Let $T:H \to H$ be a bounded linear transformation between Hilbert spaces. Let $T^*$ be the adjoint of T. Show that $\|T\|=\|T^*\|$.  I know that $\langle Tx,y\rangle=\langle x,T^*y\rangle$, but I don't know how to use it to prove $\|T\|=\|T^*\|$.

Suppose $H$ is a Hilbert space and let $T \in B(H,H)$ where in our notation $B(H,H)$ denotes the set of all linear continuous operators $H \rightarrow H$.  We defined the adjoint of $T$ as the unique $T^* \in B(H,H)$ such that $\langle Tx,y \rangle = \langle x, T^*y\rangle$ for all $x,y$ in $H$. I proved its existence as follows:  Fix $y \in H$. Put $\Phi_y: H \rightarrow \mathbb{C}, x \mapsto \langle Tx,y \rangle$. This functional is continuous since $|\langle Tx, y\rangle | \leq ||Tx||\; ||y|| \leq ||T||\; ||x||\; ||y||$. Therefore we can apply the Riesz-Fréchet theorem which gives us the existence of a vector $T^*y \in H$ such that for all $x \in H$ we have $\langle Tx, y\rangle = \langle x, T^* y\rangle$.  I now have to prove that $||T^*|| = ||T||$. I can show $||T^*|| \leq ||T||$:  Since the Riesz theorem gives us an isometry we have $||T^*y|| = ||\Phi_y||_{H*} = \sup_{||x||\leq 1} |\langle Tx, y\rangle| \leq ||T||\;||y||$ and thus $||T^*|| \leq ||T||$.  However, I do not see how to prove the other inequality without using consequences of Hahn-Banach or similar results. It seems like I am missing some quite simple point. Any help is very much appreciated!  Regards, Carlo


I've used bash in xterm on Debian Jessie for about 2 years. Just recently I sometimes get an error bash: $'\302\211[COMMAND]': command not found.  The only help I can find on the topic is  and . This sometimes happens when I type tab for command completion. Is there any way I can get rid of this without switching terminal emulators?

Sometimes when I simply type a valid command like 'find ...', or anything really, I get back the following, which is completely unexpected and confusing (... is command name I type): sh: $'\302\211...': command not found  There is some corruption going on I think. I don't use color in my prompt, I am using the Bash shell in POSIX mode as sh (chsh to /bin/sh and so on - $SHELL is sh). What is going on and why does this keep happening? Anything I can debug? I think this is more of an xterm issue than sh, or at least a combination of the two. Files, for context: My /etc/profile, as distributed with Arch Linux x86-64: # /etc/profile  #Set our umask umask 022  # Set our default path PATH="/usr/local/sbin:/usr/local/bin:/usr/bin" export PATH  # Load profiles from /etc/profile.d if test -d /etc/profile.d/; then         for profile in /etc/profile.d/*.sh; do                 test -r "$profile" && . "$profile"         done         unset profile fi  # Source global bash config if test "$PS1" && test "$BASH" && test -r /etc/bash.bashrc; then         . /etc/bash.bashrc fi  # Termcap is outdated, old, and crusty, kill it. unset TERMCAP  # Man is much better than us at figuring this out unset MANPATH  My /etc/shrc follows below. It's something I created as a way to have sh parse some file on startup, for a non-login shell; it is achieved using ENV variable set in /etc/environment with the line ENV=/etc/shrc: PS1='\u@\H \w \$ ' alias ls='ls -F --color' alias grep='grep -i --color' [ -f ~/.shrc ] && . ~/.shrc  My ~/.profile, I am launching X when logging in through first virtual tty: [[ -z $DISPLAY && $XDG_VTNR -eq 1 ]] && exec xinit -- -dpi 111  My ~/.xinitc, as you can see I am using the system as a Virtual Box guest: xrdb -merge ~/.Xresources  VBoxClient-all  awesome &  exec xterm  And finally, my ~/.Xresources, no fancy stuff here I guess: *faceName: Inconsolata *faceSize: 10 xterm*VT100*translations: #override <Btn1Up>: select-end(PRIMARY, CLIPBOARD, CUT_BUFFER0)  xterm*colorBDMode: true xterm*colorBD: #ff8000 xterm*cursorColor: S_red  Since ~/.profile references among other things /etc/bash.bashrc, here is its content: # # /etc/bash.bashrc #  # If not running interactively, don't do anything [[ $- != *i* ]] && return  PS1='[\u@\h \W]\$ ' PS2='> ' PS3='> ' PS4='+ '  case ${TERM} in   xterm*|rxvt*|Eterm|aterm|kterm|gnome*)     PROMPT_COMMAND=${PROMPT_COMMAND:+$PROMPT_COMMAND; }'printf "\033]0;%s@%s:%s\007" "${USER}" "${HOSTNAME%%.*}" "${PWD/#$HOME/~}"'                                                              ;;   screen)     PROMPT_COMMAND=${PROMPT_COMMAND:+$PROMPT_COMMAND; }'printf "\033_%s@%s:%s\033\\" "${USER}" "${HOSTNAME%%.*}" "${PWD/#$HOME/~}"'     ;; esac  [ -r /usr/share/bash-completion/bash_completion   ] && . /usr/share/bash-completion/bash_completion  I have no idea what that case statement does, by the way, it does look a bit suspicious though, but then again, who am I to know.


Can we drive low power load on high power source? For example we have source power 12 volt 60 amp and load power 12 volt 5 amp. Do we need resistor between them? If needed, what value will it be and how do I calculate its right value?  Can we drive load directly on hight power source ?

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


I want to show that for the Fibonacci numbers, $F_n$ $>=$ $2^{n/2}$ for n $>=$ 6.  My thought was to prove this via induction.  I showed the base case is true for $F_n$, n=6 and 7.  I assumed this was true for $F_{n-1}$, and $F_n$   => $F_{n-1}$ >= $2^{\frac{n-1}{2}}$ and $F_{n}$ >= $2^{\frac{n}{2}}$  => $F_{n+1}$ = $F_{n-1}$ + $F_{n}$  => $F_{n+1}$ = $2^{\frac{n-1}{2}}$ + $2^{\frac{n}{2}}$  => $F_{n+1}$ = $2^{\frac{n-1}{2}}$ $( 1 +$ $2^{\frac{1}{2}}$)  But in order to have $F_{n+1}$ >= $2^{\frac{n+1}{2}}$ I need $( 1 +$ $2^{\frac{1}{2}}$) >= 4, which is not true. This is where I get stuck.  Can anyone offer some tips? Thanks.

The Fibonacci sequence $F_0, F_1, F_2,\dots$ is defined by the rule $F_0=0, \ F_1=1, \ F_n = F_{n−1} + F_{n−2}$.  Use induction to prove that $F_n \ge \sqrt 2 ^n$ for $n \ge 6$.  So for the base case:  $F_6 = 8 \ge 2^{\frac 6 2} = 8$  $F_7 = 13 \ge 2^{\frac 7 2} = 11.31$  By definition: $F_{n+1} = F_n + F_{n-1} \ge \sqrt 2 ^n + \sqrt 2 ^{n-1}$.  This is as far as I could get and I'm not sure where to go from here. Any ideas?


Can somebody help me put this block diagram into this frame. I know there are a lot of questions about this specific diagram but I do have a project and I need your help.

I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization.


I'm launching a web app, which is currently in beta running on a "Lite" VPN account from my hosting provider. It has 2 cores and 1GB RAM.  I have only about 10 users now but Im considering whether I should just boost up the server to the "Pro" setup for $100/month, being 8 cores and 3GB RAM.   Aside from handling more LOAD..as that is not really needed for my whole 10 users, will it actually make my app any faster going from 2 to 8 cores? It's a web api written written mostly using async/await (C#) (IIS 8.5 on Win Server).  Will it have any noticable difference for my users?

This is a  about capacity planning for web sites. Related:      What are some recommended tools and methods of capacity planning for web sites and web-applications? Please feel free to describe different tools and techniques for different web-servers, frameworks, etc., as well as best-practices that apply to web servers in general.


I'm currently working on a codewars kata (Convert RGB number (0-255) to hexadecimal) and came across something interesting when trying to improve the readability of my code. I want to construct a global function to work with local variables, but when I try to run the code it throws an undefined error on the "j" variable (and also presumably the "i" variable). Code below:  function rgb(r, g, b){   let x   let y   let z   function conversion(){     switch(j) {             case 10:               j = 'A'               break             case 11:               j = 'B'               break             case 12:               j = 'C'               break             case 13:               j = 'D'               break             case 14:               j = 'E'               break             case 15:               j = 'F'           }           switch(i) {             case 10:               i = 'A'               break             case 11:               i = 'B'               break             case 12:               i = 'C'               break             case 13:               i = 'D'               break             case 14:               i = 'E'               break             case 15:               i = 'F'           }   }   if (r <= 0) {     x = '00'   } else if (r >= 255) {       x = 'FF'     } else {         let i = Math.floor(r / 16)         let j = Math.floor(r - i * 16)         conversion()         x = i.toString() + j.toString()       }   if (g <= 0) {     y = '00'   } else if (g >= 255) {       y = 'FF'     } else {         let i = Math.floor(g / 16)         let j = Math.floor(g - i * 16)         conversion()         y = i.toString() + j.toString()       }   if (b <= 0) {     z = '00'   } else if (b >= 255) {       z = 'FF'     } else {         let i = Math.floor(b / 16)         let j = Math.floor(b - i * 16)         conversion()         z = i.toString() + j.toString()       }   return x + y + z }   So as you can see, it would be nicer to use the "conversion" function rather than copy paste all that code three times. Any ideas on this topic? Thanks in advance.

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


I'm trying to get blender to render freestyle contours on objects behind a transparent material (literally transparent, not glass) and I can adjust the QI Range to max at 1, and while this does draw the freestyle lines on the occluded objects, it also draws freestyle lines on parts of the opaque mesh that really should be hidden. My major problem is I still want freestyle lines around the transparent object, and I want freestyle lines around objects occluded by this, but I don't want freestyle lines on objects occluded by opaque objects. Is this even possible considering freestyle doesn't know anything about materials? Is there something I can do to the backfaces of the transparent object to make freestyle appear through it but not through the other (opaque) objects?

Can Freestyle draw lines when an object is behind a transparent plane (or any other transparent object)? The render below shows the issue, the freestyle lines that should be drawn on lower arm and hand don't get drawn.


