Let $a,b,c$ be the lengths of the sides of a triangle. Prove that, $$a^2b(a-b)+b^2c(b-c)+c^2a(c-a) \geq 0.$$    Attempt  Using a ravi substitution I said let $a = x+y, b = y+z, c = z+x$. Then we have $$(x+y)^2(y+z)(x-z)+(y+z)^2(x+z)(y-x)+(x+z)^2(x+y)(z-y) = 2 x y^3+2 x^3 z + 2 y z^3-2 x^2 y z-2 x y^2 z-2 x y z^2.$$ Then I thought of using the rearrangement in equality, but I couldn't see how to make that work.

For any triangle with sides $a$, $b$, $c$, prove the inequality $$a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0 .$$   This is IMO 1983 problem 6.  I tried substituting $a=x+y$, $b=y+z$, $c=z+x$ but well it doesn't help in any sense except wasting 3 pages that lead to nothing (please don't mind the joke). Using $a=2R\sin A$, $b=2R\sin B$, $c=2R\sin C$ also didn't lead to anything for me. Could you give me a hint for finding the proper substitution?


At boot time I get this message:  This kernel requires an x86-64 CPU, but only detected an i686 CPU. Unable to boot- please use kernel appropriate for your CPU

To check whether I am using 32bit or 64bit Ubuntu. I looked in  and found this answer uname -a. If it is shown as i386, it will be 32bit and amd64, it will be 64 bit, but I got this result:  Linux mukund-ThinkPad-Edge-E431 3.8.0-35-generic #50-Ubuntu SMP Tue Dec 3 01:25:33 UTC 2013 i686 i686 i686 GNU/Linux   What is this i686? Is it 32bit or 64bit - I think  it is 32bit, because all the Debian packages which I installed in it are of 32bit, so can anybody please give a detailed explanation.


In my Java program I have a method that needs to return a generic array. In order to simplify things, I have made a much simpler code to reproduce my problem, which is the following:  public class Main {     public static void main(String[] args) {         Integer[] integers = toArray(1);          System.out.println(integers [0]); //should output 1     }      public static <T> T[] toArray(T element) {         T[] array = (T[]) new Object[1];         array[0] = element;         return array;     } }   But when I execute this code I get the following exception:  Exception in thread "main" java.lang.ClassCastException: [Ljava.lang.Object; cannot be cast to [Ljava.lang.Integer; at Main.main(Main.java:3)   But if I change the type of integers to Object[], it works as expected. I suppose it's due to the fact that Java only supports generics at compile time, and then performs type erasure, transforming in this case my Integer array to a Object array.  But my problem persists, and my method must return a collection of generic T values, whether the return value is a List or an array it's the same, so if it's not possible to accomplish what I want with an array, I could use an ArrayList, for example.  But... is it possible to accomplish this simply by using an array?  Thank you.

Due to the implementation of Java generics, you can't have code like this:   public class GenSet<E> {     private E a[];      public GenSet() {         a = new E[INITIAL_ARRAY_LENGTH]; // error: generic array creation     } }   How can I implement this while maintaining type safety?  I saw a solution on the Java forums that goes like this:  import java.lang.reflect.Array;  class Stack<T> {     public Stack(Class<T> clazz, int capacity) {         array = (T[])Array.newInstance(clazz, capacity);     }      private final T[] array; }   But I really don't get what's going on.


I searched and found at last that my ask question feature is not working due to repetitive questions etc. I got my mistake, after that I still continued my contributions through answering, but will i never get the chance to ask question in coming future, because i need help many time also now I got it what I should not do so  what should I do now start with another account or wait?

If you are reading this, you may have been affected by one of our post quality bans. If so, it is important that you  to understand what has happened and how to regain the permissions that you lost. While trying to ask a question, one could see:  We are no longer accepting questions from this account. See  to learn more.  Likewise, for answers:  We are no longer accepting answers from this account. See  to learn more.   Why am I getting this message? Are deleted posts taken into account too? Is a question/answer ban the same as a suspension? How do I avoid getting a question ban? How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account? Can I simply create a new account? I'll just ask somewhere else on the SE network, and they'll migrate my question to the correct site! Will a ban on one Stack Exchange site affect my standing on other sites in the network? Does this apply to meta sites too? My account is in good standing. Why am I still blocked?


Im using fontspec to have Arial in my scrartcl -document. For some reason this Arial is not applied to sectiontitle/subsectiontitle. Compiling with Xelatex  \documentclass[a4paper]{scrartcl} %%%%%%%%%%%%%%%%%% Font %%%%%%%%%%%%% \usepackage{fontspec} \setmainfont{Arial}  %%%%%%%%%%% header %%%%%%%%%%%%%%%%%% \usepackage[headsepline=0.75pt]{scrlayer-scrpage} \renewcommand*{\headfont}{\normalfont} \clearpairofpagestyles \automark[section]{section} \ihead{\headmark} \ohead{\pagemark}  \begin{document}  \tableofcontents \section{Section 1} 11111111111111111111111 \subsection{Subsection 1} 11111111111111111111111 \subsubsection{Subsubsection 1} 11111111111111111111111 \end{document}

I am setting up the layout for my bachelor thesis using scrbook as basis for a self-made documentclass with twosided print. I want a header containing the current part number and name on the outer side (left on even pages, right on odd pages), the current chapter number and name on the center of the head and the same for section on the inner side. I found this example in the KOMA-Script documentation:  \usepackage{scrlayer-scrpage} \pagestyle{scrheadings} \automark[chapter]{chapter} \automark*[section]{}   It puts the chapter on the outer side on even pages and the section on the outer side on odd pages. Sadly, I was not able to modify this to fit my needs because I do not really understand the way KOMA-Script works here. If a part starts but there is still no chapter in it, the place for the chapter shall remain empty (same for chapter and section). Can anyone help?  Furthermore, I would like to change all fonts that KOMA-Script changes (e.g. toc, section, chapter...) back to the default computer modern as I do not like the font KOMA-Script uses here. Is there a better way than changing all the fonts manually like this:  \addtokomafont{section}{\fontfamily{cmr}\selectfont}


A girl I met online says the travel agency she went to says she can't get a B2 visa to the US because she took a loan out to pay for her trip. Under Russian law she has to pay back a 680 US dollar loan to get the visa. She says the US embassy won't let her get an interview for the visa. Is this a scam? It sounds fishy to me. Can she get a visa and leave Russia?

On Travel.SE we often see questions about a person (usually a love interest) asking for money to pay for airfare, visas, permits and other expenses. For example        What general advice can be given in such situations to the person asking the question? Is it all a scam or can there be legitimate situations in which an online friend could be asking for money?


I want to write a recursive function that gives me the lenght of a list. To make it recursive, i use this pointer as default parameter in the declaration of the function in the List class header. But the compiler gives me an error... This is the code:  //Header file #include "Nodo.h"  template < class Tipo >  class Lista {      private:         Nodo< Tipo >* Prox;       public:         Lista();          bool ListaVuota();          int DimensioneLista(Lista<Tipo>* = this);          void InserisciInCoda(Tipo);  };  //CPP file  template< class Tipo >  int Lista< Tipo >::DimensioneLista(Lista< Tipo >* lista)  {      if(lista->ListaVuota())         return 0;     else         return 1+DimensioneLista(lista);  }

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


If $a$ is a positive integer of the type $3n+2$,then pove that at-least one prime divisor of $a$ is of the form $3n+2$  My try:If $3n+2$ is prime then we are done since $3n+2$ is of the form $3n+2$. What do we do in the case it isn't prime?

I have to prove that any number of the form $3n+2$ has a prime factor of the form $3m+2$. Ive started the proof  I tried saying by the division algorithm the prime factor is either the form 3m,3m+1,3m+2.  Case 1: $3m$      suppose $3m$ does divide $3n+2$. That means $3mr=3n+2$ where $r$ is some integer. But we get $mr-n= 2/3$ and since $mr-n$ is an integer that's a contradiction. Thus $3m$ does not work.  Case 2: $3m+1$ Same argument here  Case 3: $3m+2$ By the fundamental theorem of arithmetic every integer is divisible by a prime. But not sure what to do from here.


In the movie Now You See Me, the Four Horsemen rob a French bank and later reveal that the robbery was all an illusion. When Thaddeus Bradley (Morgan Freeman) was explaining it I still couldn't understand how they did this trick.  This is really driving me crazy, would someone please explain it to me so I don't go insane?

In Now You See Me, when Morgan Freeman explains to the detective on how the Four Horseman robbed the bank, he mentions that they replaced the real money (while in the secured transport truck) with flash paper.  This does not explain how the paper in the bank got ignited, and no ignition/stimulator left in the scene as evidence.  Who/What/When ignited the flash paper in the bank on time?   There had to be some timer/delay mechanism on the platform, or something similar - but in the frames we see - there is nothing.


The links share | edit | close | flag are hidden when viewing the post from a review queue. I know we don't need share, and edit is already a button above. But there are cases where we should flag, (e.g., flagging for spam or migration) instead of, or in addition, to casting a close vote. The flag link should either be shown below the question under review, and/or as a button next to 'Edit.'

I've been reviewing suggested edits lately, and have come across a problem in the queue: we don't have the normal 'flag' link for the post. I'm not talking about flagging the edit, but the post itself. Often, I will come across a post that, though the edit does improve it, still is low quality, and should be flagged as such. While I want to give the user recognition for trying to improve the post, I also want to let the mods know that it's low quality - and having to go to the question in the normal view isn't very fun for this. So, please add a flag link below posts in the Suggested Edits queue.


Is there some easy way to pad Strings in Java?  Seems like something that should be in some StringUtil-like API, but I can't find anything that does this.


I was trying to update my Ubuntu 14.04 system using terminal but I got this result  W: Failed to fetch http://in.archive.ubuntu.com/ubuntu/dists/trusty-backports/restricted/binary-i386/Packages  407  Proxy Authentication Required   Also in the top-right corner of my PC there is a red triangle which says the update information is outdated. Again when I tried to download something from software repository there comes a window which says untrusted package ,then when I select ok then another window pops out which says check your Internet connection. But I am well connected to the Internet(under proxy network),so what should I do?

For the command   sudo apt-get update   I get following error:  W: Failed to fetch http://ch.archive.ubuntu.com/ubuntu/dists/maverick-updates/multiverse/binary-i386/Packages.gz   407  Proxy Authentication Required (The ISA Server requires authorization to fulfill the request. Access to the Web Proxy filter is denied. )   I am running Ubuntu 10.10 installed on Windows XP using VirtualBox. For Internet connections I am using proxy server with an authentication. I tried to use gnome-network-proxy tool to set proxy settings system-wide.   After that /etc/environment has been updated by http_proxy variable with the format http://my_proxy:port/, there were no authentication data.  I checked this with Firefox. Browser asked my for login and password and everything was working fine. It was unfortunately not the case for apt-get. I have also tried to do as described . Unfortunately it does not work.  May it be somehow related to the fact that a proxy is in a Windows domain, any ideas?  My proxy name is http-proxy. Is '-' a special character here?


