Subadditivity of square root function Any hint to prove   $$ \sqrt{x+y} \le \sqrt{x} + \sqrt{y}, \qquad \forall x,y \ge 0 $$
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$? How do I prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$? for $x, y$ positive?  This should be easy, but I'm not seeing how.  A hint would be appreciated.
How to stop mysql from running at boot time? Currently, my MySQL server starts on every server boot. For a couple reasons, this is undesirable behavior. Is there a way to disable this behavior? Evaluate $\int\frac{1}{1+x^6} \,dx$ I came across following problem     Evaluate $$\int\frac{1}{1+x^6} \,dx$$   When I asked my teacher for hint he said first evaluate     $$\int\frac{1}{1+x^4} \,dx$$   I've tried to factorize $1+x^6$ as  $$1+x^6=(x^2 + 1)(x^4 - x^2 + 1)$$ and then writing  $$I=\int\frac{1}{1+x^6} \,dx=\int\frac{1}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx=\int\frac{1+x^2-x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$ $$I=\int\frac{1}{x^4 - x^2 + 1} \,dx-\int\frac{x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$  However $$x^4-x^2+1=\left(x^2-\frac12\right)^2+\frac{3}{4}$$ But I can't see how it helps  I've also tried to reverse engineer the   And I need to have terms similar to $$\frac{x^2-1}{x^4-x^2+1} \quad , \quad \frac{1}{1+x^2} \quad , \quad \frac{1}{(x+c)^2+1}\quad , \quad \frac{1}{(x+c)^2+1}$$ in integrand, How can I transform my cute looking integrand into these huge terms?  Since in exams I will neither have access to WA nor time to reverse engineer the solution moreover it does not seem intuitive,is there any way to solve this problem with some nice tricks or maybe substitutions? How to fetch the columns of the synonyms for linked servers in SQL server I am using two servers local (SQL Server running on my system) and remote (SQL Server running on another system). I have created synonyms in my local server for a table which is located on the remote server.  Synonym used- CREATE SYNONYM [dbo].[test] FOR remoteserver_name .[database_name].[schema_name].object_name  Requirement   I need to fetch the columns of the synonym.  I can retrieve the columns of the synonym using below query in SQL server.  select * from dbo.test   where  dbo is synonym created schema name (local server schema name) and test is synonym name.  I have tried to retrieve the columns of the synonyms using below query, but I cannot fetch the columns  SELECT sys.schemas.name   AS SCHEMA_NAME,        sys.synonyms.name  AS view_name,        sys.columns.name   AS COL_NAME,        sys.types.name     AS data_typename FROM   sys.columns        INNER JOIN sys.synonyms             ON  OBJECT_ID(sys.synonyms.base_object_name) = sys.columns.object_id        INNER JOIN sys.schemas             ON  sys.schemas.schema_id = sys.synonyms.schema_id        LEFT OUTER JOIN sys.types             ON  sys.columns.system_type_id = sys.types.system_type_id WHERE  sys.types.system_type_id = sys.types.user_type_id        AND sys.schemas.name = N'scehmaname'        AND sys.synonyms.name = N'synonymname'   Can you please suggest some other way to retrieve the columns of the synonym or correct the above query? Do we know Snoke predates the Empire? Why are certain example URLs like https://site.com/ and https://mysite.com/ blocked from post content? Why is  and  blocked from the post content on the main site? I tried to make a sample URL and I had to use  instead. I was wondering how to create a theorem environment similar to the following example:   Specifically, the environment should resemble the box that contains "Claim -- The function g is linear".  This comes from a , who has his style files uploaded  I have tried to mimic what I believed to be the relevant code (as there's a lot of stuff there that isn't related to this), to no avail. I have attached my attempt below, but it may be better to ignore it.  \usepackage{amsmath} \usepackage{amsthm} \usepackage{mdframed} \usepackage{thmtools} \usepackage{tikz} \usepackage{xcolor} \usepackage[framemethod=TikZ]{mdframed}     \mdfdefinestyle{mdgreenbox}{%         linewidth=0.5pt,         skipabove=12pt,         frametitleaboveskip=5pt,         frametitlebelowskip=0pt,         skipbelow=2pt,         frametitlefont=\bfseries,         innertopmargin=4pt,         innerbottommargin=8pt,         nobreak=true,         backgroundcolor=SpringGreen!15,         rightline=false,         leftline=false,         topline=false,         bottomline=false,         linecolor=green,     }     \declaretheoremstyle[         headfont=\bfseries\color{OliveGreen},         mdframed={style=mdgreenbox},         headpunct={\\[3pt]},         postheadspace={0pt},     ]{thmgreenbox} \declaretheorem[style=thmgreenbox]{thrm1}   This returns an error, one for xcolor not recognizing the colors, and the following.  