How to get minutes interval of two dates PHP 5.2?
How to get time difference in minutes in PHP
creating variable using variable value as part of new variable name I'm trying to create a new variable using the value of an existing variable as part of the variable name.  filemsg"$word1"=" "   I've also tried   filemsg$word1=" "  filemsg${word1}=" "   on all attempts I get the following when that line executes,  cicserrors.sh[45]: filemsgCICS= : not found [No such file or directory] An excerpt from Introduction to Analytic Number Theory by Tom M. Apostol.      I have three main concerns regarding this proof:    What is the abscissa of convergence for $\frac{1}{F(s)}$ - why can we take the product of the two series. I only know this is true if the two series are absolutely convergent.  Why can we do term by term integration? I believe its suffices to show that the series converges locally uniformly - BUT is this true?  How does the proof show that $G(s)$ converges uniformly? The following C++ code uses a ifstream object to read integers from a text file (which has one number per line) until it hits EOF. Why does it read the integer on the last line twice? How to fix this?  Code:  #include &lt;iostream&gt; #include &lt;fstream&gt; using namespace std;  int main() {     ifstream iFile("input.txt");    // input.txt has integers, one per line      while (!iFile.eof())     {         int x;         iFile &gt;&gt; x;         cerr &lt;&lt; x &lt;&lt; endl;     }      return 0; }   input.txt:  10   20   30   Output:  10   20   30   30   Note: I've skipped all error checking code to keep the code snippet small. The above behaviour is seen on Windows (Visual C++), cygwin (gcc) and Linux (gcc). How to remove symbolic link I was trying to create this symbolic link:  sudo ln -s /usr/share/phpmyadmin /var/www/phpmyadmin   but I accidentally typed:  sudo ln -s /usr/share/php,yad,in /var/www/phpmyadmin   So now I want to correct it but it says symbolic link already exist. @class vs. #import It is to my understanding that one should use a forward-class declaration in the event ClassA needs to include a ClassB header, and ClassB needs to include a ClassA header to avoid any circular inclusions. I also understand that an #import is a simple ifndef so that an include only happens once.  My inquiry is this: When does one use #import and when does one use @class? Sometimes if I use a @class declaration, I see a common compiler warning such as the following:     warning: receiver 'FooController' is a forward class and corresponding @interface may not exist.   Would really love to understand this, versus just removing the @class forward-declaration and throwing an #import in to silence the warnings the compiler is giving me. Switching window manager/desktop environments? In general what is the approach to switch the desktop environment or window manager on Ubuntu? The main difference between stock Ubuntu, Kubuntu and Lubuntu is supposedly the use of Unity vs. KDE vs. LXDE.  However, in order to try various desktop environments and window managers I don't want to have to reinstall the respective flavor from scratch just to get a particular desktop environments or window manager. There probably is an easier method than that.  The question: How can I easily test different desktop environments and respective compatible window managers (say KDE, LXDE, Unity, GNOME, XFCE and StumpWM)? Bound on the difference of two determinants Let $A$ and $B$ be two real, $n\times n$ matrices. Using Hadamard's inequality, it is not hard to show that $$ \left|\det A - \det B \right| \leq \|A-B\|_{2} \frac{\|A\|_{2}^n -\|B\|_{2}^n}{\|A\|_2 -\|B\|_2}. $$ Where $\|A\|_2=\sqrt{\sum_{i,j}a_{ij}^2}$.  From this, I can derive a sup bound, for example  $$ \left|\det A - \det B \right| \leq n^{n+1} \|A-B\|_{\infty} \max (\|A\|_{\infty}^{n-1},\|B\|_{\infty}^{n-1}). $$ Where $\|A\|_\infty=\sup_{i,j}|a_{ij}|$.   The constant $n^{n+1}$ is not the best bound possible : any reference (or proof) for a better (or the best) one? I show below that one can obtain $n^2(n-1)^{n-1}$, but that isn't much better. I just tried  $10^5$ random matrices on Maple and obtained a maximal constant (much) smaller  than one : this is not a proof, but it looks like there is room for improvement nevertheless.    