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Rule of thumb for choosing an implementation of a Java Collection? Anyone have a good rule of thumb for choosing between different implementations of Java Collection interfaces like List, Map, or Set?  For example, generally why or in what cases would I prefer to use a Vector or an ArrayList, a Hashtable or a HashMap? Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$ I am trying to prove the above with the conditions that N is normal to G and $G/N$ is abelian.  So then for $Na,Nb\in{G/N}, NaNb=NbNa$.  But $NaNb=Nab=Nba$, so then we know $ab=ba$, so G is abelian.  So if $ab\in{G}, N=abN(ab)^{-1}=abN(ba)^{-1}=baNa^{-1}b^{-1}....$ and i'm getting lost... How to find out the terminal command of an application? I want to use some applications shown on the Unity Launcher in a terminal, but I need to know the appropriate command to run them. How can I achieve that? What command(s) would you use to extract all of the usernames from a database called /etc/passwd and then sort this output alphabetically in reverse order? KDB: apply dyadic function across two lists In classical statistics, there is a definition that a statistic $T$ of a set of data $y_1, \ldots, y_n$ is defined to be complete for a parameter $\theta$ it is impossible to form an unbiased estimator of $0$ from it nontrivially. That is, the only way to have $E h(T (y )) = 0$ for all $\theta$ is to have $h$ be $0$ almost surely.   Is there a intuition behind this? Is seems like a rather mechanical way of defining this, I am aware this has been asked before, but was wondering if there was a very easy to understand intuition that would make introductory students have an easier time digesting the material. TL2018 (MacTeX) and TikZ calligraphy library How can I modify title page so that it looks like it is in  video. Please seek to 16 seconds and watch title page. I do not have permission to post images. I liked this theme and I want to make a beamer theme that looks similar. I tried with beamercolorbox but I failed to position the box to the bottom.      Edit: Here is my minimum working example  \documentclass[xcolor=dvipsnames]{beamer} \defbeamertemplate*{title page}{customized}[1][] { \usebeamerfont{subtitle} \usebeamercolor[fg]{subtitle}  {\flushright \setbeamercolor{author}{bg=white,fg=Red} \usebeamerfont{author} \insertauthor\par \usebeamerfont{institute}\insertinstitute\par }  \vspace{0.2in}  \setbeamercolor{postit}{fg=white,bg=YellowOrange}  \begin{beamercolorbox}[sep=1em,wd=1.062\textwidth,ht=3cm,dp=3cm,right]{postit} \usebeamerfont{title} {\huge \inserttitle}\par \usebeamerfont{subtitle} {\insertsubtitle} \end{beamercolorbox} } \usecolortheme[named=YellowOrange]{structure} \useoutertheme{infolines} \setbeamertemplate{navigation symbols}{}  \institute{Harvard College Professor and\\ Johnstone Family Professor in Psychology, Harvard University}  \title{SAY WHAT?} \subtitle{Linguistics as a Window to\\ Understanding the Brain} \author{Steven Pinker}  \begin{document} { \setbeamertemplate{footline}{} \begin{frame} \titlepage \end{frame} } \end{document} I have a ASUS R500A notebook.Original OS is Windows 7 64bit.Few days ago I tried to Install Windows 8.1 64 bit version.But it failed &amp; error message is,     windows cannot be installed on this disk. The selected disk is of the GPT partition style.   My Steps: First i Deleted C: Partition ( Already installed windows 7 ). Then i Formatted that partition. Tried to install Windows 8.1 64bit.  In this hard disk i have another several partitions with Important data.  How do i Install Windows 8.1 without loosing Data from the Other partitions ? If I use  two different router in the same network while both are running in the default router mode then we can access the setup page or setup interface from browser just by IP address of corresponding router. But when I use one of the router as repeater then I can only enter the setup page of the router which is running in router mode. Why router's setup page cannot be accessed when using the router as repeater? Now how can I change the settings of the router in repeater mode? The only way is to reset router with the hardware key then setup again. I want to prove or disprove this problem: If there exist $\lim\limits_{x\rightarrow \infty} (f'(x)+f(x))=L&lt;\infty$ then $\lim\limits_{x\rightarrow\infty} f(x) =L$.  