Why the intrinsic spin cannot be expressed in terms of polar vectors or the orbital variables $\bf r$ and $\bf p$?  Or, why do we need matrix representation for Spin?

This may seem like a slightly trite question, but it is one that has long intrigued me.  Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and generally rotational dynamics) can be fully derived from normal (linear) momentum and dynamics. Simply by considering circular motion of a point mass and introducing new quantities, it seems one can describe and explain angular momentum fully without any new postulates. In this sense, I am lead to believe only ordinary momentum and dynamics are fundamental to mechanics, with rotational stuff effectively being a corollary.  Then at a later point I learned quantum mechanics. Alright, so orbital angular momentum does not really disturb my picture of the origin/fundamentality, but when we consider the concept of spin, this introduces a problem in this proposed (philosophical) understanding. Spin is apparently intrinsic angular momentum; that is, it applies to a point particle. Something can possess angular momentum that is not actually moving/rotating - a concept that does not exist in classical mechanics! Does this imply that angular momentum is in fact a fundamental quantity, intrinsic to the universe in some sense?  It somewhat bothers me that that fundamental particles such as electrons and quarks can possess their own angular momentum (spin), when otherwise angular momentum/rotational dynamics would fall out quite naturally from normal (linear) mechanics. There are of course some fringe theories that propose that even these so-called fundamental particles are composite, but at the moment physicists widely accept the concept of intrinsic angular momentum. In any case, can this dilemma be resolved, or do we simply have to extend our framework of fundamental quantities?


If $f(x)$ is a real continuous function that is zero almost everywhere on the interval $[a,b]$, how can I prove that it is zero everywhere in that interval?  My apologies for the probably silly question.

Suppose $f$ and $g$ are continuous functions on $[a,b]$. Show that if $f=g$ almost everywhere on $[a,b]$, then, in fact, $f=g$ on $[a,b]$. Is a similar assertion true if $[a,b]$ is replaced by a general measurable set $E$?  I have known that the set $A=\{x \mid f(x) \neq g(x)\}$ has measure zero and we want to show that A is empty. Now let's assume $A$ is not empty. I am stuck in getting the contradiction.  Thanks for your hints and answers.


I am trying to return certain variables about the salary based employees from a txt file and the code will compile but not print out.  This is what I currently have done in my project:  public class PayrollPreparation {      private File source;     private Scanner input;     private String payrollType;     private int employeeID;     private String employeeName;     private int hoursWorked;     private double payRate;     private double straightPay;      public void printEmployeeData() {         System.out.println("Employee ID         Name        Hours Worked        Pay      Amount");          try {             source = new File("Payroll.txt");             input = new Scanner(source);             input.useDelimiter("[,\n]");         } catch (Exception e) {             System.out.println(e);         }          while (input.hasNext()) {             if (payrollType.equals("S")) {                 employeeID = input.nextInt();                 employeeName = input.next();                 hoursWorked = input.nextInt();                 payRate = input.nextDouble();                 payrollType = input.next();                 straightPay = (hoursWorked * payRate);                  System.out.println(" " + employeeID + "           " + employeeName                         + "                                                "                         + hoursWorked + "       " + straightPay);                  input.nextLine();             }         }         System.out.println("No More Salaried Employees.");     } }   The code all compiles but when tested there is an error with the if statement and it says java.lang.NullPointerException: null

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'm not an expert, I'm on Ubuntu 16.04 LTS, and I'm trying to install Stremio by following this tutorial "https://github.com/Stremio/stremio-shell/blob/master/DEBIAN.md" from source codes. So in order to make it work, I have to install the "libqt5webview5-dev" package, but unfortunately I get the error "Unable to locate package libqt5webview5-dev". (sorry the following terminal outputs are in Fench) $sudo apt-get install -y libqt5webview5 Lecture des listes de paquets... Fait Construction de l'arbre des dépendances        Lecture des informations d'état... Fait E: Impossible de trouver le paquet libqt5webview5  I tried to add the "universe" repository but it was already enabled. $sudo add-apt-repository universe Le composant de distribution « universe » est déjà activé pour toutes les sources.  Maybe my distribution is too old ? Can you help me ? Thanks!

When I try to install any package through the command line, I get an error.   $ sudo apt-get install <package> Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package <package>   Can anyone help me on this?


how do I delete just the first spaces or tabs in string?  char* DelFistSpace(char* s){     int i,k=1;     char * out=s;     for(i=0;s[i]!='\n';i++)         if((s[i]!=' ' && s[i]!='    ')  || k==0){             out[i]=s[i];             k=0;         }         out[i]='\0';         puts(out);         return out; }   For example: DelFistSpace("(space)(space)(space)a a");  expected: "a a"

Is there a clean, preferably standard method of trimming leading and trailing whitespace from a string in C? I'd roll my own, but I would think this is a common problem with an equally common solution.


That's what I want to do with C#. I have two buttons and two textboxes, and first I want to write something in textbox1, and this message is redirected to the console, and at this time, when something new appears in my console, textbox2 needs to read it, and the process should continue and continue. I want to use my simple DLL library, which works in this scenario. I know how to write messages to the console, but I can not read every new one from the console and write it to textbox2.  This is my redirecting from textbox into console, now i need to read anything new appearing in the console to my textbox2.  public partial class NativeMethods {     public static Int32 STD_OUTPUT_HANDLE = -11;      [System.Runtime.InteropServices.DllImport("kernel32.dll")]      public static extern System.IntPtr GetStdHandle(Int32 nStdHandle);      [System.Runtime.InteropServices.DllImport("kernel32.dll", EntryPoint = "AllocConsole")]     [return: System.Runtime.InteropServices.MarshalAs(System.Runtime.InteropServices.UnmanagedType.Bool)]      public static extern bool AllocConsole(); }   And somewhere else....  public void console() {     if(NativeMethods.AllocConsole())     {         IntPtr handle = NativeMethods.GetStdHandle(NativeMethods.STD_OUTPUT_HANDLE);          Console.WriteLine("type: ");     }     else     {         Console.WriteLine("Waiting...");     } }   Using these when a button is clicked.

I'm developing an Windows Forms application that requires me to call a separate program to perform a task.  The program is a console application and I need to redirect standard output from the console to a TextBox in my program.    I have no problem executing the program from my application, but I don't know how to redirect the output to my application.  I need to capture output while the program is running using events.    The console program isn't meant to stop running until my application stops and the text changes constantly at random intervals.  What I'm attempting to do is simply hook output from the console to trigger an event handler which can then be used to update the TextBox.  I am using C# to code the program and using the .NET framework for development.  The original application is not a .NET program.  EDIT: Here's example code of what I'm trying to do.  In my final app, I'll replace Console.WriteLine with code to update the TextBox.  I tried to set a breakpoint in my event handler, and it isn't even reached.      void Method()     {         var p = new Process();         var path = @"C:\ConsoleApp.exe";          p.StartInfo.FileName = path;         p.StartInfo.UseShellExecute = false;         p.OutputDataReceived += p_OutputDataReceived;          p.Start();     }      static void p_OutputDataReceived(object sender, DataReceivedEventArgs e)     {         Console.WriteLine(">>> {0}", e.Data);     }


As a physic undergraduate with some knowledge of calculus (Lebesgue integral, stochastic analysis, complex analysis) I'm interested in learning about number theory.   Anyone who has a good tip for me, with which book to start?   Thank you!

What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks.


I'm trying to convert seconds to hours , minutes and seconds.  Example:  int totalseconds = 5049;   How do i use one message box to display the results in the form:  H:1 M:24 S:9

What is the best way to convert seconds into (Hour:Minutes:Seconds:Milliseconds) time?  Let's say I have 80 seconds, are there any specialized classes/techniques in .NET that would allow me to convert those 80 seconds into (00h:00m:00s:00ms) format like to DateTime or something?


I'm new in Linux and I'm trying to make my first bash script to improve  my work at college. Im working with a software called GROMACS and I'm trying to make a script to perfom a bunch of codes at the same time, but in one of the lines I need needs an input (number) from the keyboard. What can I do to make this script work?  Here are my lines:  !#/bin/bash gmx pdb2gmx -f protein_name.pdb -o protein_name_processed.gro -water spce   And that last line needs the keyboard input (number 15)  Thanks for your help.

I'm trying to create an interactive bash script where I can collect user input variables to be used as arguments in another command. Can someone provide me an example of this?  Currently i want to do:   what type of content you want to delete? what is the status?   then feed it into a mysql delete query command.


Which sentence below is correct when using the past tense of "do"?  What I did to find out is that...  What I did to find out was that...

I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense?


I have one site made by Wix, have been seo working into this site for about 7 months. My site got ever 1st position in google search result for targeted keywords. But after 301 redirection and changing address in google search console, my site now gets in about 3~4th position. Maybe my site got ranking decreasing in google search. I want to rank my site in the 1st position. What shall I do?

What are the best ways to improve a site's position in the Google search results?


In thousands of movies, books and TV shows, vampires have to be invited inside of the house in order to attack the inhabitants. My question is why do they have to be invited inside, is there an actual reason or is this going on ancient folklore? Is there an explanation?

Its been a long time since I read Bram Stoker's Dracula, and I do not remember any instance of Jonathan Harker inviting Count Dracula to his home. I just watched the Let Me In movie and I also remember from the movie The Lost Boys that a Vampire needs the invitation of the host to enter the hosts house.This brings me to the questions:    Where in writing or a movie does this idea first originate? Was it from Bram Stoker's Dracula?


Here is an example the rip-off is apparently monetizing through add (sometime even pr0n). Is this site already known and under investigation? Rip-off :  Original:  PS: The site goes as far as duplicating a whole range of sub-sites and as one can see at top level site

of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means:   Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow:   You have to provide . Simple links to the original post and author info are just fine. You have to  and allow other people to use your content, as long as they follow these very same rules. How meta!    (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.)  There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short).  In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery.  So, the question is: what can you do if you spot a SCRAPER?