I have a question about use of static inner class in the following code, adapted from Eckel's Thinking in Java 4th edition (page 625).  The code uses a static inner class called Node.  When you create a Stack structure, you can then push the nodes onto the stack and pop them off - so far so good.  But I'm confused about why the node class is static?  Wouldn't that mean that there would be only one Node created in the LinkedStack class?  How / why is it that in fact you can push many different nodes onto the stack, and then pop them off (which of course is what the stack is supposed to do).  In fact, you can change private static class Node to 'private class Node` and it also works ... so why did Eckels choose static class Node?  In this example, the input is the three words "Phasers", "on", "stun!" and output is "stun!", "on", "Phasers".  public class LinkedStack<T> {      //generic inner class node     private static class Node<U> {          U item;         Node<U> next;         Node() {             item = null;             next = null;         }         Node(U item, Node<U> next) {             this.item = item;             this.next = next;         }         boolean isDummyNode() {             return item == null && next == null;         }     }      //initialize top of stack as a dummy first node     private Node<T> top = new Node<T>();      public void push(T item) {         top = new Node<T>(item, top);     }      public T pop() {         T result = top.item;         if(!top.isDummyNode())             top = top.next;         return result;     }      public static void main(String[] args) {         LinkedStack<String> stack = new LinkedStack<String>();         for(String s : "Phasers on stun!".split(" "))             stack.push(s);         String s;         while((s = stack.pop()) != null)             System.out.println(s);     }  }

What is the main difference between an inner class and a static nested class in Java? Does design / implementation play a role in choosing one of these?


Using biblatex I don't obtain the name of the reference but the name of the article - in the .bib - file in bold.        Here's my code:  \documentclass{beamer} \setbeamertemplate{bibliography item}{\insertbiblabel}  \mode<presentation> {\usetheme{Madrid}       }  \usepackage{graphicx} % Allows including images \usepackage{booktabs} % Allows the use of \toprule, \midrule and \bottomrule in tables  \usepackage[utf8]{inputenc} \usepackage[spanish]{babel} \usepackage{hyperref} \usepackage{pgfgantt} \usepackage[backend=biber]{biblatex} \addbibresource{presentation.bib}   %---------------------------------------------------------------------------------------- %   TITLE PAGE %----------------------------------------------------------------------------------------  \title[Short title]{Proyecto de Tesis: Holografía y sistemas integrables} % The short title appears at the bottom of every slide, the full title is only on the title page  \author{John Smith} % Your name \institute[UCLA] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space { University of California \\ % Your institution for the title page \medskip \textit{john.smith@example.com} % Your email address } \date{\today} % Date, can be changed to a custom date  \begin{document}  \begin{frame} \titlepage % Print the title page as the first slide \end{frame}  \begin{frame} \frametitle{Outline} % Table of contents slide, comment this block out to remove it \tableofcontents % Throughout your presentation, if you choose to use \section{} and \subsection{} commands, these will automatically be printed on this slide as an overview of your presentation \end{frame}  %---------------------------------------------------------------------------------------- %   PRESENTATION SLIDES %----------------------------------------------------------------------------------------  %------------------------------------------------  \begin{frame}[allowframebreaks] \frametitle{Resumen}  Las p-formas autoduales se definen en dimensión $d=2(p+1)$, donde $p$ es par . Su caso más sencillo, con $p=0$, corresponde al bosón quiral . Esta ecuación aparece como un caso particular de la denominada ``jerarquía de KdV''. Dicha jerarquía se puede formular como una acción de Chern-Simons en una dimensión extra, escogiendo condiciones de borde adecuadas para la conexión. El objetivo de esta tesis es generalizar esta construcción con el fin de generar sistemas integrables para p-formas en dimensiones superiores, con aplicaciones a supergravedad en seis dimensiones \cite{Marcus:1982yu}.  \end{frame}  %------------------------------------------------  %------------------------------------------------   \begin{frame} \Huge{\centerline{Muchas gracias.}} \end{frame}  %----------------------------------------------------------------------------------------  \end{document}    My purpose is being able to use the \footfullcite command. I've read  and  but I don't know the problem.

Running the minimal example  \documentclass{article} \usepackage{filecontents} \begin{filecontents*}{\jobname.bib} @ARTICLE{example,   author  = {Other, Anthony Norman},   title   = {Some things I did},   year    = {2014},   journal = {J.~Irrep. Res.},   volume  = {1},   number  = {1},   pages   = {1-10} } \end{filecontents*} \usepackage[backend=biber]{biblatex} \addbibresource{\jobname.bib} \begin{document} Hello\cite{example}. \printbibliography \end{document}   I get the warning There were undefined references.  I have read  and know that I need to run:   LaTeX Biber LaTeX   However, my editor is only set up to run BibTeX. How do I go about setting up my editor/IDE to be able to run Biber, and how do I run the LaTeX/Biber/LaTeX cycle?  Answers (sorted alphabetically by editor name)                    Answer guidelines   Each answer should be for one editor. If the editor is cross-platform, if possible give a single answer with notes covering the minor platform variations. Please edit the question to include new answers in the 'link list' Each answer should be 'stand alone', i.e. don't say 'It's almost the same as editor Y but ...' for the editor part Instructions for 'build tools' such as arara or latexmk are welcome but should explain how to set up the editor in question as not all editors allow simple addition of arbitrary tools


I am being happy. This sentence belongs to present continuous tense. Can we show duration or state in present continuous tense or no?  If we can? By which structure?

I am arguing with friends about this question.  According to what I learned in school, there are some adjectives that cannot be used in the progressive form.  I think this one is ungrammatical because angry describes an emotion, which is a temporary state on its own. Therefore, it is redundant to use it in the progressive form.  Am I correct?


I'm trying to make an Intent to start the NewEventActivityunfortunately the app crashejn when the floating action button is pressed. Here is my code:  MainActivity:      public class MainActivity extends AppCompatActivity {         @Override         protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_main);              }             public void newEventIntent(View v){                 Intent intent = new Intent(this, NewEventActivity.class);                 startActivity(intent);         }     }   activity_main.xml:          <android.support.design.widget.FloatingActionButton         android:onClick="newEventIntent"         android:id="@+id/add_event_fab"         android:layout_width="wrap_content"         android:layout_height="wrap_content"         android:layout_alignParentRight="true"         android:layout_alignParentBottom="true"         android:layout_marginRight="20dp"         android:layout_marginBottom="20dp"         android:src="@drawable/baseline_add_24"/>   LogCat:  java.lang.RuntimeException: Unable to start activity componentInfo{com.example.deadline/com.example.deadline.NewEventActivity}: java.lang.NullPointerException: Attempt to invoke virtual method 'void android.support.design.widget.FloatingActionButton.setOnClickListener(android.view.View$OnClickListener)' on a null object reference   I made sure that both activities are in the manifests.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I've learned that function $f:\mathbb{R}^n\rightarrow \mathbb{R}^p$, at $x \in \mathbb {R}^n$, $f(x)$ is Gateaux differentiable, then exits a linear operator $\lambda (x):\mathbb{R}^n\rightarrow \mathbb{R}^p$ such that $D_uf(x)=\lim_{t \rightarrow 0}{\frac{f(x+tu)-f(x)}{t}}=\lambda(x)(u),\forall u \in \mathbb{R}^n$. If $\lambda(x)$ is continous, $f(x)$ is Frechet differentiable.   I want to find a counterexample that $f(x)$ is Gateaux differentiable and $\lambda(x)$ is linear, not continous, but it's hard for me, help me, thank you!

Let $V,W$ be nonzero normed spaces over $\mathbb{K}$ such that $V$ is finite-dimensional.  Let $E$ open in $\mathbb{K}$ and $p\in E$.  Let $f:E\rightarrow W$ be Gâteaux-differentiable at $p$.  Is $f$ necessarily Fréchet-differentiable at $p$ in this case?  I think this is not true in general, but cannot find a counterexample. What would be a counterexample?


My understanding is, that according to GR, an apple falls to the ground not because it is being pulled but because it follows the curvature of space, caused by the mass of the Earth.  My question is - Why should it follow that curve instead of remaining where it is? Apparently, it is already in motion in Space-Time, with Zero velocity in space and a velocity of C in time? If that be so, what causes it to start moving in space, with a corresponding reduction in time? Is Gravity not a force? What about electricity, magnetism and the strong and weak nuclear forces?

I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or trampoline bending under an object, which causes other objects to come together, but I always thought this was a hopelessly circular explanation because the blanket only bends because of "real" gravity pulling the object down and then pulling the other objects down the sloped blanket. In other words, to me, it seems that curved space wouldn't have any actual effect on objects unless there's already another force present.   So how is curved space-time itself actually capable of exerting a force (without some source of a fourth-dimensional force)?  I apologize for my ignorance in advance, and a purely mathematical explanation will probably go over my head, but if it's required I'll do my best to understand.


As I saw on cppcoreguidelines page,  there is a statement like this void Value::set_text(const string& ss) {     if (type == Tag::text)         s = ss;     else {         new(&s) string{ss};   // s is a member string of class Value         type = Tag::text;     } }  I have never seen such usage before. What does this mean?

Has anyone here ever used C++'s "placement new"? If so, what for? It looks to me like it would only be useful on memory-mapped hardware.


I want to automatically (via script) add new TIF-files on the harddrive to Geoserver as a new layer. I use the REST-API for that.  In the first step I added the TIF as a coveragestore, and that step works. So I use this JSON:  {     "coverageStore":     {         "name": "test123",         "type": "GeoTIFF",         "enabled": true,         "workspace":         {             "name": "TEST"         },         "url": "file:\/\/\/data\/test123\/test123.tif"     } }   I add that via wget and that part works:  wget --user=test '--password=test123' --header='Content-Type: application/json' --post-file=coveragestore-test123.json 'http://localhost:8080/geoserver/rest/workspaces/TEST/coveragestores'   So far it s fine. But now I want to publish that as a layer, and that doesn't work. My JSON here looks like this:  {     "layer":     {         "name": "test123",         "type": "RASTER",         "defaultStyle":         {             "name": "TEST:style123",             "workspace": "TEST"         },         "resource":         {             "@class": "coverage",             "name": "TEST:test123"         }     } }   And I send it with this:  wget --user=test '--password=test123' --header='Content-Type: application/json' --post-file=layer-test123.json 'http://localhost:8080/geoserver/rest/layers'   It comes back with an HTTP-error 405.  What do I do wrong?