I have a class employee in which I have a static function with count number employee and and count to type of employee(e.g teacher ,assistant teacher,personal assistant etc) .For this purpose I have static class inside with I have a static count for number of employee and inside each subclass I want to access base class static method.  class Employee{     private static int emp;     //...code      static void IncreaseEmployeeCount()     {         emp=emp+1;     }  }  class Teacher : Employee{     private static int tchr;      //...code      static void IncreaseTeacherCount()     {         tchr = tchr + 1;     } }   How can I access base class static method using child class. It tried using following but fails with compile time error:  Teacher teacher = new Teacher(); teacher.IncreaseEmployeeCount();      'Employee.IncreaseEmployeeCount()' is inaccessible due to its protection level   Adding public access level still gives an error:     Member 'Employee.IncreaseEmployeeCount()' cannot be accessed with an instance reference; qualify it with a type name instead

Here is a little test program:   #include <iostream>  class Test { public:     static void DoCrash(){ std::cout<< "TEST IT!"<< std::endl; } };  int main() {     Test k;     k.DoCrash(); // calling a static method like a member method...      std::system("pause");      return 0; }   On VS2008 + SP1 (vc9) it compiles fine: the console just display "TEST IT!".  As far as I know, static member methods shouldn't be called on instanced object.   Am I wrong? Is this code correct from the standard point of view? If it's correct, why is that? I can't find why it would be allowed, or maybe it's to help using "static or not" method in templates?


Let $F$ be a subfield of the complex numbers (or, a field of characteristic zero). Let $V$ be a finite-dimensional vector space over $F$, Suppose that  $E_1,...,E_k$ are projections of $V$ and that $E_1+...+E_k=I$. Prove that $E_iE_j=0$ for $i$ (does not equal) $j$     (Hint: Use the trace function and ask yourself what the trace of the    projection is.)   Attempt: If $E$ is projection then $V = R \bigoplus N$ where $R = im E$ and $N$ is nullspace of $E$. If $\{ \alpha_1, ... , \alpha_r \}$ is base of $R$ and $\{ \alpha_{r+1}, ... , \alpha_n \}$ is base of $N$, then the matrix of $E$ is  $\left(\matrix {I&0\\0&0} \right)$,   where I is the identity matrix $r \times r$. Then see that $Trace(E)=dimR$.  Now  $E_1+...+E_k=I \rightarrow E_1^2+...+E_1E_k=E_1\rightarrow E_1E_2+...+E_1E_k=0 $  applying the trace operator and using its linearity  $tr(E_1E_2)+...+tr(E_1E_k)=tr(0)=0 $  now using the observation from the beginning  $dim Im(E_1E_2)+...+dim Im(E_1E_k)=0 $  it is $E_1E_k=0=0 ,\,\ \forall k$. And the other cases would be analogous. Is it right? Any better suggestions?

Let $X$ be a finite dimensional real linear space, or more generally a finite dimensional vector space over a field of characteristic $0$.  Let $(P_i)_{i=1}^n$ be a finite sequence of linear mappings $P_i :X\rightarrow X$ such that    $P_i^2=P_i$ for $i=1,...,n$,  $(P_1+...+P_n)^2=P_1+...+P_n$.   I wish to show that  $$P_i\circ P_j=0 \textrm{ for } i \neq j.$$  I know how to prove it only for $n=2$: if  $(P_1+P_2)^2=P_1+P_2$ then   $$P_1P_2+P_2P_1=0. \tag{$\ast$}$$  By multiplying both sides this equality by $P_1$ from left and by $P_1$ by right and obtain two equalities: $P_1 P_2+P_1P_2P_1=0$ and $P_1P_2P_1+P_2P_1=0$. By subtracting:   $$P_1P_2-P_2P_1=0. \tag{$\ast\ast$}$$  From $(\ast)$, $({\ast}\ast)$, we get $P_1P_2=0$, $P_2P_1=0$.


I want to print a text file in terminal with numbered paragraphs using the cat command.

I have a text file for which I need to do three things:   Modify the "cat" command to highlight keywords whilst showing the complete contents of the file.  Modify the "cat" command to automatically number the paragraphs. These are separated by a single blank line.  Modify the "cat" command to display the final paragraph only.    The tricky part is that all of these need to be done by modifying the cat command.   I've seen many forum posts explaining that cat is not meant for this - and I can entirely see why. However, the challenge is that I have to use cat!


minzaw@Dell-PC:~$ sudo start mysql [sudo] password for minzaw:  start: *Unable to connect to Upstart: Failed to connect to socket /com/ubuntu/upstart: Connection refused* minzaw@Dell-PC:~$ sudo restart mysql restart: Unable to connect to Upstart: Failed to connect to socket /com/ubuntu/upstart: Connection refused

I read about how to enable and disable services in Ubuntu and it seems that there are different possibilities to manage them.  The first method I found is update-rc.d to add new services to startup, which aims on the /etc/init.d folder and its contents.  The other one I found is to edit .conf files in the /etc/init folder.  What's the recommended way to enable / disable / add services and why?  Could you please give a short bulletproof step by step example on how to add a service in Ubuntu and enable and disable it?


In Python I am trying to make a function that can accept 1 or more arguments. For simplicity let's say I want to make a function that prints all the arguments that are passed  def print_all(**arguments**):     print(arg1, arg2, ..., argN)   so print_all("A", "B") would output AB.  The number of arguments passed could be 1 or more strings.  What is the best way to do this?

In the following method definitions, what does the * and ** do for param2?  def foo(param1, *param2): def bar(param1, **param2):


Suppose we have a table that shows the vacation destinations for some people with their vacation date (in January). Date       |   Name   |   Destination 01/01/2021 |   Andy   |   Thailand 01/01/2021 |   Ben    |   Singapore 02/01/2021 |   Andy   |   Japan 02/01/2021 |   Andy   |   Canada 03/01/2021 |   Ben    |   USA 04/01/2021 |  James   |   Thailand 05/01/2021 |  James   |   Thailand 06/01/2021 |  James   |   Japan 07/01/2021 |  Ben     |   Canada 08/01/2021 |  James   |   Canada  How do we list down those who have destinations in the exact following order: Thailand - Japan - Canada? (If someone has destination in the same country multiple times in sequential order then it counts as one appearance) The expected output is the name of the person: Name       Andy     James

I am looking for a way to concatenate the strings of a field within a group by query. So for example, I have a table:  ID   COMPANY_ID   EMPLOYEE 1    1            Anna 2    1            Bill 3    2            Carol 4    2            Dave   and I wanted to group by company_id to get something like:  COMPANY_ID   EMPLOYEE 1            Anna, Bill 2            Carol, Dave   There is a built-in function in mySQL to do this


I would like to redefine a short command (without \begin ... \end) for single line code examples using the listings package.  Here is what I tried:  \documentclass{article} \usepackage{listings}  \newcommand{\my}[1]{ \begin{lstlisting} #1 \end{lstlisting} }  \begin{document} \my{code} \end{document}   However, it gives the following error:  ! Emergency stop. <*> example.tex *** (job aborted, no legal \end found)   Using lstlisting directly works, though:  \documentclass{article} \usepackage{listings}  \begin{document} \begin{lstlisting} code \end{lstlisting} \end{document}

This code fails with Emergency stop:  \documentclass{scrbook} \usepackage{listings} \newcommand{\demo}{% \begin{lstlisting} foobar \end{lstlisting} }  \begin{document} \demo \end{document}   Why?


Please consider the following MWE:  \documentclass{article}  \PassOptionsToPackage{usenames,dvipsnames,svgnames,table}{xcolor} \usepackage{xcolor} \usepackage{tikz}  \begin{document}  \par Text before  \begin{center}     \begin{tikzpicture}         \node[text=blue] {test};  %% This line produces the error     \end{tikzpicture} \end{center}  \par Text after  \end{document}   Before the new year's MiKTeX update, I was able to write :  \node[blue] {test};   and the text within the node would be rendered blue. Since the update, however, this syntax creates a GhostScript (ps2pdf) Error: /undefined in XC@..  For some reason, at certain places in my documents, I now have to explicitly write \draw[draw=red] instead of \draw[red] or I get a similar error.  I have therefore tried using \node[text=blue], but to no avail. I know I could simply use \textcolor{blue}{...} inside the node to achieve the same effect, but my question is as follows: is this currently a bug in TiKz or MiKTeX, or is it a new change in syntax/features? (or alternatively, is my MiKTeX installation just fubar-ed...)  As with similar TikZ/PGF/PSTricks issues since the MiKTeX update, the .ps file seems to be properly generated (no actual errors during compilation), but the PDF conversion that ensues fails miserably, thus not producing a viable output document.

I use tikz (and tikzpicture) a fair bit, but files that used to compile fine before the latest slew of updates to pgf, and pstricks, no longer seem to do so (at least, on my MikTeX installation). The MWE (below) seems to compile correctly, but the DVI can't be rendered using yap, and dvi -> ps -> pdf fails (the dvi -> ps seems to be ok -- to the extent it isn't throwing errors), but ps2pdf fails miserably, with the following errors:   Error: /undefined in XC@.  Operand stack:    --nostringval--   --nostringval--   --nostringval--   --nostringval--   -  -nostringval--   --nostringval-- Execution stack: %interp_exit   .runexec2   --nostringval--   --nostringval--   --  nostringval--   2   %stopped_push   --nostringval--   --nostringval--   --  nostringval--   false   1   %stopped_push   2045   1   3   %oparray_pop    2044   1   3   %oparray_pop   2025   1   3   %oparray_pop   1884   1   3    %oparray_pop   --nostringval--   %errorexec_pop   .runexec2   --nostringval-  -   --nostringval--   --nostringval--   2   %stopped_push   --nostringval-- Dictionary stack:   --dict:979/1684(ro)(G)--   --dict:1/20(G)--   --dict:87/200(L)--   --    dict:182/300(L)--   --dict:58/200(L)--   Current allocation mode is local   Current file position is 99615   GPL Ghostscript 9.26: Unrecoverable error, exit code 1   Here is the MWE:  \documentclass[12pt,letterpaper,oneside]{article}  \usepackage{tikz}  \usetikzlibrary{decorations,shapes,arrows,matrix,positioning}  \begin{document}  \begin{center} \begin{tikzpicture}[x=0.175cm,y=0.175cm,scale=1]  % set up maximum and minimum x- and y-coordinates \def\xmin{0} \def\xmax{23.5} \def\ymin{0} \def\ymax{23.5}  % draw and label axes    \draw[->,thick] (\xmin,0) -- (\xmax,0) node[below=8pt,near end]  {\small{abundance ($N$)}};   \draw[->,thick] (0,\ymin) -- (0,\ymax) node[above=12pt,near   start,rotate=90] { \small{birth rate ($b$)}};  % draw vertical reference line at K/2=50   \draw[color=black, thick,  smooth] (0,20) -- (20,0)  node[below=6pt,midway,rotate=-45] {\small{slope~$=a$}};  % draw circle around point where function intersects x-axis \draw [red] (0,20)  ellipse (0.2cm and 0.2cm) node[right=3pt,black] {$b_0$};   \end{tikzpicture}  \end{center}   \end{document}


Hi I'm looking to get the value from a HTML Tables Cell and then display it into a JQuery Dialog Window when the user has clicked in that cell How can I achieve this ? Here's my code currently  <script> $(function() {     $( ".dialog" ).click(function(){            $('#dialog').dialog({             resizable:true,             modal:true,         });     }); </script>

I am trying to work out how to get the value of table cell for each row using jQuery.  My table looks like this:

     Customer Id	     Result

     123

     456

     789

   I basically want to loop through the table, and get the value of the Customer Id column for each row.  In the code below I have worked out that I need to do this to get it looping through each row, but I'm not sure how to get the value of the first cell in the row.  $('#mytable tr').each(function() {     var cutomerId =  }


const myWord = "ölkorv";  myWord.replace(/\w\S*/g, function(txt) {         return txt.charAt(0).toUpperCase() + txt.substr(1).toLowerCase(); });   This returns: "öLkorv". So basicly I understand that \w will only match on latin letters, how would I accomplish the same thing but allow of ÅÄÖ?

