How electron movement produces current,instead of having a slow drift speed?
How fast does electricity flow?
A real $2 \times 2 $ matrix $M$ such that $$M^2 =  \begin{pmatrix} -1&amp;0 \\ 0&amp;-1-\epsilon  \\   \end{pmatrix}$$ (a) exists for all $\epsilon &gt; 0$. (b) does not exist for any $\epsilon &gt; 0$. (c) exists for some $\epsilon &gt; 0$. (d) None of the above is true.  Attempt: I couldn't think of any theory base to prove / disprove the existence of such a matrix. Could someone please give me a hint on how to go about this problem? Thank you very much for your help in this regard. I am trying to monitor multiple JVMs running on different servers through an ssh tunnel.  Thanks to one of the UNIX gurus here, I have managed to get this running for a single server by:   Run jstatd on the target server Set up Visual VM to use 9696 as its socks proxy port. On my local PC, run:  ssh -L 2222:server1:22 bastion-host  On my local PC, run:  ssh -o port=2222 -D 9696 -L 1099:localhost:1099 localhost    This does the trick. Now when I try and tunnel to a second server I try:   On my local PC, run:  ssh -L 3333:server2:22 bastion-host  On my local PC, run:  ssh -o port=3333 -D 9696 -L 2099:localhost:1099 localhost    However, the last step complains with:  bind: Address already in use channel_setup_fwd_listener: cannot listen to port: 9696   Has anyone managed to do something similar?  Update:  The reason this is so complex is that jstatd is an RMI server application:    As with RMI applications, these register with an rmiregistry. Using rmi through a firewall requires me to use SOCKS as described here:    Unfortunately, visualvm only lets me set the SOCKS proxy port once, and the -D option won't allow me to forward the same local port to both servers... Is there a modal command for MakeLowercase? Analog to  question I've been wondering WHAT is to \lowercase as \bfseries is to \textbf? (... and for uppercase, or \MakeLowercase and MakeUppercase, etc., which also seem to be text-block commands as explained .)  Is there a "switch"/"declaration"/"modal command" (what is the correct term here?, is there a difference between them?) that would allow one to turn something into lowercase/uppercase in the same way that one would use \scshape for example, i.e., not as text-block command with the curly braces?  Or how to create such a command?  I couldn't find any clue on the forum. Consistent, complete, and generalized description of the quantum harmonic oscillator Currently I'm running Linux-3.0 and I want to update it to Linux-3.3.1 the latest stable kernel release as mentioned at . Can I update to 3.3.1 in Ubuntu without any risk of crashes? I'm updating my kernel regularly as provided by the Update Manager..Currently I have Linux-3.0.0.17..Can I update?  NOTE:  The latest kernel version any user is supposed to use in Ubuntu is updated automatically via the Update Manager, so no action is normally required by user regarding kernel upgrades. What the question author is referring to is mainline kernel, see: Elsevier article with APA references I'm writing an article for Elsevier Journal which follows APA6e references; everything is fine except that the article starts from page 2 leaving page 1 blank with just double hyphen (==) in the middle. Here is how I write.  \documentclass[preprint,12pt,authoryear]{elsarticle} \usepackage[natbibapa]{apacite} \usepackage{float} \usepackage{hyperref} \usepackage[ruled,vlined,commentsnumbered]{algorithm2e} \journal{Expert Systems with Applications}  \begin{document} \begin{frontmatter}  \bibliographystyle{apacite} \bibliography{myrefers}  \end{document}   How Can I rectify the problem? Residuals correlated positively with response variable strongly in linear regression Let $G$ be a group and $\{H_i\}_{i\in I}$ a family of subgroups. I would like to find a condition that will imply that $\cup_{i\in I} H_i$ is a subgroup. I know that it's not true in general, I need help to find this condition.  Any help is welcome.  Thanks a lot. How can I get my external IP address in a shell script? I need to find my external IP address from a shell script. At the moment I use this function:   myip () {      lwp-request -o text checkip.dyndns.org | awk '{ print $NF }' }   But it depends on perl-libwww, perl-html-format, perl-html-tree installed. What other ways can I get my external IP? Multiple runnable classes inside JAR, how to run them? Here is the problem:  Suppose that $*$ is an associative binary operation on a set $S$. Let  $$H:= \{a \in  S\mid a * x = x * a \mbox{ for all }x\in S\}.