So, simple thing as it seems but I can't seem to make it work! I'm trying to add a raster data file (GeoTIFF) to geoserver via REST API, using curl on linux. REST API is working, since I created a new workspace using it:  curl -u admin:geoserver -v -XPOST -H 'Content-type: text/xml' \  -d '<workspace><name>restProba</name></workspace>' \  http://localhost:8080/geoserver/rest/workspaces   It's correctly created as shown by Geoserver's admin ui, but when I try to add a coveragestore to that workspace by executing  curl -u admin:geoserver -v -XPOST -H 'Content-type: text/xml' -d '<coverageStore><name>int_dec</name><enabled>true</enabled> <type>GeoTIFF</type> <url>$home/int_dec.tif</url></coverageStore>'      "http://localhost:8080/geoserver/rest/workspaces/restProba/coveragestores?configure=all"   even though it is correctly loaded, it goes directly into the default workspace, which is not the one I want it in. Is there any way of defining which workspace i want it in? I thought it'd enough by mentioning it in the URL where I point to restProba's workspace URI but it seems to be omiting it.  Thanks for your help :-)  pd: newbie with geoserver, I've tried searching for this but either i'm not using the correct search criteria, im a fool or it's just too simple for anyone to ask that i'm even fooler for asking it :p


Root not avaliable?    So far all of Rooting APK's Either don't download (Just disappears) Or say Root failed or not available.   So far These are what ive used. KingRoot KingoRoot OneClickRoot  -    If possible can someone tell me Rooting programs that I haven't used that might work.

This is a common question asked by those who want to root their phones. How exactly do I root my Android device? Are there risks involved?


I can't get my copy of cad eagle to create tag type of label for a wire or a net. Instead I get simple text type of label. GND label is what I am trying to get.    I have tried turning xref on and off, and changing size or font. In the end, all I get is simple plain text label. So, how do I get the fancy tag type of label?

In  they've somehow created "wireless" networks, meaning networks that connect two components but don't have an actual wire in the schematics.  What are these called, and how can I create them in Eagle Cad 6.5?


Assume $n$ and $r$ are nonnegative integers where $$0\le r\le n$$How can one simplify $$S=\binom{n}{0}-\binom{n}{1}+\binom{n}{2}-...+(-1)^r\binom{n}{r}$$ ?  I think that this combinatorial expression should be either solved using a combinatorial way but I don't know how. Probably It's also useful one tries to represent somehow using binomial representation of $(a+b)^n$.  I appreciate any idea given!

It is easily checked that $\displaystyle\sum_{i\ =\ 0}^{n}\left(\, -1\,\right)^{i} \binom{n}{i} = 0$, for example by appealing to the binomial theorem.  I'm trying to figure out what happens with the truncated sum $\displaystyle\sum_{i\ =\ 0}^{D}\left(\, -1\,\right)^{i}\binom{n}{i}$.  How far away from $0$ can this get, as a function of $D$ ?.  I'm mostly interested in the case of when $D \ll n$, such as $D \sim \,\sqrt{\,n\,}\,$.  Thanks !


Find a normal subgroup in $A_4$ and identify the quotient of $A_4$ by this normal subgroup  How do you find a normal subgroup in $A_4$? What I did is that I listed all the combinations of two cycles. For example, $(12)(34), (13)(24)..(34)(12)$. So there are 12 elements in $A_4$ From here, how do I find a normal subgroup other than trivial ones? I can't check every element that satisfies $gH = Hg$ where $H$ is a normal subgroup and $g \in A_4$.

Klein's $4$ group, $\{1\}$ and $A_4$ are three normal subgroups of $A_4$. I want to know about any other normal subgroups of $A_4$. Do these exist?


I was trying to solve questions from "Mathematical Analysis" by "Apostol" and came across this question which states  ""If $a, b, c$ and $d$ are rational and if $x$ is irrational, prove that $\dfrac{\left( ax + b \right)}{\left( cx + d \right)}$ is usually irrational.""  Now, the problem with this is that how can we prove something is usually True? All we can do is to show some cases where this is not true. Like in this example, we can give the solution as:-  The only time it will be rational is when the numerator is some integer times the denominator or vice - versa. The rest of the times, when this is not true, it will be irrational.  Is this the correct way of proof or there is some other war to prove something usually true?  Note: My question is not about finding the possibilities that the given expression is rational. The question is about how to prove something usually True? Because, as far as I have learnt about logic, we may prove something to be True (completely) or False (by just giving one counter example). So, here, I am asking that if such a statement comes, what does it mean to prove it? In fact, I have solved the question and its solution is written in the explaination. All I want to know is that if my solution is correct or is there a proper way to prove something usually True?

If a.b.c,d are rationals and x is irrational number, then prove that $\frac{ax+b}{cx+d}$ is usually a irrational number. When do exceptions occur?  This is a homework Question. i did this by assuming that given fraction is rational say $\frac{p}{q}$. Now i write $$\frac{ax+b}{cx+d} = \frac{p}{q}$$. After cross multiplying i get   $$\frac{qb-pd}{pc-qa}=x$$  So this contradiction as right hand side is rational and left hand side is irrational. Now the question asks where does exceptions occur. I see that exceptions can occur when $a=c=0$ and $a=b=c=d$. But what are other exceptions and is my working method correct?  Thanks


Prove that if $A$ is an $m\times n$ matrix and $B$ is an $n\times p$ matrix, then $\operatorname{rank} AB$ is less than or equal to $\operatorname{rank} B$.  The hint is: prove that if the $k$th column of $B$ is not a pivot column, then the $k$th column of $AB$ is not a pivot column of $AB$.  I don't think I am allowed to use row space, column space or the Sylvester's inequality as we haven't learned them yet in the class.  I have been stuck here for ages, so hints or solutions are very appreciated.  Thank you for your time.

Let $A$ and $B$ be two matrices which can be multiplied. Then $$\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B)).$$   I proved $\operatorname{rank}(AB) \leq \operatorname{rank}(B)$ by interpreting $AB$ as a composition of linear maps, observing that $\operatorname{ker}(B) \subseteq \operatorname{ker}(AB)$ and using the kernel-image dimension formula. This also provides, in my opinion, a nice interpretation: if non-stable, under subsequent compositions the kernel can only get bigger, and the image can only get smaller, in a sort of loss of information.  How do you manage $\operatorname{rank}(AB) \leq \operatorname{rank}(A)$? Is there a nice interpretation like the previous one?


With respect to Thomas Young's double-slit experiment, I have heard that it can be done with a single photon.  But how does the single photon go through both slits?  And how far apart are the slits?

I just recently watched  where they were explaining the double slit experiment.  I understand that the interference pattern would be observed if you send photons or electrons one after the other. The conclusion that the author seems to make is that it is as though the particle/packet of energy travels through both the slits after somehow splitting into two.  Has anyone done an experiment where they send just one particle? (And end the experiment) Do you observe two points on the screen in that case or just one?


Can you give any idea regarding the evaluation of the following limit?   $\lim_{n\to \infty}\left(1 - \frac {1}{n^2}\right)^n$  We know that $\lim_{n\to \infty}\left(1 - \frac {1}{n}\right)^n = e^{-1}$, but how do I use that here?

I'm trying to find the limit of $a_n = \left(1-\frac{1}{n^2}\right)^n$ for $n \rightarrow \infty$.  It seems that the limit is $1$, since $a_n = 0.999...$ for large $n$. The presentation $a_n = \frac{(n^2-1)^n}{n^{2n}}$ and expanding was my first idea, but I couldn't get the result from there. Any ideas?


I've not opened any $.. and i'm not using any mathematical command (apart \pm but this is not the problem because it doesn't work the same). The first error is just after the first \end{tabular}. I created a table and subtable environement, maybe I can't manage them well, please help me.   \begin{table}[H]  \centering     \subtable{       \begin{tabular}{ll}      \multicolumn{2}{c}{\textbf{Molla 1}}\\     \hline     $R_s$ &      1.48\pm0.01 cm\\     $n_s$   & 41 \pm1\\     \multicolumn{2}{l}{$l_0=23.2 \pm 0.2$cm}\\     \hline     massa (g) & $\delta{l}$ (cm)\\     \hline     38.8\pm0.1      & 9\pm0.5\\     148.1\pm0.2     & 13.5\pm0.5\\     235.6\pm0.3     & 21.2\pm0.5\\     336.6\pm0.4     & 30.3\pm0.5\\     \hline     \end{tabular}     }     \qquad \subtable{     \begin{tabular}{ll}     \multicolumn{2}{c}{\textbf{Molla 2}}\\     \hline     $R_s$   &    0.93   \pm0.01 cm\\     $n_s$   & 66 \pm1\\     \multicolumn{2}{l}{$l_0=19.1 \pm 0.2$cm}\\     \hline     massa (g) & $\delta{l}$ (cm)\\     \hline     87.5\pm0.1      & 3\pm0.5\\     188.5\pm0.2     & 6.5\pm0.5\\     237.5\pm0.3     & 8.2\pm0.5\\     336.6\pm0.4     & 11.8\pm0.5\\     \hline     \end{tabular}      }     \end{table}     \clearpage

\begin{table}     \begin{tabular}{|c|c|c|c|c|}     \hline     \multicolumn{5}{|c|}{\textbf{Table 1:}Unfiltered Water}\\     Concentration of analyte in sample   & Avg & Std Dev &  RSD & 90\% CI \\      \hline     Total hardness (ppm $CaCo_3$ equiv)  & 97  &    2   &  2\%  & \pm 5   \\     Calcium hardness (ppm $Ca^{2+}$)     & 57  &    3   &  5\%  &  \pm 5   \\     Magnesium hardness( ppm $Mg^{2+}$)   & 40  &    3   & 7.5\% &  \pm 5 \\     \hline     \end{tabular}   This table is giving me an error. That says   ! Missing $ inserted. <inserted text> $ l.41 ...Co_3 equiv\) & 97 & 2 & 2\% & \pm 5 \I've inserted a begin-math/end-math symbol since I think   you left one out. Proceed, with fingers crossed.  What is the cause of this error?  I can't seem to find any thing that is mismatched.


Suppose that $f:    [0,1 ] \to \mathbb{R}$ has a continuous second derivative, $ f(0)=f(1)=0$ and $f(x)>0$ for all $x\in (0,1)$. Prove that $\int_0 ^1 |f''(x)/f(x)|dx> 4.$ I have no idea how to proceed with this problem, how does one approach such a problem? Any hints will be appreciated.