When I assume problem below:  If there exist $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L&lt;\infty$, There exists $\lim\limits_{x\rightarrow\infty} f(x)$?  I can use mean-value theorem to show that.  So my question is:     If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x))=L&lt;\infty$, does $\lim\limits_{x\rightarrow\infty} f(x)$ exist? How do I force TeX to completely use the 1st column? How do I force TeX to completely use the 1st column before writing to the second column?  Right now I dont have enough content to fill one whole page. So the left and right columns are equally filled, leaving 25% symmetrical empty page at bottom. How do I fill the left column first, and then the right?  \documentclass{article}  \usepackage{multicol} \usepackage[scale=0.9]{geometry} \usepackage{amssymb} \renewcommand{\labelitemi}{\tiny$\blacksquare$} \begin{document} \begin{multicols}{2}      %lots of text goes here  \end{multicols} \end{document} I've been dealing with this problem for almost 2 hours now, with hardly any progress. I'm to prove the following inequality using induction   $$\sqrt[n+1]{n+1}&lt;\sqrt[n]{n}$$ where $n≥3$, $n∈\mathbb{N}$. How can this be done? Show that there's no continuous function that takes each of its values $f(x)$ exactly twice. I need to prove the following:  There's no continuous function $f:[a,b]\to \mathbb{R}$ that takes each of its values $f(x)$, $x\in [a,b]$  exactly twice.  First of all, I didn't understand the question. For example $x^2$ takes $1$ twice, in the interval $[-1,1]$. Is it saying that it does not occur for all $x$ in the interval? But what about $f(x) = c$? Is it saying that it does not occur only exactly $2$ times, then? I have no idea about how to prove it. I know that for $f(x)$ such that $f(a)&lt;f(x)&lt;f(b)$, if $f$ is continuous then there is a $c\in [a,b]$ such that $f(c) = f(x)$.  Now, there's the following proof in my book and I really wanted to understand it, instead of just getting a new proof  Since the interval $[a,b]$ has only $2$ extreme points, then the maximum or minimum of $f$ must be in a point $c\in int([a,b])$ and and in another point $d\in [a,b]$. Then, there exists $\delta&gt;0$ such that in the intervals $[c-\delta, c), (c,c+\delta)$ (and if $d$ is not extreme of $[a,b]$, $[d-\delta, d]$) the function takes values that are less than $f(c) = f(d)$. Let $A$ be the greatest of the numbers $f(c-\delta), f(c+\delta), f(d-\delta)$. By the intermediate value theorem, there are $x\in [c-\delta, c), y\in (c, c+\delta]$ and $z\in [d-\delta, d)$ such that $f(x)=f(y)=f(z)=A$. Contradiction.   Well, why the last part? Why is it that I can apply the intermediate value theorem to these values? For example, $&lt;f(c-\delta)&lt;p&lt;f(c)$, then by the theorem I know that there exists $m\in [c-\delta, c)$ such that $f(m) = p$. Same for the other intervals. But what guarantees thhat the greatest of the values between  $x\in [c-\delta, c), y\in (c, c+\delta]$ will be inside the intervals $[c-\delta), c), (c,c+\delta), [d-\delta, d)$? Laplace transform of $1/t$ How can I make something that looks like this?  --------   Text   ---------  where the horizontal rules extend to the margin on either side? 80's Animated movie: An old man joins mission to save a boy stranded on a hostile world What do you call something that is not first in a sequence? Is there a word to describe something that is not the first element in a sequence, but can be in any other position? A synonym of "not first", in fact.     This element is __ in this sequence. How do I use an NBT editor to modify item properties? problem with using loop inside the tabular environment