I hope that this is not a duplicate. Consider the MWE  \documentclass[tikz]{standalone} \standaloneconfig{border=-3cm 0cm 0cm 0cm}  \begin{document} \begin{tikzpicture} \draw(0,-5) grid (10,5); \foreach \X in {0,...,10} \node[circle,fill,label=45:{\X}] at (\X,0){}; \node at (5,2) {border=\{$\langle\mbox{length}~(\mbox{left})~\rangle$ $\langle\mbox{length}~(\mbox{right})~\rangle$ $\langle\mbox{length}~(\mbox{bottom})~\rangle$ $\langle\mbox{length}~(\mbox{top})~\rangle$ \}}; \end{tikzpicture} \end{document}     The image gets cut at the left, which is consistent with the manual (top of page 9)    However, if I do  \standaloneconfig{border=0cm -3cm 0cm 0cm}    instead, I get     i.e. the image gets cut at the bottom (rather than right side).  Overall, I think that the standalone crops according to   border={left bottom right top}   What am I doing wrong?

I tested a MWE given in question . Following the documentation (page 9) I used the class option border={left right bottom top} with left=right=top=0pt and bottom=20pt (20pt only to show the effect here).  With the version 2012/09/15 v1.1b of standalone and the following MWE I get no 20 pt margin at the bottom of my picture.  What is the problem?  MWE:  \documentclass[% % border=1pt   border={0pt 0pt 20pt 0pt} %left right bottom top ]{standalone}% http://ctan.org/pkg/standalone \begin{document} $2^5 = x_5 \times y^8$ \end{document}


Assume there is an infinitely large plane with a charge density $\sigma$. I understand how to derive, using Gauss' Law, that $E = \frac{\sigma}{2\epsilon_0}$ is the electric field at a distance $r$ from the plane.  However, intuitively, I don't understand how this could be true. Shouldn't the electric field be more powerful closer to the plane, since the electric field falls of as $\frac{1}{r^2}$? The larger I make $r$, the further it is from every point, meaning the electric field should decrease - shouldn't it?  Any help understanding this would be appreciated.

For an infinite line charge, $E$ falls off with $1/r$; for an infinite sheet of charge it's independent of r! The infinitesimal contributions to $E$ fall off with $1/r^2$, so why doesn't the total $E$ fall off the same way for the infinite line and sheet charges?


How can I generate alphanumeric unique userId's of 5/6 digits reducing the chances of collision upto 10 lac values with Java? I don't want to make calls every time  to the DB so as to check whether that ID already exists there.

I've been looking for a simple Java algorithm to generate a pseudo-random alpha-numeric string.  In my situation it would be used as a unique session/key identifier that would "likely" be unique over 500K+ generation (my needs don't really require anything much more sophisticated).    Ideally, I would be able to specify a length depending on my uniqueness needs. For example, a generated string of length 12 might look something like "AEYGF7K0DM1X".


Let $R$ be an integral domain, and let $a \in R, a \neq 0$. Let $f_a: R \rightarrow R$ be defined by $f_a(r)=ar$. Prove that $f$ is injective.   Then prove that every finite integral domain is a field.   My ideas and concept:   Can someone help articulate my understandings into a proper solution?

This is how I'm approaching it: let $R$ be a finite integral domain and I'm trying to show every element in $R$ has an inverse:   let $R-\{0\}=\{x_1,x_2,\ldots,x_k\}$,  then as $R$ is closed under multiplication $\prod_{n=1}^k\ x_i=x_j$,  therefore by canceling $x_j$ we get $x_1x_2\cdots x_{j-1}x_{j+1}\cdots x_k=1 $,  by commuting any of these elements to the front we find an inverse for first term, e.g. for $x_m$ we have $x_m(x_1\cdots x_{m-1}x_{m+1}\cdots x_{j-1}x_{j+1}\cdots x_k)=1$, where $(x_m)^{-1}=x_1\cdots x_{m-1}x_{m+1}\cdots x_{j-1}x_{j+1}\cdots x_k$.   As far as I can see this is correct, so we have found inverses for all $x_i\in R$ apart from $x_j$ if I am right so far. How would we find $(x_{j})^{-1}$?


Bangla (Eng. Bengali) is a language common in Bangladesh and part of India (West Bengal) with a rich history of literature and cultural heritage.   How would it be; if on  site is opened for discussion about question and answer about Bengali language? The functions like tagging etc. and main portion of the question and answers will be basically written in English (so that everyone can understand and participate) but users will be allowed to quote in Bengali; with an English transcript of pronunciation and an English translation.  Initially the site would include all aspects of Bengali language; such as starting from Literature, riddles, metaphor-cracking through grammar, spelling, etymology, pronunciation, translation etc. to typing softwares, encoding types, problems in encoding, fonts, optical character recognition, etc.   Later on, if the site can survive and cross the beta stage; then further branching can be decided.   Update: The proposal has been submitted at

I have an idea or subject that should have a Q&A, and want to propose a new site. How can I do this?  Related:


Conjectures are often based on inference from a few cases.  A famous example is the Riemann Hypothesis which states that all zeros of the zeta function have real part 1/2. All the zeros that we've found on the zeta functions had real part 1/2.  In the same fashion, the abc conjecture has been verified for a lot of large cases.  Can you think of any conjecture true for a "large" number of cases but was still proved wrong?

I just came back from my Number Theory course, and during the lecture there was mention of the Collatz Conjecture.  I'm sure that everyone here is familiar with it; it describes an operation on a natural number – $n/2$ if it is even, $3n+1$ if it is odd.  The conjecture states that if this operation is repeated, all numbers will eventually wind up at $1$ (or rather, in an infinite loop of $1-4-2-1-4-2-1$).  I fired up Python and ran a quick test on this for all numbers up to $5.76 \times 10^{18}$ (using the powers of cloud computing and dynamic programming magic).  Which is millions of millions of millions. And all of them eventually ended up at $1$.  Surely I am close to testing every natural number? How many natural numbers could there be?  Surely not much more than millions of millions of millions. (I kid.)  I explained this to my friend, who told me, "Why would numbers suddenly get different at a certain point?  Wouldn't they all be expected to behave the same?"  To which I said, "No, you are wrong!  In fact, I am sure there are many conjectures which have been disproved by counterexamples that are extremely large!"  And he said, "It is my conjecture that there are none! (and if any, they are rare)".  Please help me, smart math people.  Can you provide a counterexample to his conjecture?  Perhaps, more convincingly, several?  I've only managed to find one! (Polya's conjecture). One, out of the many thousands (I presume) of conjectures. It's also one that is hard to explain the finer points to the layman. Are there any more famous or accessible examples?


A common strategy that is sometimes used when a person asks questions that pertains to themselves, but wants to disassociate from (for any reason), is to frame the question as being about somebody else, or otherwise externalizing it. "My friend" is a classic example of this:     A friend of mine wrecked into their boss's brand new car in the parking lot. What should they do?   Another example often starts with "let's say", presenting a real situation as a hypothetical one in order to artificially distance the asker from a questionable   situation:     Let's say a teacher unfairly gave a student a poor grade on an assignment. How can that student get revenge?   Note that we assume through context that the above examples actually pertain directly to the asker (i.e. they do because I said they do, it's the basis of this question).  Is there a name for this strategy / style of presentation (applies to both speaking and writing) / whatever it is? I'm not even certain that "by proxy" was the correct phrase to use in the title.

Is there a word that describes the phenomenon, often seen on SE sites, where someone says they are asking a question "for a friend", but actually mean themselves?


I saw this  and see that it has  in the end of tag list (it should in the beginning).    If I go to revision history I'm also facing some oddities:  was replaced by itself two times!    How is that possible?

On  (but I remember seeing it in other cases) the diff shows the same tag being both added and removed.


I've defined a generic type as following:  public class RelevanceGroup<T> {     public string Name;     public List<Relevance<T>> Relevances { get; set; } = new List<Relevance<T>> { };      public RelevanceGroup(string name)     {         this.Name = name;      }     public RelevanceGroup(List<Relevance<T>> relevances, string name)     {         this.Name = name;         this.Relevances = relevances;     }      public bool ChangesHasBeenMade(List<Relevance<T>> newRelevances)     {         return !(newRelevances.All(o => this.Relevances.Any(w => w.ItemId == o.ItemId)) && (this.Relevances.All(o => newRelevances.Any(w => w.ItemId == o.ItemId))));     }   My question is regarding the last method:  I get an compile error message in my linq expression saying that "operator == cannot be applied to operands of type T and T". I have to do a foreach loop to make it work. Can i do something to make the method work with the linq expression?  Thanks in advance.

According to the documentation of the == operator in ,      For predefined value types, the   equality operator (==) returns true if   the values of its operands are equal,   false otherwise. For reference types   other than string, == returns true if   its two operands refer to the same   object. For the string type, ==   compares the values of the strings.   User-defined value types can overload   the == operator (see operator). So can   user-defined reference types, although   by default == behaves as described   above for both predefined and   user-defined reference types.   So why does this code snippet fail to compile?  bool Compare<T>(T x, T y) { return x == y; }   I get the error Operator '==' cannot be applied to operands of type 'T' and 'T'. I wonder why, since as far as I understand the == operator is predefined for all types?  Edit: Thanks, everybody. I didn't notice at first that the statement was about reference types only. I also thought that bit-by-bit comparison is provided for all value types, which I now know is not correct.  But, in case I'm using a reference type, would the == operator use the predefined reference comparison, or would it use the overloaded version of the operator if a type defined one?  Edit 2: Through trial and error, we learned that the == operator will use the predefined reference comparison when using an unrestricted generic type. Actually, the compiler will use the best method it can find for the restricted type argument, but will look no further. For example, the code below will always print true, even when Test.test<B>(new B(), new B()) is called:  class A { public static bool operator==(A x, A y) { return true; } } class B : A { public static bool operator==(B x, B y) { return false; } } class Test { void test<T>(T a, T b) where T : A { Console.WriteLine(a == b); } }


Let  $E$, $F$ be complex Hilbert spaces. The algebraic tensor product of $E$ and $F$ is given by $$E \otimes F:=\left\{\xi=\sum_{i=1}^dv_i\otimes w_i:\;d\in \mathbb{N},\;\;v_i\in E,\;\;w_i\in F \right\}.$$  In $E \otimes F$, we define  $$ \langle \xi,\eta\rangle=\sum_{i=1}^n\sum_{j=1}^m \langle x_i,z_j\rangle_1\langle y_i ,t_j\rangle_2, $$ for $\xi=\displaystyle\sum_{i=1}^nx_i\otimes y_i\in E \otimes F$ and $\eta=\displaystyle\sum_{j=1}^mz_j\otimes w_j\in E \otimes F$.  The above sesquilinear form is an inner product in $E \otimes F$.     Why $(E \otimes F,\langle\cdot,\cdot\rangle)$ is not a complete space?   Thank you!!