Assume that $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$ and $f$ is positive on the interval $(0,1)$ and $0$ at the endpoints.    I want to prove that $$\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4. $$  I could not make any progress. Since the unit interval is compact, we know that the continuity of $f, f'$ and $f''$ are uniform and they attain their maximum and minimum values. Moreover, I tried to apply the Mean Value Theorem but I failed.


How is the below code is printing true?  string x = new string(new char[0]); string y = new string(new char[0]); Console.WriteLine(object.ReferenceEquals(x,y));   I expected this to print False, because I expected two separate objects to be constructed and then their references compared.

I collect a few corner cases and  and would always like to hear more. The page only really covers C# language bits and bobs, but I also find core .NET things interesting too. For example, here's one which isn't on the page, but which I find incredible:  string x = new string(new char[0]); string y = new string(new char[0]); Console.WriteLine(object.ReferenceEquals(x, y));   I'd expect that to print False - after all, "new" (with a reference type) always creates a new object, doesn't it? The specs for both C# and the CLI indicate that it should.  Well, not in this particular case. It prints True, and has done on every version of the framework I've tested it with. (I haven't tried it on Mono, admittedly...)  Just to be clear, this is only an example of the kind of thing I'm looking for - I wasn't particularly looking for discussion/explanation of this oddity. (It's not the same as normal string interning; in particular, string interning doesn't normally happen when a constructor is called.) I was really asking for similar odd behaviour.  Any other gems lurking out there?


I'm learning Javascript and am told setting a variable equal to a function is done all the time.  I'm trying to figure out why.  Below is sample code that suggests there is no advantage.  What am I missing?  <script type="text/javascript">           var  addVar =  function() {             var myTemp = 0;              for(i=0; i< arguments.length;i++){                myTemp+=arguments[i];             }             return myTemp;          }           function addFunc() {             var myTemp = 0;              for(i=0; i< arguments.length;i++){                myTemp+=arguments[i];             }             return myTemp;          }           function addTwo(first,second){             return first+second;          }           alert( addTwo(addVar(1,2,3),addVar(1,2,3)) );          alert( addTwo(addFunc(1,2,3),addFunc(1,2,3)) );   </script>

I've recently started maintaining someone else's JavaScript code. I'm fixing bugs, adding features and also trying to tidy up the code and make it more consistent.  The previous developer used two ways of declaring functions and I can't work out if there is a reason behind it or not.  The two ways are:  var functionOne = function() {     // Some code };     function functionTwo() {     // Some code }   What are the reasons for using these two different methods and what are the pros and cons of each? Is there anything that can be done with one method that can't be done with the other?


In a faraway country, they have a strange culture where they favor girls over boys. Additionally, they know that boys are trouble, so they settle for one in a family. Thus, each family give birth until their first son is born, and then they stop (they never take the risk of having two boys – double trouble ...). As a result, families in this country are of the following types:  a. Boy  b. Girl, Boy  c. Girl, Girl, Boy  d. Girl, Girl, Girl, Boy  e. … Are there more girls or more boys in this country? You may assume that 𝑃𝑟(𝑏𝑜𝑦)=𝑃𝑟(𝑔𝑖𝑟𝑙)=0.5  Is the answer is that it is equal number of boys and girls because the Expected Value is 2, what means that for every boy there will be born a girl ?

Puzzle  In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?  My solution (not finished)  If we assume that the probability of having a girl is 50%, the set of possible cases are:  Boy (50%)  Girl, Boy (25%)  Girl, Girl, Boy (12.5%)  ...  So, if we call G the number of girls that a family had and B the number of boys that a family had, we have:  $B = 1$  $P(G = x) = (1/2)^{x+1}*x$  So  $G = \Sigma (1/2)^{x+1}*x$  I feel like the sum of this infinite serie is 1 and that the proportion of girls/boys in this country will be 50%, but I don't know how to prove it!  Thanks!


Their planet is dying or something and they all go in different directions, and he crash-lands on Earth on a farm I think. His ship is about the size of a bowling ball to us, and he's the size of an insect. He's exploring the area when a human picks him up, and he uses his laser on the human but the human just thinks it's a bug bite and squashes him. I think it was like he was writing in a "captain's log" sort of thing. It was a paperback, I can't remember if it was the first story of the collection but I think it was more in the middle of the book, and I thought they were all the same author but now I'm not sure. I thought it was Asimov but now I'm not sure.

This story was in one of the first SF anthologies I ever read, in the mid-1960s. A meteor lands near to a house. The householder finds it and carries it into his house (meteor is grapefruit/football sized). It’s actually a crashed spaceship, crewed by beings the size of beetles or cockroaches. They emerge, and are spotted by the householder, who of course thinks they’re insects, but notices one seems to be holding a tiny tube. He reaches towards it and the alien shoots his hand (the tube being a gun, of course), stinging him. I can’t recall how the story ends, but I’d love to know what the story was called, and who its author was, as I’m trying to assemble a list of the early SF that fired my enthusiasm for the genre.


Which of the following are quadratic integers in $Q[√−5]$?  EDIT: THANKS TO THE COMMUNITY FOR DIRECTING ME TO THE ORIGINAL QUESTION! I DID NOT KNOW THIS QUESTION ALREADY EXISTED ON MATH.SE  (a) $3/5$   (b) $2 + 3√−5$   (c) $(3 + 8√−5)/2$  (d) $(3 + 8√−5)/5$  (e) $i√−5$  Prove your result in each case.  Here's what I've got so far (I'm not even sure if this is half  right):  $\{1,i\sqrt{5}\}$ forms a basis for the field  $\mathbb{Q}(\sqrt{-5})$ viewed as a vector space over  $\mathbb{Q}$. We note that, $\mathbb{Q}\leq \mathbb{Q}(\sqrt{-5})$ Meaning, that the rationals are contained in this simple extension.  a)Yes, as just explained all rationals are contained in this field.  d)Yes, it is  $\frac{3}{5}+\frac{8}{5}\sqrt{-5}$ so if we select  $a=3/5$, $b=8/5$ in $\mathbb{Q}$ as a linear combination for  $a+b\sqrt{-5}$ then it works!  e)No, unless we are asking for  $i\sqrt{5}$.  I am having trouble on how to explain (b) and (c).

Can someone tell me if $\frac{3}{5}$, $2+3\sqrt{-5}$, $\frac{3+8\sqrt{-5}}{2}$, $\frac{3+8\sqrt{-5}}{5}$, $i\sqrt{-5}$ are all quadratic integers in $\mathbb Q[\sqrt{-5}]$. And if so why are they in $\mathbb Q[\sqrt{-5}]$.


If $b$ is a unit mod $p$, show that $(\frac{b}{p})+(\frac{2b}{p})+\cdot \cdot \cdot +(\frac{(p-1)b}{p})\equiv 0$.  Since $b\in U_p$ then $(\frac{1}{p})+(\frac{2}{p})+\cdot \cdot \cdot +(\frac{(p-1)}{p})$.  (So I'm not sure if I'm stating this part correctly) Therefore for each $(\frac{i}{p})$ for $i=1,...,p-1$, $i$ is either in $Q_p$ or not. Since $|Q_p|=\frac{\phi(p)}{2}=\frac{p-1}{2}$. Half will be in $Q_ p$ and the other half will not. So we get $(\frac{1}{p})+(\frac{2}{p})+\cdot \cdot \cdot +(\frac{(p-1)}{p})=1-1+1-\cdot\cdot\cdot +1\equiv0$.  Is this okay?

I have a question about Legendre symbol.  Let $a$, $b$ be integers. Let $p$ be a prime not dividing $a$. Show that the Legendre symbol verifies: $$\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0.$$  I know that $\displaystyle\sum_{m=0}^{p-1} \left(\frac{m}{p}\right)=0$, but how do I connect this with the previous formula?  Any help is appreciated.


Are there vector spaces with uncountable basis ? I was thinking about something as $L^1(\mathbb R)$. A could imagine that $\varphi_x:\mathbb R\to \mathbb R$ defined as $\delta_x(y)=1$ if $y=0$ and $0$ otherwise can generate all function and is uncountable. Moreover there are linear independent (but I'm not sure).  But for an uncountable basis, how we would write for example $\sum_{x\in\mathbb R}f(x)\delta_x$ ? It looks weird, no ?   In general if $V$ has an uncoutable basis $\{e_t\}_{t\geq 0}$, and if $v\in V$, how write $$v=\sum_{t\geq 0}v_te_t,\ \ ?$$ I guess that the previous notation has no sense.

I was reading up on the difference between countable and uncountable sets, and was wondering if there was a basis of uncountable size.  I now know there are, however they all seem to be covering rather high level areas in math.  So I was wondering; what is the simplest example of a basis of uncountable size for a vector space over a field?


Sometimes when I try to install something using sudo apt-get install it shows results looks like ---  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?   Now, I want to know the process(name , id) which is using it. If the process is no more needed I can kill it.  How can I know the process id?

I get this error when trying to use apt-get:  E: Could not get lock /var/lib/dpkg/lock - open (11 Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/) is another process using it?     How can I fix this?


Asp.net MVC5 and WebApi2 have Authorize attributes on controllers that let you filter on roles. For example:  [Authorize(Roles="HomePageUser")] public ActionResult Home(){     return View(); }   But this emits a 401 status code if the user is authenticated but not in the correct role. My question is simply: is this the best approach or should I write a filter that sends 403 if they are authenticated but in the wrong role?  To see why this is an issue, consider: the user who is not in role HomePageUser logs in and tries to go to the Home page. The Authorize filter emits a 401 code which the Owin context then intercepts and turns into a 302 redirect to the login page. But, the user is in fact logged in and no amount of logging in can rectify the fact that the user's identity lacks the permissions to view the page.  In practical terms, this all means frustration for the users because the automatic redirecting never gives them any information about why they can't see the page--they are likely to assume they typed in their password incorrectly.  It seems to me that the key failure here is that the Authorize filter lied--the user was not unauthorized but forbidden, and it should have issued a 403.  Here's the code I have in mind to fix this. For MVC actions:  using System.Web.Mvc;  public class AuthorizeOrForbidAttribute : AuthorizeAttribute {     protected override void HandleUnauthorizedRequest(AuthorizationContext filterContext)     {         if (filterContext.HttpContext.User.Identity.IsAuthenticated)         {             filterContext.Result = new HttpStatusCodeResult(403);         }         else         {             filterContext.Result = new HttpUnauthorizedResult();         }     } }   and for Web Api actions:  using System.Web.Http; using System.Diagnostics.CodeAnalysis; using System.Diagnostics.Contracts; using System.Linq; using System.Net; using System.Net.Http; using System.Security.Principal; using System.Web.Http.Controllers; using System.Web.Http.Filters; using System.Web.Http.Properties;  public class AuthorizeOrForbidAttribute: AuthorizeAttribute {     protected override void HandleUnauthorizedRequest(System.Web.Http.Controllers.HttpActionContext actionContext)     {         if (actionContext.RequestContext.Principal.Identity.IsAuthenticated)         {             actionContext.Response = actionContext.ControllerContext.Request.CreateErrorResponse(HttpStatusCode.Unauthorized, actionContext.RequestContext.Principal.Identity.Name+" does not have permissions for this request.");         }         else         {             actionContext.Response = actionContext.ControllerContext.Request.CreateErrorResponse(HttpStatusCode.Unauthorized, "Authorization has been denied for this request.");         }     } }   From there it is easy enough to redirect these status codes to the appropriate error pages depending on what you want the user to see.  Is this a good approach? I'm worried because I'm wondering if there's a good reason Microsoft didn't do this in the first place.

