My question is which one is correct:   a) I have been awarded the science award 5 times   or b) I was awarded the science award 5 times   Thank you :)
Possible Duplicate:          As a English non-native speaker it is difficult for me to understand when I must use present perfect or past simple because in my official language there isn't the present perfect tense. I know that present perfect is related to something that happened in the past but its result is important now. But for instance:        The message has been sent.   The message was sent.      Please help me point me out any examples/contexts where I should use 1. instead of 2.
For gravity, we have    General Relativity, which is a geometric theory for gravitation.  Is there a similar analog for Electromagnetism? How to preserve bookmarks when rearranging pages of a PDF file with tools like pdftk? I am using pdftk to rearrange pages of a pdf file with bookmarks/outlines, but after that, the output file lost the bookmarks of the original.   My command is pdftk in.pdf cat 1-22 43 23-42 44-end output out.pdf.  I was wondering how I could keep the bookmarks while rearranging pages? Number theory counting sums of squares modulus This is an extra question from an old examination paper:     VI. Let $n&gt;1$ in $\mathbf{Z}$ and let $r(n) = \#\{(a,b)\in \mathbf{Z}^{2};n=a^{2}+b^{2}\}$ Let also $n=n&#39;n&#39;&#39;n&#39;&#39;&#39;$ where $n&#39;,n&#39;&#39;,n&#39;&#39;&#39; \in \mathbf{N}$ and   $p|n&#39; \Longrightarrow p\equiv 1\mod 4 ; p|n&#39;&#39; \Longrightarrow p=2 ; p|n&#39;&#39;&#39; \Longrightarrow p\equiv 3 \mod 4$   for $p\in \mathbf{N}$ prime.   i) Show that if $n&#39;&#39;&#39;$ is not a square, then $r(n)=0$.  ii) Show that if $n&#39;&#39;&#39;$ is a square and $n&#39; = 1$, then $r(n)=4$  iii) Show that if $n&#39;&#39;&#39;$ is a square and $1&lt;n&#39;=p_{1}^{e_{1}}\ddots p_{k}^{e_{k}}$ where $p_{1},...,p_{k}$ are different primes in $\mathbf{N}$ and $e_{1},...,e_{k} \in \mathbf{N}$, then it holds that $r(n)=r(n&#39;)=4(e_{1}+1)\ddots (e_{k}+1)$    I am completely dumbstruck and can't see how to begin (and neither did an older student who took this exam and whom I asked for hints). Help is greatly appreciated. Raise bounty on question MySQL cartesian product between two SELECT statements I want to block access to my web server by default as a precaution but I keep getting the following errors showing up in my error log.      [Wed Jun 27 23:30:54 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Edu.jar      [Wed Jun 27 23:32:40 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/REST.jar      [Wed Jun 27 23:35:39 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Set.jar      [Thu Jun 28 01:01:17 2012] [error] [client 58.218.199.227] client denied by server configuration: /home/www/default/proxyheader.php      [Thu Jun 28 02:34:57 2012] [error] [client 58.218.199.227] client denied by server configuration: /home/www/default/proxy.php      [Thu Jun 28 05:41:33 2012] [error] [client 58.218.199.227] client denied by server configuration: /home/www/default/proxyheader.php      [Thu Jun 28 06:55:10 2012] [error] [client 180.76.6.20] client denied by server configuration: /home/www/default/      [Thu Jun 28 07:31:26 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Edu.jar      [Thu Jun 28 07:32:25 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/REST.jar      [Thu Jun 28 07:36:10 2012] [error] [client 86.77.20.107] client denied by server configuration: /home/www/default/Set.jar   I don't really want these errors to show up but whatever I do, I can't get rid of them. Does anyone know how I can achieve this?  Here is a copy of my configuration.  &lt;VirtualHost *:80&gt;     DocumentRoot /home/www/default      &lt;Directory /&gt;            AllowOverride None            Order Deny,Allow            Deny from all     &lt;/Directory&gt;      #ErrorLog /var/log/apache2/error.log     #LogLevel warn     CustomLog /var/log/apache2/access.log combined &lt;/VirtualHost&gt; How to recover deleted files? Are there any tools, methods, incantations to recover recently deleted files on Ubuntu?  If it makes any difference, I want to recover a  2.x database file. But would be better to have a method/tool that works on any kind of file. line 56 syntax error: unexpected end of file I have typed out the code for this mychoice.sh bash example and I keep getting the syntax error: unexpected end of file.  