This question has been modified...  Problem  Given Hilbert spaces.  In general, their algebraic tensor product isn't complete: $$\mathcal{H}\hat{\otimes}\mathcal{K}=\mathcal{H}\otimes\mathcal{K}\iff\dim\mathcal{H}<\infty\lor\dim\mathcal{K}<\infty$$ How to prove this from scratch?  Attempt  Choose orthonormal bases: $$\mathcal{S}\otimes\mathcal{T}:=\{\sigma\otimes\tau:\sigma\in\mathcal{S},\tau\in\mathcal{T}\}$$  One obtains some candidates: $$\sigma_k\otimes\tau_l\in\mathcal{S}\otimes\mathcal{T}:\quad\sum_{kl=1}^\infty\frac{1}{kl}\sigma_k\otimes\tau_l\quad\sum_{k=1}^\infty\frac{1}{kl}\delta_{kl}\sigma_k\otimes\tau_l$$ However the former one drops out: $$\sum_{kl=1}^\infty\frac{1}{kl}\sigma_k\otimes\tau_l=\left(\sum_{k=1}^\infty\frac{1}{k}\sigma_k\right)\otimes\left(\sum_{l=1}^\infty\frac{1}{l}\tau_l\right)$$ So it is not obvious at all wether the latter one works out!  Reference  Build-up on:


I have setup streaming replication on Postgres 9.1.6 running on a debian server and it's going on fine.  When I try to run a query on the replica DB I get the error below:  ERROR:  index "tbl_cust_id_idx" contains unexpected zero page at block 0 HINT:  Please REINDEX it.   What might be causing this error?  The question is also posted in


I am using Zotero to manage my references. Then, I export the .bib file (Biblatex) from Zotero. The issue is there is an empty parentheses if there is no author. Also, if it is a web-page citation, there is an empty parentheses after the author's name.     @online{shotts_learning_nodate,     title = {Learning the shell - Lesson 1: What is the shell?},     url = {https://linuxcommand.org/lc3_lts0010.php},     author = {Shotts, William},     urldate = {2020-12-14},}  The .bib code above results in an empty parentheses after the author's name. @online{noauthor_what_nodate,     title = {What is Linux?},     url = {https://www.linux.com/what-is-linux/},     titleaddon = {Linux.com},     urldate = {2021-01-20},     langid = {american},}       The .bib code above results in an empty parentheses, if there is no author. Here is my LateX code \documentclass[12pt,a4paper]{report} \begin{document} \usepackage[style=ieee]{biblatex} \addbibresource{Exported_Items.bib} \printbibliography[title={REFERENCES}] \include{Chapter1} \include{Chapter2} \end{document}  The result is:  [1] (). “What is linux?” Linux.com, [Online].  Available:https://www.linux.com/what-is-linux/(visited on 01/20/2021).  [2] W. Shotts. (). “Learning the shell - lesson 1: What is the shell?”  [Online]. Available:https://linuxcommand.org/lc3_lts0010.php(visited  on 12/14/2020).  Thank You.

By using biblatex ieee style, I found that the reference will display empty brackets even though the field "year" is undefined. How can I remove it without having to change the biblatex.bst?  \documentclass{article}  \usepackage[style=ieee,backend=bibtex]{biblatex}  \usepackage{filecontents}  \begin{filecontents}{\x.bib} @ELECTRONIC{MEMSnet,   title = {What is {MEMS}?},   organization = {MEMSnet},   url = {http://www.memsnet.org/mems/what_is.html},   urldate = {Dec. 01, 2013} } \end{filecontents}  \addbibresource{\x.bib}  \nocite{*}  \begin{document}  \printbibliography  \end{document}   I got   (). What is MEMS? MEMSnet, [Online]. Available: .  which is not a correct citation style. I would like to have:  What is MEMS? MEMSnet, [Online]. Available: .  Many Thanks


How can I prove that the blue line is always less than or equal to the red line when X is greater than or equal to one?  This is a crucial algebraic step in a proof by mathematical induction. In order to complete my proof,  I have to show that this is true. How do I do this?

Hey so while doing exercises this popped up. My idea is to put everything under $\sqrt{x+1}$ and then multiply it by $\sqrt{x+1}$. and then square both sides to get that $x \leq 0$. But this is a very ugly method. The one in the answer is using the fact that $4(x^2+x) \leq (2x+1)^2$ but how in the world am i supposed to come up with that... This is actually the result i come up with at the end. It seems as if they did my method and then reverse it. Any other good ideas to solve it? Not graphically. Is it actually viable to calculate the function of area between the functions and maximize the function? Seems ugly here but in general?


I am a Ghanaian citizen. I made a mistake in filling out the application for a UK standard visitor's visa. When asked 'if I have been refused a UK visa before,' I checked no but I was refused a UK visa last year. I have submitted the form online and will be making a submission tomorrow. What should I do?

I'm from Lebanon and I've been working in Saudi Arabia for nine years. In 2012, I put the money that I collected from my job as a teacher in my father's Lebanese account since I didn't have one in Lebanon. During the interview, my interviewer told me that my application will be rejected because I don't have proof that this money is mine and clearance officer will think someone else gave me the money. I didn't know that I had to bring with me from Saudi Arabia an employment letter and bank statements to prove that this money is mine and I earned it by working in Saudi Arabia. Anyways, my visa did get refused as my interviewer had told me it would be.    Last May, I was granted a US visitor visa Multi Entry for 5 years. I wanted to visit the US in August for 10 days but my mom entered the hospital so I had to postpone it. Now I'm applying for a teacher training program in the UK. I received an invitation letter from Brighton University and so I applied for a UK Standard Visitor visa. After I paid and printed the application, I realized that I answered the question Any previous visa rejections ... with "NO" and I don't know how should I fix this.  Please note that I still didn't give my biometrics, I still didn't use my US visa which I received on May 2016, I paid for my application so I can't amend it online. I'm supposed to give my biometrics and submit my documents this Monday.  If I don't say anything will they check it and refuse me?    Will my US visa be an advantage and they will disregard the previous rejection or should I correct it when I submit my documents this Monday?


In a Windows file system, we cannot created a folder or file with the same name. For example, New Folder. If there is a existing folder already named as "New Folder" and if we create another folder with the same name, it prompts or creates "New Folder 2". I recently deleted various folders named New Folder.  Recycle bin does not complaint if both folders have same names. I wanted to know how "Recycle bin" is functioning. It is a file system as well. How is it implemented, what is the data structure used. I want to implement a similar file system at work.  I can think that even though it shows the users that files are deleted but the reference is to the same place from where it got deleted and allowing same file names.

What does the Recycle Bin in Windows actually do?  Is it just a glorified folder and a holding place for soon to be deleted files, or does it do something specific?  Specifically, are files that are "moved" to the Recycle Bin actually moved on the hard disc, or are just the pointers to the files moved?  I am a fairly experienced user, I just wanted a more depth explanation of the Recycle Bin.


I have a Lenovo laptop running Ubuntu 18.10 with kernel 4.19.0-041900-generic.  Only Ubuntu is installed.  When I turn on the laptop it directly boots into Ubuntu. I want to go to Advanced Options to boot a different kernel.  Pressing Shift or Esc is not working for me.

I read here at  that holding Shift during boot can bring up the GRUB menu. However I try holding one or the other Shift keys, tapping, tapping then holding, nothing works. Am I missing something? How does one access the GRUB menu during boot time?   No dual boot here, just standard Lubuntu 14.04 install.


I tried Ubuntu Gnome and liked it and I want to stay on it but It directly boots without Grub screen, But a Grey background with slightly darker borders appear while booting, It takes a lot of time. how can I bring the grub menu back?

On every boot up I get this:    For about 10 seconds (or more) before the "normal" Ubuntu Gnome loading screen and the login screen comes up.  I've read some questions and a bug report about this already, but this problem was dismissed as a minor inconvenience or there were no real solutions (that worked for me). For me, this problem leads to an unacceptable slow boot compared to Ubuntu (Unity) or Windows.  Does anybody know how to fix this or is this a "feature" of Ubuntu Gnome and not a bug?


struct triangle { triangle( vertice * p0,  vertice * p1,  vertice * p2)     :tv1(0)     ,tv2(0)     ,tv3(0) {     m_Vertices[0] = p0;     m_Vertices[1] = p1;     m_Vertices[2] = p2;     //SetCircumCircle();  };  triangle *tv1,*tv2,*tv3;}   struct vertice  {         vertice (  int init_val=0) :id (init_val) {};     vertice (double xx, double yy=0):x(xx),y(yy) { };     int id;     double x,y; };  std:: vector <triangle> triangles;  void cre_triangle() {     triangle r(0,1,2);     triangle r2(3,4,6);     r.tv1= &r2;     r.tv2=0;     r.tv3=0;     cout << r.tv1->m_Vertices[0]->id << r.tv1->m_Vertices[1]->id << r.tv1->m_Vertices[2]->id;           //the result is  3 4 6      triangles.pushback(r); }  int main () {     cre_triangle();     cout << triangles[0].tv1->m_Vertices[0]->id <<triangles[0].tv1->m_Vertices[1]->id       <<triangles[0].tv1->m_Vertices[2]->id << endl ;        // problem here  (....exe has stopped working)       return 0; }     i went to access to the ids and the coordinates of vertices of triangle r2 by r (tv1 is the neighbor 1) and modify its but i have a problem ( appilcation.exe has stopped working) please can you help me ..

This question attempts to collect the few pearls among the dozens of bad C++ books that are published every year. Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book. It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles. Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in . (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list.  Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review. *Note: FAQs and other resources can be found in the  and under .