In ASP.NET MVC, you can mark up a controller method with AuthorizeAttribute, like this:  [Authorize(Roles = "CanDeleteTags")] public void Delete(string tagName) {     // ... }   This means that, if the currently logged-in user is not in the "CanDeleteTags" role, the controller method will never be called.  Unfortunately, for failures, AuthorizeAttribute returns HttpUnauthorizedResult, which always returns HTTP status code 401. This causes a redirection to the login page.  If the user isn't logged in, this makes perfect sense. However, if the user is already logged in, but isn't in the required role, it's confusing to send them back to the login page.  It seems that AuthorizeAttribute conflates authentication and authorization.  This seems like a bit of an oversight in ASP.NET MVC, or am I missing something?  I've had to cook up a DemandRoleAttribute that separates the two. When the user isn't authenticated, it returns HTTP 401, sending them to the login page. When the user is logged in, but isn't in the required role, it creates a NotAuthorizedResult instead. Currently this redirects to an error page.  Surely I didn't have to do this?


As Taylor's series give $e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$  Similarly, can someone please help me to find expansion of the term $\frac{1}{(1 - e^{-x})}$? Where $0 < e^{-x} < 1$  Thank you.

How do you find the Taylor expansions of the expressions:   $\frac{1}{sin2x}$ and $\frac{1}{1-e^{-x}}$ I'm not sure what to do since all the terms are in the denominator. Thanks in advance for any help.


\begin{center} \begin{tabular}{|c|c|c|} \hline & polarity & $\displaystyle \frac{\textrm{charge}}{\textrm{mass}}$\\ \hline \textbf{A} & negative & $\displaystyle \frac{E}{g}$\\ \textbf{B} & negative & $\displaystyle \frac{g}{E}$\\ \textbf{C} & positive & $\displaystyle \frac{E}{g}$\\ \textbf{D} & positive & $\displaystyle \frac{g}{E}$\\ \hline \end{tabular} \end{center}

The table that I'd like to make does not display fractions with enough space between lines. What's the reasoning for this? (Not enough rep to be able to post a picture yet unfortunately.)  \documentclass{article} \usepackage{amsmath,amsfonts} \usepackage{booktabs}  \begin{document} \begin{table} \centering \begin{tabular}{lcccc} \toprule \textbf{Care type} & $\mathbb{P}(Pat \cap H)$ & $\mathbb{P}(Pat \cap H')$ & $\mathbb{P}(Pat' \cap H)$ & $\mathbb{P}(Pat' \cap H')$\\ \midrule Direct care  &$\displaystyle \dfrac{58}{197}$  &  $\displaystyle \dfrac{48}{197}$  & $\displaystyle \dfrac{21}{197}$* &$1-\displaystyle \dfrac{58}{197}$ \\ Housekeeping &$\displaystyle \dfrac{12}{17}$  &  $\displaystyle \dfrac{2}{17}$  & $\displaystyle \dfrac{5}{17}$* &$1-\displaystyle \dfrac{12}{17}$\\ \bottomrule \end{tabular} \caption{Probabilities of hand hygiene given direct patient contact} \label{tab:handwash_given_pat} \end{table} \end{document}   Edit: Image added and MWE completed.


I have some problems with my Bluetooth headset. It works fine if I connect it when Ubuntu runs via an installation medium in trial mode. After installation, it is not possible to connect it anymore. It works fine with my Android phone and with another Windows computer. Does anybody have an idea how to fix this?  Best regards

I'm trying to use mt SONY MDR-XB950BT headphones on Ubuntu 16.04 but not having any luck. I've managed to get them connected but it doesn't seem like I can actually listen to music/videos out of them. I tried setting the audio output to the headphones, but sound keeps coming out of the speakers instead. I also installed Pulse Audio Volume Control, but that doesn't seem to make a difference. I briefly managed to get it so that the test sound would play through the headphones, but when I tried to watch an online video, the video wouldn't even play until I changed the sound output device.  Does anyone have any advice/experience with this kind of thing? Any help would be greatly appreciated.


So I am building a simple user authentication system, users will input their name into username and password fields and then the code should test what the user enters against a database. I have used a string comparator to do this but it does not execute code in the if statement when correct user and pass are fed through it.  Here is a snippet of the code  Boolean authpassed = false while(rs.next() && (authpassed == false)){           int id  = rs.getInt("id");          String first = rs.getString("first");          String last = rs.getString("last");          String username = rs.getString("username");          String password = rs.getString("password");            System.out.print("ID: " + id);          System.out.print(", First: " + first);          System.out.print(", Last: " + last);          System.out.print(", Username: " + username);          System.out.println(", Password: " + password);           if((authuser == username) && (authpass == password) ) {              System.out.println("Logged In!");              authpassed = true;          }       }   When code is executed with correct login details the "Logged in" is not displayed?  Thanks for having a look :)

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


According to euler's formula \begin{equation} e^{i\pi}=-1 \tag{1} \label{1} \end{equation} \begin{equation} e^{-i\pi}=-1 \tag{2} \end{equation} Comparing $(1)$ and $(2)$, we get $$ e^{i\pi}=e^{-i\pi} $$ Comparing the exponents on both sides, $$i\pi=-i\pi$$ Simplifying yields $$i=-i$$ Is this correct? If not, what is the mistake?

We know that $e^{\pi i} = -1$ because of de Moivre's formula. ($e^{\pi i} = \cos \pi + i\sin \pi = -1).$  Suppose we square both sides and get $e^{2\pi i} = 1$(which you also get from de Moivre's formula), then shouldn't $2\pi i=0$? What am I missing here?


I have a table with some fields (time, text, type). I want to build a query to return for every type the text that was introduced with the maximum value of time. Oracle has some restrictions and it is not simple to build the query without some tricks.  I am struggling to get the right query, can anyone help me with it?  TIME TEXT TYPE -------------------------- 03.05.2020 AA 2 02.04.2020 BB 2 01.04.2020 CC 1   I want a query that returns  03.05.2020 AA 2 01.04.2020 CC 1

Table:   UserId, Value, Date.   I want to get the UserId, Value for the max(Date) for each UserId. That is, the Value for each UserId that has the latest date. Is there a way to do this simply in SQL? (Preferably Oracle)  Update: Apologies for any ambiguity: I need to get ALL the UserIds. But for each UserId, only that row where that user has the latest date.


I'd like to ask the user for their first and last name by using a string variable, then use the first name they entered in that string and print it out.  string name;  cout << "What is your first and last name? "; cin >> name; cout << "Thank you " << name  << " for shopping with us!";   Where the name variable is in the second cout statement I'd like to just use their first name, with the current setup i have, it outputs both their first and last names.

I'm trying to iterate over the words of a string.  The string can be assumed to be composed of words separated by whitespace.  Note that I'm not interested in C string functions or that kind of character manipulation/access. Also, please give precedence to elegance over efficiency in your answer.  The best solution I have right now is:  #include <iostream> #include <sstream> #include <string>  using namespace std;  int main() {     string s = "Somewhere down the road";     istringstream iss(s);      do     {         string subs;         iss >> subs;         cout << "Substring: " << subs << endl;     } while (iss); }   Is there a more elegant way to do this?


If I play Lucio, can I heal the teammates located at a different height? (roof, upstairs, hovering Pharah... )  In other word is that aura strictly horizontal? Or does it work more like a bubble like Winston's barrier?  If it's horizontal, does it require Line Of Sight or not? (will I heal a nearby ally right behind a wall?)


I'm doing an exercise from a python for beginners book. The project I'm stuck on is as follows: "Write a function that takes in a list of value as an argument and returns a string with all the items separated by comma and a space. Your function should be able to work with any list values passed to it"  Here is my code:  def passInList(spam):        for x in range(len(spam)):            z = spam[x] + ', '             print(z,end= ' ')  spam=['apples', 'bananas', 'tofu', 'and cats'] passInList(spam)   Expected output is - 'apples, bananas, tofu, and cats'.  My output is- 'apples, bananas, tofu, and cats,'  The issue I'm having, is that I can't seems to get rid of the comma at the end of "cats".    Thanks for suggestions.

What would be your preferred way to concatenate strings from a sequence such that between every two consecutive pairs a comma is added. That is, how do you map, for instance, ['a', 'b', 'c'] to 'a,b,c'? (The cases ['s'] and [] should be mapped to 's' and '', respectively.)  I usually end up using something like ''.join(map(lambda x: x+',',l))[:-1], but also feeling somewhat unsatisfied.


For a quick and dirty project, what are some of the simplest ways to reduce the power use of an Arduino?  Imagine the following setup:   A typical Arduino Nano, hooked up to a pair of DS18B20s and one of the mini OLED screens. Power comes from a cellphone battery hooked to a TP4056 board, which then runs to a small 0.9V >> 5V boost board, both common eBay items.  The idea is to make a basic platform, to which additional functionality will be slowly added, such as a wireless link and data-logging. For now, though, the situation is as described above.  The obvious start would no doubt be killing off unnecessary LEDS , or at least, tacking on extra resistance to make them fainter. Maybe finding how to reduce the brightness of the OLED screen would also be an obvious step, and that green LED next to the ON switch isn't necessary...   But beyond this, what simple steps could be done in coding or hardware load-out could help get more battery time?  (This question relates to a specific level of embedded system enthusiast, namely, the intermediate level, someone who isn't yet confident enough to dive into the depths of the AVR assembly language, but rather someone who already grasps the basics of how electronics and embedded devices are put together in a system (In other words, myself..). There are differences compared to the  question, and more specific to the actions I practically can take.)

