\relax    a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or l\or m\or    n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or y\or z\else    #1\fi }  \def\explower#1{%   \doexplowerchar#1\relax }  \def\doexplowerchar#1{%   \ifx#1\relax   \else     \explowerchar{#1}\expandafter\doexplowerchar   \fi }  %%%%%%%%%%%%%%%%%%%%%%%%%%%% STEVE'S HACKY PACKAGE APPROACH  \usepackage{stringstrings}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%  \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t}  \begin{document}  \textbf{Steve's hacky approach}  \caselower[q]{S}\csname macro\thestring\endcsname\par \caselower[q]{T}\csname macro\thestring\endcsname  \textbf{egreg's less hacky approach}  \edef\lcstring{\explowerchar{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\explower{T}}\csname macro\lcstring\endcsname  \textbf{L3 approach}  \edef\lcstring{\Xexplower{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\Xexplower{T}}\csname macro\lcstring\endcsname  \end{document} Why won't SparseArray let me store values with the head List? Where can I find historical data on arrival and departure times of a particular flight? Where can I find historical data on flights, specifically Delta international flights?  I need to find out about cancellations, diversions and any other flight data pertaining on particular route at a given time.  This source has to be official and stand up to legal scrutiny. How do you end with a single quote followed by a double quote? I have my A* pathfinding algorithm right now working such that given a graph it can find the route from one starting node to one goal node.   This works well for many problems, but sometimes I find that multiple goal nodes are valid.  For example, in a game, an NPC might have to go to a switch to shut a door. If there are multiple switches that shut the door in question, it doesn't matter which switch it goes to - it just needs to go to one of them.  How can I augment my pathfinding algorithm to find the path to the best goal (the shortest path)? As in, the algorithm searches for multiple goals and when it finds just one, it returns the path to that one.  One solution would be to run the algorithm as many times as there are valid goals, but you can guess why that might be inefficient. Use LaTeX to produce Epub If I have $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f$ is onto and $f\circ f\circ f = f$, how can I prove that $f$ is bijective? I know that I only have to prove that it is 1-to-1 because I'm given the fact that it's onto, but how can I use the fact that $f\circ f\circ f=f$ to prove that it is 1-to-1?  Thanks!