Am I missing something?  mychoice.sh  #!/bin/bash  E='echo -e';e='echo -en';trap ";exit" 2 ESC=$( $e "\e") TPUT(){ $e "\e[${1};${2}H";} CLEAR(){ $e "\ec";} CIVIS(){ $e "\e[25l"} DRAW(){ $e "\e%\e(0";} WRITE(){ $e "\e(B";} MARK(){ $e "\e[7m";} UNMARK(){ $e "\e[27m";} R(){ CLEAR ;stty sane;$e "\ec\e[37;44m[J";}; HEAD(){ DRAW     for each in $(seq 1 13);do     $E "   x                    x"     done     WRITE;MARK;TPUT; 1 5     $E "BASH SELECTION MENU         ";UNMARK;}     i=0; CLEAR; CIVIS;NULL=/dev/null FOOT(){ MARK;TPUT 13 5     printf "ENTER - SELECT,NEXT         ";UNMARK;} ARROW(){ read -s -n3 key 2&gt;/dev/null &gt;&amp;2      if [[$key = $ESC[A ]];then echo up;fi      if [[$key = $ESC[B ]];then echo dn;fi;} M0(){ TPUT  4 20; $e "Login info";} M1(){ TPUT  5 20; $e "Network";} M2(){ TPUT  6 20; $e "Disk";} M3(){ TPUT  7 20; $e "Routing";} M4(){ TPUT  8 20; $e "Time";} M5(){ TPUT  9 20; $e "About  ";} M6(){ TPUT 10 20; $e "Exit   ";} LM=6 MENU(){ for each in $(seq 0 $LM);do M${each};done;} POS(){ if [[ $cur == up ]];then ((i--));fi     if [[ $cur == dn ]];then ((i++));fi     if [[ $i -lt 0 ]];then i=$LM;fi     if [[ $i -gt $LM ]];then i=0;fi;} REFRESH(){ after=$((i+1)); before=$((i-!))     if [[ $before -lt 0 ]];then before=$LM;fi     if [[ $after -gt 0 ]];then after=0;fi     if [[ $j -lt $i ]];then UNMARK;M$before;else UNMARK;M$after;fi     if [[ $after -eq 0 ]] || [$before -eq $LM ];then          UNMARK; M$before; M$after;fi;j=$i;UNMARK;M$before;M$after;} INIT(){ R;HEAD;FOOT;MENU;} SC(){ REFRESH;MARK;$S;$b;cur='ARROW';} ES(){ MARK;$e "ENTER = main menu ";$b;read;INIT;};INIT while [[ "$0" != " " ]]; do case $i in     0) S=M2;SC;if [[ $cur == "" ]];then R;$e "\nS(w     )\n";ES;fi;;     1) S=M2;SC;if [[ $cur == "" ]];then R;$e "\nS(ifconfig  )\n";ES;fi;;     2) S=M2;SC;if [[ $cur == "" ]];then R;$e "\nS(df -h )\n";ES;fi;;     3) S=M2;SC;if [[ $cur == "" ]];then R;$e "\nS(route -n  )\n";ES;fi;;     4) S=M2;SC;if [[ $cur == "" ]];then R;$e "\nS(date  )\n";ES;fi;;     5) S=M2;SC;if [[ $cur == "" ]];then R;$e "\nS($e by oTo )\n";ES;fi;;     6) S=M2;SC;if [[ $cur == "" ]];then R;exit 0;fi;;  esac;POS;done; What counts as "entering a zone"? There are many actions that create persistent zones and have a trigger for their effect of among others: "...enters the zone..." What are the things that qualify as entering the zone?  Things that would seem to fit this would be:   Willing movement into the zone. Forced movement into the zone. Teleporting into the zone. Appearing inside the zone. Having the zone moved to include the square you occupy.   Do any of those listed not count as having entered the zone and why? And are there any that are not listed that would count as having entered the zone?  This is for D&amp;D 4e. Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential? The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they?  If yes, can we look for bound states in any of these $\delta'^{(n)}(x)$ potentials? Are there explicit formulae for them (and for the scattering states)?  To be more precise, I am asking for explicit solutions of the 1D Schroedinger equation with point potential,  $$- {\hbar^2 \over 2m} \Psi_n''(x) + a \  \delta'^{(n)}(x) \Psi(x) \ = E_n \Psi_n(x) $$  I should add that I have read at least of three set of boundary conditions that are said to be particular solutions:   $\Psi'(0^+)-\Psi'(0^-)= A \Psi(0)$ with $\Psi(0)$ continuous, is the zero-th derivative case, the "delta potential". $\Psi(0^+)-\Psi(0^-)= B \Psi'(0)$ with $\Psi'(0)$ continuous, was called "the delta prime potential" by Holden. $\lambda \Psi'(0^+)=\Psi'(0^-)$ and $\Psi(0^+)=\lambda\Psi(0^-)$ simultaneusly, was called "the delta prime potential" by Kurasov   The zero-th derivative case, $V(x)=a \delta(x)$ is a typical textbook example, pretty nice because it only has a bound state, for negative $a$, and it acts as a kind of barrier for positive $a$. So it is interesting to ask for other values of $n$ and of course for the general case and if it offers more bound states or other properties. Is it even possible to consider $n$ beyond the first derivative?  