Scenario I have created a nice electronic door lock for my dorm room. It is currently an Arduino Diecimila with a servo [un]locking the door. It has a numerical keypad with 3x4 buttons and 5 LED's (2 serie pairs and one single LED). It also currently runs on a cellphone charger. I have now redesigned it to run on a standalone Arduino (ATmega328), but would really like to have it run on AA batteries or even a 9V battery. For the software part, I figured I could put sleep calls for certain times inside the loop method to keep the ATmega power consumption as low as possible. And let the LED's "flash" with as long as possible time off. Question 1 When a button is pressed during the few milliseconds which the board sleeps, will it be "remembered"/"held" until it comes out of sleep and then be picked up as a button press? What would be the best way to handle this button press on sleep? Can I code it to wake up upon button activity, or must I just let it sleep for e.g. 10m.s. in every loop? Question 2 How would I approach the math of calculating how many AA batteries are needed to run this device for 10 months? Also, I don't know how to measure the average power usage per minute or so, since it alternates quickly etc. The Device


So when I code, say in C++, I like to separate blocks of code with spacing, etc. This makes it easier to navigate and interpret. When I separate out a block, it becomes clear that that is a unit that serves some particular purpose.  In Latex, I do this for navigation reasons and clarity. However this causes undesired consequences: New paragraphs when I don't want them. For example, I like to write proofs as follows:  \begin{proof} etc. etc. etc. (blank line) \end{proof}   This way it's easy to see where the end of a long proof is. However, this causes the QED symbol to be on a new line: Not ideal.  Also, I like to separate an eqnarray environment with new lines too.  Is there any way to attain better clarify with space? Or is this something I should just live without?

I have been using LaTeX for about a year now, and I quite like it.  However, I like to space out my source code. In most languages, this doesn't cause an issue, as extra newlines don't affect meaning.  However, in LaTeX, two newlines in fact changes the document, by creating a new paragraph.  I'm wondering, is there a way to turn this feature off in latex, and require me to specify new paragraphs manually? If not, is there an alternative to LaTeX (preferably similar i.e. still TeX based) which isn't so sensitive?


I found my four independent variables have a high positive association with my depepednet variable. However, except one independent variable, P value of all other indepdent variables are not significant in my regressino analysis. My hypothesis is that each of my independent variables separately has a postive relationship with my dependent variable, so I have four hypothese. I was wondering if I should reject three of my hypothese under such situation?  Sorry, forgot to say, There is no collinearity problem with my independent varibales Thank you.  More information:Please see attached picture. It is my research model. After bivariate correlation analysis and partial correlation, all independent variables are positively associated with dependent variable. A hierarchical regression was used with control variable.I first put control variable in first block of SPSS, and then add the 4 other independent variables in second block. The results are in attached docuement. Three independent variables are not significant.... Correlation table:

I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out.  I have a least squares regression model, with one independent variable and one dependent variable. The relationship is not significant. Now I add a second independent variable. Now the relationship between the first independent variable and the dependent variable becomes significant.  How does this work? This is probably demonstrating some issue with my understanding, but to me, but I do not see how adding this second independent variable can make the first significant.


We have two Microsoft Private Clouds: one consists of 8 nodes (each with two processors) and the other consists of 4 nodes (each with two processors). Call them Private Cloud A and Private Cloud B. Each node is currently licensed on our EA with a Windows Server 2012 R2 Datacentre license.  Some production services are hosted on A, with DR instances for those services existing on B (i.e. SQL availability group with primary on A, one secondary on A (for HA) and one secondary on B (for DR), Exchange cross-site DAG). We also have some production services running on B, with DR instances running on A.  Private Cloud A hosts about 70 VM's (95% Windows Server 2012, rest are Linux based) and Private Cloud B hosts about 30 VM's.  We'd like to implement SCCM (more specifically, SCVMM) to help us manage the virtual environment (which is currently done mostly through Powershell scripts and manual intervention on Failover Cluster Manager and Hyper-V console).  How should we license SCCM 2012 R2 in this environment? Would I need to purchase a Datacentre License for each of the 12 hosts (which would be an exorbitant amount)? Or, do I only license one host with a Standard license, and host all my VM's that run SCCM components on that one host? Or should I rather put down a physical machine to host these components, and license with a Standard license?

This is a  about Licensing.    Questions on licensing are off-topic on Server Fault.  If your question has been closed as a duplicate of this question, then this is because we want to help you understand why licence questions are off topic rather than just telling you "it just is". In all likelihood, this question will not address your question directly, it was not meant to.    I have a question regarding software licensing. Can the Server Fault community please help with the following:   How many licenses do I need? Is this licensing configuration valid? What CALs do I need to be properly licensed? Can I run this product in a virtual environment? Can I downgrade this product to an earlier version? Am I entitled to feature X with license Y?


I have created a business page for my restaurant. My boss's wife has nearly 5,000 people who like her business page. Is there a way to "invite" all of the people who like her page to like my page?

I'm the admin of a certain Facebook page, "A". Some people I don't know personally and I'm not friend with liked this page.  Now I created a 2nd page, "B". Since the topics are similar, I'd like to invite all the people from page "A" to also like page "B".  Is this possible?


I really do have a doubt. Actually I'm making Vplotter and for that I'm using 333nNm 0.31 A Stepper motor NEMA 17. And I'm giving an external supply of 5V and 1 A to motor driver sheild. Will L293D heat.

This question is about the following three integrated H-bridge drivers: -    or L293D (D = protection diodes added)  (protection diodes included)  (no protection diodes)   Time after time the same question keeps coming up - someone is using one of these devices (on a low voltage, usually around 6V or less) and they are just not performing adequately. The reasons are listed further below but my question is this: -  What H-bridge drivers are preferred when controlling a low-voltage motor?   Information  The L293 and the SN754410 are nearly identical and crucially, if you try and control a 1 amp load, you are faced with dismal performance: -    The tables tell you (typical conditions) that the upper transistor drops (loses) about 1.4 volts when driving a 1A load and, the lower transistor drops (loses) about 1.2 volts when driving a 1A load. The upshot is that if you have a 6V, 1A motor and 6V battery, don't expect to see more than 3.4 volts across the motor: -  \$V_{OUT} = 6V - (1.4V + 1.2V) = 3.4V\$  Worst case scenario is you might only see 2.4 volts across it.  What about the L298? It's got a nice big heat-sink whereas the L293 and SN754410 are regular-looking chips. Here's what the volt drop (losses) look like: -    It's the same story - for a 1A load, you can expect to lose up to 3.2 volts and, what you thought might be 6V across your motor, is at best 4.2 volts and at worst only 2.8 volts.  Clearly none of the devices listed are suitable for low voltage applications where the motor might be expected to draw in excess of 0.5 amps.


Those Command Are Present In 'help' Command They Are Internal Command Or Not....

I'm running Bash scripting, but sometimes I get confused which of these commands I use belong to who. Sometimes man xxx works, sometimes doesn't, so I use --help or info, mostly one of these works to show description of the command. Can anyone tell me how I would know what command belongs to what? Bash builtin, GNU utility, etc.


Take an example:  Me : Where can I find the best pizza in the city?   Friend:1000s of people are dying of hunger and all you care about best pizza.  In this case he does reply to my question but it doesn't help me.  Is there a word/group of words to express this?

When some one is asked a question, sometimes if they are trying to avoid answering the question, they respond with something unrelated. What is the word for that response?  Eg. A: Why were you late?     B: This bagel tastes good.  What I am looking for is the name of that response, not the action.


I came across a website/facebook page which posts famous quotes and i wonder what does "Porn" mean in this situation ? I also search many websites but they all believe that it has something to do with pornography but i don't think it's relevant to that .. what do you think ?

On   while browsing Meta Stack Overflow, I have encountered the phrase information porn, typically used by Jeff Atwood. What does it mean?


I attempted to test out Lutrix on ubuntu 17.10 with League of Legends. Everything worked fine and well.  After testing it out I no longer needed Lutrix, Wine, or the game so I purged both Lutrix and Wine and deleted the Wine directory along with its contents.  However I can still see the League of Legends and Uninstall League of Legends launcher in Dash.  I have searched in /usr/share/application and in /usr/local/share/applications but can't find anything. I also performed a full system search and came up with no *.desktop files that fit the description.  Is there any other way that Ubuntu registers launchers in Dash that I am missing?

I have installed Chromium and Tweet Deck on it (trough Chrome Store), now I uninstalled Tweet Deck and after that Chromium, the problem is, when I installed Tweet Deck it asked me if I want to create a shortcut to it and I chose YES. Now that both are uninstalled the Tweet Deck icon still appears on Unity Menu over Internet.    I tried to remove the icon from the menu but I can't figure out how to do this. It should be a simple thing to do, but is giving me headaches :P  What I have to do to remove the shortcut and possible junk files from Chromium?  Also my Ubuntu version is 11.10 x64.  (Sorry if I write something wrong)


Take a website such as  where users can reply to a post, and then users can reply to that reply, etc.     I'm building a mobile application that deals with a similar situation with nested replies. However, I'm really stuck on how to implement it efficiently.  Mobile screens have such a narrow width. I feel this "indentation" pattern encounters problems very quickly. (Can't show very many comments deep, text boxes get narrower and narrower, etc.)  Does anyone have any alternative ideas on how I could implement this?

Websites such as  have tiered comments. In tiered comments, a response is indented one step past its parent comment. How can tiered comments be adapted for the mobile screen? I forsee the following problems from transferring this website idiom directly to mobile:   The narrow screen width limits the depth of conversations. The narrow screen height limits the user's global mental map of the conversation. That is, the user may lose track of who is responding to who when the originating comment is not visible on the screen. The indentation is ostentatious use of white space on mobile screens. Are there other ways to show hierarchy without using vast amounts of white space?


I need to show the value of the fields of the objects being created on the error page. i tried to do it via add error but it doesn't output dynamic data trigger checktime on Appointment__c (before insert, before update) {     Time startDate;     Datetime endDate;     String Name;           //Fetch all appointment records to compare     List<Appointment__c> listOfAllAppointments = [SELECT Id,Appointment_Data__c,Appointment_Data_End__c,Doctor__c                                                   FROM Appointment__c];                                                        for(Appointment__c newAppointment : Trigger.new) {         for(Appointment__c appointment : listOfAllAppointments) {             if(appointment.Appointment_Data__c <= newAppointment.Appointment_Data_End__c                 && appointment.Appointment_Data_End__c >= newAppointment.Appointment_Data__c                 && appointment.Doctor__c == newAppointment.Doctor__c)              {                //  newAppointment.addError('Your Error Message'+newAppointment.Doctor__r.Name);                             newAppointment.Appointment_Data_End__c.addError('Bad');                 break;             }         }     }  }

This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, navigate to the  tag. This question and answer is owned by the community! If you can improve it and make it more useful, you're welcome to edit it. I am building a trigger, a unit test, or other Apex code. I'm working with sObject records, and trying to access related record information. For example, I might have a structure like this: Account a = new Account(Name = 'Test'); insert a;  Opportunity o = new Opportunity(Name = 'Donation', AccountId = a.Id); insert o;  System.assertEquals(o.Account.Name, 'Test', 'Correct Account associated'); // Assertion fails!  Or, in a trigger, I might be aiming for something like this: trigger ContactTrigger on Contact (after insert) {     for (Contact c : Trigger.new) {         if (c.Account.Name == 'Test') {             // Take some action here         }      } }  Why doesn't this work? Why am I getting null values, or NullPointerExceptions?


