Hi, I want to convert the comma separated nvarchar to int list in sql
How do I split a string so I can access item x?
Static Classes In Java Is there any way I can specify a standard or custom numeric format string to always output the sign, be it +ve or -ve (although what it should do for zero, I'm not sure!) How can I understand and prove the "sum and difference formulas" in trigonometry? The "" formulas often come in handy, but it's not immediately obvious that they would be true.  \begin{align} \sin(\alpha \pm \beta) &amp;= \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \\ \cos(\alpha \pm \beta) &amp;= \cos \alpha \cos \beta \mp \sin \alpha \sin \beta \end{align}  So what I want to know is,    How can I prove that these formulas are correct? More importantly, how can I understand these formulas intuitively?   Ideally, I'm looking for answers that make no reference to Calculus, or to , although such answers are still encouraged, for completeness. I have 2 graphics cards on my laptop. One is IGP and another discrete.   I've written a shell script to to turn off the discrete graphics card.  How can I convert it to systemd script to run it at start-up? Age of universe? Well relativity teaches us that time interval between two events is a frame dependent quantity, then how can we say that our universe is 13.8 billion years old? Should it not depend on who is asking this question? How can I narrow down these gaps? I am writing my curriculum vitae, but I have one question.  In the first image, there are spaces between different sections.  (Between contact and phone, between education and Seoul~~,....)  Thus, I want to narrow down these gaps.  How can I solve this problem??  \documentclass[margin,line,letterpaper,11pt]{res}  \usepackage{times}  \usepackage{enumitem}   \setlength{\topmargin}{0.1in} \setlength{\textheight}{11in}  \setlength{\textwidth}{6in} \setlength{\oddsidemargin}{-.55in}  \setlength{\evensidemargin}{-.55in}  \oddsidemargin -.25in \evensidemargin -.49in \textwidth=5.4in  \newcommand{\ts}{\textsuperscript}  \newcommand{\block}[1]{     \vspace{.1in} \section{\sc #1} }  \newcommand{\subblock}[1]{     \vspace{-.2in}\subsection*{#1} }  \newenvironment{enum}{     \begin{enumerate}[leftmargin=5mm]     \setlength{\itemsep}{1mm} }{     \end{enumerate} }   \begin{document}   \name{\sc \LARGE  }   \begin{resume}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \block{Contact} Phone:  \\ Email:  \\\vspace*{-6mm} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \block{Education}  University : \\  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \block{Other\\ Activities}  Club : \\   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \end{resume} \end{document} Idempotent linear operators are projections I'm working on this problem: Suppose $V$ is a Hilbert space and $P : V \to V$ is a linear map such that $P^2= P$ and $\Vert Pf \Vert \leq \Vert f \Vert$ for every $f \in V$. Prove that there exists a closed subspace $U$ of $V$ such that $P = P_U$. I did do some searching online and I know that $P$ is an idempotent matrix and I know that $U$ is supposed to be $\text{range}P$, which I can show is closed. However, I'm having a hard time showing $P_{\text{range}P} = P$. I know that I can decompose $f = g + h$, where $g \in \text{range}P$ and $h$ is in the orthogonal complement of $\text{range}P$. I'm not sure how to proceed. Most of the online searches require that $P$ be self-adjoint, but this question doesn't have this condition. Can I get some help? I just upgraded linux-firmware package and after that I used $ sudo update-initramfs -u -k all but I got some errors:  $ sudo update-initramfs -u -k all [sudo] password for piotrek:  update-initramfs: Generating /boot/initrd.img-4.4.0-34-generic Warning: No support for locale: en_US.utf8 update-initramfs: Generating /boot/initrd.img-4.4.0-31-generic Warning: No support for locale: en_US.utf8 update-initramfs: Generating /boot/initrd.img-4.4.0-13-generic WARNING: missing /lib/modules/4.4.0-13-generic Ensure all necessary drivers are built into the linux image! depmod: ERROR: could not open directory /lib/modules/4.4.0-13-generic: No such file or directory depmod: FATAL: could not search modules: No such file or directory Warning: No support for locale: en_US.utf8 depmod: WARNING: could not open /var/tmp/mkinitramfs_LJbkti/lib/modules/4.4.0-13-generic/modules.order: No such file or directory depmod: WARNING: could not open /var/tmp/mkinitramfs_LJbkti/lib/modules/4.4.0-13-generic/modules.builtin: No such file or directory   I'm sure I don't have kernel 4.4.0-13. I might have had it some time ago but removed it:   $ apt list --installed | grep linux-  WARNING: apt does not have a stable CLI interface. Use with caution in scripts.  linux-base/xenial,xenial,now 4.0ubuntu1 all [installed,automatic] linux-firmware/now 1.159 all [installed,local] linux-headers-4.4.0-31/xenial-updates,xenial-updates,xenial-security,xenial-security,now 4.4.0-31.50 all [installed] linux-headers-4.4.0-31-generic/xenial-updates,xenial-security,now 4.4.0-31.50 amd64 [installed] linux-headers-4.4.0-34/xenial-updates,xenial-updates,xenial-security,xenial-security,now 4.4.0-34.53 all [installed] linux-headers-4.4.0-34-generic/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-image-4.4.0-31-generic/xenial-updates,xenial-security,now 4.4.0-31.50 amd64 [installed] linux-image-4.4.0-34-generic/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-image-extra-4.4.0-31-generic/xenial-updates,xenial-security,now 4.4.0-31.50 amd64 [installed] linux-image-extra-4.4.0-34-generic/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-libc-dev/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-sound-base/xenial,xenial,now 1.0.25+dfsg-0ubuntu5 all [installed] syslinux-common/xenial,xenial,now 3:6.03+dfsg-11ubuntu1 all [installed] syslinux-legacy/xenial,now 2:3.63+dfsg-2ubuntu8 amd64 [installed]   How to fix those update-initramfs errors? As you can see from the image below, I have an issue with the text alignment of extra long chapter names. How can I fix it so that the text will not go further left than the start of the chapter name? That is, I don't want any text to be underneath the "Appendix A" part.  I added that red line just to show how I'd like it aligned, if possible.    Here's my MWE:  \documentclass{book} \let\cleardoublepage\clearpage  \RequirePackage{titletoc} \RequirePackage{tikz} \RequirePackage[explicit]{titlesec} \RequirePackage{DejaVuSansCondensed} \RequirePackage[normalem]{ulem} \RequirePackage[   left=2.25in,   right=0.75in,   top=1.25in,   bottom=1.25in,   marginparwidth=1.75in,   marginparsep=.25in,   asymmetric]{geometry}  \renewcommand*\familydefault{\sfdefault} % Set default font  %%% Table of Contents ---------------------------------------------------------- \setcounter{tocdepth}{1} % Show only Chapters and Sections  %%% Change font/color/layout of TOC \makeatletter \titlecontents{chapter}[-2em] {\color{cyan}\bfseries\LARGE\addvspace{3mm}} {\makebox[4.4em][r]{\@chapapp}\contentslabel{-0.25em}\hspace{1.9em}} {} {\hspace{3em}\contentspage} \g@addto@macro{\appendix}{%   \addtocontents{toc}{\protect\renewcommand*{\protect\@chapapp}{\protect\appendixname}}% } \makeatother  \titlecontents{section}[5.3em] {\color{cyan}\large\itshape\addvspace{3mm}} {\contentslabel{0em}\hspace{3.2em}} {} {\hspace{3em}\contentspage} [\addvspace{0mm}]  %%% Chapter Header ---------------------------------------------------------- \makeatletter \titleformat{\chapter}   {\normalfont\sffamily\Huge\scshape}   {}{0pt}   {\thispagestyle{empty}    % Remove page number on new chapters   %\setcounter{definition}{0}   \begin{tikzpicture}[remember picture,overlay]     \node[yshift=-3cm] at (current page.north west)       {\begin{tikzpicture}[remember picture, overlay]         \draw[fill=cyan] (0,-1) rectangle           (25cm,3cm);         \draw[fill=cyan] (0,-24) rectangle           (25cm,-25cm);         \ifttl@label% &lt;---------------------- Added condition on \ifttl@label           \node[anchor=west,xshift=.21\paperwidth,yshift=-.01\paperheight,rectangle]               {\color{white}\LARGE \MakeUppercase{\@chapapp} \Huge\thechapter};         \fi% &lt;------------------------------- end condition on \ifttl@label        \end{tikzpicture}       };    \end{tikzpicture}\endgraf   \vskip-.7cm   \color{cyan}\Huge\raggedright\leftskip-1cm    \noindent\MakeUppercase{#1}\endgraf   } \makeatother  \titlespacing*{\chapter}{0pt}{10pt}{0pt}{}  \titleformat{\section}{\color{cyan}\itshape\LARGE}{\llap{\thesection} #1}{1em}{}[\titleline{\color{cyan}\titlerule[1pt]}] \titleformat{\subsection}{\color{cyan}\normalfont\large}{\; #1}{1em}{}  \begin{document}   \tableofcontents   \chapter{Turing Machines}     \section{The Turing Machine}     \section{Variations of the Turing Machine}       %\subsection{Non-deterministic Turing Machines}     \section{The Church-Turing Thesis}   \chapter{Decidability}     \section{The Universal Turing Machine}    \appendix   \chapter{ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM} \end{document} Why does minimizing the MAE lead to forecasting the median and not the mean? From the , specifically :     A forecast method that minimizes the MAE will lead to forecasts of the   median, while minimizing the RMSE will lead to forecasts of the mean   Can someone give an intuitive explanation of why minimizing the MAE leads to the forecasting the median and not the mean? And what does this means in practice?  I have asked a customer: "what is more important for you to make mean forecasts more accurate or to avoid very inaccurate forecasts?". He said that to made mean forecasts more accurate have higher priority. So, in this case, should I use MAE or RMSE? Before I read this citation I believed that MAE will be better for such condition. And now I doubt. I just finished a test as part of a job interview, and one question stumped me, even using Google for reference. I'd like to see what the StackOverflow crew can do with it:  The memset_16aligned function requires a 16-byte aligned pointer passed to it, or it will crash. a) How would you allocate 1024 bytes of memory, and align it to a 16 byte boundary? b) Free the memory after the memset_16aligned has executed.  {        void *mem;    void *ptr;     // answer a) here     memset_16aligned(ptr, 0, 1024);     // answer b) here     } How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$? For $\alpha \in \mathbb{R}$, define $\displaystyle I(\alpha):=\int_{0}^{2\pi}e^{\alpha \cos \theta}\cos(\alpha \sin \theta)\; d\theta$. Calculate $I(0)$. Hence evaluate $\displaystyle\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta)\; d\theta$.  Hint: To evaluate the integral that expresses $\displaystyle\frac{dI}{d\alpha}$, consider $\displaystyle\frac{\partial}{\partial \theta}(e^{\alpha \cos \theta}\sin(\alpha \sin \theta))$.  How do I do this question? I think this might have something to do with the Fundamental Theorem of Calculus, but I'm not sure.  I computed $\displaystyle I(0)=\int_{0}^{2\pi} d\theta=2 \pi$, and $\displaystyle I(1)=\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$. Following the hint I get  $$\begin{align} \frac{\partial}{\partial \theta}(e^{\alpha \cos \theta}\sin(\alpha \sin \theta)) &amp; =\alpha e^{\alpha \cos \theta} \sin (\alpha \sin \theta) + e^{\alpha \cos \theta}\cos(\alpha \sin \theta) \alpha \cos \theta \\ &amp; =  \alpha e^{\alpha \cos \theta} \sin (\alpha \sin \theta) + \frac{dI}{d \alpha} \cos \theta. \\ \end{align}$$  Is this correct so far?  The answers in the question referred as a duplicate does not help. I'm in a course dealing with real values, not complex. Are recommendation questions an acceptable kind of list-type question or should they be closed? Recommendations are a recurring topic on multiple Stack Exchange (SE) sites. Some sites allow recommendations (ex: ), some do not (ex: ). There are many reasons for that and I can still remember animated discussions on this subject on the Gaming meta. Then there is that existential problem with Sci-Fi SE, &quot;What problems does answering a question on this site solve?&quot;  The only common problem I can think of is What to read/watch next?, which obviously led to a big number of recommendation questions, later slightly disguised as list question. And the main trouble with these questions isn't objectivity at all, some of them aren't even subjective. It's the fact that they don't have an answer - they are open ended. -  Those questions are monstrously popular because:  There's an actual problem to be solved,  or  This problem is quite common.  