l.17        \mdfdefinestyle                       {mdgreenbox}{% The package mdframed has already been loaded with options:   [] There has now been an attempt to load it with options   [framemethod=TikZ] Adding the global options:   ,framemethod=TikZ to your \documentclass declaration may fix this. Try typing  &lt;return&gt;  to proceed.  Package thmtools Info: Key `mdframed' (with value `style=mdgreenbox') (thmtools)             is not a known style key. (thmtools)             Will pass this to every \declaretheorem (thmtools)             that uses `style=thmgreenbox' on input line 39. Package thmtools Info: Automatically pulling in `thmdef-mdframed' on input line 40. (/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thmdef-mdframed.sty Package: thmdef-mdframed 2014/04/21 v66 ) \c@thrm1=\count282 (/compile/output.aux) \openout1 = `output.aux'.   I am looking for a way to mimic the environment more than to fix my methods.  Thank you in advance! Convert HTML to PDF in .NET I want to generate a PDF by passing HTML contents to a function. I have made use of iTextSharp for this but it does not perform well when it encounters tables and the layout just gets messy.  Is there a better way? How can I convert from a SID to an account name in C# I have a C# application that scans a directory and gathers some information.  I would like to display the account name for each file.  I can do this on the local system by getting the SID for the FileInfo object, and then doing:  string GetNameFromSID( SecurityIdentifier sid ) {     NTAccount ntAccount = (NTAccount)sid.Translate( typeof( NTAccount ) );     return ntAccount.ToString(); }   However, this does not work for files on a network, presumably because the Translate() function only works with local user accounts.  I thought maybe I could do an LDAP lookup on the SID, so I tried the following:  string GetNameFromSID( SecurityIdentifier sid ) {     string str = "LDAP://&lt;SID=" + sid.Value + "&gt;";     DirectoryEntry dirEntry = new DirectoryEntry( str );     return dirEntry.Name; }   This seems like it will work, in that the access to "dirEntry.Name" hangs for a few seconds, as if it is going off and querying the network, but then it throws a System.Runtime.InteropServices.COMException  Does anyone know how I can get the account name of an arbitrary file or SID?  I don't know much about networking or LDAP or anything.  There's a class called DirectorySearcher that maybe I'm supposed to use, but it wants a domain name, and I don't know how to get that either - all I have is the path to the directory I'm scanning.  Thanks in advance. \nameref breaks for the star versions of section, paragraph when titlesec is loaded. I have a document that numbers paragraphs by default, but I have a few I do not want to number but would like to refer to. These are marked with \paragraph*, however, if the titlesec package is loaded at the same time, it causes nameref to display an empty string (the link box of hyperref is still visible).  MWE:  \documentclass[12pt]{article} \usepackage[sf]{titlesec} %comment this out and it works fine. \usepackage{hyperref} \begin{document} \section{Sections} \label{sec} This is \nameref{sec} \paragraph{A named Paragraph} \label{par} This is \nameref{par} \paragraph*{A starred named Paragraph} \label{par:star} This is \nameref{par:star} \end{document}   I suspect titlesec causes this defect for ALL star variants of sectioning commands but have not tested this. For me only paragraph* is relevant however a fix for all variants would be the best.  I have a hunch it might be related to this:  however this happens to go way beyond my latex knowledge and is just "magic" for me. How can I get the current working directory? I want to have a script that takes the current working directory to a variable. The section that needs the directory is like this dir = pwd. It just prints pwd how do I get the current working directory into a variable? WPF textblock binding with List does anyone know if there is a simple way to bind a textblock to a List. What I've done so far is create a listview and bind it to the List and then I have a template within the listview that uses a single textblock.  what I'd really like to do is just bind the List to a textblock and have it display all the lines.  In Winforms there was a "Lines" property that I could just throw the List into, but I'm not seeing it on the WPF textblock, or TextBox.  Any ideas?  did I miss something simple?  