On my device (running Stack Exchange Android app v1.0.95), the Stack Exchange sites sidebar lists "Unknown Site cogsci" with the default Stack Exchange icon.    (Sorry, no freehand circle to highlight the problem entry. It's in the middle, between Community Building and Biology.)  When I tap this icon, the app crashes with (what I believe is) a null pointer exception.  I believe that the site formerly known as Cognitive Science (that is, cogsci.stackexchange.com) was renamed or otherwise migrated sometime in the past few months.  I see a twofold problem:   It looks like the app missed this migration, leaving my sidebar pointing to a non-existent site. In addition, the app crashes when visiting non-existent sites (instead of showing "site not found" or similar).

I let Android submit the crash report several times since the site was renamed to Software Engineering.  The side drawer icon is labeled "Unknown Site programmers".  Are other people seeing this problem?   App Version: 1.0.89 Device Manufacturer: LGE Device Model: Nexus 5X OS Version: 7.0 (3425233)


I'm new to Ubuntu 15.04 and I experienced problems with Temaker, namely the keyboard shortcuts did not work after some time. However, manually installing the version compiled with Qt4 fixed the problem, but according to this  the problem recurs if Ubuntu automatically updates to the new version, which indeed happened. My question is if it is possible to disable automatic updates just for Texmaker to stay with the working Qt4 version.

Because of  I'd like to prevent apt-get upgrade and Update Manager from updating the "libgtk2.0-0" package.   How can this be achieved?


We’re going to the pub. Want to come with?”    I have heard this from an American colleague. Though this sounds odd to the majority of us, however, since I am not sure of the usage, I am asking how common is it to use the phrase “come with” without specifying with whom.

Do you want to come with? Can I come with?  I seem to hear this construction more often in recent years, but it still grates on my ear. I know it's often said that one shouldn't , but I class that rule along with  (i.e. — pedantic tosh). Is it always informal/casual speech to end a sentence with "with"? Was it ever thus?


In my module notes, if $A$ is a Borel and $m(A)=0$, then it is not necessarily true that any subset $B$ of $A$ (with $m(B=0)$) is Borel.  So I am wondering if there is a null set that is not a Borel set?

I'm trying to find a set which is Lebesgue measurable but not Borel measurable.  So I was thinking of taking a Lebesgue set of measure zero and intersecting it with something so that the result is not Borel measurable.  Is this a good approach? Can someone give a hint what set I would take (so please no full answers, I want to find it myself in the end ;-))  Also, I seem to remember that to construct a non-Lebesgue measurable set one needs to use the axiom of choice. Is this also the case for non-Borel measurable sets?


I am new to Java, could you please tell me -  "what is the purpose of the protected variable and method in Java".  Thanks in advance. JP.

In Java, are there clear rules on when to use each of access modifiers, namely the default (package private), public, protected and private, while making class and interface and dealing with inheritance?


I don't do math a long time, so I completely don't remember how to prove that: $$ \sum_{i=1}^\infty \frac{i}{2^i} = 2 $$  Can anybody help me?

I have put his on wolfram and obtained answer as follows:  $\sum_{n=1}^{\infty}\frac{n}{2^n} = 2$  And the series is convergent too because $\lim_{n\to\infty} \frac {n}{2^n} = 0$  However I am wondering if there is a convenient way to solve this; I don't think you can represent it by a geometric progression either. So how do we have to do it on paper?


Question: I was looking for natural numbers with same number of odd and even Divisors.Then I observed that, every second number in the list $2,4,6,8,10,12,14,...$ is such a number. Following list shows that, $2,6,10,14,...$ are even natural numbers that have same number of odd and even Divisors. $2 \qquad 1 \qquad 1\quad\ast$ $4 \qquad 1 \qquad 2$ $6 \qquad 2 \qquad 2\quad\ast$ $8 \qquad 1 \qquad 3$ $10 \qquad 2 \qquad 2\quad\ast$ $12 \qquad 2 \qquad 4$ $14 \qquad 2 \qquad 2\quad\ast$ $16 \qquad 1 \qquad 4$ $18 \qquad 3 \qquad 3\quad\ast$ ......... How we can prove this in general? Is there is something special about this? Note: I just copied the above list from  answer given here,

With given number N, how to determine first number after N with same amount of odd and even divisors? For example if we have N=1, then next number we are searching for is :   2 because divisors: odd : 1 even : 2   I figured out that this special number can't be odd and obviously it can't be prime. I can't find any formula for this or do i have just compute it one by one and check if it's this special number ? Obviously 1 and number itself is divisors of this number. Cheers


I have a problem with qgis 2.8.1 (Wien). Whenever I change the project SRC to WGS84-World Mercator (EPSG 3395), the area is calculated as zero.  How can I solve this problem? Is this a known bug?  The answer from  don't solve the problem, since the problem only appears with a metric CRS.

I am using Qgis 1.7.4 to calculate the area of polygons. My shapefiles have been projected using the coordinate system WGS 1984 UTM fuseau 35 Sud, but my area calculations are still displayed in degrees. how do I get them in metres?


I am applying to statistics and biostatistics PhD programs for next year, and I just got my GRE scores back, and they weren't at all what I expected.  I ended up with a 159V/156Q/6.0AW, which corresponds to 83rd/61st/99th percentile in the verbal/quantitative/analytical writing sections, respectively. So, I have a combined score of 315 with a 6.0 writing.  I understand that most statistics programs place a premium on the quantitative score, and so I am a little worried about my low quantitative score, but I am wondering if the relatively high verbal/writing can offset the weakness there.  For some idea of what kind of student I am, I have about a 3.5 GPA with an applied math major, with a full course in real analysis, mathematical statistics and some graduate level regression theory, and potentially an honors thesis (pending). Since my scores are so atypical compared to other applicants (who typically have much stronger quantitative and lower verbal/writing), I am unsure of what my score means for my application as a whole.  I suppose the question of "do stats programs care?" can be generalized to "do quantitative programs care?". While I see there are some threads on low quantitative scores, there aren't too many about a low quant score combined with a high(er) verbal/writing score.

Question: I got general GRE scores of VR (verbal reasoning), QR (quantitative reasoning), and AW (analytical writing).  Is this a good score to apply for entry to postgraduate degree in field X?  How will this score look to the selection committee?    Note: This is an intentionally generic GRE question (with unspecified scores and field of study) which is intended as a template for a large number of questions asked on this forum regarding evaluating the scores on the general GRE test (e.g., , , , , , , , and ).  This question seeks answers that are applicable for an applicant for graduate-level programs in any field, based on any scores in the GRE general test.  The goal of this question is to provide a general reference to avoid the need for specific questions with particular scores/field of study.


I selected a group of photos and added them to an album.  But now, I want to exclude those photos from my search, because I don't want to add them to another album by mistake and vice versa - I want to add all photos to some album.  I searched on Google, but found nothing.  Do you know any solution?

Go to  Add a few photos to a photo album Go back to All Photos   See all of the photos there, even ones you copied to the Album. No problem here, per se. At least not yet.  What if you want to delete photos that you did not copy to that album?  Where is the selector or filter that filters those "in an album already" photos from this main view?  Or is there a way to create such a filtered view such that I can then cherry-pick photos for deletion?


Will Stack Overflow ever implement a feature that allows users to see if someone is actively answering their question?  I feel like this feature would help make the site feel more active and give users a reason to wait for an answer longer if they see someone is in the middle of composing a long response.  Quora has this feature, and when I see someone is in the middle of answering my question I tend to stay on the site longer to wait for their response.

I ask a lot of question on SO, so this recommendation/idea comes from that experience. I'm not really sure how this would fit in with the current structure of SE.   Oftentimes after asking a question, maybe after an hour or so, I end up finding the answer I needed somewhere. And it comes time for me to answer the most difficult question of all: do I delete this question, or do I keep it in case someone answers and others may benefit from it. The problem is, if I don't delete it and no one answers, my acceptance rate goes down. So usually I'll just delete it.  However, sometimes I fear that someone is typing a really really long answer to my question since itäs only been an hour, and so I imagine the nightmare that person experiences when they find out their essay will be gone to waste. Overall, this never-to-be-seen-again answer could have benefitted many people had the question remained.  Since SE has gone "live-happy" lately, where answers and comments refresh live, I thought it might be interesting if the original asker of the question (or anyone else for that matter) could see how many people are currently responding to the question (just count, not necessary to display their names). This way, if I know someone is replying, I won't delete the question, and others can benefit from it.


I'm not sure what I did, but now my KDE desktop is just a blank screen.  I am still able to log onto a gnome session, and the guest account has a perfeclty fine Kubuntu session, but no matter what I do I can't get a Kubuntu session with my own login.

I have updated my kubuntu 14.10 to kubuntu 15.04. And now after boot, when I enter my password on welcome screen, I will get black screen. It's looks like screen powered off. No cursor, no change brightness. Nothing. And when I try switch to text consoles (Ctrl+Alt+F1) nothing happening. If I doesn't login in welcome screen I can switch to text console.