Just for completeness (and in case someone sees a factor I missed), to get the first bound, writing $A=[A_1,\ldots,A_n]$ in terms of its column vectors, an expansion shows \begin{eqnarray*} \det A &amp;=&amp; \det (A_1 -B_1,A_2,\ldots,A_n) + \det (B_1,A_2,\ldots,A_n) \\   &amp;=&amp; \sum_{j=1}^n \det (B_1,\ldots, B_{j-1}, A_j -B_j,A_{j+1},\ldots,A_n) \\ &amp;&amp; + \det B,  \end{eqnarray*} Thus by Hadamard's inequality, \begin{eqnarray*} \det A -\det B &amp;\leq&amp;  \sum_{j=1}^n \prod_{i=1}^{j-1} \|B_i\|_{2}\prod_{i=j+1}^{n} \|A_i\|_{2} \|A_j-B_j\|_{2} \\ &amp;\leq&amp;  \|A-B\|_{2} \sum_{j=1}^n \|B\|^{j-1}_{2}\|A\|^{n-j}_{2} \\  &amp;=&amp; \|A-B\|_{2} \frac{\|A\|_{2}^n -\|B\|_{2}^n}{\|A\|_2 -\|B\|_2}. \end{eqnarray*}  The second bound is just that $x^n -y^n\leq n \max(|x|^{n-1},|y|^{n-1}) |x-y|$ and $\|A\|_2 \leq n\|A\|_\infty$.    Another approach is calculus, namely, to write that $\det B - \det A = f(1)-f(0)$, with $f(t)=\det(A + t(B-A))$.   By the mean value theorem $f(1)-f(0)\leq \max |f^\prime (t)|$.   We can compute that $$f^\prime(t) =  {\rm trace}\left({\rm Cofm}(A +t(B-A))(B-A)\right)$$  (if I did not mess up, using the formula for the differential of a determinant, where Cofm means the matrix of Cofactors).   Then, it should deliver something better, if there is a nice way to bound it. The simplest thing is to use Cauchy-Schwarz, namely $$ \left|{\rm trace}\left({\rm Cofm}(A +t(B-A))(B-A)\right)\right|\leq \|B-A\|_{2} \|{\rm Cofm}(A +t(B-A))\|_{2} $$ and then, by lack of a better idea,  $$ \|{\rm Cofm}(A +t(B-A))\|_{2}\leq n \max_{ij} |{\rm Cof}_{i,j}(A +t(B-A))|, $$ and brutally, $|{\rm Cof}_{i,j}(A +t(B-A))|\leq ((n-1) \max(\|A\|_\infty,\|B\|_\infty))^{n-1}$ gives a slightly better constant, namely $$ n^2(n-1)^{n-1} &lt;n^{n+1} $$ but that still seems a very rough way to bound a determinant, as it is never sharp, since to attain this bound all coefficients should be equal, and therefore the cofactor would be zero. They are of the same order in $n$, and I suspect this order is wrong. What does my internet provider know about my online activities? What does my internet service provider know about my online activites in these cases?   plain server (www, ftp, whatever) connection and provider's DNS secured (e.g. TLS) server connection and provider's DNS plain server (www, ftp, whatever) connection and an non-provider non-logging DNS secured (e.g. TLS) server (www, ftp, whatever) connection and non-provider non-logging DNS   In case 4) does my provider know anything more about my online behaviour than "IP w.x.y.z was assigned to Foo Bar between connect-time and disconnect-time" (i.e. only the duration my router was connected)?  What traffic does need to go through the provider's infrastructure to make my connection work at all? How to disable the Windows8 volume On-Screen-Display? Here is a picture of what i am talking about.    I am at my wits end with that annoying thing, please somebody help me. How to downgrade a package via apt-get? How long does it take to unlock another frame by playing one of the base frames? I'd like to get an advanced frame in Firefall. I've been told that I can use "Pilot Tokens" to unlock other frames without having to pay money.  How soon would I be able to unlock an advanced frame? Do I have to level a base frame all the way to level 40? More than once? Here's my preamble:  \documentclass[11pt]{amsart} \usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots. \geometry{letterpaper}                   % ... or a4paper or a5paper or ...  %\geometry{landscape}                % Activate for for rotated page geometry %\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent \usepackage{graphicx} \usepackage{amssymb} \usepackage{epstopdf} \usepackage{float} \usepackage[normalem]{ulem}  \DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}  \title{\emph{Research Proposal:}\\Perceptual Effects of Cross-Contextualized Soundscapes within the Built Environment}   Here's what happens:    Any ideas? Why didn't Harry Potter tell Aunt Petunia he was rich to improve how he was treated by Dursleys? This is a follow-up question to   One reason Aunt Petunia mistreated Harry was that she did not know he was rich. If she knew, she would naturally have treated this golden goose nicely. Her retirement would be secured if Harry financially supported her in old age.  Why didn't Harry tell Aunt Petunia he was rich? Surely every boy wants to be treated nicely by his family. Save entire process for continuation after reboot I developed an algorithm for a fairly hard problem in mathematics which is likely to need several months to finish. As I have limited resources only, I started this on my Ubuntu 12.04 (x86) laptop. Now I want to install some updates and actually restart the laptop (the "please reboot" message is just annoying).  Is there a way to save an entire process including its allocated memory for continuation beyond a reboot?  