A sequence of positive integers, a[1], a[2], a[3], . . . , a[n] is called a Special Sequence, if a[1] divides a[2], a[2] divides a[3], and so on until a[n−1] divides a[n], and if all the elements are distinct. For example, (2, 4, 8, 32) is a Special Sequence. But (4, 2, 8) is not, because 4 does not divide 2. Similarly (2, 4, 4, 8) is also not Special, because the elements are not distinct. You need to find the number of Special Sequences such that all the elements of the sequence are from the set {1, 2, . . . , K}. Suppose K = 3. The Special Sequences possible are (1), (2), (3), (1, 2), (1, 3). So the answer would be 5. Find the answer for K = 19. My Approach Core Concept: {a, b} and {b, c} are two special sequence sets, then so will be {a, b, c} I can use this and solve the cardinality for every number up to 19 and that would give me the answer but it takes too much manual effort so I think there is another way to do this.

Hello everybody! The problem you see above is a combinatorial problem that I could not solve. :(  Since we are to choose distinct numbers from $\{1,2,3 \ldots K\}$, the numbers must be in increasing order because they are all positive. I think that the difficulty of this problem is in the fact that the Special Sequence can be of any length. We can go about choosing say $n$ elements in $\binom{K}{n}$ ways but again how do we control that? Talking about a recursive solution, I think that is the way to go but I can't get how to do that (that is get a recursive formula for that).  Any help in solving this problem would be much appreciated. Thanks.


When using algorithmx you get "Algorithm 1 algorithm name". How can you change the label "Algorithm"? I do not mean individually for each algorithm, but instead changing it globally the whole latex project. The reason for this is because I rather want it to say "algoritme", which is algorithm in Norwegian.     \documentclass{article} \usepackage[norsk]{babel}  \usepackage{tabularx} \usepackage{apacite} \usepackage{hyperref} \usepackage{enumerate} \usepackage[normalem]{ulem} \usepackage{color} \usepackage[noend]{algpseudocode} \usepackage{algorithm} \begin{document}  \begin{algorithm} \begin{algorithmic}[1] \State a \label{a} \caption{name} \end{algorithmic} \end{algorithm}  \end{document}

I've been trying to use this answer  to no avail. I use the packages:  \usepackage{algorithm} \usepackage{algpseudocode}   And this code for defining new environment:  \newenvironment{megaalgorithm}[1][htb]{     \renewcommand{\algorithmcfname}{MegaAlgorithm}% Update algorithm name    \begin{algorithm}[#1]%   }{\end{algorithm}}   But then it tells me that there is an error:      Latex Error: \algorithmcfname undefined   I can't use algorithm2e as in previous example as it breaks my current code.


I am posting from a new account I have created, as I have been unable to access my Stack Exchange account for several days.  My account is tied to my AOL OpenID exclusively. For quite some time, when signing into SE with AOL, one needed to write their AOL username without the @aol.com.  When one wrote one's username with the @aol.com, SE has historically given an error saying canceled. This has not been an issue, as AOL has routinely accepted AOL usernames on their OpenID authentication page without the @aol.com portion.  It appears to me that AOL has changed something in their authentication system, at least for some accounts. Now, AOL does not allow me to sign into my account when I omit the @aol.com portion, so I am forced to write username@aol.com.   However, with this arrangement, Stack Exchange gives me the cancelederror (although AOL allows me to sign in). I assume this is because Stack Exchange stores my account credentials as type: AOL, username: username (without the @aol.com). However, AOL will only authenticate me now with username:username@aol.com.  Note that AOL only seems to be doing this for OpenID authentications, rather than all logins to their system. When merely signing into my AOL account (without using their OpenID authentication system), I can access the account by merely entering my username without the @aol.com portion.  Is there a way to fix or circumvent this problem?

NOTE: Signing up or Logging in via OpenID is no longer officially supported from any of our sites. Currently,  is still on the internet, but we are in the process of completely removing it.    Stack Overflow was an early and strong supporter of . We built our sign up/log in flow around it. We were idealistic and had , but these hopes weren't realized. Over the years people have wondered if  is . We've had to remove support as OpenID providers  or .  The time has come to part ways. The reality is OpenID support has created a ton of complexity in our codebase and the number of users actively using OpenID simply don't justify that cost. Users have spoken with their actions. You prefer Google, Facebook and Stack Exchange (aka email/PW) based account auth.     Of our 9,813,747 accounts around one-tenth of a percent are actively using OpenID (defined as having visited a site in the past 12 months). If you include all the inactive accounts it is still less than 2.9% of all accounts.  So, what is the plan?   DONE - Remove the ability to create a new account with most OpenID providers DONE - Add the ability to  DONE - Convert Launchpad (used on  ) to OAuth DONE - Remove creating new accounts with Steam from  (Steam removed support for OAuth. Only 454 accounts that use Steam have visited Arqade in the past 6 months.) DONE - We will email all users that rely on deprecated OpenID credentials and request that they  DONE - Run an announcement banner for any user who signs in with deprecated OpenID credentials urging them to  DONE - End support for logging in via OpenID  In progress - Remove  (note: only 0.2% of authorized sites in the last year have been non-Stack Exchange sites.)   Obviously, if your account relies on OpenID, then make life easy and go now and .   If you've forgotten what you credentials you use to login, then  to refresh your memory. If you don't see one of the three account types shown in the image below (Google, Facebook or Stack Exchange) then click the "add more logins" button to add one of them to your account.    Remember, SE OpenID accounts are really email/pw accounts handled through complicated OpenID code path. They will be migrated to a simpler email/pw only code path as a part of this change. No extra work required on your part.


I am a Filipino currently holding a Greece National Type D visa. Before traveling to Greece, however, I would like to stay in Italy for 3 weeks.   Will I have any problems at the Italian airport if I show up with this visa only? I was told I need to go to Greece before I could travel to Italy. I would like to know if anybody had a similar experience before.

I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France?


Find the infinite Sum of the series with general term $\frac{1}{n(n+1)(n+2)}$.  I decomposed the fraction upto this $1/(2n)-1/(n+1)+1/(2n+4)$. But I find no link about cancelling terms. So how should I find the infinite Sum?   Please don't say that this is off topic or homework.  if wanna say that this is homework, at least give a hint if I am going the right way?

I got this question in my maths paper     Test the condition for convergence of $$\sum_{n=1}^\infty \frac{1}{n(n+1)(n+2)}$$   and find the sum if it exists.   I managed to show that the series converges but I was unable to find the sum. Any help/hint will go a long way. Thank you.


I'm using Lyx, and adding a floating image always add a "Figure X" at the left of the image, I'd like to show this 'caption' (I don't know if is caption or not) under the image, how should I do? What should I add in preamble?

In LyX, how can I set a float that contain figure so that the caption is under the figure? By default the caption is always on the left side of figure.


I'd like to know what's the difference between for example myself and by myself. it would be great if you made some example to be easier to understand. Thank you everyone.

Could you please explain me which option should I use?     I would like to have a green house with rare plants from all over the world. I could take care of them (myself / by myself)?   And why?


So Q(x) is a predicate in some domain of discourse. I am given $\neg$($\forall$y Q(y)) and I want to make a formal proof that shows that $\exists$x (Q(x) $\rightarrow$ $\forall$y Q(y)) follows from it. How would one approach it?   I tried moving the negation all the way to the center with De Morgans. Then I did Elim $\exists$ for some special c that satisfies Q. Then I did Intro $\exists$ to introduce x. I am not sure where to go from there.

Why is this true?  $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$


I want Ctrl-Alt-T to focus (bring back to front) an existing terminal window if there is no running process in it (e.g. top). If there is no terminal window without a running process, a new window should be opened. Is that possible?  Edit: It's not a duplicate. The further going idea is the following: I do not want to get a terminal where I can not execute a command right now because it's busy (a process is running in it, e.g top). So my wish was to get only a already opened terminal if there is no process in it.

I tend to use the terminal a lot,  So I wondering if there is a way I can make Ctrl+Alt+T focus the existing terminal if there is one, otherwise create a new terminal?


i'd like to know how to prove that following sequence  $$\sqrt{2\sqrt2},\sqrt{2\sqrt{2\sqrt2}},\sqrt{2\sqrt{2\sqrt{2\sqrt2}}},...$$  Is convergent, and that it's limit equals two.   In other words, that $$\sqrt{2\sqrt{2\sqrt{2\sqrt2...}}}=2$$  I imagine it's supposed to be simple and straightfoward, but i cant figure it out. I would be grateful for any help you could give me.

(Fitzpatrick Advanced Calculus 2e, Sec. 2.4 #12)  For $c \gt 0$, consider the quadratic equation $x^2 - x - c = 0, x > 0$.  Define the sequence $\{x_n\}$ recursively by fixing $|x_1| \lt c$ and then, if $n$ is an index for which $x_n$ has been defined, defining  $$x_{n+1} = \sqrt{c+x_n}$$  Prove that the sequence $\{x_n\}$ converges monotonically to the solution of the above equation.  Note: The answers below might assume $x_1 \gt 0$, but they still work, as we have $x_3 \gt 0$.    This is being repurposed in an effort to cut down on duplicates, see here: .  and here: .


Recently there are a lot of news about the plans to build the FCC accelerator, with many claims of possibilities to find new particles, for example like those suggested by theories of supersymmetry. However, this theory has been around for decades already, with no signs of experimental confirmation.   So my questions is - can there be an experiment, which we may perform with our current means, whose results will disprove supersymmetry, or at least will make it very unlikely?

A question in four parts.   What are the main problems which supersymmetry purports to solve?  What would constitute lack of evidence for SUSY at the proposed LHC energy scales (e.g. certain predicted superpartners are not in fact observed)?  Are there alternative theoretical approaches which would address the SUSY problem set and which would still be credible in such an LHC no-SUSY-scenario? Where would LHC-disconfirmation of SUSY leave String Theory?   I would like to think that these four points could be taken together as one question.


When I walk up to a Mac, and open a Terminal.app window, what options do I have for editing text files?  I see that both  and  text editors are included with macOS Sierra, along with  and , but apparently not the ee text editor bundled in FreeBSD.   What other options for command-line text editors are built into macOS?