How can I use Unicode-aware regular expressions in JavaScript?  For example, there should be something akin to \w that can match any code-point in Letters or Marks category (not just the ASCII ones), and hopefully have filters like [[P*]] for punctuation, etc.


I just got a new laptop and I installed the TeX Live installation of LaTeX. My favorite editor is TeXstudio so I downloaded that as well. I spent a day working on a document and compiled it a bunch of times. When I subsequently checked the working directory, I found that a lot of files had been created. These files end up as, for example, "NAME".tex.AFi688, "NAME".tex.ALw688, etc... with every compilation creating a new set of files with a different, but similar, file extension.  In the start of my document I have the line "%& -aux-directory=AuxOut", which should take care of the auxiliary files, but upon closer inspection, the auxiliary files don't appear in in this directory, but rather in the directory that contains the source file itself.  This is not a problem when compiling on my desktop computer, so it might be that some of my settings are different on my laptop, but I am unable to identify which settings to modify.  Has anyone experienced something similar?  Thank you

I need to compile between two and four times before I see changes I make in the editor (TeXstudio) and each time I compile, a new .tex file is created with random letters and numbers at the end.   For example, If I create the file hello.tex and compile two to four times I'll get the file,   hello.tex.QU6664      then I make some small changes in the editor and compile two to four times I'll get the additional file,   hello.tex.Ak6664   After continuing to do this (each time compiling between two to four times before I see the changes I made), I now have many files that look like  hello.tex.QU6664, hello.tex.Ak6664, hello.tex.YX6664, hello.tex.sN6664, hello.tex.Ss6664, ...   A little bit of additional information (in case it's relevant): Everything was working fine up until a few days ago, i.e. only needed to compile once and only the file hello.tex was created. I still only get one .aux,  .synctex and .pdf files. I use TeXstudio to write and compile. I don't think it has anything to do with the bibliography (I tried removing bibliography altogether and still having the same problem).  How do I prevent these additional files from appearing and only compiling once like I used to? Has anyone had a similar problem?


I want to highlight some software commands as code in my text without any line break or any new paragraph for the code. Is there any possible way to do so?

What is the command to insert inline code words into the text like this?   I know there are packages for inserting snippets into the code, but I need to insert keywords within the main text. I was wondering if there is a more convenient way to do that.


I am learning the basics of Natural Deduction and I meet a problem about the role of context.   In Natural Deduction, if we have $\vdash A\rightarrow B$, we also have $A\vdash B$; if we have $A\vdash B$, we obtain $\vdash A\rightarrow B$.   My question is: if we have $\Gamma\vdash A$ where $\Gamma$ denotes a context, do we have $\vdash\Gamma\rightarrow A$; and if we have $\vdash\Gamma\rightarrow A$, do we have $\Gamma\vdash A$? I ask this because I didn't see any occurrence of contexts written as $\Gamma,\Delta$ after $\vdash$, is it wrong to write in that way?  Thank you in advance!

I am really lost trying to understand the difference between the logical connective "implies", $\to$, and the metalogical symbol (or maybe it's also a connective?) $\vdash$. (This is all focusing on prepositional logic here).  In metalogical terms, for example with modus ponens, it is said that $P, P \to Q \vdash Q$, which means "If we have a proof of $P$, and we have a proof of $P \to Q$, then we can infer / make a proof of $Q$". But I don't understand what the difference is between that and saying something like $P \land (P \to Q) \to Q$ which is similar but uses $\to$ instead of $\vdash$.  For example the $P \to Q$, at least in my experience, means "it is possible to go from $P$ to $Q$" but I don't see how "going to $Q$" is different from "inferring $Q$." Simply telling me that one is metalogical and one is not doesn't really help me understand what's going on.   I've also been given the example of  but I don't understand this, either. It sounds like the tortoise is constantly rejecting implications because "who says I have to accept conclusions just because the premises are true?" but then somehow introducing a metalogical $\vdash$ solves this? "We use the metalogical symbol $\vdash$ to basically force that stubborn tortoise to accept the conclusions and we've now circumvented the issue."  Unless I've grossly misunderstood something I just don't see why that's even a thing. Who says then I have to accept $\vdash$? Is $\vdash$ just a stronger form of $\to$, like a "sudo $\to$" or something (to borrow a Linux term), a form of implies that forces the conclusion to be accepted from the premise(s)?   What's the difference? How are they working here? Why do we need them? Are there any concrete examples showing the difference of both?


I was reading ISLR and came across this claim. Can someone elaborate mathematically.

Looks like the rationale behind the accepted answer of  is incorrect.   Under leave one out cross validation(LOOCV), the variance of its MSE estimator is $$var [\frac{\Sigma_i x_i}{n}] = \frac{var[\Sigma_i x_i]}{n^2}$$ where $x_i$ is an estimate of MSE from one particular iteration.   I agree that LOOCV has a higher enumerator (b/c of the covariance terms), but the denominator is larger as well because there are essentially n estimates (greater than k estimates as in the k-fold case).  Given this, why does LOOCV still have higher variance in estimating MSE and why does it have lower bias?  (This is against intuition b/c increasing sample should decrease variance and leaves bias unchanged for $\hat\theta$ and $\hat{y}$)


For an ideal gas, we can relate temperature to the average kinetic energy of the gas molecules.  What if we view a container of this gas from a reference frame that is translating at constant speed relative to the container.  $$E[X^{2}] = Var[X] + E[X]^{2}$$  The distribution of speeds is the same, but since the mean is larger (it is zero in the rest frame of the container), then the observer would view a higher average kinetic energy. Does the moving observer say that the container of gas is hotter?  If bulk translation doesn't relate to temperature, is there some hidden zeroing that's not present in the simple statement of "average kinetic energy"?

In ideal gas model,  is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?  Furthermore, if we accelerate a block of metal with ultrasonic vibrator so that the metal is vibrating in very high speed with cyclic motion, can we say the metal is hot when it is moving but suddenly become much cooler when the vibration stop?


Here is a bare-bones example of my code: def function():   var_a = 1   var_b = 2   var_c = 3   return var_a, var_b, var_c  function()  (Apologies for wonky formatting). Basically, the function takes in no arguments and its single job is variable assignment. I need to be able to call on the function for quick assignment and then be able to use those variables in the rest of my code. The problem is that I can't get those variables out of the function. So if I use the above code and put a print(var_a) line after, then it will tell me that var_a is not defined. If I say values = function() , print (values) then I will get only the values printed in a list, but I won't be able to access them in the way I want.  Is there an easy way to fix this?

The canonical way to return multiple values in languages that support it is often . Option: Using a tuple Consider this trivial example: def f(x):   y0 = x + 1   y1 = x * 3   y2 = y0 ** y3   return (y0, y1, y2)  However, this quickly gets problematic as the number of values returned increases. What if you want to return four or five values? Sure, you could keep tupling them, but it gets easy to forget which value is where. It's also rather ugly to unpack them wherever you want to receive them. Option: Using a dictionary The next logical step seems to be to introduce some sort of 'record notation'. In Python, the obvious way to do this is by means of a dict. Consider the following: def g(x):   y0 = x + 1   y1 = x * 3   y2 = y0 ** y3   return {'y0': y0, 'y1': y1 ,'y2': y2}  (Just to be clear, y0, y1, and y2 are just meant as abstract identifiers. As pointed out, in practice you'd use meaningful identifiers.) Now, we have a mechanism whereby we can project out a particular member of the returned object. For example, result['y0']  Option: Using a class However, there is another option. We could instead return a specialized structure. I've framed this in the context of Python, but I'm sure it applies to other languages as well. Indeed, if you were working in C this might very well be your only option. Here goes: class ReturnValue:   def __init__(self, y0, y1, y2):      self.y0 = y0      self.y1 = y1      self.y2 = y2  def g(x):   y0 = x + 1   y1 = x * 3   y2 = y0 ** y3   return ReturnValue(y0, y1, y2)  In Python the previous two are perhaps very similar in terms of plumbing - after all { y0, y1, y2 } just end up being entries in the internal __dict__ of the ReturnValue. There is one additional feature provided by Python though for tiny objects, the __slots__ attribute. The class could be expressed as: class ReturnValue(object):   __slots__ = ["y0", "y1", "y2"]   def __init__(self, y0, y1, y2):      self.y0 = y0      self.y1 = y1      self.y2 = y2  From the :  The __slots__ declaration takes a sequence of instance variables and reserves just enough space in each instance to hold a value for each variable. Space is saved because __dict__ is not created for each instance.  Option: Using a  (Python 3.7+) Using Python 3.7's new dataclasses, return a class with automatically added special methods, typing and other useful tools: @dataclass class Returnvalue:     y0: int     y1: float     y3: int  def total_cost(x):     y0 = x + 1     y1 = x * 3     y2 = y0 ** y3     return ReturnValue(y0, y1, y2)  Option: Using a list Another suggestion which I'd overlooked comes from Bill the Lizard: def h(x):   result = [x + 1]   result.append(x * 3)   result.append(y0 ** y3)   return result  This is my least favorite method though. I suppose I'm tainted by exposure to Haskell, but the idea of mixed-type lists has always felt uncomfortable to me. In this particular example the list is -not- mixed type, but it conceivably could be. A list used in this way really doesn't gain anything with respect to the tuple as far as I can tell. The only real difference between lists and tuples in Python is that lists are , whereas tuples are not. I personally tend to carry over the conventions from functional programming: use lists for any number of elements of the same type, and tuples for a fixed number of elements of predetermined types. Question After the lengthy preamble, comes the inevitable question. Which method (do you think) is best?