Here's the code  &lt;UserControl x:Class="QSTClient.Infrastructure.Library.Views.WorkItemLogView" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"          Width="500" Height="400"&gt; &lt;StackPanel&gt;     &lt;ListView ItemsSource="{Binding Path=Logs}" &gt;         &lt;ListView.View&gt;             &lt;GridView&gt;                 &lt;GridViewColumn Header="Log Message"&gt;                     &lt;GridViewColumn.CellTemplate&gt;                         &lt;DataTemplate&gt;                             &lt;TextBlock Text="{Binding}"/&gt;                         &lt;/DataTemplate&gt;                     &lt;/GridViewColumn.CellTemplate&gt;                 &lt;/GridViewColumn&gt;             &lt;/GridView&gt;         &lt;/ListView.View&gt;     &lt;/ListView&gt; &lt;/StackPanel&gt;     and the WorkItem Class  public class WorkItem {     public string Name { get; set; }     public string Description { get; set; }     public string CurrentLog { get; private set; }     public string CurrentStatus { get; private set; }     public WorkItemStatus Status { get; set; }     public ThreadSafeObservableCollection&lt;string&gt; Logs{get;private set;}   I'm using Prism to create the control and put it into a WindowRegion          WorkItemLogView newView = container.Resolve&lt;WorkItemLogView&gt;();         newView.DataContext = workItem;         regionManager.Regions["ShellWindowRegion"].Add(newView);   thanks Why can't I seem to grasp interfaces? Could someone please demystify interfaces for me or point me to some good examples? I keep seeing interfaces popup here and there, but I haven't ever really been exposed to good explanations of interfaces or when to use them.  I am talking about interfaces in a context of interfaces vs. abstract classes. How many switches can be stacked/interconnected? I would like to know how many switch can be stacked with fiber channel to get a best transfer rate between computers.  I have 200 computers connected to 12 3Com switches. All switches have two fiber ports.  Is the best way to have fiber backbone switch and connect fiber channel from every switch to the backbone? Or connect switch 1 to switch 2 to switch 3 to ... switch 12 to switch 1 again?  Thanks! Please help me prove this. I'm not sure how to apply the parallelogram law to the norm. Cannot use polyglossia/babel with biblatex in LuaTeX: etoolbox Toggle undefined This is an example test.tex document. Both babel and polyglossia failed and produce the same error: \documentclass{book}  %\usepackage[vietnamese]{babel} \usepackage{polyglossia} \setdefaultlanguage{vietnamese}  \usepackage{biblatex}   \title{Sth}  \begin{document}  \maketitle  \end{document}   is the full log. And my config for VS Code: &quot;latex-workshop.latex.recipes&quot;: [     {         &quot;name&quot;: &quot;lualatex-&gt;biber&quot;,         &quot;tools&quot;: [             &quot;lualatex&quot;,             // &quot;biber&quot;,         ]     } ], &quot;latex-workshop.latex.tools&quot;: [     {         &quot;name&quot;: &quot;lualatex&quot;,         &quot;command&quot;: &quot;lualatex&quot;,         &quot;args&quot;: [             &quot;--shell-escape&quot;,             &quot;-synctex=1&quot;,             &quot;-interaction=nonstopmode&quot;,             &quot;-file-line-error&quot;,             &quot;-pdf&quot;,             &quot;%DOC%&quot;         ]     },     {         &quot;name&quot;: &quot;biber&quot;,         &quot;command&quot;: &quot;biber&quot;,         &quot;args&quot;: [             &quot;%DOCFILE%&quot;         ]     } ],  I installed all Vietnamese-related package I found using tlmgr search, notably babel-vietnamese and vntex, to no avail. When I use English language, it works. When I paste the exact document to Overleaf, it also works. So it's something on my part. How can I fix this? The volume on my macbook pro has suddenly become greyed out. I haven't installed any updates or made any modifications to the computer, it just suddenly became greyed out after waking the macbook up from sleeping.  I've tried resetting the PRAM, but I don't hear any chime at all when I start up my computer, no matter how long I wait/how many times the computer re-restarts itself.  There also seem to be no internal speakers detected when I go into system preferences. For both input and output the computer detects 0 devices.  Thanks so much in advance for any help!! What's the terminal command for finding out a process's id I want to exit a process using the command line, but I can't recall the command to look up the process's ID.  Does anyone know it? Pause button started working for Chrome / Youtube, messing with audio player controls How do I use RelativeSource with WPF bindings and what are the different use-cases? Integrating $\frac{1}{\sqrt{ax^2+bx+c}}$ for $a<0$ I'm trying to integrate the function $\frac{1}{\sqrt{ax^2+bx+c}}$ for $a&lt;0$ and $b,c&gt;0$.   From a list of integrals of irrational functions from Wikipedia I know the result should contain arcsin or arcos, but I don't understand how to get there.  I've tried Euler's substitution and trigonometric substitution but I always stumble over the fact that $a$ is negative.  Can please someone help me?