Graphs for complex numbers
Plotting in the Complex Plane
I'm trying to show that if $f$ is a continuous function on $[0,1]$ and $\int_0^{1} f(x)e^{nx}\,{\rm d}x = 0$ for all $n = 0, 1, 2, \dots$, then $f(x) = 0$.  I'd like to use Weierstrass approximation theorem to find a sequence of polynomials $p_m$ that converge uniformly to $f(x)$. Then we could say $\lim\limits_{m\to \infty} \int p_m(x)e^{nx}\,{\rm d}x = \int f(x)e^{nx}\,{\rm d}x = 0$, but I'm struggling to deduce that then all the $p_m$ are zero which would give the result. A better serial voting trap According to the , you can harden a MySQL server by adding passwords, or removing the anonymous accounts.      If you want to prevent clients from connecting as anonymous users   without a password, you should either assign a password to each   anonymous account or else remove the accounts.   Before hardening, my users table looked like this.   mysql&gt; select user,host,password from mysql.user; +------------------+-----------+-------------------------------------------+ | user             | host      | password                                  | +------------------+-----------+-------------------------------------------+ | root             | localhost | *F3A2A51A9B0F2BE246XXXXXXXXXXXXXXXXXXXXXX | | root             | gitlab    |                                           | | root             | 127.0.0.1 |                                           | | root             | ::1       |                                           | |                  | localhost |                                           | |                  | gitlab    |                                           | | debian-sys-maint | localhost | *95C1BF709B26A5BAXXXXXXXXXXXXXXXXXXXXXXXX | | myuser           | localhost | *6C8989366EAF75BB6XXXXXXXXXXXXXXXXXXXXXXX | +------------------+-----------+-------------------------------------------+   I've remove all anonymous accounts, so that the user table now looks like this.  (I'm using puppet to manage the users, but puppet effectively performs a DROP USER command).   mysql&gt; select user,host,password from mysql.user; +------------------+-----------+-------------------------------------------+ | user             | host      | password                                  | +------------------+-----------+-------------------------------------------+ | root             | localhost | *F3A2A51A9B0F2BE246XXXXXXXXXXXXXXXXXXXXXX | | debian-sys-maint | localhost | *95C1BF709B26A5BAXXXXXXXXXXXXXXXXXXXXXXXX | | myuser           | localhost | *6C8989366EAF75BB6XXXXXXXXXXXXXXXXXXXXXXX | +------------------+-----------+-------------------------------------------+   Why is it that I am still able to login to my test system without a username or a password? What do I need to do to prevent any unwanted users from logging in?   root@gitlab:~# mysql Welcome to the MySQL monitor.  Commands end with ; or \g. Your MySQL connection id is 98 Server version: 5.5.32-0ubuntu0.12.04.1 (Ubuntu) .... mysql&gt;    Update:  I've also just discovered that I can login as root, without entering a password.  Update2: I found  which has some good information, but does not solve the issue.   There are no anonymous users.  mysql&gt; select user,host,password from mysql.user where user=''; Empty set (0.00 sec)   I login as root@localhost.  mysql&gt; select USER(),CURRENT_USER(); +----------------+----------------+ | USER()         | CURRENT_USER() | +----------------+----------------+ | root@localhost | root@localhost | +----------------+----------------+    I do not have a default password, or skip-grant-tables defined in my.cnf  root@gitlab:~# cat /etc/mysql/my.cnf |grep -i 'skip-grant-tables'|wc -l 0 root@gitlab:~# cat /etc/mysql/my.cnf |grep -i 'pass'|wc -l 0   Update3:  I have tried performing these steps with puppet, (which should perform a flush privileges automatically). I have also manually flushed privileges and also tried restarting mysql.   Update4: I've also tried changing the mysql root password and flushed privileges. No luck, I can still log in as any user without a password. I am drawing a 3D array like the attached picture, which actually describes a multidimensional array. However, I can not put the name of the axis and take the value from the matrix like the attached picture.  This is the code that I have:  \documentclass[margin=5mm]{standalone} \usepackage{tikz} \usetikzlibrary{matrix,calc}  \begin{document} \begin{tikzpicture}[every node/.style={anchor=north east,fill=white,minimum width=1.4cm,minimum height=7mm}] \matrix (mA) [draw,matrix of math nodes] { (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ };  \matrix (mB) [draw,matrix of math nodes] at ($(mA.south west)+(1.5,0.7)$) { (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ };  \matrix (mC) [draw,matrix of math nodes] at ($(mB.south west)+(1.5,0.7)$) { (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ };  \draw[dashed](mA.north east)--(mC.north east); \draw[dashed](mA.north west)--(mC.north west); \draw[dashed](mA.south east)--(mC.south east); \end{tikzpicture}   \end{document} "Calling dibs" - what does it imply? The term "to have dibs on something" or "to call dibs on something" plays a recurring role in American film and television (e.g. ), so it gets exported a lot.   describes "dibs" as     [...] a common, "informal" convention to reserve or declare full or partial ownership of a community resource, such as a chair [...]   