Is there a built-in text editor in the terminal on Lion?  (Like, for example, nano on Linux.)


I've had Windows 7 installed for a while now and decided to install XP on another drive. It appears that XP has overwritten 7's boot loader, so XP boots up by default. I popped in my Windows 7 install disc to repair the loader. After selecting the repair option, it shows me this:    I clicked Repair and Restart and it still boots into XP by default. Luckily, I can go into my BIOS and do a manual override to get it to boot from the Windows Boot Manager on the drive that 7 is installed on. My goal is to have Windows 7/XP dual boot, but, for now, I just want to get the Windows 7 loader working properly.  And I am aware that there are several nearly- identical questions on here (I anxiously await the onslaught of "possible duplicate" comments and close votes), but they're all about 10 years old except for one where the answer is a link to a 20-minute YouTube video. None of them address my issue anyway.  Edit: As expected (and predicted in the paragraph preceding this one), it was closed as a dupe. I've seen all those questions/answers and I do not have an option to open a command prompt. I am literally only able to select Repair and Restart.  Also, when I remove the drive that has XP installed on it from the boot priority in BIOS and attempt to use my Windows 7 disc, I get this:

It seems pretty straightforward to dual boot those versions of Windows when the newest is installed after Windows XP. But the inverse isn't happening on my machine. I tried even editing the BOOT.INI file, but the boot just freezes or displays that a file is missing when I try to boot another partition.  Currently I'm stuck with Windows XP, and I need to boot my Windows 7 instead.  What is the solution?


This cartoon was recently posted on Facebook. My sister (who is a retired HS English teacher) says the grammar is wrong and that the correct wording should be: "Neither one of us is." but I disagree.   I am not an English teacher but I believe that "US" relates to "WE" and the correct wording for that pronoun is "WE ARE". On the other hand "ONE OF US" relates to "I" and "YOU" but the correct wording for those pronouns would be "I AM" or "YOU ARE" ... There absolutely is no place in English where we correctly use "I IS", "YOU IS", or "WE IS" so why would "US IS" be correct?

Bob: "Can I set the font color? Can I customize the text?"  Frank: "Neither of these options is available. Sorry!"    Is "neither is" always correct or should one use "neither are" in some cases and what are the exact rules?  of this-is-why-stackexchange-exists :P


My understanding is that interferometers can detect distance changes on the order of the wavelength of light being used. LIGO uses 808 nm light but has a sensitivity of 10^-18 m. Where do those 11 orders of magnitude come from?

The currently proposed Gravitational wave detection apparatus consists of Michelson Interferometer which is supposed to measure distances of the order of $10^{-22}$m. But the wavelength of the light used is in the order of micrometers ($10^{-6}$m). How is this possible? The conventional way to measure distance is by counting the interference fringes. But for path difference smaller than wavelength of laser light this is not possible.


I am a Indian citizen holding a work residence permit from Norway for two years.  I want to make some trips in the rest of the Schengen area. I am planning my first trip to Portugal on 22/08/18 till 26/08/18, a second trip to Italy from 22/11/18 to 27/11/18, and again to Portugal from 06/02/19 to 16/02/19.  I will stay permanently  inside Norway after each trip to other Schengen countries.  How does the 90/180 rule work in this case?  Am I allowed to make all those trips while holding my residence permit in Norway? Can you let me know if I'm exceeding the 90-day limit with these trips?

I am an Indian citizen, holding a residence permit in Norway valid for 2 years. I want to know about the 90/180 rule.   Can I travel to Portugal for one week, come back to Norway and travel again for vacation for 2 weeks to Italy, and again come back to my residence country?  Does time spent in my residence country also count against my total stay in the Schengen area? Does Iit mean that the clock stops tickkng when person comes back to their residence country?


$X_1$ and $X_2$ are i.i.d random variables and the pdf of each of them is $e^{-x}$ for $x>0$ and $0$ otherwise. $Y = X_1-X_2$ and the question asks to find the pdf for $Y$? I took the approach of going from the cdf to pdf. $P(Y\le y) = P(X1-X2\le y) = P(X1\le y+X2)$. The integral boundaries would be different, depending on the sign of $y$. The integrand is $e^{-X_1-X2}$ and I did it in the order $dX_1dX_2$. In the case of $y>$0 I set the boundary for $dX_1$ from $0$ to $y+X_2$ and $0$ to $\infty$ for $dX_2$. For $y\le0$ I have $dX_1$ set from $0$ to $y+X_2$. And the boundary for $dX2$ from $-y$ to $\infty$. I tend to make mistakes when setting boundaries for these types of piecewise functions, so was wondering if I made any here? Before I proceed any further in this problem.

Suppose we have $v$ and $u$, both are independent and exponentially distributed random variables with parameters $\mu$ and $\lambda$, respectively.   How can we calculate the pdf of $v-u$?


Let $d_1(x,y)$ and $d_2(x,y)$ be any two metrics on $\mathbb{R}^n$. Can it be shown that,  $$c\cdot d_2(x,y) \le d_1(x,y) \le C\cdot d_2(x,y)$$  for all $x,y \in \mathbb{R}^n$ for some fixed positive constants $c,C$? If not, under what conditions could such a relation hold (for a compact set it seems straightforward)? If yes, does this result hold for two arbitrary topological metric spaces as well?  Thanks!

The following is a well-known result in functional analysis:     If the vector space $X$ is finite dimensional, all norms are equivalent.     Here is the standard proof in one textbook. First, pick a norm for $X$, say  $$\|x\|_1=\sum_{i=1}^n|\alpha_i|$$ where $x=\sum_{i=1}^n\alpha_ix_i$, and $(x_i)_{i=1}^n$ is a basis for $X$. Then show that every norm for $X$ is equivalent to $\|\cdot\|_1$, i.e.,  $$c\|x\|\leq\|x\|_1\leq C\|x\|.$$ For the first inequality, one can easily get $c$ by triangle inequality for the norm. For the second inequality, instead of constructing $C$, the  is applied to construct a contradiction.   The strategies for proving these two inequalities are so different. Here is my question,      Can one prove this theorem without Bolzano-Weierstrass theorem?   UPDATE:     Is the converse of the theorem true? In other words, if all norms for a vector space $X$ are equivalent, then can one conclude that $X$ is of finite dimension?


I think its still in debate    Normally when I have a question and a answer, but have doubt with my own attempt, I tend to put the solution within my question. And I'll only post the question (if without a solution in my mind), and could post my solution afterwards separately as a answer to my own question (if I can found out one).  But today I met  and been enlightened to always post them separately, is this the case? Maybe its there but I really can't find it in FAQ, and even it is, I still feel a question for suggestions of your own answer should include the solution in the question.

I showed up here to write a perfectly normal rant about misaligned pixels, and there's a big fat checkbox cluttering up the "Ask" page:    WHAT THE EEEEK IS THIS NEW ABOMINATION?


If I make a tunnel in the earth through its center from one place to the antipode place and throw a ball into the hole, what will happen? So far I can think, the ball will oscillate with SHM motion Making such a tunnel is not possible. I have just assumed it.

...And you jumped in.  What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up?


What are the two formulae to convert between the two?  For example, I have a z critical value of 3.00. With what formula can you convert this to 0.9973?  And, for example, you have a confidence level value of 0.9973. How do you convert it to 3.00?

Does anyone know what the Inverse Cumulative Distribution Function of Normal Distribution is? Does it have a closed form expression? I did not find any good answer using Google.


When I try to install Audacity through Ubuntu Software Center, the screen initially shows:  Available from the "universe" source   Then, I click on Use This Source button on the right, and it asks for a  password. But, after I enter my login password, the  System shows Progress 1 and later on gives the following error:   Failed to download repository information Check your Internet connection   I have also tried to install VLC Player but with similar results. Can anyone help me in this respect as I am quite new to Ubuntu platform?

How do I get to the Universe Repository in supported versions of Ubuntu?


Below is a C program:    #include<stdio.h>  void func(int a[]) {   printf("%d\n",sizeof(a)); }  int main() {   int arr[10];   printf("%d\n",sizeof(arr));   func(arr);   return 0; }   Now the problem is that the sizeof() operator returns 40  when I use sizeof(arr) but 8 when I use sizeof(a). What is the reason for this behavior?

First off, here is some code:  int main()  {     int days[] = {1,2,3,4,5};     int *ptr = days;     printf("%u\n", sizeof(days));     printf("%u\n", sizeof(ptr));      return 0; }   Is there a way to find out the size of the array that ptr is pointing to (instead of just giving its size, which is four bytes on a 32-bit system)?


I downloaded the deb file from http://brackets.io/ and ran  sudo dpkg -i ~/Downloads/Brackets*  and getting following error:   dpkg: dependency problems prevent configuration of brackets: brackets depends on libgcrypt11 (>= 1.4.5); however: Package libgcrypt11 is not installed.   This occurred after fresh install.

How do I install a .deb file via the command line?


since James Jeans was that famous British physicist, shouldn't there be:  Jeans's instability    instead of:   Jeans instability      I have read couple (maybe not all) of saxon genitive related topics here but I haven't found the answer.

When does a noun can be used as a adjective avoiding the use of saxon genitive? I am writing a tittle that states: "FDA's, EPA's, and TTB's regulations", but I would like to avoid using the saxon genitive (if possible) because the tittle looks longer and more complicated. I would prefer to say "FDA, EPA, and TTB regulations." Is the second sentence correct? Can we use FDA, EPA, and TTB as if they were adjectives?  Note: FDA, EPA, and TTB are US Regulatory Agencies.  Thank you,


In order to sign up for a developer account, I'll need my parents credit card. However, after going through the signup process, my Dad's name shows up because he is the credit card holder. How can I publish an app under my name, if I don't have access to my own credit card? Should I buy a prepaid one?

So now I have an "identity cannot be verified" message whenever I activate it from the activation code Apple gave me via email.  Is there anything I can do about this or is my $99 "doomed"?