In any $∆ABC$, prove that: $$r^2+ r_1^2+ r_2^2 +r_3^2=16R^2-a^2-b^2-c^2$$ where $r$ is the inradius, $r_1,r_2,r_3$ are the exradii of the triangle respectively, and $R$ is the circumradius of the triangle. I tried to solve the question by replacing $r$ by $∆/s$ and $r_1$ by $∆/(s-a)$, and similarly for $r_2$ and $r_3$, but the answer is too long and I think there must be another short method.

From SL Loney Trigonometry:     Prove that   $$r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2$$   for a triangle with sides $a$, $b$, $c$, circumradius $R$, inradius $r$, and exradii $r_1$, $r_2$, $r_3$.   This one is a really dirty question.   I have tried a lot of stuff like $r=4R\times \Pi(\sin\frac{A}{2}$) and  $r_1=4R\times\sin\frac{A}{2}\cos\frac{B}2\cos\frac{C}2$ etc..  There are other ways like $-r+r_1+r_2+r_3=4R$,  but all these are way too cumbersome or clumsy.   Anything more intuitive?


I have been alerted to by our system that a PHP shell has been found in the /tmp directory. Firstly - I would like to know how it could have got here and why it would be here - is there any way PHP can be executed at this level?  Secondly it has somehow been uploaded through a WordPress installation - tracing how this happened won't be easy but does anybody have a general idea how this might have been? There are no public facing upload forms on the site.  Thanks, Chris.

This is a  about Server Security - Responding to Breach Events (Hacking)   See Also:                  Canonical Version I suspect that one or more of my servers is compromised by a hacker, virus, or other mechanism:   What are my first steps? When I arrive on site should I disconnect the server, preserve "evidence", are there other initial considerations? How do I go about getting services back online? How do I prevent the same thing from happening immediately again? Are there best practices or methodologies for learning from this incident? If I wanted to put a Incident Response Plan together, where would I start? Should this be part of my Disaster Recovery or Business Continuity Planning?   Original Version       2011.01.02 - I'm on my way into work at 9.30 p.m. on a Sunday because our server has been compromised somehow and was resulting in a    attack on our provider. The servers access to the Internet   has been shut down which means over 5-600 of our clients sites are now   down. Now this could be an FTP hack, or some weakness in code   somewhere. I'm not sure till I get there.      How can I track this down quickly? We're in for a whole lot of   litigation if I don't get the server back up ASAP. Any help is   appreciated. We are running Open SUSE 11.0.            2011.01.03 - Thanks to everyone for your help. Luckily I WASN'T the only person responsible for this server, just the nearest. We managed   to resolve this problem, although it may not apply to many others in a   different situation. I'll detail what we did.      We unplugged the server from the net. It was performing (attempting to   perform) a Denial Of Service attack on another server in Indonesia,   and the guilty party was also based there.      We firstly tried to identify where on the server this was coming from,   considering we have over 500 sites on the server, we expected to be   moonlighting for some time. However, with SSH access still, we ran a   command to find all files edited or created in the time the attacks   started. Luckily, the offending file was created over the winter   holidays which meant that not many other files were created on the   server at that time.      We were then able to identify the offending file which was inside the   uploaded images folder within a  website.      After a short cigarette break we concluded that, due to the files   location, it must have been uploaded via a file upload facility that   was inadequetly secured. After some googling, we found that there was   a security vulnerability that allowed files to be uploaded, within the   ZenCart admin panel, for a picture for a record company. (The section   that it never really even used), posting this form just uploaded any   file, it did not check the extension of the file, and didn't even   check to see if the user was logged in.      This meant that any files could be uploaded, including a PHP file for   the attack. We secured the vulnerability with ZenCart on the infected   site, and removed the offending files.      The job was done, and I was home for 2 a.m.            The Moral   - Always apply security patches for ZenCart, or any other CMS system for that matter. As when security updates are released, the whole   world is made aware of the vulnerability.   - Always do backups, and backup your backups.   - Employ or arrange for someone that will be there in times like these. To prevent anyone from relying on a panicy post on Server   Fault.


I bought a new Samsung galaxy S Advance(GT-i9070). It came with Gingerbread. It was actually . I clearly verified this with the shop when I bought it. Last day I upgraded my phone to Jell bean with official Russian firmware and reset to factory default settings. But now the phone seems very slow . Also full RAM Capacity seems 521 MB at Application manager. All applications are now consuming  memory from total 521 MB memory. My question is- where is remaining memory? How can I obtain the remaining memory to speed my phone? Some people on the web say to root the phone, install ROM manager etc. Are these approaches good? Please give me a solution

I have a Nook Color with Cyanogenmod 7.2 (on mSD), and Nook Color is supposed to be 512MB of RAM (says so on product's page).  When I open Menu (on bottom bar, while on desktop) > Manage Applications > Running, it says on the bottom left 95MB used, and on the bottom right it says 174MB free. These are about 270MB, does that mean my RAM is corrupted? Why is it not utilizing all 512MB of RAM?


Is there some way in which I can view/edit what the contents of a symbolic link are? I don't want to view the destination the link points to, but the symbolic link itself.  Suppose I have a file, file.txt and I create a link to file.txt as      ln -s $HOME/path/to/file.txt .   Now, if I copy this link to a different system, this link will point to nothing if $HOME expands to something different on the other system, even if the path after $HOME is still the same. Is there some way to edit the link file so that $HOME is not expanded before creating the file, but is a part of the file itself?

I have built my app for different architectures and would like to create a "dynamic symlink" which takes me to the right version based on a variable.   If the machine I am currently logged in to, is x86, then the symlink should take me to that build.  A mocked example of what I want to do:  $ uname -i x86_64  $ ls -ltr  lrwxr-xr-x  1 dogbane gg     4 Feb 16 15:40 mylink -> @sys/ drwxrwxr-x  2 dogbane gg  2048 Feb 16 15:40 x86_64/ drwxrwxr-x  2 dogbane gg  2048 Feb 16 15:40 i386/  $ cd mylink  $ pwd -P ~/x86_64   Is this possible?   I know I can use cd $(uname -i), but want something simpler.


I wrote some code that sets a marker on a current location when clicked. Unfortunately, the entire application crashes when no current location is given and the button is clicked. The error states:  java.lang.NullPointerException: Attempt to invoke virtual method 'double java.lang.Double.doubleValue()' on a null object reference  Is there a way implement a try catch exemption within the button?  Here is the on click instruction for the button:      markerBtn.setOnClickListener(new View.OnClickListener() {         @Override         public void onClick(View view) {               LatLng myCurrentLocation = new LatLng(myCurrentLatitude, myCurrentLongitude);             marker = mMap.addMarker(new MarkerOptions().position(myLocation).title("New Marker"));             markerBtn.setTag("yo");          }     });

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 have only recently started getting into the SE network of sites. As a new user it was a little confusing that I had to create a new account for each site, as I would have imagined that these would be combined into one account. I now understand why, Open ID requires new authorization for each site so it is out of SE's control.  The SE drop box on the top left corner is nice, but is it possible to get a feed of information about activity, my own and others, from all the SE sites which I am a member of in one area.  I know this will probably sound similar to this question, , but instead of only getting a feed of network wide replies I think it would be good to get a feed of information from each site that I have an account, all consolidated into one overall feed on the SE website. This way I could view the interesting, featured and hot feeds of multiple sites at one time. For example I could see SO and Tex questions together.  "But you can already view multiple site feeds at once by choosing sites in the right hand side of the SE page!!" Yes, that is true. I couple of problems with this: I have to manually select the sites (not a big deal, but automatic select of the sites that you are a member seems like a smart option). It is also displayed in a different style to the feeds in the full sites, there is no way to switch between the interesting or month viewing modes etc.  The other area of improvement is the User page, which again could consolidate statistics, activity, favourites etc into one place. This is very similar to the suggestions in the previous question that was linked above, but it is something that I think would be a very useful feature, which would still benefit from more discussion.

I think its good if we have one user account for all the SE sites(i.e. a StackExchange Profile).   Profile page should facilitate (from account owners pov):   List all the SE sites we have subscribed and we can visit the site account by clicking on the link. A summarized status of each account (e.g. whether there are new replies and comments) List SE sites we have not subscribed and instant subscription capability to any SE site.  Facility for grouping and using separate names.(It seams, some users don't like the idea of one profile . If a user doesn't want others to see all his/her accounts, then user can use separate names per group or account and set-up visibility settings so only the accounts with a similar screen names will be shown together. Yet account owner can manage them at one place )   Having a SE profile page will allow users to have separate accounts for each site, still managing them will be much easier. I am not suggesting to remove the profile pages we have at SE Q&A sites, I think separate profiles should be there since each site serves a different cause. Adding a link on each SE Q&A profile page, which will direct the user to SE main profile will be sufficient.  In the prevailing system visiting a SE site, which we don't use often, is a 3 step process. Lets say one wants to visit SE TeX but he/she has bookmarked StackOverflow only. Then steps should be StackOverflow > accounts > SE TeX. But if we have a Profile page at StackExchange, then it will be a 2 step process SE Profile > SE TeX.  If we have a SE site that we visit very often then we can bookmark it in our computer. But bookmarking all the SE sites we have signed up is pretty messy thing to do. So if SE provides a "StackExchagne Profile" page we simply can bookmark our profile page instead of bookmarking everything.  From StackExchange's point of view, enabling grouping facility will reduce the size of the user database.  Similar ideas were discussed in following pages, but I opened a different Question since the facilities I am requesting are different to them.   (1)  (2)  (3)


Translated to English using Google:  I bought a notebook asus f552cl that has the ability to use either the integrated video card or video card intel nvidia geforce 710m with optimus technology. Now on ubuntu 12.04 (the only one that does not give me problems with the network adapter atheros), is used only the intel integrated card, but I would always use the nvidia. How do I install the drivers for the nvidia card and make it usable by default? Thanks and sorry for the problem possibly even stupid    Original question:     Ho comprato un notebook asus f552cl che ha la possibilità di utilizzare o la scheda video integrata intel o la scheda video nvidia geforce 710m grazie alla tecnologia optimus. Ora su ubuntu 12.04 (l'unico che non mi da problemi con la scheda di rete atheros), viene utilizzata solo la scheda intel integrata, mentre io vorrei utilizzare sempre la nvidia. Come devo fare ad installare i driver per la scheda nvidia e renderla utilizzabile di default? Grazie e scusate per il problema possibilmente anche stupido