From the usages in the media I have seen, this convention also seems to contain some moral concept which is not described in dictionaries. For me, it looks like by calling dibs (or ), the caller actually receives the (implicit, moral) right to that resource, and this typically goes undisputed by their rivals.  Can you confirm the existence of this concept? Is this something that varies between groups of people (or maybe between regions), or is there a concensus on how to respond to this? Java Manifest.mf classpath issues I've been trying to run a jar file - let's call it test.jar - that uses the Sybase jconn3.jar on a Unix system.  I have created a MANIFEST.MF file that has the following:  Class-Path: $SYBASE/jConnect-6_0/classes/jconn3.jar commons-net-1.3.0.jar   This gives a ClassNotFoundError. $SYBASE is the system variable that points to /opt/sybase13; I've also tried the following:  Class-Path: /opt/sybase13/jConnect-6_0/classes/jconn3.jar commons-net-1.3.0.jar   and  Class-Path: opt/sybase13/jConnect-6_0/classes/jconn3.jar commons-net-1.3.0.jar   However, if I copy the jconn3.jar file from the $SYBASE/jConnect-6_0/classes to the same directory as test.jar, and update my MANIFEST.MF to read as follows:  Class-Path: jconn3.jar commons-net-1.3.0.jar   The application runs as expected.  Now, I've been able to verify the jconn3.jar file works by copying it locally; my MANIFEST.MF file includes the path to my Main-Class, so that's not at issue here.  What do you think could be the problem? I've been looking at this thing for too long now. Thanks! Running out of inodes Why doesn't the frequency of light change during refraction? Word for an event that will likely never happen again I've read , but none of them are what I am looking for. I once read a book that used a word to describe an event that has happened in the past, but the odds were so astronomical that it will likely never happen a second time. The context I read these words in were the creation of the first life on earth (without any theological ideas). Basically, the text said that the scenario for the creation of the first living organism happened on a planet where conditions were just right by complete chance, and that the odds of this were so astronomical that it would likely never happen again anywhere in the universe over any length of time.  Sample sentence: "The creation of the first organisms was incredibly unlikely, the event can be called a _________ event, or an event that will likely never happen again."   I can't pretend to understand the validity of the claims by the text, but the words they used to describe these events were quite clever (and scientific sounding) that it would make a fun hyperbole.  I thought it was something along the lines of singularity event, but that doesn't sound quite right. Winter Bash 2014 Secret Hats Is there a term for when just by saying that something is broken and showing it to someone fixes the issue? This seems to be a common enough occurrence that it would merit its own phrase. I imagine it might be some sort of subset of Murphy's Law. But it's specific enough that Murphy's Law doesn't quite address it.  Do you know when you are banging your head against a wall for hours trying to fix something? And then when you finally give up and try to get someone else to come fix it (or even just look at it to see that it's broken), it's working perfectly as if nothing had ever happened? And at this point, you're just trying to convince the other person that it was broken in the first place.  It'd at least take some of the frustration out of the experience if you could both just laugh about &lt;insert the phrase for it here&gt;. But as it is now, I basically have to go through the whole paragraph above to say it, and at that point the joke is kind of lost. I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course, it's always good to give as much intuition about the material.  Some things I'd be happy if it includes (but again, it mostly just needs to be a clear book even if it doesn't contain these) are:   As much justifications for the postulates if possible, I'm very interested in reading more about how Liouville's theorem connects to the postulates. Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas. What exactly does Perl's "bless" do? I understand one uses the "bless" keyword in Perl inside a class's "new" method:  sub new {     my $self = bless { };     return $self; }       But what exactly is "bless" doing to that hash reference ? SEO Removal Time? I was searching about removing the a domain/site being listed in Web Search Results (like, Google Search) and i found solution, .  I believe it will be the solution but what i still need to know is:   How long will it take to bring down my Website being listed from Search Engine Results? Labeling Multiple Equations Per Row of a Table I am trying to create a table with two columns of independently labelled equations (1-6). Unfortunately, everything I have found so far either has not worked or would number them as sub-equations (1a, 1b, etc).  