I simply want to use the \multimapboth symbol, which belongs to the \txfonts package; however I don't want to install this package, as it changes some formatting on my document... How can I do this? Thank you in advance.  EDIT: I'm looking for something like the answer to  question, just don't know how can I find more details about my symbol...
Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way?
Elliptic Curves of different forms Looking at  to find a safe curve, I find that most curves described here are of a different form from that generally used.  In , for example, FpCurves take curves of the form $y^2 = x^3+ax+b$ (Weierstrass), whereas the (safe) curves found on the above linked have different forms, such as $y^2 = x^3+ax^2+x$ (Montgomery) - how do I translate between the two? How do I use the second form of curve with, for example, Bouncy Castle?  (Or do I simply have to accept that no safe curves of the Fp form exist?)    What else have I tried? Guide to Elliptic Curve Cryptography (Hankerson et.al.) covers curves of the forms $y^2 = x^3+ax+b$ for fields with characteristic > 3, and only offer alternatives (that are not interchangable with the safe curves, either) for lower characteristics, that are not very useable in my situation. Even then, some curves on the safe curves website are of forms that I cannot immediately find explained anywhere. If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field. List sections of chapter at beginning of that chapter How can one have a mini table of contents for the current chapter appear just after the chapter name listing all sections of that chapter? Categorical Principal Component Analysis - using Count, Continuous, Ordinal variables together I have some variables and I want to reduce their number for further analysis. I initially thought of combining them using factor analysis. But since the variables are of all kinds (rating, count, ordinal, continuous dollar amount) I am thinking about using CATPCA for it. However, I have some questions about the technique -   Is CATPCA the right approach or Latent Class Factor Analysis would be the better one? By using the different kinds of variables together - how will the object scores be interpreted? For example - The rating question is on a 10 point scale but the dollar amount ranges from 0 to 1000s, so what will the object score obtained after CATPCA represent? And is it comparable to the Factor Score obtained from traditional PCA? For ordinal variables - Do all of them need to be in the same form, e.g. 1 meaning lowest and 10 meaning highest? Or can they be used in whatever form they are? Is it good to categorize the count and continuous variables based on their distribution and then treat then as ordinal/categorical variables?   I would highly appreciate any help you can provide! My computer is loud: How do I tell which fan is the issue? On my new computer, my fan(s) is/are plain LOUD! Using SpeedFan, I find that my temps are all under 32 degrees C under my normal use (IDK how accurate that is but the CPU itself says 27 C).  The fan doesn't sound unbalanced and it isn't making sounds in rhythm (Not the usual rrrrrrrRRRRRR... rrrrrrrRRRRRR... rrrrrrrRRRRRR... rrrrrrrRRRRRR), just a constant fan. I am thinking about oiling the fans, but I can't decide if it is the PSU fan or a case fan or the CPU fan. If it's the CPU fan I will most likely just replace that with a quiet fan. How can I tell which fan is making the noise (if not multiple)?  One thing that I am thinking may be the problem is my CPU fan isn't PWM so would swapping that out help? There is no "linear voltage" or etc thing in BIOS so I think it may be running at full speed. Also, I could have too much airflow because it is also making a whistling noise that you can hear close to it that sounds like when I accedentially put part of the side cover over my floor vent to get it out of the way. Further customize color of hyperref links I have tried to find a way to customize how internal links are colored, but I don't yet have the expertise in finding and redefining commands. In the LaTeX example below, I describe how I would like to change the colors of various links. Any ideas or examples are much appreciated.  \documentclass{article}  \usepackage[backref=true]{biblatex} \begin{filecontents}{refs.bib} @book{cit1, title = {The backreferences should be yellow}, author = {Last, First} } \end{filecontents} \bibliography{refs.bib}  \usepackage{color} \usepackage[usenames,dvipsnames,svgnames,table]{xcolor} \usepackage[colorlinks=true,             linkcolor=red,             urlcolor=blue,             citecolor=gray]{hyperref}  \begin{document}  \title{Title} \maketitle \tableofcontents \listoffigures  \section{Table of content's links should be green} \label{s1} All text, captions, and section headers after the list of figures should be black. The citation links should be gray.\autocite{cit1} \subsection{Table of content's subsections links should be orange} Internal links like this section link \ref{s1}  or this figure link \ref{f1} should be blue.  \begin{figure}[h] \caption{List of figures links red} \label{f1} \end{figure}  \printbibliography  \end{document} How to run .sh script with keybind Sorry if this is very basic but here's a question.   Let $\mathbf{v}=(v_1,\ldots, v_n)\in k^n$ where $k=\bar{k}$.      Why do we have   $$ \sqrt{\sum_{i=1}^n |v_i|^2} \leq \sum_{i=1}^n |v_i|,  $$   where the left-hand side can be thought of as the $2$-norm $\|\mathbf{v}\|_2$ on $L^2(k^n)$?   $\mathbf{General \; case}$: If this is true for $p=2$-norm, I am guessing that this is true for all $p\geq 1$:  $$ \left( \sum_{i=1}^n |v_i|^p\right)^{1/p}\leq \sum_{i=1}^n |v_i|.  $$     In fact, does this inequality hold when $p$ is a rational number? How do I show that:  $$\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$$  This is actually problem B $4371$ given at this . Looks like a very interesting problem.   My attempts: Well, I have been thinking about this for the whole day, and I have got some insights. I don't believe my insights will lead me to a $\text{complete}$ solution.   First, I wrote $\sin\frac{5\pi}{14}$ as $\sin\frac{9 \pi}{14}$ so that if I put $A = \frac{\pi}{14}$ so that the given equation becomes, $$\frac{1}{\sin^{2}{A}} + \frac{1}{\sin^{2}{3A}} + \frac{1}{\sin^{2}{9A}} =24$$ Then I tried working with this by taking $\text{lcm}$ and multiplying and doing something, which appeared futile. Next, I actually didn't work it out, but I think we have to look for a equation which has roots as $\sin$ and then use $\text{sum of roots}$ formulas to get $24$. I think I haven't explained this clearly.         $\text{Thirdly, is there a trick proving such type of identities using Gauss sums ?}$ One post related to this is:  I don't know how this will help as I haven't studied anything yet regarding Gauss sums. Server 2012 Core (no GUI): Remote Server manager not working I am trying cmd --> MMC --> Server Manager and then connecting to my Server 2012 no GUI  but i keep getting the following error The WinRM client cannot process the request  I am unable to upload images right now  This is not related to other post "How to Remote Manage Windows Server 2012 in Server Manager?" because title and description of that post is quite different from what i am asking What is the 'Badlock Bug'? A user on the Ask Ubuntu General Room posted a link to . After some googling around, all I can find is that it is a mysterious security bug, that uses the same website template as Heartbleed.  I manage Linux Servers, a mysterious security bug does not sit well with me. What exactly is it, and how can I protect my servers from it? Indefinite integral $\int(\sin x)^2/(x\cdot\cos x-\sin x)^2\,dx$ How to find the antiderivative of $\dfrac{(\sin x)^2}{(x\cdot\cos x-\sin x)^2}$? I know that series theory can solve the problem. But I wish to solve the problem by the antiderivative way. The numerator and denominator divide the $x^2$ at the same time, don't they? I have been using Ubuntu 12.04 for quite a while and have never had a problem come at me out of the blue like this. I'm trying to install python 3.2 on my Ubuntu system and every time I run the code to compile the python source, I get this error:  'Command 'sudo' is available in '/usr/bin/sudo' The command could not be located because '/usr/bin' is not included in the PATH environment variable. sudo: command not found'   I've also tried running gksudo command to view what my environment shows but I pretty much get the same error. Current code is:  \begin{enumerate}[label=LEVEL \arabic{*},leftmargin=*]     \item Description of Level 1 \quad L1 \\ \emph{more text}     \item Description of Level 2 \quad L2 \\ \emph{more text}  \end{enumerate}   but the \quad does not align L1 and L2 uniformly vertically. I want to replace \quad with a tab but the tabbing environment does not allow mixing with an enumerate! How to derive this binomial identity? Can I install Microsoft Office? If so, how? I want to know how to install Microsoft Office (specifically, Microsoft Office 2010) in Ubuntu?   I am a die hard fan of MS Office and I want to know if there is a way I can use it in Ubuntu. How can I apply a -p0 patch from any working directory? Almost sure convergence of the Poisson process Let $N = \{N(t) \}_{t\geq 0 }$ be a Poisson process. I already know that $N(t)- \lambda t$ is a martingale where $\mathbb{E} [ N(t) ] = \lambda t$.   I want to prove that $$ \frac{N(t)}{t} \rightarrow \lambda, \quad t \rightarrow \infty \quad \text{ a.s.}. $$  To prove this I received a hint that I should use the martingale law of large numbers which states that:  Theorem: (Martingale LLN)  Let $S= (S_n = \sum_{k=1}^n X_k)_{n=1,2,\ldots}$ be a martingale with respect to the filtration $(\mathcal{F}_n)_{n=1,2,\ldots}$. Then $\sum_{k=1}^n X_k/k$ converges almost surely on the set $\left\{ \sum_{k=1}^\infty k^{-2} \mathbb{E}\left[ X_k^2 \mid \mathcal{F}_{k-1} \right] &lt; \infty \right\}$. Hence $S_n/n \rightarrow 0$ a.s. on the same set.  Now to use this theorem I think I need to use Doob-Meyer to decompose $N(t)$ as the sum of a martingale and an increasing process. Which would be the martingale $M(t) = N(t) - \lambda t$ and increasing process $A(t) = \lambda t$. But how is $M(t)$ the sum of a martingale? And I do not know how this exactly relates to the thing I have to prove. Thanks for any help. Essentially, I have a csv file that contain multiple columns, called cols.csv  1,a,100 2,b,200 3,c,300 4,e,400   and I have a new csv file that has one column, called col.csv  f g h i   I want to copy the items in col.csv and append them to the end of each line in cols.csv so that, cols.csv now contains those  1,a,100,f 2,b,200,g 3,c,300,h 4,e,400,i   is that possible at all? i tried join, paste, nothing worked I am moving from Egypt to the Netherlands and I need to take my PC with me. I won't be taking the monitor, just the case, but I'm wondering what the best way would be.  Am considering taking it as carry-on because I'm allowed 8kg and at least then I can handle it myself. Has anyone done this before and can give me tips or warn me that this doesn't work? Would putting it in my normal suitcase as checked baggage be a better idea?