Related questions  (If you recall a related question, feel free to suggest it in the comments, or even to edit directly if you have privileges for it)  For the delta prime, including velocity-dependent potentials, the question has been asked in   In the halfline $r&gt;0$, the delta is called "Fermi Pseudopotential". As of today I can not see questions about it, but  seems to be the same potential.  A general way of taking with boundaring conditions is via the theory of self-adjoint extensions of hermitian operators. This case is not very different of the "particle in 1D box", question  A general take was the question  A related but very exotic question is  because obviosly the point-supported interacctions have a peculiar scaling  Comments  Of course upgrading distributions to look as operators in $L^2$ is delicate, and it goes worse for derivatives of distributions when you consider its evaluation $&lt;\phi | \rho(x) \psi&gt;$. Consider the case $\rho(x) = \delta'(x) = \delta(x) {d\over dx}$. Should the derivative apply to $\psi$ only, or to the product $\phi^*\psi$? Minimal polynomials and cyclic subspaces I'm trying to make my way through two problems in Curtis's Linear Algebra, chapter 25.  One of the two problems is this one, #5:     Prove that $V$ is cyclic relative to a linear transformation $T \in \mathcal{L}(V)$ if and only if the minimal polynomial of $T$ is equal to the characteristic polynomial.   Part of the issue is that I'm not really sure what it's asking. The statement that $V$ is cyclic seems to suggest that the entire vector space (say it has dimension $n$) is generated by some vector $v \in V$, along with $Tv, T^2v, \ldots T^{n-1}v$; Curtis's definition of a cyclic subspace (as opposed to a space, though I can't see why there should be a difference) seems to reinforce this:     A $T$-invariant subspace $V_1$ of $V$ is called cyclic relative to $T$ if $V_1 \neq 0$ and there exists a vector $v_1 \in V_1$ such that $V_1$ is generated by $\{ v_1, Tv_1, T^2v_1, \ldots T^kv_1 \}$ for some $k$.   However, I've seen several examples that seem to directly contradict this interpretation. For example, we recently had a take-home midterm that required we find elementary divisors, rational canonical form, etc., of a $6\times 6$ matrix; a classmate who received a perfect score on her test found that her matrix's characteristic polynomial was equal to its minimal polynomial &#151; it was $(x+8)^2 (x+14)^2 (x^2+61x+80)$ &#151; and yet the vector space could be written as $\left&lt; v_6 \right&gt; \oplus \left&lt; v_4 \right&gt; \oplus \left&lt; -v_2+v_3+v_6 \right&gt;$ &#151; i.e., as the direct sum of three cyclic subspaces, not as one cyclic subspace.  So that suggests that "$V$ is cyclic" might mean the direct sum of cyclic subspaces. However, while working on the exercise that follows (#6), I came across this:  $$S= \left(\begin{array}{ccc} -1 &amp; 0 &amp; 0 &amp; 0\\ 0 &amp; 1 &amp; 0 &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; 0\\ 0 &amp; 0 &amp; 0 &amp; 2 \end{array}\right)$$  Here, the characteristic polynomial is not equal to the minimal polynomial, which is $m(x) = (x-1)(x+1)(x+2)$. The eigenspace associated with $\lambda = 1$ has dimension $2$. And so it seems as though, if $V$ has basis $\{ v_1, v_2, v_3, v_4 \}$, we can write $V = \left&lt; v_1 \right&gt; \oplus \left&lt; v_2 \right&gt; \oplus \left&lt; v_3 \right&gt; \oplus \left&lt; v_4 \right&gt; $. This would seem to contradict my second interpretation of the original question.  Obviously I'm missing something. Could someone fill me in on what it might be? (I've tried to be thorough, but I'm also trying not to make this ridiculously long; if I've left out necessary information, I'll be happy to append it.) $\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show? Graph with Cycle and Two-Colorable i think if the graph G has an odd cycle, it's not two-colorable, otherwise it can be two colorable.   i read in one notes that the following is True: we couldent two-colorable any graph G that has cycle.    anyone could clarify me ? $$L~=~ \frac{1}{2} \dot{q}  \sin^2{q} $$  Is it zero or not defined? cd to previous directory without echo of directory name This  gave me cd - as shorthand to change to my previous directory in Bash. It does have a major problem: it prints the directory it changes to, wasting my screen space, as that directory is then repeated in the prompt on the next line.  I know I can do cd $OLDPWD, also mentioned in that answer, and cd - &gt;/dev/null but that is much more typing.   In the bash man page it says:     ... or if - is the first argument, and the directory change is successful, the absolute path name of the  new  working  directory  is written to the standard output.   How can I make - not to be the first argument? By using any of the cd optional arguments? Any other way to suppress the echo or minimise typing without the need for defining functions/aliases on every machine I work with? How do I parse command line arguments in Java? Search favorite questions by tag Favorite questions on Stack Overflow I feel is highly unused feature of all the features provided on the site. (This again is my personal opinion)  I have favorited around 90 question till date and it gets very very very difficult if I want to search for a question which I remember I have favorited, which defeats the entire purpose of one favouriting a question, so here is my small suggestion.  Favorites by tags  Screen 1        Screen 2        Please share your opinions on this. How can I run a Minecraft Server on multiple CPU cores? I am working on setting up a Minecraft server on a machine I have at home. This particular machine has two quad-core CPUs running at 2.0Ghz so I would like to take advantage of the number of cores and run a server with 4 or 6 of the cores. My server of choice is CraftBukkit, the latest version of which is craftbukkit-1.4.7-R1.0 and launched with a start-up script of:  "C:\Program Files\Java\jre7\bin\java.exe" -Xms1G -Xmx8G -jar craftbukkit-1.4.7-R1.0.jar"   The  says:     Minecraft servers, as of 1.1.0, can use multiple cores, so now they will not sit idle.   but does not really expand on this.  My questions, then:   Is it possible to set the number of cores the server uses? How do I do it - via start-up options, or other methods? Is it really worth it and would it make that much of a difference with a lot of players? More than one 'Open xxxxx here as Administrator' I want the option to open a Command window or Powershell window as Administrator from the drive and directory context menus in Windows.   I can have either by creating and populating the special 'runas' registry keys shown below, but is there a way I can have both listed on the context menu and have both run as Administrator?  [HKEY_CLASSES_ROOT\Drive\shell\runas] ... [HKEY_CLASSES_ROOT\Drive\shell\runas\command] ... [HKEY_CLASSES_ROOT\Directory\shell\runas] ... [HKEY_CLASSES_ROOT\Directory\shell\runas\command] ... [HKEY_CLASSES_ROOT\Directory\Background\shell\runas] ... [HKEY_CLASSES_ROOT\Directory\Background\shell\runas\command] ... How can one motivate the relativistic momentum? Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where it is moving). Now, in Special Relativity the momentum changes. The new quantity of motion becomes $$\mathbf{p} = \dfrac{m\mathbf{v}}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Or, using $\gamma$ the Lorentz factor $$\mathbf{p} = \gamma(v) m\mathbf{v}$$ where I write $\gamma(v)$ to indicate that the velocity is that of the particle relative to the frame in which the movement is being observed. The need for this new momentum is because the old one fails to be conserved and because using the old one in Newton's second law leads to a law which is not invariant under Lorentz transformations. So the need for a new momentum is perfectly well motivated. What I would like to know is how can one motivate that the correct choice for $\mathbf{p}$ is the $\gamma(v)m\mathbf{v}$. There are some arguments using the mass: considering a colision, requiring momentum to be conserved, transform the velocity and then find how mass should transform. Although this work, it doesn't seem natural, and it is derived in one particular example. On my book there's even something that Einstein wote saying that he didn't think it was a good idea to try transforming the mass from $m$ to $M = \gamma(v)m$, that it was better to simply keep $\gamma$ on the new momentum without trying to combine it with the mass. So I would like to know: without resorting to arguments based on transformation of the mass, how can one motivate the new form of momentum that works for special relativity?