I am considering buying a Dell XPS 15 laptop. The laptop has a Nvidia 420m card which should work with Linux but I keep reading that the Nvidia Optimus technology isn't supported on Linux. I am not really interested in switching from Nvidia to Intel to save power but need to know that the Nvidia card will in fact work if I installed Ubuntu.  If anyone has experience using a Nvidia card with Optimus technology or even better the exact laptop in question (Dell XPS 15 with 1GB NVIDIA® GeForce®  GT 420M) it would be great.  A major problem holding people back from adopting Linux is this sort of hardware issue. I am a long term Ubuntu user and supporter who can't afford to make a mistake with a purchase like this. I don't want to spend £500+ to find I have no graphics acceleration because Windows 7 is not an option.


player_health = 10  def add(num):   return num + player_health  def monster_room():   print(player_health) # Error on this line   player_health -= 1 # Doesn't crash without this line, even though the error is thrown on the previous line.   print(add(6)) # works monster_room() # doesn't work   I get an error if I try to modify player_health:  UnboundLocalError: local variable 'player_health' referenced before assignment on line 10 in main.py  How the variable is possibly not assigned when I can use it in the add function just fine? Does it not recognize that it's a class-level variable because I'm attempting to modify it inside the function? Does Python have to pass every class-level variable you want to use to the functions so it can do everything at the local scope?

The following code works as expected in both Python 2.5 and 3.0:  a, b, c = (1, 2, 3)  print(a, b, c)  def test():     print(a)     print(b)     print(c)    # (A)     #c+=1       # (B) test()   However, when I uncomment line (B), I get an UnboundLocalError: 'c' not assigned at line (A). The values of a and b are printed correctly. This has me completely baffled for two reasons:   Why is there a runtime error thrown at line (A) because of a later statement on line (B)? Why are variables a and b printed as expected, while c raises an error?   The only explanation I can come up with is that a local variable c is created by the assignment c+=1, which takes precedent over the "global" variable c even before the local variable is created. Of course, it doesn't make sense for a variable to "steal" scope before it exists.  Could someone please explain this behavior?


There is one question which is bothering me alot: It is said that data can only be held on magnetic disks for about 5 years. After that, it could get lost because the magnetic force on the disk gets "weak" (I do not really know how to describe it better ;))  Do disks counteract against this? For example: Do they rewrite all their bits from time to time when they are idling?  Regards Christian

Do you guys know how much time needs to pass until the data stored on a hard drive starts to degrade?   To keep the data intact for long periods of time, I heard you need to periodically rewrite it on the hard drive, like every 5 years or so. Is it true?


How does one keep fried food hot while staying crispy for delivery? There are plenty of heating bags but I need one especially for French fries and other fried foods. Are there any techniques that keep french fries fresh during transportation?

If I'm deep-frying foods and want to hold batches of them so I can serve a large amount all at once, or even prepare a couple hours ahead, what's the best way to hold them until ready to serve?  Should I put them on wire racks above a drip pan, or should I place them on paper towels?  Or even in a paper cone?  Should I keep them warm or should I let them cool and reheat them in a very hot oven (450F)?  Or does it depend on the type of food, its shape, or the batter?  What I'm looking for here is someone who's done some comparison testing between different methods of holding over deep-fried foods.  Some example foods: garlic & pepper shrimp, tempura vegetables, latkes, felafel, and french fries.


I want to install Ubuntu/Linux on my laptop because I really hate windows 10!! I think windows 10 is not totally compatible with the hardware of my laptop or I do not know what happen, but I have several issues such as slow initial booting, it is slow to turn off the laptop and more issues. I have a dell inspiron with 16 GB RAM, 128GBSSD (OS installed there) and 1TB SATA, core i7 and nvidia 4GB, so pretty good stuff for using google chrome and couple other softwares.   I am really decided to change to linux as my OS, but after reading several experiences the best solution is to either dual boot windows and linux or install LInux on a external hard disk. I am not a computer expert, so I need some guidance to know the best option (preserve windows and not mess the internal hard disk) and to install linux.  Thank you.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


This is a newbie question. I read that JVM's execution starts from searching for the methodname from lowest class in the hierarchy and if the method is not available in that class it traverses to the parent class looking for the method.  If this is the case then why do we need to use "@override" for adding custom logic to the inherited class ?  The below example illustrates my question  class superclassA {  method() { }  }  class subclassB extends superclassA {  @Override  //While executing if JVM starts looking for the method name from the lowest hierarchy //then why do we have to use "override" as the methodname will be matched from the lowest level itself? method()  { --custom subclass specific code... }   }

What are the best practices for using Java's @Override annotation and why?     It seems like it would be overkill to mark every single overridden method with the @Override annotation.   Are there certain programming situations that call for using the @Override and others that should never use the @Override?


$\text {let}\ p(z)=a_0+a_1z+......+a_{n-1}z^{n-1}+z^n,a_i\in\mathbb{C}.$ if $|p(z)|=1 \forall |z|=1$ is it true that $p(z)=z^n$ for n=1,this is true.but is it also for higher value of n ???

Given a polynomial $ P(z) = z^n + a_{n-1}z^{n-1} + \cdots + a_0 $, such that   $\max_{|z|=1} |P(z)| = 1 $      Prove: $ P(z) = z^n $      Hint: Use cauchy derivative estimation    $$ |f^{(n)} (z_0)| \leq \frac{n!}{r^n} \max_{|z-z_0|\leq r} |f(z)| $$ and look at the function $ \frac{P(z)}{z^n} $     It seems to be maximum principle related, but I can't see how to use it and I can't understand how to use the hint.


Show that $f_{n}(x)$ is monotonically increasing on $(0, \infty)$ where, $$f_{n}(x)=\left(1+\frac{2x}{n}\right)^n$$ I considered the difference of consecutive terms, that is $$\left(1+\frac{2x}{n+1}\right)^\left(n+1\right)-\left(1+\frac{2x}{n}\right)^n$$ For any x in $(0,\infty)$ My goal is to show this portion is positive. What about induction method?I'm kind of stuck in here.

Note: I don't want to get the full solution, but only a hint.  I have to show that for $x \in [0, \infty)$, the sequence $\left(1+\frac xk\right)^k$ is monotonically increasing. We were already given the hint that we could use the inequality of arithmetic and geometric means, but I don't see how to apply it yet.   I tried to do it by induction. While the case $k = 1$ works easily, I don't know how to start further from here. I already tried to use the definition of the binomial theorem, but it didn't lead me anywhere.


More specifically, how would you evaluate the below formula? $$\lim_{n\to\infty}\sum_{k=n/2}^{n}\frac{1}{k}$$ I know that the harmonic series starting at any point diverges, but when we limit it in this way, does the series diverge or converge?   If it diverges:   How might you determine that? Is there some $d$ that we can replace with $2$ to make the sequence converge?   If it converges:   What does it converge to, and how might you determine that? The sequence must converge for any $d>2$. Is there a formula for the series generalized for any $d$?

What is the sum of the 'second half' of the harmonic series?  $$\lim_{k\to\infty}\sum\limits_{n=k+1}^{2k}{\frac{1}{n}} =~ ?$$  More precisely, what is the limit of the above sequence of partial sums?


Below is the code I made for a simple html table. My goal is to center the entire table vertically in the center of the page based on the users height of the device. I tried to make a div with the height as 100% and width as 100% and placing the table 50% from top and left and no luck. Any ideas?    body {     background-color: #a00000; } table {     margin: 50px auto 25px auto;     padding: 0px;     background-color: #fff;     border-radius: 10px; } td {     background-color: #fff;     padding: 10px;     background-color: #fff;     border-radius: 10px; } img {     max-width: 120px;     max-height: 120px;     border: solid 5px #a00000;     border-radius: 5px;     background-color: #a00000; } <!DOCTYPE html>               <meta charset="UTF-8">         <title>Bobcat Menu</title>         <meta content='width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=0' name='viewport' />         <link rel="stylesheet" href="css/style.css">

I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support.
Div to be aligned vertically
   How can I center a div vertically in all major browsers, including Internet Explorer 6?


using System.Collections; using System.Collections.Generic; using UnityEngine;  public class Enemy : MonoBehaviour {     public Animator Wall;     public AudioSource hurtSound;     public Animator animator;     public int maxHealth = 100;     int currentHealth;     public int points = 0;     public GameObject camera;     void Start()     {         currentHealth = maxHealth;     }           public void TakeDamage(int damage)     {         currentHealth -= damage;         animator.SetTrigger("hurt");         hurtSound.PlayOneShot(hurtSound.clip);         if(currentHealth <= 0)         {             Die();         }     }      void Die(){         Wall.Play("goDown");         animator.SetBool("isDead", true);         GetComponent<Collider2D>().enabled = false;         this.enabled = false;         points += 1;         Debug.Log(points);              }       } using System.Collections; using System.Collections.Generic; using UnityEngine;  public class door : MonoBehaviour {          void Update(){         if(Enemy.points == 3){             print("yeee");         }     }  }  i want to refrence the points int to a diferent script but i cant because of this error An object refrence is required for non-static field, method, or property Enemy.points. here is the points int public int points = 0;  here is where i am tring to refrence it void Update(){         if(Enemy.points == 3){             print("yeee");         }     }  but it doesnt work help

Consider:  namespace WindowsApplication1 {     public partial class Form1 : Form     {         public Form1()         {             InitializeComponent();         }          private void button1_Click(object sender, EventArgs e)         {             //int[] val = { 0, 0};             int val;             if (textBox1.Text == "")             {                 MessageBox.Show("Input any no");             }             else             {                 val = Convert.ToInt32(textBox1.Text);                 Thread ot1 = new Thread(new ParameterizedThreadStart(SumData));                 ot1.Start(val);             }         }          private static void ReadData(object state)         {             System.Windows.Forms.Application.Run();         }          void setTextboxText(int result)         {             if (this.InvokeRequired)             {                 this.Invoke(new IntDelegate(SetTextboxTextSafe), new object[] { result });             }             else             {                 SetTextboxTextSafe(result);             }         }          void SetTextboxTextSafe(int result)         {             label1.Text = result.ToString();         }          private static void SumData(object state)         {             int result;             //int[] icount = (int[])state;             int icount = (int)state;              for (int i = icount; i > 0; i--)             {                 result += i;                 System.Threading.Thread.Sleep(1000);             }             setTextboxText(result);         }          delegate void IntDelegate(int result);          private void button2_Click(object sender, EventArgs e)         {             Application.Exit();         }     } }   Why is this error occurring?     An object reference is required for the nonstatic field, method, or property 'WindowsApplication1.Form1.setTextboxText(int)


On the new Meta Stack Exchange, if I select help from the top of the screen, the Return to the main site link goes to Stack Overflow, and the text says, "Back to Stack Overflow".  Shouldn't this say "Back to Stack Exchange" and link back to ?