$$  In other words, $H$ is consisting of all the elements of $S$ that commute with every element in $S$.  Show that $H$ is closed under $*$. How to Start Web Mapping? I want to start working on a web map at work to map some of our statistics by city.    I have an idea, but I'm not exactly sure where to start.   Are there any definitive resources that provide step by step guidance on how to do this? How to make sure I'm not using any proprietary software after installation? I know I can check the currently installed non-free software with the following command (assuming aptitude is FOSS):  aptitude search '?installed (?section(restricted) | ?section(multiverse))'   And I can remove the "restricted" and "multiverse" sources (and not add any PPA's) to keep that list empty. I'm assuming from this point, whenever I apt install something, that something is either in the allowed sources or it is not found.  Is this enough? Does this make sure all software I'm running (in Ubuntu) is open-source? Occasionally, when I'm installing stuff, I get an error like the following:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  package1 : Depends: package2 (&gt;= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this? This is not a duplicate of this .  The linked question says that it suffices to show that if $(x_n)\to x$ then $(\frac{x_1+\cdots+x_n}{n})\to x$ to prove my question, but how so? I tried using the same strategy as how one proves that if $(x_n)\to x$ then $(\frac{x_1+\cdots+x_n}{n})\to x$, by "splitting" the product in th $N$th term:  $$\sqrt[n]{x_1x_2\cdots x_n}=\sqrt[n]{x_1x_2\cdots x_Nx_{N+1}\cdots x_n}=\sqrt[n]{x_1x_2\cdots x_N} \sqrt[n]{x_{N+1}\cdots x_n}$$  but it seems I can't use for now the definition of convergence of $(x_n)$ because of the $n$th root. I also tried to use a result: if $(x_n)\to x$ then $(\frac{x_n}{n})\to 1$ but don't know if this is true. Sadly I've had no real progress. Any help will be greatly appreciated, thanks in advance! Is it possible to browse a chatroom under invisible mode? E.g.  I know that I can browse the chat when I'm not logged on. But what if I am logged on and want to spare the inconvenience of logging off/multiple browsers? external variable in awk Calculate the area of an irregular cyclic convex polygon I have seen a few  here on Meta&nbsp;Stack&nbsp;Exchange that cover parts of this, but they are often too local, and none of them seem to cover all the relevant scenarios.  I will break it up into multiple parts in order to make this more specific:     When should I vote on a question:   What are the qualifications for a question to be deserving of being up-voted? When shouldn't I vote up on a question? What are the things that would cause a question to need to be down-voted?   How should I go about down-voting the question (do I wait a little while to give the OP a chance to change it, or do I down-vote it immediately)?  When shouldn't I vote down on a question?  When should I vote on an answer:   What are the qualifications for an answer to be deserving of being up-voted? When shouldn't I vote up on an answer? What are the thing that would cause an answer to need to be down-voted?   How should I go about down-voting the answer (do I wait a little while to give the OP a chance to change it, or do I down-vote it immediately)?  When shouldn't I vote down on an answer?  When should I vote on a comment:   While votes on comments do not affect reputation points, it might be useful to new users to know when to up-vote them.    It seems that a full, comprehensive list of these would be invaluable to new users looking to figure out how the voting system works, but this list seems to be missing from the meta site. After reinstalling TeXLive distribution (install-tl-20160318, Ubuntu 14.04), a issue occurs with the updated version of the titlesec package: the section numbering is lost.  What could it be missing? Is there a modification I have not seen?  Below is a MWE comparison of the two versions. The prevtitlesec package is a reinstall of the previous version (2011/12/15).  \documentclass{book} \usepackage[margin=2cm,a4paper]{geometry} %\usepackage{prevtitlesec}% 2011/12/15 version \usepackage{titlesec}% 2016/03/15 version \usepackage{lipsum}  \begin{document}  \chapter{Title of the first chapter} \lipsum[1] \section{A test section} \lipsum[4] \subsection{A test subsection} \lipsum[4] \subsection{A test subsection} \lipsum[4]  \end{document}   titlesec package 2011/12/15:    titlesec package 2016/03/15: