How to make an empty list inside a module program? It consatly spews errors
Is there a guideline about when to end expressions with semicolons?
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ How can the contact point of rolling body have zero velocity? They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion? Assume that $X$ and $Y$ are two random variables such that $Y=E[X|Y]$ almost surely and $X= E[Y|X]$ almost surely. Prove that $X=Y$ almost surely.   The hint I was given is to evaluate: $$E[X-Y;X&gt;a,Y\leq a] + E[X-Y;X\leq a,Y\leq a]$$  which I can write as: $$\int_A(X-Y)dP +\int_B(X-Y)dP$$ where $A=\{X&gt;a, Y\leq a\}$ and $B=\{X\leq a,Y\leq a\}$.  But I need some more hints. How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access? What limits a motherboard from supporting more memory? My specific question is with the ASUS M3N78-VM motherboard that my home server uses. I currently have 4x2GB installed for a total of 8GB but I was hoping to upgrade to say 16GB (4x4GB). The official specifications of that motherboard says it only supports up to 8GB but it was released back when only 2GB sticks were available. What, if any, would prevent it from working with 4GB sticks now that 4GB sticks are available?  My general question is with motherboards in general... what would prevent a motherboard from working with bigger sticks if its all just the same type (DDR2 for example and same speeds) of memory? Connect two computers with SSH in a home LAN I have two ubuntu computer shared the same wifi and desire to reach another from one's terminal.  First create an user on the second computer named "Second" and hostname "Algorithms"    Then tried to reach it from the other with SSH,  but get error report as   $ ssh second@Algorithms   ssh: Could not resolve hostname algorithms: nodename nor servname provided, or not known   The solution I tried is based on   What's the problem with my experiment? MacTEX-2014, TeXShop 3.36.1 on Mac OS 10.9.5 -- when using hyperref I do not see the colored border that should appear around the hyperlinks in the pdf.  for example, when compiled with pdflatex, the code below should produce a pdf with a green border around the link on the right of "abc", but it does not. Any idea how to check where the problem is?  \documentclass{article} \usepackage{hyperref} \hypersetup{colorlinks=false,pdfborder=0 0 1,citebordercolor={0 1 0}} \begin{document}  abc \cite{123}  \begin{thebibliography}{99} \bibitem{123} efg \end{thebibliography} \end{document}    this is the list of files from the generated .log     File List   article.cls    2007/10/19 v1.4h Standard LaTeX document class   size10.clo    2007/10/19 v1.4h Standard LaTeX file (size option)   hyperref.sty    2012/11/06 v6.83m Hypertext links for LaTeX   hobsub-hyperref.sty    2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO)   hobsub-generic.sty    2012/05/28 v1.13 Bundle oberdiek, subset generic (HO)     hobsub.sty    2012/05/28 v1.13 Construct package bundles (HO)   infwarerr.sty    2010/04/08 v1.3 Providing info/warning/error messages (HO)    ltxcmds.sty    2011/11/09 v1.22 LaTeX kernel commands for general use (HO)   ifluatex.sty    2010/03/01 v1.3 Provides the ifluatex switch (HO)     ifvtex.sty    2010/03/01 v1.5 Detect VTeX and its facilities (HO)    intcalc.sty    2007/09/27 v1.1 Expandable calculations with integers (HO)      ifpdf.sty    2011/01/30 v2.3 Provides the ifpdf switch (HO)   etexcmds.sty    2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)   kvsetkeys.sty    2012/04/25 v1.16 Key value parser (HO)   kvdefinekeys.sty    2011/04/07 v1.3 Define keys (HO)   pdftexcmds.sty    2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO)   pdfescape.sty    2011/11/25 v1.13 Implements pdfTeX's escape features (HO)   bigintcalc.sty    2012/04/08 v1.3 Expandable calculations on big integers (HO)     bitset.sty    2011/01/30 v1.1 Handle bit-vector datatype (HO)   uniquecounter.sty    2011/01/30 v1.2 Provide unlimited unique counter (HO)   letltxmacro.sty    2010/09/02 v1.4 Let assignment for LaTeX macros (HO)    hopatch.sty    2012/05/28 v1.2 Wrapper for package hooks (HO)   xcolor-patch.sty    2011/01/30 xcolor patch   atveryend.sty    2011/06/30 v1.8 Hooks at the very end of document (HO)   atbegshi.sty    2011/10/05 v1.16 At begin shipout hook (HO)   refcount.sty    2011/10/16 v3.4 Data extraction from label references (HO)    hycolor.sty    2011/01/30 v1.7 Color options for hyperref/bookmark (HO)     keyval.sty    2014/05/08 v1.15 key=value parser (DPC)    ifxetex.sty    2010/09/12 v0.6 Provides ifxetex conditional    auxhook.sty    2011/03/04 v1.3 Hooks for auxiliary files (HO)   kvoptions.sty    2011/06/30 v3.11 Key value format for package options (HO)     pd1enc.def    2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO)   hyperref.cfg    2002/06/06 v1.2 hyperref configuration of TeXLive        url.sty    2013/09/16  ver 3.4  Verb mode for urls, etc.    hpdftex.def    2012/11/06 v6.83m Hyperref driver for pdfTeX   rerunfilecheck.sty    2011/04/15 v1.7 Rerun checks for auxiliary files (HO)    nameref.sty    2012/10/27 v2.43 Cross-referencing by name of section   gettitlestring.sty    2010/12/03 v1.4 Cleanup title references (HO) Split string on spaces in Java, except if between quotes (i.e. treat \"hello world\" as one token) Prove $| \sum_{i \leq n} \frac{\mu(i)}{i} | \leq 1$ So I am trying to prove the above stated formula. I am completely new to number theory so I thank you in advance for baring with me. I start off by using the definition:  $\frac{\phi(n)}{n} = \sum_{d|n} \frac{\mu(d)}{d}$  Where $\phi$ is Eulers function, and $\mu$ is the Mobius mu function. From here, I use the Mobius inversion formula to give:  $\frac{\mu(n)}{n} = \sum_{d|n}d\frac{\phi(\frac{n}{d})}{n}\mu(d)$  Now summing $n$ up to $x$:  $\sum_{n \leq x}\frac{\mu(n)}{n} = \sum_{n \leq x}\sum_{d|n}d\frac{\phi(\frac{n}{d})}{n}\mu(d)$  Now I'm not fully sure on how I can rearrange things inside the two summations on the right hand side, so leaving things as they are; using that $\sum_{d|n} \mu(d) = 1$, if and only if $n =1$. Hence:  $\sum_{n \leq x}\frac{\mu(n)}{n} = \sum_{d|1}d\phi(\frac{1}{d})\mu(d)$  Thus $d=1$. Subbing this in:  $\sum_{n \leq x}\frac{\mu(n)}{n} = \phi(1) = 1$  I am not sure what I have missed (or done wrong) as to have an equality and not a triangle relation. Any suggestions or ideas would be greatly appreciated Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian? Is the following statement true or false:  If $G$ is a group with the property that $g=g^{-1}$ for all $g \in G$, then $G$ is abelian.   I believe it is false since I know that abelian or commutative property implies that every element in $G$ must have an inverse. Thus $g\cdot g^{-1}= g^{1}\cdot g = e$. I need someone to check my attempt. Separators for author group (IF conditon) I am new to LaTeX, just a beginner, basically a Perl developer.  I have created a LaTeX file  \begin{document}  \cont{\iname{\isurname{Name1}\ifname{K. C. G.}}\iname{\isurname{Name11}\ifname{Y. Q.}}\iname{\isurname{Name111}\ifname{C.-Z.}}\ititles{Some title Text}\ipage{995}}  \end{document}   Now my need is to define LaTeX commands so that the output should appear as below     Name1 K. C. G., Name11 Y. Q. and Name111 C.-Z. Some title Text - 995.   \iname - Person Name will repeat several times \isurname - Surname of a person \ifname - First Name of a person    \iname will repeat any number of times, say 1 to ...  If only one \iname found inside \cont, display should be like the below     Name1 K. C. G. Some title Text - 995.   If only two \iname found inside \cont, display should be like the below     Name1 K. C. G. and Name11 Y. Q. Some title Text - 995.   If more than two \iname found inside \cont, display should be like the below (and should come after last \iname)     Name1 K. C. G., Name11 Y. Q. and Name111 C.-Z. Some title Text - 995.   I can define input for \iname separated by commas, but I don't know how to write a macro to define \iname with different outputs based on the if condition.  I hope to have clearly explained my doubt. Loading OpenStreetMap data in QGIS? In QGIS 1.8 I used the openstreetmap plugin to request data from the server, or open a .osm XML file, which produced 3 layers (polygons, polylines and points) in QGIS.  This was great (give or take the 64bit bug which highly affects the freshly mapped area I work on), but how do I do that in QGIS 2.x?   I can't find any updated documentation about it.  In the vector menu, I've tried importing from osm servers, I get a .osm file, but then I'm stuck. There's a menu option for loading an XML file, but it produces a spatialite db, which apparently only has non-geometry tables when I try to add it as a spatialite layer. If I open the attribute table, I can see node ids, ways and so on, but I can't figure out how to actually make use of them.  I've also tried adding a vector layer from a .osm XML file. I get a gpsbabel window that shows nothing, then finally an invalid data source message in QGIS. Closed-loop function question How do I find the   How do I find the transfer function of Gd(s)?  I am able to find the transfer function of Gr(s) but I am not really sure about Gd(s)? and how do i determine which order is this closed system? Is the Formula Logically Valid? Why does speed of light have to be constant? My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.  My motivation for asking this question is thinking about Special Theory of Relativity. One way of understanding why time dilation and length contraction happen is to look at it from the perspective of constancy of speed of light. Alice who is on the moving source of light and Bob, a fixed observer see the speed of light as constant. In order for Alice to see the speed of light as a constant value, time slows down and length expands (in forward direction) thus keeping the speed constant.   In the  I'm doing, the Professor tells that this constancy of speed of light could be more generally referred to as, "Principle of wave constancy". That is, the speed of any wave is a property of the medium (and thus it remains constant). So, the speed of a wave in water, for example, remains constant even if the source of the waves (say a paddle keeps moving). Frequency and wavelength may change but the speed remains constant. In a similar fashion, light is an electromagnetic wave and thus its speed is constant. And the constant speed is defined by the medium (which happens to be vaccum i.e., no medium for light).   My questions are twofold now -    Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general) Theoretically, could there be other waves that could travel through vaccum at a different speed? If yes, time dilation and length contraction will have to be different.   I'd appreciate it if the answer is kept non-technical (essential math is okay). More importantly, I request you to try and explain without using General Theory of Relativity. Because I'm thinking how the scientific understanding by 1905 had already knew that speed of light has to be constant. Position of the adverb "substantially" "become a President" or "become President" If he had not been a film star, he would not have become President.     In my opinion, "a President" is correct. Examples:     "My dream is to be a teacher"   "My dream is to be a President"   Which is correct usage? President or a President? I´d like to enable the ssh root access on Ubuntu 14.04. Editing the /etc/ssh_config (PermitRootLogin yes) didn't affect anything. \includegraphics PDF, color problem I'm using pdflatex, and use \includegraphics to include content of figures from PDF. PDF are exported from InkScape.  \begin{figure} [!h]     \centering     \includegraphics[height=3cm]{fig/SUSAN.pdf} \end{figure}   Included PDF or source SVG has same colors. Green has always RGB value (0, 255, 0). Problem occurs when I include this files from LaTeX. In output PDF on some pages colorspace is darker. Even same image on other page has different colourity.  My PDF  . As you can see on page 7 (11 in PDF) USAN areas are bright green, but then on page 5 (9 in PDF) are green points on corners more darker. How many ways can $b$ balls be distributed in $c$ containers with no more than $n$ balls in any given container?