When clicking help, you get this:    First, it shouldn't have a button to return to the main site, as this site isn't attached to any other site. Second, What's Meta's wording should be changed, because again, there is no main site.


My Camera model is Canon EOS 60D. I am using this last three years. How can I know the shutter count for my camera ?  Thanks in advance.  Jayanta P.

I'm selling a 60D body, and I want to check the reported shutter-release count. But I can't find it on the menu anywhere. Does someone know how to find it?  Note that the next assigned filename is not it. It notes the largest numbered file on the card and jumps ahead to that, so the numbers continued from my previous camera body.


I was trying to make a code like this def no(t=.001):     print("N", end='')     for i in range(1000):         print('o', end='')         time.sleep(t)     print()  So that when I call no() I would print a long "Nooooo...", waiting some time between each 'o'. What happens instead is that the function halts, for the whole total time (1 second with the default argument), then prints the whole list. Is this intended? And if not how should I obtain my intended effect?

How do I force Python's print function to output to the screen?


What do  I do with the iso?  I did install with Wubi last year but now I have a new computer.

I would like to see a full how-to guide on how to install Ubuntu.


Which of these is correct:         I didn't realize how much clothes you had on the floor   I didn't realize how much clothing you had on the floor      Any additional explanation about clothes versus clothing would be helpful.   This other question discusses the meaning of the two words, but doesn't help with the grammar problem above:

Do some google I find that clothes work like objects like:        You should pack your clothes.  → Yes   You should pack your clothing. → No      Can you tell me the main difference between clothing and clothes?


I have a very simple run.sh script which looks like this:  #!/bin/sh echo "Hello, let's start!" cd /Users/c/Dev/App/Code/ . venv/bin/activate cd Backend export FLASK_APP=app.py export FLASK_DEBUG=1 export CONFIG=Local flask run   After I run it, I get the following:   Saving session... ...copying shared history... ...saving history...truncating history files... ...completed.  [Process completed]   Instead, I would like to get the active session as I would if I type the script manually, so simply the virtualenv active where I can then run pip install and see Flask's output.  How can I do that?

I python script called scrape.py. As the name suggests it is a web crawler and I want it to run continuously on my Linux machine even after I log out and end the ssh session. I read a lot around here and there were many suggestions of using nohup python scrape.py &. This worked well but the script execution stopped as soon as I logged out. I also explored the supervisor application but I don't have root permissions so it fails too. Can you suggest me a way to solve this problem? Thank you.


I'm writing my graduation project and suddenly it won't compile anymore. I'm getting the following error in the .bbl file: Package inputenc Error: Unicode char − (U+2212)(inputenc) not set up for use with LaTeX.  If anyone could help me, I would be very grateful.

My beamer presentation presents this problem Package inputenc Error: Unicode char − (U+2212)(inputenc) not set up for use with LaTeX. \end{frame}. I tried remove some elements and I see that problem appear when I use - in equation. I'd like one hint about this problem.   \documentclass[pt]{beamer} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage[utf8]{inputenc} \usepackage[brazil]{babel} \usepackage{upgreek} \usepackage{mathtools} \usetheme{Berlin}  \begin{document} \begin{frame}{Convergência - Prova}     %\justifying     Sem perda de generalidade a demonstração foi focada numa partícula unidimensional. Reescrevendo a Equação, tem-se que     \begin{equation}     x_i(t + 1) + \alpha_1 x_i(t) + \alpha_2 x_i(t − 1) = \alpha_3     \end{equation}     onde     \begin{equation}     \begin{aligned}     \alpha_1 &= (1 + \omega) + u(r_1 - r'_1)c_1 + u(r_2 -r'_2)c_2 + c_1r{'}_1 + c_2r'_2 \\     \alpha_2 &= \omega \\     \alpha_3 &= u(r_1 - r'_1)c_1p + uc_2(r_2g - r'_2n) + c_1r'_1p + c_2r'_2n                         \end{aligned}     \end{equation} \end{frame} \end{document}   Sorry by english


Is there a way to create a centreline in QGIS from two other lines (such as a river bank) which won't always be equally apart? I am aware that in ArcGIS Desktop there is Collapse Dual Line to Centerline which sounds like it is what is needed, but I have not found an equivalent in QGIS.

How do I create a centerline (vector data) from two parallel polylines (vector data) in QGIS? For example, if the distances between two parallel lines are 14m, then I want to create a centerline at 7m from both lines.


I have this interface:  interface ILooperable<in TASK_TYPE, in CALLBACK_TYPE>   I would like to set the first parameter to implement foo and second parameter to boo, something like this:  interface ILooperable<in TASK_TYPE, in CALLBACK_TYPE> where TASK_TYPE: foo, CALLBACK_TYPE : boo   But it doesn't work,  It says:     Syntax error   What am I doing wrong?

I have a generic method which has two generic parameters. I tried to compile the code below but it doesn't work. Is it a .NET limitation? Is it possible to have multiple constraints for different parameter?  public TResponse Call<TResponse, TRequest>(TRequest request)   where TRequest : MyClass, TResponse : MyOtherClass


I want to add the following code to my class:  static private final ILogic_P logicInstanceI =     (ILogic_P)Factory.CreateAnon("some.path.ILogic_P" + (SomeClass.isIMDB() ? "1" : "2"));  public static ILogic_P getLogicInstanceI(){     return logicInstanceI; }   I can't figure it out if the initialization of the static variable is thread safety or not. Is there a chance that two threads will try to initialize this attribute simultaneously?

Let's say I have some Java code:  public class SomeClass {     static {         private final double PI = 3.14;         private final double SOME_CONSTANT = 5.76;         private final double SOME_OTHER_CONSTANT = 756.33;     }    //rest of class }   If a thread is initializing SomeClass's Class object and is in the middle of initializing the values in the static block when a second thread wants to load SomeClass's Class again, what happens to the static block?  Does the second thread ignore it assuming it's already initialized even though the first thread is not done? Or does something else happen?


I have a question, that asks me to find the following limit  $$\lim_{x\to 0}\bigg\lfloor\frac{x^2}{\sin x \tan x}\bigg\rfloor$$  Now, here's what I know, that, $$\lim_{x\to 0} \frac{\sin x}{x} = 1$$ and $$\lim_{x\to 0} \frac{\tan x}{x} =1$$  But according to that, the answer to my question should be $1$, but it is given as $0$  Now, my book states that $$\lim_{x\to 0} \frac{\sin x}{x} \to 1^-$$ and $$\lim_{x\to 0} \frac{\tan x}{x} \to 1^+$$  or, $$\lim_{x\to 0} \frac{\sin x}{x} = 1-h$$ $$\lim_{x\to 0} \frac{\tan x}{x} = 1+h$$ How do they get this? How do I analyse the behavior of a function near around a point? A detailed explanation would really help.

Find $$\lim_{x\to0}  \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$$ where $\lfloor\cdot\rfloor$ is greatest integer function   I am a high school teacher. One of my students came up to ask this limit.  For $\lfloor\frac{\sin x}{x}\rfloor$, I have used $\sin x > x$ using increasing decreasing functions.  I tried to prove $x^2 > \sin x \tan x$ using increasing /decreasing  function but I am not getting it.


Is there nay way to generate random String using this code but with size 42 symbols?  public static final String RANDOM_STRING = UUID.randomUUID().toString();

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".


Is that the same as the ways can one select a team of five students out of ten students which is ten choose two or I misunderstand this point

In how many different ways can you split $10$ people into two groups with the same amount of people?  My attempt: Since the order in which you choose someone doesn't matter, I chose to calculate the combinations: $10 \choose 5$


I noticed that Command-X (cut and paste) is greyed out on finder in El Capitan. Is there any way to get it back?  EDIT: WITHOUT Command-Option-V. If possible, way to map command-option-v to command-x would be great....

On OS X 10.6 (Snow Leopard), I don't seem to be able to us the "Cut" command on a file in the Finder, like you can do in Windows Explorer on Microsoft Windows. (In Windows, once you select a file and "cut" it, you can then move to a different directory and "paste" the file to that location.)   The only way I can move a file using keyboard or contextual menu commands is to copy the file to another drive or location and then delete the old version of the file.   In the Finder's 'Edit' menu, 'Cut' is in the list but if a file itself is selected, it is always greyed out. 'Copy' is not. Why is this?


Show that if $\int_0^1 f(x) v(x) dx = 0$ for every function v for which $\int_0^1 v(x) dx = 0$, then f is constant. I do not know how to do it.

Let $f\in C[0,1]$ be such  that $\forall \phi\in C[0,1]$ with $\int_0^1\phi \, dx=0$,we have $\int_0^1f\phi \, dx=0$.  Then $f$ is constant.  May be someone can help me proof this problem. Thanks!


Lets say I have a siccative object that’s attached to a rope and it’s moving in a vertical circular motion around some circumcenter. If along the motion the rope will happen to reach maximum tension, intuitively it’ll tear, but will it? If it’ll tear the object will proceed at the direction of its velocity? Thanks for assuring that, and if it’s wrong thanks for correcting me

I know this is a basic question, but question:  A rock is connected to one end of string and is in circular motion with the center being the other end of the string. Now the string gets released at some point. How do we know the direction in which the rock is going to fly?


I have an assumption for which I have to answer true or false to: "The energy Es of the system cannot increase with time." To which the answer is false with the motivation that it is the appropriate free energy that has to decrease with time. I am not sure if I understand it completely. Why does free energy always have to decrease over time?

Why is it that, at equilibrium, certain potentials are minimised? That is, for a system at constant temperature and pressure, the Gibbs free energy is minimised, and for fixed volume and temperature, the Helmholtz free energy is minimised. I haven't been able to find a reason for this.