Define the events $A$ = "both children are girls", $B$ = "at least one of the children is a girl"   What is the probability $Pr(A|B)$?  Can someone explain how to do this?  Both children are born independently

Assume that a newborn baby is a girl with probability $p$ and a boy with probability $1-p$. Also assume that the genders of dierent newborns are independent of each other. Consider a person who has two children. Define the following two events:  A = "both children are girls"  B = "at least one of the children is a girl"  What is the conditional probability $Pr(A \vert B)$?    My attempt is to use the conditional probability formula $P(A\vert B) = \frac{P(A\cap B)}{P(B)}$  $S = \{ BB, GG, GB, BG \}$  $P(A) = p\cdot p$ since for both children to be girls  $P(B) = 2\cdot\{(1-p)\cdot p\} + (p)^2 = 2p - p^2$ since the probability for at least one girl means the probability $GG$ plus $GB$ and $BG$, with NO $BB$   $P(A\cap B) = ?$ How do I get the intersection? I know the only intersection is $GG$ which is $\frac{1}{4}$ but I need to express it as a probability.   My guess is that the intersection is $p^2$ since that is the $P(A)$, but I'm not sure, can some one convince me if I'm right?  $P(A\vert B) = \frac{p^2}{2p-p2} =\frac{p}{2-p}$  Is this correct?


I have started using R recently, along with the caret package. I note that there is an option to preprocess data so that it is scaled and centered. I am interested in  multiple linear regression. What can go wrong mathematically in the case when data is not scaled and centered? One guess is that we could have a very bad condition number for the 'system matrix'? Is this what scaling and centering tries to remedy, or is it something else? A related question is should we ALWAYS scale and center for any predictive model we decide to use? Is there any downside to scaling and centering the data?

My understanding is that when some features have different ranges in their values (for example, imagine one feature being the age of a person and another one being their salary in USD) will affect negatively algorithms because the feature with bigger values will take more influence, is it a good practice to simply ALWAYS scale/normalize the data?  It looks to me that if the values are already similar among then, then normalizing them will have little effect, but if the values are very different normalization will help, however it feels too simple to be true :)  Am I missing something? Are there situations/algorithms were actually it is desirable to let some features to deliberately outweigh others?


I'm trying to understand what is exactly a file system. I found various answers on the web including the ones provided here: . While these answers provide valuable informations, it's still unclear to me whether a file system is: a - A collection of data structures (inodes, master file table, file allocation table, ...) that index files and directories . b - A collection of data structures that index files and directories and the file tree. c - A file tree (mounting a file system, mounting a network file system, the /proc file system).

I have used Windows since childhood, and when I hear the phrase "Windows filesystem" I think of directories (folders) within directories, a folder called SYSTEM, a folder called PROGRAM FILES etc. Is this what the system is? Just the layout of the folders?  And then I recently started using Linux, and my reference book says in the linux filesystem everything starts at root and branches off from there. How is that really different from Windows? I mean, it seems the linux system and the windows system are just two ways of setting up a directory tree.  Is this what file system means?


After re-watching the movie, I realised that although Snape is revealed to be the 'Half-Blood Prince' - it is never explained as to how he got his name.   I assume 'Half-Blood' would be Half Muggle?   Anyone know the answer?

My question comes from what I learned in the movies, considering I have not yet been able to read the books. I would just like to know why Severus Snape called himself the Half-Blood Prince? Did many people call him that or did he just think that it was a cool nickname? This question might be answered in the books so feel free to quote from it.


Yesterday, I created my  and I tried to add in the google search index. Here's what I did:    I went to  google search console and added new "property" with "URL prefix".  Then I added the meta tag on my github-pages site (html-head) as described, it looked like   Then I pasted my page URL (kirusha05.github.io) to the "search bar" on the top of the search console  I was redirected to URL adress verification page, where I saw "URL adress is not on Google". I clicked "request indexing". A live test started , then a message like "The live test failed" showed up.    I saw again "URL adress is not on Google" . This page is not included in index , but not because of an error. And under that a Coverage section, near it I saw "Google doesn't know the URL adress" . What is wrong ? How can I get my site indexed ? Thanks in advance!

This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it?


I have somewhere the concepts of left groups (A non empty set with an associative binary operation, a left identity and each element has left inverse) and right groups. I have also studied some basic properties of identities and inverses .  Now I have a question.  Does there exist a left group which is not right group?

Related Link:    Reference: Fraleigh p. 49 Question 4.38 in A First Course in Abstract Algebra     I will present my proof (distinct from those in the link) for critique and then ask my question.  $G$ is a set and $ \times $ is an associative binary operation.  Suppose that there exists a $e \in G$ such that, for all $a \in G$, $ea = a$ and $a^{-1}a = e$ for some $a^{-1} \in G$.  Show that for the same $e$, $ae = a$ and $aa^{-1} = e$.  $a^{-1}(aa^{-1})a = (a^{-1}a)(a^{-1}a) = ee = e = a^{-1}a = a^{-1}(a^{-1}a)a$  Since $a^{-1} \in G$, it has a left inverse; apply it to both ends, and we have $(aa^{-1})a = (a^{-1}a)a$.  As a result, $ae$ = $a(a^{-1}a) = (aa^{-1})a = (a^{-1}a)a = ea$.  For the right inverse, start with $aa^{-1} = a(a^{-1}a)a^{-1} = (aa^{-1})(aa^{-1})$.  Since $\times$ is a binary operation, $aa^{-1} \in G$ and has a left inverse; apply it to both ends, and we have $e = aa^{-1}$.  In second comment following the question in the link, Mr. Derek Holt pointed out that the requester did not word his/her question correctly.  Specifically, the identity in the second axiom is not well-defined.     Let $(G, *)$ be a semi-group. Suppose    1. $ \exists e \in G$ such that $\forall a \in G,\  ae = a$;    2. $\forall a \in G, \exists a^{-1} \in G$ such that $aa^{-1} = e$.    How can we prove that $(G,*)$ is a group?    This formulation makes the same technical error as many textbooks. The $e$ in your second axiom is not well-defined. "But obviously it's intended to be the same $e$ as in the first axiom" you reply. But the first axiom does not necessarily specify a unique element $e$. So should we interpret the second axiom as meaning "for some $e$ as in 1" or "for all $e$ as in 1"? –  Derek Holt Sep 17 '11 at 15:31   Was he saying that if, in axiom 1, we have $ae_1 = a, ae_2 = a$, but $e_1 \neq e_2$,  when we get to axiom 2, do we have $aa^{-1} = e_1, aa^{-1} = e_2$, or two different inverses so that $aa_1^{-1} =  e_1, aa^{-1}_2 = e_2$?  I think my wording eliminated the ambiguity.  It does not imply that $e$ is unique, but if $e$ is a left identity and produces left inverses, then it is also a right identity and produces right inverses. I tried really hard on this one; please kindly point out my mistakes.


Find the zero divisors of the ring $R=C[0,1]$ the continuous functions $f:[0,1] \to [0,1]$.  I could thought of a set $S$ that I think is included in the set of zero divisors, but I am not sure if $S$ contains all the zero divisors. $S=\{f:[0,1] \to [0,1]: \text{there is} \space \epsilon>0, (x_0-\epsilon,x_0+\epsilon) \subset [0,1], f((x_0-\epsilon,x_0+\epsilon))=0\}$  I would like some help to find the zero divisors. Is the set $S$ a subset of the set of zero divisors? How can I show that?

Suppose you have a ring $(C[0,1],+,\cdot,0,1)$ of continuous real valued functions on $[0,1]$, with addition defined as $(f+g)(x)=f(x)+g(x)$ and multiplication defined as $(fg)(x)=f(x)g(x)$. I'm curious what the zero divisors are.  My hunch is that the zero divisors are precisely the functions whose zero set contains an open interval. My thinking is that if $f$ is a function which is at least zero on an open interval $(a,b)$, then there exists some function which is nonzero on $(a,b)$, but zero everywhere else on $[0,1]\setminus(a,b)$. Conversely, if $f$ is not zero on any open interval, then every zero is isolated in a sense. But if $fg=0$ for some $g$, then $g$ is zero everywhere except these isolated points, but continuity would imply that it is also zero at the zeros of $f$, but then $g=0$, so $f$ is not a zero divisor.   I have a hard time stating this formally though, since I'm only studying algebra, and not analysis. Is this intuition correct, and if so, how could it be rigorously expressed?


So the idea I had is that I want to create a partition with only or at least all the damaged sectors on a HDD (if only damaged sectors are not possible, then a few normal ones are ok as well) and the main partition would be the undamaged sectors.  Is such a thing possible to do? I can't imagine why not.

I've seen a lot of hard drives with only a few bad (unrecoverable) sectors (as indicated by SMART). Of course the proper thing to do with a bad drive is replace it, as there's a good chance of the drive crashing completely in the near future; I'm aware of that. However, in the interim, or for those who don't want to spend $70 to save data they don't value highly anyway (sigh, non-technical people), or just to get some use out of old hardware instead of throwing it away, I'm wondering if there's a way to identify where the unrecoverable sectors are ("where" meaning numerically, from 0 to the number of sectors on the drive), so I could stick a blank partition in that general area. Yes, this would involve low-level-formatting the drive and reinstalling the OS, of course.  So:  Would partitioning around unrecoverable sectors even be a workable way of reducing the disk of losing data?  If so, is there a way to find the location of these unrecoverable sectors?


In the classic example of a charging capacitor I can see how an Amperian loop with a surface going between the capacitor's plates would feel a changing electric flux, as the electric field between the plates changes with time.  However, considering the same Amperian loop but with a flat surface crossed by the wire leading to the capacitor, there is no displacement current, only conducting current.  The fact that there is no displacement current tell us that there is no change in the electric field across that flat surface.  Can someone elaborate more to me why there is no changing electric field across the flat surface too? I can't understand it...