Since High School, I have cheated a lot in exams. But in college it became a habit and I developed successful ways of doing it, without getting caught throughout first and second year. But I eventually got caught, and I feel horrible about it, it was the most humiliating thing ever, but I guess karma comes to us all.  A lot of the other students know that I've cheated a lot throughout the course and lost respect for me, so they'll be happy now. This time, I cheated in the same way that has worked a lot for me in the past. I recorded full essays on my phone, put it in my pocket with earphones hidden up my jumper and sleeves, and I rested my head on my hand with the earbud in my ear, listening to the recorded material. I knew early on that this invigilator was more wary of my body language than any others have been before, she was a lot younger than any others and probably more alert about technology. I became a bit unsettled, and she noticed that as well. When the first essay finished, I put my arm down and she immediately came over to me and investigated me. My major mistake this time was that, instead of putting my phone in my pocket and covering the wire with my jumper, I had it between my legs with the wire sticking down the middle of my trousers. She saw the wire, bent down and pointed at it asking 'what's this?' then rolled up my sleeve and found the ear socket inside. I was busted, so I gave her my phone and earphones, then she took my paper of me and gave me a new one to restart. It wasn't subtle, the whole class knew about it and I saw a lot of them turning around to look at me. She then phoned her invigilator boss and told her about it to make sure she handled it correctly, and she said clearly 'I just caught a student cheating' in front of everyone. I just sat there for the rest of the time, not knowing anything because I didn't study for it, and wrote a letter to the marker about it. At the end, everyone left the room staring at me while she took a photo of the evidence.  I burst into tears when I was left with the invigilator on my own, and she told me to speak to my tutor. He told me that I'd fail the module, and I emailed the programme leader about it, who said he would wait for the invigilator's report. I think I'm going to have to go through a disciplinary hearing, but I have to protect myself. I can't admit that I've cheated in just about every exam in the three years I've been there, I'll have to say that this was a one off thing because of personal problems and lack of preparation.  But it's not a good feeling having a conscience guilty of such dishonesty, and more lies to tell. I can't get expelled from the course, because I want to get my degree, but I'll deal with failing the module and having a disciplinary record.  Am I just an evil person by nature? I know I don't deserve to be on the course having not been caught so many times, yet I'm doing everything I can to stay. A lot of people say honesty is the best policy, but I don't believe that is true within the business of living and getting success.  Also, how will a disciplinary record affect my future? Will employers/other education institutions know of it after I leave?

I got caught cheating in a two-hour engineering exam consisting of 100 multiple choice questions which was done online through the  e-learning software. I feel like my life is almost over.  Having not studied well and having no time to study, I decided to cheat. I know there are no excuses for cheating. Before the exam I dug up research about moodle exams, and it turned out you can take the exam anywhere you want to as long as you have the quiz password. Taking advantage of this, I went up to my engineering library and asked a close friend who was taking the exam to send me the quiz password before he starts.  What I had prepared:   Calculator (was not allowed during the quiz). Printed material (consisted of more than 200 pages). Google search engine (on a laptop ready to help). Whatsapp (to ask questions for a friend who took the quiz last year).   As I sat down, I did the first 50 questions, suddenly the quiz froze and moodle told me:      you are not allowed to take the exam from this location.   While I was leaving, one instructor responsible for the course (there are 5) came and found me. She accused me of cheating, took my mobile and made come with her to a huge office where two instructors searched all my mobile (took the name of my friend who gave me the password), and started talking to me, asking for all details of this crime. They took and confiscated my phone and looked at everything: Whatsapp conversations, all my emails, and images. The instructor took the mobile from my hand without asking me and kept it with her. It seems that the instructors are going to report me as well as my friend who sent me the password for the exam.  The university's Student Code Conduct said that cheating will result in one of the following: a Dean's Warning, Suspension, or Expulsion. If any of that happens, my future is over. A dean's warning will cancel my financial aid. A suspension would be for at least two years, and coming back would require a lot of work. An expulsion will be definite.  I've learned the lesson about cheating, now how can I fix this? How can I prevent the five instructors from reporting me? It's obvious that I should speak to them, but what should I say? What can I do? My future is almost over, but many of you are teachers and instructors here, what can I do to fix this?    EDIT: Wow, it has been almost 3 years. I would like to update on how I dealt with the situation.   Lesson: It was obvious to never ever cheat under any circumstances, and it was not whether you'd get caught or not.    Consequences: I received a Dean's warning but the financial aid wasn't revoked. However, I couldn't stay in the department as engineering was not for me and I was even ashamed to stay in the university.  What happened next: I transferred to an ABET-accredited Computer Science institution and I graduated with distinction in 2.5 years. It was extremely stressful as I had taken 6 major courses (18 credits) in one semester, but I had to do it.  Future plans: I'm going for an MSc in Computer Science in St Andrews next year.


Let an even function $f:\mathbb{R}\to\mathbb{R}$ which is even and differentiable. We define $F:\mathbb{R}^n\to\mathbb{R}$  as $F(x) = f(\|x\|)$. Show that $F(x)$ is differentiable on $\mathbb{R}^n$.   My Work:    Let $x_0\in\mathbb{R}^n$.   If $x_0\ne 0$ then the partial derivatives of the norm are well-defined and: $$ \frac{\partial \|.\|}{\partial x_i} = \frac{x_i}{\|x\|}$$ $\frac{x_i}{\|x\|}$ continuous and since $f$ is differentiable it's partial derivatives are continuous. So we can conclude that $\frac{\partial F}{\partial x_i}$ is continuous and therefore $F$ is differentiable. If $x_0=0$ then the $\|x_0\| = 0$ and since $f$ is even $f(0)=0$ and it must be an extremum point. Therefore, $F'(0)=0$.   I'd like to get a critique of my work. Am I being right/rigorous?  Thanks.

I have tried an attempt on the following:  Let $F:U\in \Bbb{R}^n\to \Bbb{R}$ and $f:\Bbb{R}\to \Bbb{R}$ where $f$ is an even function. Now $F(\mathbf{x})=f(|\mathbf{x}|)$, where $|\ . |$ is the Euclidean norm. Given $f$ is $C^r$, I have to show that $F$ is $C^r$.  My attempt was to argument by induction. I showed that $F$ is $C^1$, basically using univariate chain rule on $\frac{\partial f\left(\sqrt{x_1^2+\dots+x_n^2}\right)}{\partial x_1}$ and arguing that it would be continuous using the fact that $f$ is $C^r$. Since the argument works for all $x_i$, it establishes first-differntiability for $F$ and continuity of the operator $DF(\mathbf{x})$. Then I moved on to show $F$ is $C^r$ assuming $F$ is $C^{r-1}$ and $f$ is $C^r$. Now what I did was partially differentiate:  $$ {\partial \over \partial x_2} \left[\frac{\partial ^{k-1}f}{\partial x_1^{k-1}}\right] = \underbrace{{\partial \over \partial |\mathbf{x}|} \left[\frac{\partial ^{k-1}f}{\partial x_1^{k-1}}\right]}_{(1)} . \underbrace{{\partial |\mathbf{x}| \over \partial x_2}}_{(2)} $$  My argument runs as follows: this partial derivative is continuous since $f$ is $C^r$ and hence $(1)$ is continuous. Continuity of $(2)$ is establishd in a similar manner, since $\sqrt{\mathbf{x}}$ is $C^r$ if $\mathbf{x} \neq \mathbf{0}$. Then the product would be continuous. I am uneasy on multivariate arguments and dont know if my approach is completely off track. I didnt use the even function property, so I am sure I might me missing something. Any hints and references would be welcome. Thanks!


I just fresh installed 13.10, but now the teamviewer.deb file won't install due to an unresolvable dependency: lib32asound2. I found a download link  but also this package won't install due to an unresolvable dependency: libasound2 (= 1.0.25-4ubuntu4)  and help ??

I was trying to install Teamviewer, but I was getting a dependency error. I tried to install the required packages, but with no luck.  I'm getting this error:  Unpacking teamviewer (from teamviewer_linux_x64.deb) ... dpkg: dependency problems prevent configuration of teamviewer:  teamviewer depends on lib32asound2; however:   Package lib32asound2 is not installed.  teamviewer depends on lib32z1; however:   Package lib32z1 is not installed.  teamviewer depends on ia32-libs; however:   Package ia32-libs is not installed.  dpkg: error processing teamviewer (--install):  dependency problems - leaving unconfigured Errors were encountered while processing:  teamviewer   I tried   sudo apt-get -f install   Getting   Package ia32-libs is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   lib32z1 lib32ncurses5 lib32bz2-1.0  Package lib32asound2 is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'lib32asound2' has no installation candidate E: Package 'ia32-libs' has no installation candidate   I can't even get to the   sudo dpkg -i teamviewer_linux_x64.deb   If I force installation  sudo dpkg --force-depends -i teamviewer_linux_x64.deb   Although it's "Setting up Temviewer" it gives me this:    How can I fix this problem?


I've often come across people saying from a quantum physics standpoint that an electromagnetic wave necessarily contains many photons. But doesn't the double-slit experiment conducted one photon at-a-time suggest that an electromagnetic wave corresponds with a single photon?  EDIT: This question is solely about the numerical relation between electromagnetic waves and photons.

At the end of this nice video (), she says that  is a chain reaction of electric and magnetic fields creating each other so the chain of wave moves forward.  I wonder where the  is in this explanation. What is the relation between electromagnetic wave and photon?


I have 3 colors, I need to find a 4th that is complementary of these three:  #d9bba3 #72737b #b0aca8   I have so far found #d7d6db but it is only my guess, not based on any tool, is there a way to find a common complementary color? Do they have one in common?

I often find myself trying to determine which colour is the "complementary" one of (or would nicely fit with) two colours imposed by the client brand. At times, only one colour is imposed, and I want to find two colours that would fit it.  Is there a quick and easy way to figure it out?


My request is as follows:  I have 93 pages of my book. I want to have my text on even pages and blank pages on odd ones. I want to have something like this:  page 1: my text page 2: blank page 3: my text page 4: blank page 5: my text page 6: blank page 7: my text page 8: blank [...] page n: my text page n+1: blank   My intended structure is like a one-sided book, where one reads the right side only.  Probably some command exists to leave odd pages empty, but I didn't find anything to do it automatically.

I wrote my thesis and my school wants an one-sided print. The printing and binding will be done by a professional bookbinder. They only accept only two sided manuscripts.    My \documentclass:  \documentclass[ 11pt, ngerman, onehalfspacing, headsepline, oneside ]{MastersDoctoralThesis}     Because of that I need to add a blank page after every page of content. I don't want to do this manually using \newpage or \clearpage because there are too many pages. Is there any LaTeX command (or package) to do this (automatically)?  Thanks for your help!


I understand that there are infinitely many primes and (obviously) infinitely many integers, but is there any way to calculate the total percentage of integers that are primes? Thanks

How high is the percentage of primes in $\mathbb{N}$?  ($\mathbb{N} := \lbrace { 1, 2, 3, \ldots \rbrace }$ ; a prime is only divisible by itself and 1 in $\mathbb{N}$)  The percentage has to be lower than 50% as all even numbers (except for 2) aren't primes. So the percentage has to be lower than $1 - (\frac{1}{2} + (\frac{1}{3} - \frac{1}{6})) = 1 - (\frac{1}{2} + \frac{1}{6}) = 1 - (\frac{1}{2} + \frac{1}{2 \cdot 3}) = \frac{1}{3}$  I guess it will be something like that:  $$\frac{\text{primes in } \mathbb{N}}{\text{numbers in } \mathbb{N}} = 1 - \sum_{i=\text{first Prime}}^\text{primes} \frac{1}{\prod_{j=\text{first prime}}^{i\text{-th prime}} j}$$  But calculating this (exact) value goes definitely beyond my math skills. Can somebody help me?