(EDIT: I've marked this question as answered in order that I can go away and come up with a better one. Thanks to everybody for the helpful answers.)     Is it possible to describe the RH in language comprehensible to a non-mathematician?   In my experience (as a non-mathematician) the answer is a definite 'no'. But before I give up on it I thought I'd ask for some views.   By 'explain' I do not mean explain fully. I mean explain the basic structure of the hypothesis. Something like - we feed values into a function and the output is plotted to create a landscape and a critical line appears and we conjecture that all zero outputs fall on this line. I expect even this is wrong but it's this level of explanation that I'm after, with just a bit more detail added.   I've spent a long time trying to understand the relationship between the inputs and outputs of the Zeta calculation and got nowhere. Yet I'm not stupid. There's something I'm missing but none of the explanations I've been offered allow me to understand what it is.             I know a bit about the primes but must ask for answers in a more or less natural language or will not be able to cope. I know such requests annoy mathematicians but I can only ask.  I have read Du Sautoy, Derbyshire and much more but never found an explanation that doesn't assume I'm a graduate mathematician. I need a children's book on the topic that describes it in very general terms.  Is such a thing possible?    EDIT: Vincent has suggested a similar but perhaps interestingly different question. This is - is there an intuitive explanation why the Riemann zeta FUNCTION (rather than hypothesis) contains interesting information about the distribution of primes in language comprehensible to a non-mathematician?    My intuition is that the explanation would be the harmonic series and its role in determining the distribution of primes. I'll hesitatingly ask if this makes any sense. Or are there other reasons? As it happens I'm coming at this as a musician and have an interest in the musical aspect of the distribution or primes, or rather in the distribution of non-primes that determines the primes.             EDIT 2: I see that similar questions have been asked previously. Thanks to the members who have provided links to them. I've been checking them and so far they have been helpful but not so much as to persuade me to take this one down. This may change as I keep reading and I'll withdraw this one if so.

I've read so much about it but none of it makes a lot of sense. Also, what's so unsolvable about it?


The point of an NS record is to tell client which name server will know for sure the actual IP address for a domain name. So for instance, the following query tells you that if you want to get an authoritative answer about facebook.com you must ask a.ns.facebook.com:   > dig ns facebook.com                                                                                19:58:27  ; <<>> DiG 9.9.5-3ubuntu0.8-Ubuntu <<>> ns facebook.com ;; global options: +cmd ;; Got answer: ;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 32063 ;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 0  ;; QUESTION SECTION: ;facebook.com.          IN  NS  ;; ANSWER SECTION: facebook.com.       65000   IN  NS  a.ns.facebook.com. facebook.com.       65000   IN  NS  b.ns.facebook.com.  ;; Query time: 13 msec ;; SERVER: 127.0.1.1#53(127.0.1.1) ;; WHEN: Sun Mar 20 19:58:40 CET 2016 ;; MSG SIZE  rcvd: 65   This seems cool and useful but I'm wondering why the ANSWER section contains the hostname and not IP of the authoritative source? Wouldn't it be easier for the client to get the actual IP address of the authoritative source and not the hostname?  I mean if it gets the hostname it will have to make another query to resolve this hostname into an IP and then ask this new IP about the initial facebook.com domain it was looking for. Isn't this inefficient?   I'd be interested in answer that points me to some paragraphs in some RFC that explains this problem.

This is a  about DNS glue records.   What exactly (but briefly) is a DNS glue record?  Why are they needed and how do they work?


As the title suggests, I'm wondering if a PC race (for example, the  with the winged option) would have the ability to hover in regards to the  condition.  The      If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as the fly spell.   All the winged option for the Variant Tiefling states is     Winged. You have bat-like wings sprouting from your shoulder blades. You have a flying speed of 30 feet while you aren’t wearing heavy armor. This trait replaces the Infernal Legacy trait.   From  we know a PC can stay in place in air. However, since nothing states it has to keep moving to continue to fly, is it considered to have the hover ability? Specifically, if it is knocked prone will it fall or not?

Some creatures have a fly speed.  Some creatures with a fly speed also have the ability to hover specified.  The PHB, in Chapter 9: Combat, Movement and Position, Flying Movement says:     Flying creatures enjoy many benefits of mobility, but they must also deal with the danger of falling. If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.   The conditions in this paragraph that would result in the creature falling have to do with having movement involuntarily removed or restricted.  That might suggest that if you don't have "hover" in your flying speed, you can't hover.  But there is a difference between being knocked unconscious, or frozen, or webbed, or otherwise rendered unable to move, and choosing to hover, by flapping your wings, or standing on your jets, or whatever.  So, can flying creatures choose to hover, even if they don't have hover in their flying speed?


I noticed today that the "StackExchange" dropdown on the top left of the main meta site, when open doesn't lay out correctly - see the image below:     The right column (reputation, etc) is shifted outside the div.  This is Firefox 24 on OS X Mountain Lion.

EDIT Dec 4 -  We're doing it live! Please post bugs or concerns as questions tagged [top-bar]  We have rolled out our 95% completed top bar for feedback.  Note:   We are still adding a few final features, so if you have a request for a feature that is not there you might hold off on that for a day or two Yes, the bar is black1. Also give that a day or two to sink in.   I also want to specifically address the meta/main/chat links.  I'm very aware that many of you like having the links at the top of the page and that this new version is different.  The thought process behind moving these links is that the "site switcher" should be an automatic place to go when you are on a site and want to go to another one. If you haven't already developed the muscle memory for these links, getting between them required a bit of a cognitive load: You must first decide that you want to switch sites and then you have to decide which area to go to to switch.  Also, we find that less familiar users aren't entirely clear what a standalone link that says "main" or "meta" actually does... Not to mention that it hurts my UX sensibilities that we are dynamically changing links in an element that should be fixed.  It is true that we have added a click in the process, but we have also removed a lot of clicks for other common actions that are much more frequent than switching between main and meta.  All I ask is that you give it a few days and see if the new "switch sites at the top left" paradigm grows on you.  What do you think?  1.  points out that technically it's not quite black.


I just downloaded and installed the latest security patch for Ubuntu 16.04 LTS using Update Manager as instructed.    I was under the impression that the new kernel version after upgrade would be 4.13, however when running this command uname -r in my terminal, it is still showing 4.10.0-42-generic  Is this correct? Is there a way to confirm that the patch has been successful?

Any questions relating to status updates, or asking if anything is going to be patched for these vulnerabilities should be closed as duplicates of this question.    are in the news right now and sound pretty severe. I don't see any security updates from Ubuntu that cover these vulnerabilities.  What is Ubuntu doing about these vulnerabilities, and what should Ubuntu users be doing?  These are CVE-2017-5753, CVE-2017-5715 and CVE-2017-5754.


Let $f$ be a Lebesgue measurable function defined on a set $E\subset \mathbb{R}^d$. Let $\{x\in E\mid f(x)\neq 0\} $ be the support of the function on $E$.  Stein and Shakarchi claim without proof that the support is measurable. But why is this true? It's not just due to the fact that the support is a subset of a measurable set.

Could someone please check if I'm saying something that make sense? I am trying to check the following:     If $f$ is a measurable function, then $\text{supp}(f)$ is measurable set?   Is it simply because, if we consider $E_1 = (0,\infty)$ and $E_2 = (-\infty,0)$, since they are open, they are measurable. So their union $\mathbb{R}-\{0\}$ is measurable as well. Since $f$ is measurable, then the preimage $f^{-1}(\mathbb{R}-\{0\})$ is measurable. But the preimage is just the support?


Following . I have just run into . It seems to be fitting perfectly to the Programmers, it is a nearly perfect example of an off-topic question at SO  and yet, it can't be migrated, because it is too old.  How and why came with the idea of questions being to old for migration? What is the reason behind this? If some questions fits badly here and fits perfectly there, what value do we have from blocking their migration only because of their age?  Note: This question is not a duplicate of . I don't want to know, why questions too old for a migration, are migrated even so. I want to know, what is the idea in marking question as too old for migration, at all.

This has come up    : migrating old questions causes problems.   The most popular solution to this to date has been to . This is do-able, but frankly it feels like treating a symptom, and doing so in a way that penalizes folks who answer what are by all appearances valid, on-topic questions.   Migration works best as a way to salvage good but off-topic questions and give them new life on a site where they can thrive. But shuffling old, answered, on-topic questions around for the hell of it is a waste of everyone's time.   Therefore, I think the real solution is much simpler: just disable the migration of old questions. They're rarely welcomed or heavily improved post-migration, often overtly disliked by folks on the destination site, and can end up causing a rather bad experience for folks who were participating in good faith on the original.   I suggest that questions older than 601 days should not be eligible for migration, either by normal user close-votes or by moderators. In extreme cases, we can perhaps provide an alternate means of moving old questions, but under normal circumstances these should be done quickly or not at all.   1 60 days is actually based on a  introduced this past spring: migrated and then rejected questions older than 60 days cause the authors to suddenly gain (permanent) reputation on the destination.


I am very curious to find if there is any reason that why are we in 3 dimensions not in any other like 1D would be hard almost impossible but 2D could have been possible, or what about 4D or in additional dimensions?

I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. There is a  on Wikipedia.  For example, a common argument for why >3 dimensions is too many is that the gravitational law cannot result in stable orbital motion. A common argument for <3 dimensions being too few is that one cannot have a gastrointestinal tract, or more generally, a hole that doesn't split an organism into two.  Am I being overly skeptical in thinking that while the force of gravity may not be able to hold objects in stable orbits, there most certainly exist sets of physical laws in higher dimensions which result in formation of stable structures at all scales? It may be utterly different to our universe, but who said a 4D universe must be the same as ours with one extra dimension?  Similarly, isn't it very easy to conceive of a 2D universe in which organisms can feed despite not having any holes, or not falling apart despite having them? For example, being held together by attractive forces, or allowing certain fundamental objects of a universe to interpenetrate, and thus enter a region of the body in which they become utilized. Or, conceive of a universe so incomprehensibly different to ours that feeding is unnecessary, and self-aware structures form through completely different processes.  While I realise that this is sort of a metaphysical question, is 3+1 dimensions really widely acknowledged to be particularly privileged by respected physicists?


How can I create a shortcut for URL in my desktop? I want to use them in Firefox or Chrome.   If a copy and paste didn't work.   What script I have to use?

I want to create an internet shortcut within a specified folder in Ubuntu 12.04. How do I do this?