I'm currently studying from "Introduction to Electromagnetics" by D.J. Griffiths. In the book the significance of the displacement current term is explained by looking a non-steady capacitor circuit (shown below).  Using the integral equation and balloon-shaped surface, it is said that $I_{enc}=0$ but $\int \partial\vec{E}/\partial t \cdot d\vec{a}=I/\epsilon_0$. This statement makes sense to me - there is no physical current flowing between the plates but there is a changing electric flux through the balloon surface.  My misunderstanding is with the flat Amperian loop surface where it is mentioned that $\vec{E}=0$ and $I_{enc}=I$ in this case. Obviously there is a current flow $I_{enc}$ in the Amperian loop, but why is $\vec{E}=0$? Just looking at the equations directly, I would have thought there would be a combination of both current terms (including displacement current due to changing electric field in the wire) in a capacitor charging/discharging situation.  I've attempted to seek other explanations on this from other texts,  and elsewhere in this stackexchange site, but this has made me more confused. Clarification on this would be appreciated.     Differential form of Ampere's-Maxwell's equation: $$\nabla \times \vec{B}=\mu_0\vec{J}+\mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}$$  Integral form of Ampere's-Maxwell's equation: $$ \oint\vec{B}\cdot d\vec{l} = \mu_0I_{enc}+\mu_0\epsilon_0 \int \frac{\partial \vec{E}}{\partial t} \cdot d\vec{a} $$


I have this interesting piece of code: def get_unit_sigmoid_func(alpha: float) -> Callable[[float], float]:     return lambda x, alpha=alpha: 1. / (1 + (1 / np.where(x == 0, 0.01, x) - 1) ** alpha)  I just don't understand what the point of this is. Why wouldn't they write something like: def get_unit_sigmoid_func(alpha,x):     return 1 / (1+(1/np.where(x==0,0.01,x)-1)**alpha)  Is there any advantage to the way it's written in the first way?

I've seen references to curried functions in several articles and blogs but I can't find a good explanation (or at least one that makes sense!)


I have some issues with my viewport. It only shows a small area of my scene with solid shading. Also only vertices within this area can be selected. In object mode a pyramid shows up. It limits the viewable area. I added two screenshots, one with viewport shading, to show you, that only a view vertices are selectable, and one with solid shading in object mode to show you the pyramid.  Has anyone an idea how this could be fixes?  Thank you! Janek

When looking at my objects in 3d view I'm seeing a gray cone that seems to be hiding other objects.   Can anyone help me turn this off and explain what it is please.  Screenshots attached.


I'm beginning to envy Fielding, of all people. Here are a few quotes from his novel:  I'll buy the gayest gown I can get ... He was besides active, genteel, gay, and good-humoured ... Among the gay young fellows who were at this season at Bath, Mr Fitzpatrick was one. ... for I have observed, the more merry and gay and good-humoured my husband hath at any time been in company, the more sullen and morose he was sure to become at our next private meeting. From The History of Tom Jones, a Foundling, 1821: ; ; ;   Take a closer look at the last part: according to Fielding "merry" and "gay" aren't synonymous or he wouldn't use the two words together. So what would a modern writer use instead of "gay"? Should someone write a novel on the same themes today, what word would you have them use?

Dictionary.com lists , with “merry, lively” as the first entry.  Microsoft  for listing  (a real place) as his hometown:   Xbox Live considered the term gay absolutely inappropriate in any context.     As a non-native English speaker, my question is whether in contemporary English, does gay always mean homosexual? Are British and American English the same in this respect?


I am having an issue while trying to show the coordinates in the print layout in QGIS. While the coordinate format is in decimal and suffix, it is ok.  I need the format in degree, minutes, and suffix. But when I had selected that option, it was showing both north and south points in the latitude, and also the east and west in the longitude.  How to solve this problem? There was a  like this one, but could not solve my problem.

I am using QGIS 3.12. I am new to QGIS after having worked with ArcGIS Desktop for a while. I am having issues with adding a grid to my project. I am using CRS ESPG:3587 WGS 84 / Pseudo-Mercator and noticed that the grid is showing the wrong coordinates and have included the parameters I have set for the grids.


I've got an array of arrays like this :  Array(     [id1] => Array (            /* details */            [unique] => 3           )     [id2] => Array (            /* details */            [unique] => 5     [id3] => Array (            /* details */            [unique] => 1     ) )   Question : How could I sort it by the unique field, so that it is converted like the one following?  Array(     [id2] => Array (            /* details */            [unique] => 5           )     [id1] => Array (            /* details */            [unique] => 3     [id3] => Array (            /* details */            [unique] => 1     ) )

I have CSV data loaded into a multidimensional array. In this way each "row" is a record and each "column" contains the same type of data.  I am using the function below to load my CSV file.  function f_parse_csv($file, $longest, $delimiter) {   $mdarray = array();   $file    = fopen($file, "r");   while ($line = fgetcsv($file, $longest, $delimiter))   {     array_push($mdarray, $line);   }   fclose($file);   return $mdarray; }   I need to be able to specify a column to sort so that it rearranges the rows.  One of the columns contains date information in the format of Y-m-d H:i:s and I would like to be able to sort with the most recent date being the first row.


I learned that historical event like "Korean war broke out in 1950." should be described with past tense.        But when a past event influences present situation, could we use 'present perfect'?    Like this,'Korean war has broken out in 1950.' or 'Edison has invented the electric bulb.'  please, tell me.

In Korea, we learned that we should use the past tense when the subject is an historical event, as in "The Korean war broke out in 1950."  However, I think that when the event continues to affect the present (now), we should use the present perfect.  So I think that we can say 'The Korean war has broken out in 1950.'  Am I right?


Naruto's naming system always confuses me. Naruto is named Uzumaki, after his mother. But Boruto is named Uzumaki, after his father. So whose surname is taken while naming a child in Narutoverse? Are there some governing factors?

Is there any logical and canonical reason to why Naruto used his mother's family name, Uzumaki, instead of his father's family name?


Its pretty much clear that switch statements can take string value in Java and something like this :  String s="diljit" switch(s){  ..  ....}   will always compile.. s is a object of type String.... but on the other hand switch statement cannot take  objects of other classes? Why is this happening and How will i validate this question with a suitable answer..  Can switch statement take objects or not?

Is this functionality going to be put into a later Java version?  Can someone explain why I can't do this, as in, the technical way Java's switch statement works?


If dark matter interacts gravitationally and not electromagnetically, then dark matter should orbit a mass like normal. But thier orbits are not restricted to outside the mass.   Would dark matter just accumulate in the center of masses in virtue of collapsing orbits and not being repelled by EM?  If a bigger mass were nearby it would 'steal' the dark matter from the smaller, or rather it will collect at the center of the masses. Why dont we detect dark matter flowing between two large masses, instead of the more 'cluster' distribution we see?  side question: how can dark matter have a temperature above 0k if its not giving off light?

As far as we know, the particles of dark matter can interact with each other only by gravitation.  No electromagnetics, no weak force, no strong force.  So, let's suppose a local slight concentration of dark matter comes about by chance motions and begins to gravitate.  The particles would fall "inward" towards the center of the concentration. However, with no interaction to dissipate angular momentum, they would just orbit the center of the concentration and fly right back out to the vicinity of where they started resulting in no increase in density.  Random motions would eventually wipe out the slight local concentration and we are left with a uniform distribution again.     How does dark matter form lumps?


Hi I'm trying to deply a webapp to my server who currently runs Centos and I have the issue that I can not write to files inside the public app dir. My directory structure is as follows, there you can see permissions on each directory. The list runs from the index.php file to the root directory.  -rwxrwxr-x. 1 myuser apache 102 Mar 28 08:08 /var/www/mypage/public/index.php drwxrwxrwx. 2 myuser apache 4096 Mar 28 07:39 /var/www/mypage/public drwxrwxr-x. 3 myuser apache 4096 Mar 28 07:39 /var/www/mypage drwxr-xr-x. 9 myuser apache 4096 Mar 28 07:38 /var/www drwxr-xr-x. 20 myuser apache 4096 Nov  6 09:16 /var   The server throws an error that says that the server has no permissions to  write to a file inside the public directory.  The server runs as apache and the user myuser is on the apache group.  So, what can be happening? I have other projects inside the same directory and they have the same folder structure and permission but with no permissions error.

SELinux is preventing the apache user from writing to a log file which it owns. When I do setenforce 0 it works. Otherwise it shows this error  IOError: [Errno 13] Permission denied: '/var/www/webapp/k/site/k.log'   The security context of the file:  $ ll -Z k.log  -rw-r--r--. apache apache system_u:object_r:httpd_sys_content_t:s0 k.log   The file was created when the SELinux mode was set to permissive.  How to set the security context so the apache user can write in that directory? I did set that directory security context using chcon but I can't find a suitable file type.  From audit.log:  type=AVC msg=audit(1409945481.163:1561): avc:  denied  { append } for  pid=16862 comm="httpd" name="k.log" dev="dm-1" ino=201614333 scontext=system_u:system_r:httpd_t:s0 tcontext=system_u:object_r:httpd_sys_content_t:s0 tclass=file type=SYSCALL msg=audit(1409945481.163:1561): arch=c000003e syscall=2 success=no exit=-13 a0=7fa8080847a0 a1=441 a2=1b6 a3=3 items=0 ppid=15256 pid=16862 auid=4294967295 uid=48 gid=48 euid=48 suid=48 fsuid=48 egid=48 sgid=48 fsgid=48 tty=(none) ses=4294967295 comm="httpd" exe="/usr/sbin/httpd" subj=system_u:system_r:httpd_t:s0 key=(null)


I have a question about the "AV Rule 33" in [1].  It says "The #include directive shall use the <filename.h> notation to include header files.".   The document "explains" it by "divergence in vendor implementations", but I have problems believing it. A "local header" file is a local header file?!  Do compiler differ that much in the definition of "local"?  [1]

In the C and C++ programming languages, what is the difference between using angle brackets and using quotes in an include statement, as follows?   #include <filename>  #include "filename"


I was playing around with the oscilloscope and noticed when I measure between two points on my hand, I see about a 1 V signal at about 60 Hz.  Do I oscillate at 60 Hz?  Does this have anything to do with lighting or main's hum?  Where does this 60 Hz signal come from?

I bought a new PicoScope USB oscilloscope and noticed that when I touch the tip of the probe with my hand I see a 50 Hz signal of 2 volts on the screen. What is causing this? (Or rather, how is the mains 50 Hz sine wave getting through me to the scope?)


If I wanted to print an image found online and get a typical 27" x 40" sized poster what resolution image do I need? 4000 x 6000 or double that? I am confused over DPI and PPI.