My current attempt is:  \documentclass{article} \usepackage{graphicx, verbatim, tabularx} \usepackage{amsfonts} \usepackage{amsmath, amssymb}  \newcommand{\grad}{\vec{\nabla}}       \newcommand{\prtl}[2]{\frac{\partial #1}{\partial #2}}  \newcommand{\curl}{\grad\times} \begin{document}  \begin{tabular}{p{5cm}p{5cm}}  $\curl\vec{E} = -i\omega\mu\vec{H}$ &amp;   $\curl\vec{H} = i\omega\mu\vec{E}$ \\  \begin{equation}  \label{eq:curlHx}   \prtl{E_z}{y} +\gamma E_y= -i\omega\mu H_x  \end{equation}  &amp;  \begin{equation}  \label{eq:curlEx}    \prtl{H_z}{y} +\gamma H_y= i\omega\mu E_x  \end{equation}\\  \begin{equation}  \label{eq:curlHy}    -\prtl{E_z}{x} -\gamma E_x= -i\omega\mu H_y  \end{equation}  &amp;  \begin{equation}  \label{eq:curlEy}    -\prtl{H_z}{x} -\gamma H_x= -i\omega\mu E_y  \end{equation}  \\  \begin{equation}  \label{eq:curlHz}   \prtl{E_y}{x}-\prtl{E_x}{y} = -i\omega\mu H_z  \end{equation}  &amp;  \begin{equation}  \label{eq:curlEz}    \prtl{H_y}{x}-\prtl{H_x}{y} = -i\omega\mu E_z  \end{equation}  \end{tabular}  \end{document}   Is there an environment other than tabular that would make this work? Tabularx came close (got the numbering correct), but the formatting/spacing was horrific. How do I prevent and/or handle a StackOverflowException? I would like to either prevent or handle a StackOverflowException that I am getting from a call to the XslCompiledTransform.Transform method within an Xsl Editor I am writing. The problem seems to be that the user can write an Xsl script that is infinitely recursive, and it just blows up on the call to the Transform method.  (That is, the problem is not just the typical programmatic error, which is usually the cause of such an exception.)  Is there a way to detect and/or limit how many recursions are allowed?  Or any other ideas to keep this code from just blowing up on me? Finding my house in minecraft "Writ large", "Writ small", and others I have seen this used with other words besides "large" and "small".  What other words can be used? Can this structure be used more generally with other adjectives? Protect .NET code from reverse engineering? Obfuscation is one way, but it can't protect from breaking the piracy protection security of the application. How do I make sure that the application is not tampered with, and how do I make sure that the registration mechanism can't be reverse engineered?  Also it is possible to convert a C# application to native code, and  is too costly.  C# provides lot of features, and is the ideal language for my code, so writing the whole codebase again in C++ is out of the question.  Secure certificates can be easily removed from the signed assemblies in .NET. Let's stop displaying a user's accept rate My feature request (or anti-feature-request perhaps) is the following: Let's stop displaying a user's accept rate.  For those of you who know "Fawlty Towers", the whole issue of a visible accept rate and our behavior towards it starts to feel like .   We generally seem to agree that harassing a user about it is not appropriate and that our decision to answer a question should not depend on it, yet we display it in varying terrorist-threat-levels of color. Yes dear users, please don't pay any attention to the brightly orange colored percentage you see there. And whatever you do, don't bring it up.  But as long as you're displaying the accept rate, people will comment on it, criticize users for it and possibly reconsider answering because of it. And while I'm of the opinion that a low accept rate should not stop you from answering (we're here to make the internet better after all) and that the possible reputation gain (or lack thereof) should not factor in either, I can't blame users for considering it. It's in their face after all. And we're only people.   So let's take the issue off the table. Or at least partially. Information about a user's acceptance behavior can still always be gathered from the profile. But at least that would be less in-your-face.   "But it helps me to see if a user is a help vampire!" I'm still wondering if those are of the sparkly variety as well, but I digress. So what? If the question is bad, downvote it. Evaluate a question on its individual value. There is no need to take a user's history into account. There might be a correlation between the quality of a question and a user's accept rate, but there doesn't have to be. And if there is, the bigger problem is the question's quality.  "Exactly! A user with a low accept rate might indicate there's a problem!" I'm not arguing we should get rid of the accept-rate value within SO/SE. After all, this Q&amp;A works based on up and downvotes, as well as the acceptance of an answer. But why not use it behind the scenes to (very occasionally) nudge the user with a statement like:      "You have received several answers to your questions, yet have not accepted an answer as correct or helpful in a while. You might want to evaluate them and where possible ".    After all, in the various questions with regards to comments on low accept rates, if any comments are encouraged at all, then they are of this soft variety. So why not let the system take care of that?  I feel this would take the whole issue of accept rate off the table, while still providing the user with the information he might have missed or needs. (As a bonus, it would reduce the frequency with which the topic is brought up here on Meta) And those users who would ignore this information are most likely not convinced by a displayed percentage either.