With the following code, I get TWO errors on the line \begin{abstract}, one saying "Misplaced alignment tab character &" which doesn't make sense because I'm not citing anything, so no & is misplaced in my citations and Package hyperref Warning: Token not allowed in a PDF string (PDFDocencoding): remove \unskip on input line 61 - which is the \begin{abstract} line I understand perhaps \texorpdfstring would be a solution here, but I'm unclear how to input that exactly into this type of "bookmark"      \documentclass[runningheads]{llncs} \fontfamily{ptm}\selectfont \usepackage{hyperref} \hypersetup{     linktocpage,     colorlinks=true,     linkcolor=blue,     citecolor= red,     filecolor=red,           urlcolor=cyan} \usepackage{graphicx} \graphicspath{{figures/}} \usepackage{array} \usepackage{longtable}  \usepackage{makecell} \usepackage{cite} \usepackage[utf8x]{inputenc}  \usepackage[english]{babel} \renewcommand\theadalign{bc} \renewcommand\theadfont{\bfseries} \renewcommand\theadgape{\Gape[4pt]} \renewcommand\cellgape{\Gape[4pt]} \usepackage{geometry} \geometry{letterpaper, portrait, margin=1in}  \begin{document}  \title{The Ethics of Software: A Systematic Mapping Study of Ethical Concerns  in Software Engineering \thanks{Supported by my school.}}  \titlerunning{The Ethics of Software: A Mapping Study \& Focus Group}  \author{My name\inst{1}\orcidID{2643038}}  \authorrunning{my name}  \institute{my school \email{my email}} \maketitle \begin{abstract} \end{abstract}   \end{document}

When compiling a beamer presentation and using the following \author command  \author{Name \\ \texttt{my.email@domain.com}}   I get the following hyperref warning in my logfile  Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `\\' on input line 15.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `\new@ifnextchar' on input line 15.   I understand that this has to do with hyperref setting the PDF metadata, where the linebreak does’t make much sense and should be removed.  Trying to set  \hypersetup{pdfauthor={Name}}   does’t change the situation, seems like hyperref is still looking at the author command.  How do I get the desired display of author name with email and still keep hyperref happy?


The Decision  I have refused your application for a visit visa because I am not satisfied that you meet the requirements of paragraph(s) V 4.2-10 of Appendix V because:  I am aware that you were previously refused entry clearance. I have studied your previous application in addition to the information provided today. When assessing your application on the whole, I am not satisfied that you have met the requirements of the Immigration Rules on this occasion.  Although I note your sponsor states an intention to fund your trip I must also take into account the stated reason for your trip and your personal situation.   You claim to be employed and propose to stay in the UK for 10 weeks whilst undertaking a PLAB Test. Although you have submitted a letter from your employer purporting to give you leave for 10 weeks no credible explanation has been provided as to why they would grant you 10 weeks leave of absence. Furthermore I note you have only worked for your employer since March 2019. Given the short period of your employment I am not satisfied that you would have accrued 10 weeks of holiday time. Furthermore you have not provided a satisfactory explanation why you would seek to spend 10 weeks in the UK in order to undertake a short test. Because of this, I am not satisfied that you are seeking entry just as a visitor for the length of time you say. Therefore I am not satisfied that you are genuinely seeking entry as a visitor for a period not exceeding 6 months or that you intend to leave the United Kingdom at the end of the period as stated by you. This also leads me to doubt the purpose of your application as stated.   You state that you have worked as an ICU Medical Officer since March 2019 and that you have a current monthly income of 50000 NPR (£330) from all sources. You state you have personal savings of £2194 in support of your application. On the basis of the information and documents provided you appear to have no dependant relatives and little in the way of personal income or assets in your own country. In light of all the above I consider that you have failed to show sufficiently strong family, social or economic connections to your country of residence to satisfy me, on the balance of probabilities, that you intend to leave the United Kingdom on completion of a short visit.  For the reasons stated above I am not satisfied on a balance of probabilities that you are genuinely seeking entry as a general visitor for a limited period as stated by you, not exceeding 6 months; and I am not satisfied that you intend to leave the UK at the end of the period of visit as stated by you as  Please suggest me, for my next visa applications.

Over the course of time here on TSE, I have observed individuals whose pattern of visa applications is best described as ''...     serial refusals - Two or more consecutive visa refusals issued by the same regime to the same person. Commonly for the same, or nearly the same, reasons. In some visa regimes Serial refusals can have a cumulative effect wherein the applicant's credibility is increasingly eroded, especially when the application pattern suggests a secondary agenda.   A common thread appears to be the need to visit the destination country (especially Schengen, the USA, or the UK) with a special sense of urgency. Also common in these cases are the following types of questions...   Should I just reapply once again? What are my chances? What can I do to improve my odds in the future? Can I somehow address the previous refusals to avoid them being a burden on all future applications? How can I break the pattern?      NB: This question is intended as a canonical about serial refusals. I have never been personally denied a visa.


I am looking for less jargons from predicate logic and more prominence on simple language. Also, please hint me as to what approach should I use in establishing the implication both way. I know that's the way to get around it.

I just started to learn induction in my first year course. I'm having a difficult time grasping the concept. I believe I understand the basics but could someone summarize simple induction and strong induction and explain what the differences are? The video I'm watching explains that if $P(k)$ is true then $P(k+1)$ is true for simple induction, and for strong induction if $P(i)$ is true for all $i$ less than equal to $k$ then $P(k+1)$ is true. I don't really know what that means.


Let ${a_n}$ be the sequence where $a_1 =\sqrt{2}$, and $a _{n+1} = \sqrt{2+ \sqrt{a_n}}$ for all n ∈ N. Prove that ${a_n}$ is bounded above by 2, and then prove that ${a_n}$ converges.  My thought is to generally employ the monotonic convergence theorem:  Proof.  Because $a_1= \sqrt{2}$, and the sequence is increasing, we see that it is bound below by $\sqrt{2}$. And, if we take the limit as n approaches infinity, we see the limit equals 2, so it is bounded above by 2.  Further by the monotonic convergence theorem, as we see that the sequence is monotonically increasing and bounded above and below, it follows through the M.C.T. that it converges. QED  My question really has to do with showing that it is monotonically increasing, which I believe I need to use induction for, however, I am not sure how exactly to do that, as my book glosses over the subject in a generic review of the concept, i.e. noting the notion that you do $s(n)$ and then show that $s(n+1)$ is also true for all n, but I'm fuzzy on the subject. Moreover, am I correct with my bound assumptions?

(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: .


Here is the proof problem: Prove that: $$\forall a \in \mathbb{N} \ \ \forall p \in \mathbb{N}\setminus \{0\} \ \exists x \in \left\{ a+k \ | \ k \in 0.. (p-1)\right\}(p|x)$$ First, I need some help translating this. I think I've done it correctly. $x$ would belong to the set cardinality $1$ of $a+k$, which would mean x is either the one element, or the empty set, which doesn't work. Then, I know that this isnt true of all a and p, plenty of counterexamples. So, what strategy would I use to tackle this nonexistence proof?

If $x$ is positive integer, prove that for all integers $a$, $(a+1)(a+2)\cdots(a+x)$ is congruent to $0\!\!\!\mod x$.  Any hints? What are the useful concepts that may help me solve this problem?


I have table test and it has columns id,name and age.I want the id so I am querying like it  select id from test where age=12   After I get the id I am updating the name using update query  Now lets say if age=13 not present then I will insert a row(insert into test(age) values(13)) and after it is inserted I will get the id(as id is autoincremented).So is it possible to do insert and select simultaneously?

When an insert statement is executed one or more rows is inserted into the table, is there any way to extract the last inserted row in SQL Server?


We have a website math.tutorvista.com.   We use dynamic serving web pages.  Desktop URL:    Mobile URL:    I have a couple of questions on this:  1) Is it a Bad SEO to use Dynamic serving than Responsive web pages? 2) Should we use  "?view=simple" on to the URL to differentiate?  Thanks in advance!

I've heard a variety of opinions regarding the pros and cons of using responsive web design recently and was wondering whether it was necessary for small businesses that target small geographical areas to implement responsive web design?   Some sub-questions I have regarding this include:   Is it better to use responsive web design as opposed to having separate code utilized for different dimensions/devices? Can it potentially affect SEO (positively or negatively)? What are the main problems I could run into when optimizing a website for a business using this design method?


I've been working with some C# legacy code and I've been seeing a lot of @ symbols in front of variable names. What does this signify or do?  Currently I'm seeing it a lot in front of variables with common names that aren't reserved. E.g.:  MyProcedure(@step.LoadInstanceId, @step.ResultCode, @step.StatusCode);   Given that step isn't a reserved word, is there any reason that they should be escaped?

I discovered that you can start your variable name with a '@' character in C#.  In my C# project I was using a web service (I added a web reference to my project) that was written in Java. One of the interface objects defined in the WSDL had a member variable with the name "params". Obviously this is a reserved word in C# so you can't have a class with a member variable with the name "params". The proxy object that was generated contained a property that looked like this:  public ArrayList @params {     get { return this.paramsField; }     set { this.paramsField = value; } }   I searched through the VS 2008 c# documentation but couldn't find anything about it. Also searching Google didn't give me any useful answers. So what is the exact meaning or use of the '@' character in a variable/property name?


I am using a USB with an embedded device running linux. The issue is that in some cases when I unmount the usb by giving the command umount /media/sda1 the unmount is successful but when I proceed to remove the usb I get an error saying unable to mark fs as dirty and when I plug it back in I get the error  Volume was not properly unmounted. Some data may be corrupt. Please run fsck. Is there any other command on the linux terminal which I can use to safely eject the usb? so that the usb device is powered off before I unplug it.  Update: I tried using sync but the error is still there as shown below:  root@(none):~# sync root@(none):~# umount /media/sda1 root@(none):~# ls /media/sda1 root@(none):~# [  296.021241] usb 2-1: USB disconnect, device number 3 [  296.026879] sd 1:0:0:0: [sda] Synchronizing SCSI cache [  296.031175] sd 1:0:0:0: [sda] [  296.033743] Result: hostbyte=0x01 driverbyte=0x00 [  296.048283] FAT-fs (sda1): unable to read boot sector to mark fs as dirty

I'm using Ubuntu 12.04, and when I rigth click on a my flash drive icon (in the Unity left bar) I get two options that have me confused: eject and safely remove.  The closer I came to an answer was , which concludes that (for a flash drive) they are both equal and also equivalent to use the umount command. However, this last assertion seems to be false.  If I use umount from the console to unmount my flash dive, and then I use the command lsblk, I still see my device (with nothing under MOUNTPOINT, of course). On the other hand, if I eject or safely remove my flash drive, lsblk does not list it anymore. So, my question is, what would be the console command/commands that would really reproduce the behaviour of eject and safely remove?