Here is some information about the process you might need. Please feel free to ask for further information if needed.   I called the process in a terminal with the command "./binary &gt; ./somefile &amp;" or "time ./binary > ./somefile &amp;", I cannot really remember. It's printing some debug information to std::cerr (not very often). It's currently using roughly 600.0 kiB and even though this will increase, it's unlikely to increase rapidly. the process runs with normal priority the kernel is 3.2.0-26-generic-pae, the cpu is an AMD, the operating system is Ubuntu 12.04 x86. it runs since 9 days and 14 hours (so too long to cancel it ;-) ) Could you help me to point out the differences in the following sentences. for me both sentences imply same meaning.      The Restaurant , offers a broad range of locally caught fresh seafood,   prime steak and meat dishes      The Restaurant , offers a wide range of locally caught fresh seafood,   prime steak and meat dishes Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition Show that the bounded function $f(x) = \sin(x^2)$ is continuous, but not uniformly continuous, on the interval $[0,\infty)$.  The problem should be solved using the following definitions: Definition of Continuous Function Let $X$ and $Y$ be metric spaces. We sat that a function $f:X\rightarrow Y$ is continuous if given any open set $V \subseteq Y$, its inverse image $f^{-1}(V)$ is an open subset of $X$. Definition of Uniformly Continuous Function Let $(X,d_x)$ and $(Y,d_y)$ be metric spaces. If $E \subseteq X$, then we say that a function $f: X\rightarrow Y$ is uniformly continuous on $E$ if for every $\epsilon &gt; 0$ there exists a $\delta &gt; 0$ such that for all $x,y \in E$ we have $$d_x(x,y) &lt; \delta \longrightarrow d_y(f(x),f(y)) &lt; \epsilon$$ For the continuity part it is clear that $f^{-1}(a,b), (a,b) \subseteq (-1,1) = \{x:f(x) \in (a,b)\}$ which appears to be an open set however I doubt this is sufficient as a proof since it holds for any function $f$. Not sure how to go about proving $f$ not uniformly continuous. Seems to be difficult to prove from the definition alone. Property of $\{0^n, 1^n, \ldots\}$ The differences between adjacent squares are the odd numbers:  0 1 4 9 16 25 …  1 3 5 7  9 …  The differences between adjacent odd numbers are 2 = 2!  I found that this truth is more general: If the differences between adjacent powers of $n$ are written out, and the differences of those differences etc, the $(n+1)$th sequence is {n!, n!, …}  Is this a well-known theorem? Does it have an easy proof? "I have" vs "I have got" I don't know what is the difference between using "I have got" and "I have" For example:      He's got broad shoulders.    Is it possible to say:      He has broad shoulders.    If yes, so what is the difference? Prove the existence of an analytic function Let $\Delta=\{z\in \mathbb C: |z| &lt; 1\}$. Let $f: \Delta \rightarrow \mathbb C$ be a one-to-one analytic function fixing the origin. Prove that there is a one-to-one analytic function $g: \Delta \rightarrow \mathbb C$ such that $[g(z)]^2=f(z^2)$. Further, show that such a function is odd.  The only idea which comes to my mind is the following (not sure whether it is the right direction though). Let $h: \Delta \rightarrow \Delta \rightarrow \mathbb C,\ z\mapsto z^2\mapsto f(z^2)$. Note that $h'(0)=0,\ h''(z)=2f'(z^2)+4z^3f''(z^2)$; since $f$ is one-to-one and analytic, its derivative never vanishes, so $h''(0)\ne 0$. So $h$ is an analytic function of $\Delta$ with a zero of order two at the origin. Then there is an analytic function $g$ defined in an open disc about the origin with a simple zero at the origin such that $[g(z)]^2=f(z^2)$.   This is the only thing I came up with, but it seems to be a little bit irrelevant since I don't see any way of extending this $g$ to the whole $\Delta$, and also the injectivity and oddness of such a $g$ are unclear. When did The Doctor start running so much? Thanks to Netflix Streaming, I've been watching some random classic Doctor Who stories.  One thing that strikes me as different between the modern Who and old Who was that in modern Who, they do an awful lot of running.  It's become a sort of running gag that they've referenced in-universe.  In the classic Who I've seen, he tends to drive around quite a bit instead.  In addition, The Doctor in modern Who is incredibly reliant on his sonic screwdriver, which I often don't see at all in classic Who stories.  Did the Doctor running and the sonic screwdriver get introduced over time in classic Who, or were they both added as part of the modern Who revival?