(This question is meant to be a resource to direct others to given that this is a common question.)  Given the task of creating an image that will be printed at a certain size, what pixel dimensions and resolution should I be setting my file at?


I can prove this, if $f$ is continuous on $[a, b]$, using $g(x) = f(x) - x$. But can't figure out, how can I prove it, if $f(x)$ is only monotonically increasing.

Let $\mathbb{F} $ be a ordered field and a function $f:\mathbb{F}\to \mathbb{F}$ is called monotonically increasing if $\forall x,y \in \mathbb{F} $: $ x \leq y \Rightarrow f(x) \leq f(y)$. Let $ a,b \in \mathbb{F} $: and $a <b$ and $f:\mathbb{F}\to \mathbb{F}$ a monotonically increasing function with $f(a) > a$ and $f(b) < b$.  Is there for 1) $\mathbb{F}   = \mathbb{R } $ 2) $\mathbb{F}   = \mathbb{Q }$ a point with $f(x) = x$ ?  Until now we have : Infimum and supremum, axiom of real numbers,intervals etc. but no theorems about monotonically  functions


I am using statsmodels.formula.api to preform linear regression. I have used three independent variables for prediction. In some cases I am getting negative value but all the output should be positive.  Is there any way to tell the model that the output can not be negative?  import statsmodels.formula.api as smf  output1 = smf.ols(formula= 'y ~A+B+C', data= data).fit() output = output.predict(my_data)

I have created a multiple linear regression model to predict prices and about 17% of the predicted prices have come out to be negative.  Is there a way to correct for this error, or does it mean that the independent variables are not good predictors?  The R^2 coefficient is 0.865.


I'm trying to create a script to assign each keyboard layout to a different keyboard shortcut, seeing as to how I'm using way too many of them to go through them one at a time whenever I need a specific one. How should I go about this?

Can I set up keyboard shortcuts for each input language? For example I want to set "Ctrl + 8" for English, "Ctrl + 9" for Ukrainian and "Ctrl + 0" for Russian languages. I don't want to switch and search language I need. It takes time. I want directly to turn language I want. I had this ability  in Windows. Maybe I need to install some plugin?


I recently received an iPhone as a gift. It had not been used in a while, and as such, had been left un-updated on iOS 6.0.1. I am a jailbreak enthusiast, and since there may not be an iOS 8.4.1 - iOS 9 jailbreak, would it be possible to update to iOS 8.3 with its IPSW file (despite it not currently being signed)?

I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?


Show that set of all invertible $n\times n$ matrices with real entries (denoted by $GL_n(R)$) is open set in $M_n(R)$.   My attempt: by open set I think it means neighborhood of every point in set is contained in set, but this definition doesn't seem to help solve this question. Any other approach?

I want to prove, that $GL(n,K)$ is open in $M(n,K)$, where ($K=\{\mathbb{R},\mathbb{C},\mathbb{H}\}$.  For the prove I don't want to use that the determinant is continous. Alternativly I assume a submultiplicative norm.  First step: Define $U_A:=\{B\in M(n,K):\Vert A-B\Vert<\frac{1}{\Vert A^{-1}\Vert}\}$ and show that it is a neighbourhod of $A$ in $M(n,K)$.  Second step: I show that the series $\sum_{k\ge0}(1-A^{-1}B)^kA^{-1}$ converges absolutely and the limit is inverse to $B$.  For the second step I should use the Neumann series, right? But I have some problems with the first step. Any help?


David would give it about 5 minutes even if it met every one of his criterion.  David would give it about 5 minutes  even if it met his criteria.  Are both of the sentences grammatically correct and are they semantically equivalent?

I came across several forums and articles saying that criteria is plural and criterion is singular. Some gave me the impression that criterion is used to denote a set of rules.  What is the correct use of these two words?


I want to give a pictureBox the shape of an image I have. The image off course is rectangular, but there is the backgroundcolor that should be ignored, which leads to the desired form. So if there is a picture of a banana on a white background, I should have a pictureBox in shape of a banana at the end.. This is needed so that I can move shaped PictureBox in front of a AxWMPLib Mediaplayer without having the rectangle surrounding the banana covering all of the video.  My approach is to create a new class that extends PictureBox and then setting the region to the shape. Problem is, I don't know how to get the shape.  class ShapedPBox : PictureBox {     public ShapedPBox()     {          this.Paint += this.shapedPaint;     }      void shapedPaint(object sender, paintEventArgs e)     {         System.Drawing.Drawing2D.GraphicsPath gP = new System.Drawing.Drawing2D.GraphicsPath();         //do something to give gP.addPicture? perhaps something with transparency key?          this.Region = new Region(graphicsPath);     }     public Image image; }

What is the easiest way to do this? Is it possible with managed code?


A number n will always end in some digit of the set {$0,1,2,3,4,5,6,7,8,9$}. The last digit of $n^2$ is the last digit of its last squared digit. Like this:  $$\ldots 0^2 = \ldots 0$$  $$\ldots 1^2 = \ldots 1$$  $$\ldots 2^2 = \ldots 4$$  $$\ldots 3^2 = \ldots 9$$  $$\ldots 4^2 = \ldots 6$$  $$\ldots 5^2 = \ldots 5$$  $$\ldots 6^2 = \ldots 6$$  $$\ldots 7^2 = \ldots 9$$  $$\ldots 8^2 = \ldots 4$$  $$\ldots 9^2 = \ldots 1$$  Therefore, no perfect square ends in $8.$  I think my proof is pretty bad, is there anything more formal than that?

I want to prove that $$ w^2 \equiv 2 \quad (\bmod{5})$$ has no solutions in integers.  What I tried: $$ w^2 \equiv 2 \quad (\bmod{5})$$ $$ \Rightarrow w^2 =  2 + 5k,  \quad k \in \mathbb{Z} $$  Now, I don't know what to do, so I considered $x^2 = 2+ 5y$ over $\mathbb{R}$.  We can solve this to see if the solutions are integers.   If it has no solutions in integers, can I then say that this implies that $ w^2 \equiv 2 \; (\bmod{5})$ has no solutions? Is there a different approach to this problem?


Should we say:     I am a great fan of Shakespear's and Enid Byton's writing   or      I am a great fan of Shakespeare and Enid Blyton's writing

Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better.


How to prove the following statement: If $m \equiv m'$ mod $n$, then gcd$(m,n) = 1$ $\Longleftrightarrow$ gcd$(m',n) = 1$. I have never learned number theory before, for me it's already hard to prove g.c.d of two integers is 1, not to mention the whole statement above. These kinds of facts jump out frequently in my abstract algebra course. Is there any good introductory number theory book that has clear and illuminating proof for these "basic" facts? Then I can remember the proof technique and these "basic" results by rote.

Given: $a = qb + r$. Then it holds that $\gcd(a,b)=\gcd(b,r)$. That doesn't sound logical to me. Why is this so?    Addendum by LePressentiment on 11/29/2013: (in the interest of  and averting a duplicate)  What's the intuition behind this result? I only recognise the proof and examples solely due to algebraic properties and formal definitions; I'd like to apprehend the result naturally.


I understand that the harmonic series diverges because of the comparison test: $$1+\frac12+\frac13+\frac14+\frac15+\frac16+\frac17+\frac18+\cdots\\\ge1+\frac12+\frac14+\frac14+\frac18+\frac18+\frac18+\frac18+\cdots$$However, I cannot intuitively understand why this is the case if $$\lim_{n \to \infty}\left(\frac{1}{n}\right)=0$$ Previosly, I thought an easy way of checking whether a series is convergent is if the above condition is true. However, the harmonic series has shown to me that this is not always the same the case—sometimes a series can diverge even if the terms approach $0$. Why does the harmonic series diverge but series such as $1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots$ do not?

I am struggling understanding intuitively why the harmonic series diverges but the p-harmonic series converges. I know there are methods and applications to prove convergence, but I am only having trouble understanding intuitively why it is. I know I must never trust my intuition, but this is hard for me to grasp. In both cases, the terms of the series are getting smaller, hence are approaching zero, but they both result in different answers. $$\sum_{n=1}^{\infty}\frac{1}{n}=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\cdots = \text{diverges}$$   $$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2}=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\cdots =\text{converges}$$


I was studying this chapter lately, and this part of chapter always confuse me. I often think why $3d$ orbital in transition metal is higher in energy than 4s orbital? (the whole question will refer to transition elements). My confusion arises when I look at the explanation on a website (attached below), it says that because ionization energy always removes the electron from the highest, which mean that first removed electron is the last electron being put in the orbital, so I conclude that $4s$ is higher than 3d in transition element. But I found another website (attached below) stating that the highest orbital is $3d$. Now my question which one is the correct one? First link:  Second link:

I'm currently taking Quantum Mechanics in school and I came across a table displaying the following in the given order:   $E_n (\text{energy levels}), g_n (\text{eigen functions})$   $n \ l, [m]$  $E_1, 1$   $1s, [0]$  $E_2, 4$   $2s, [0]$ $2p, [-1,0,1]$  $E_3, 9$   $3s, [0]$ $3p, [-1,0,1]$ $3d, [-2,-1,0,1,2]$    Now, as I understand $n$ defines the size of the orbital, $l$ the shape and $m$ the orientation.  My question is, how does the atoms shell model fit into this if one can have two electrons per orbital? Are $1s$ the same as the orbital $2s$, but just renamed for the sake of higher energy levels? Or do two similarly looking orbits exist for different energy levels? For example two "layers" of spherical electron clouds for an atom with $4$ electrons.  I just can't see how $2$, $8$, $18$ becomes $2$, $8$, $8$ as we were taught in Physics at high school? Am I missing something?


Let $X$ and $Y$ be iid. $U(0,1)$ random variable .Then $ E(X|X>Y) $ equal: I know that $ E(Y|X=x) = \int_{0}^{1} y *f(y|x) *dy $ Should we find the joint distribution X and Y to solve this question How do we solve this question?..

$X$ and $Y$ are independent $U(0,1)$ random variables.   I have to find $E[X|X>Y]$.   I found it out by integrating $\int_0^1 \int_y^1 x dxdy$ to get $\frac{1}{3}$ as the answer but this is wrong according to the answer key. What is the mistake that I have made?