In view of the  blog post, a recommendation question fails the &quot;real questions have answers, not items or ideas or opinions.&quot; criteria. But it's still a &quot;practical, answerable questions based on actual problems that you face. &quot; and it requires expertise to answer. The problem is that there are multiple acceptable answers, and the asker is not the best person to evaluate the best answer because he doesn't know which one is the best compared to the others, and he cannot test it in short term. Even the need to accept an answer is questionable. So, is a recommendation question an acceptable kind of list-type question or should it be closed just like any other list-type questions? Access to our computer (not only to the internet) needs to be restricted for the accounts of my kids (7, 8) until they are old enough to manage this by themselves. Until then we need to be able to define the following:   the hours of the day when computing is o.k. (e.g. 5 - 9 pm) the days of the week when computing is not o.k. (e.g. mondays to fridays) the amount of time allowed per day (e.g. 2 hours)   In 11.10 all of the following that used to do the job don't work any more:   : for > 11.10 no more available through the ppa. : command line alternative, but from 11.10 removed from the repositories. : Looks great but repeatedly crashes to force restarting X-server. So we can't use or recommed this program at the moment.   Are there any other alternatives? I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); Proof of continuity of Thomae Function at irrationals. In :  $$ \begin{align} t(x) = \begin{cases} 0 &amp; \text{if $x$ is irrational}\\ \frac{1}{n} &amp; \text{if $x = \frac{m}{n}$ where $\gcd(m,n) = 1$} \end{cases} \end{align} $$  I can prove the discontinuity at rational $b$ by taking a sequence of irrationals $x_n$ which converge to $b$.   But while going through an argument for continuity at irrationals.  I found this in a book.      On the other hand if $b$ is an irrational number and $\epsilon &gt; 0$   then there is a     natural number $n_0$ such that $1/n_0 &lt; \epsilon$.   There are only finite number of rationals with denominator less than   $n_0$ in the interval $(b-1,b+1)$. Hence we can find a $\delta &gt; 0$   such that $\delta$ neighbourhood of $b$ contains no rational with   denominator less than $n_0$.   I understand the rest of the proof. But I am unable to prove the emphasized text. Although I find it intuitive. How to solve "sudo: /etc/sudoers.d is world writable" iPad 1 update from 5.1.1 to 7.1 How can I update iPad 1 from iOS 5.1.1 to iOS 7.1?  I tried checking for updates but I get a message "your software is up to date". How will old M42 lenses work on a Nikon camera? I have a Windows Server 2012 R2 Domain.  Yesterday, a computer’s (running Windows 10 Pro) network drive stopped working.  After further investigation (gpresult /h) it appears ALL group policy objects are failing with the reason Inaccessible, Empty, or Disabled.  I have confirmed that all the GPOs still exist and are enabled on both (redundant and local) domain controllers.  Furthermore, there are 20 other machines on the same domain and LAN with absolutely no problems.  However, there is one other computer that I tested which presented with the same problem!  Does that mean the problem is with the servers?  gpresult /r reports that one client is getting GPOs from local DC1, and the other from DC2.  So it is not a problem related to a specific DC.  gpupdate /force fixed nothing (though it claimed that policies were applied).   I tried deleting the registry entries for local policies (following this guide ) and rebooting - same problem.    I found this support page from Microsoft (), but it claims it only applies to Windows 7 or earlier clients.  All my machines (both server and client) are running 64-bit versions and are fully updated.  I have rebooted all of them just to be sure.