Given $a,b,x>0$, $x (a^y+b^y)^{1/y}$
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
This is a school-network.  Official (outside reachable domain name) is  bgschwechat.ac.at (www.bgschwechat..., mail.bgschwechat... and ftp.bgschwechat..)  Internally the windows domain is named bgs.ac.at  We need (possibly cheap) SSL certificates for Webserver and Exchange-Server  From our firewall (www.bgschwechat.ac.at) (Sophos UTM9) requests get NATed to virtual machines - some of them need SSL   Webserver (running CENTOS - www.bgschwechat.ac.at) Exchange Server (named xch.bgs.ac.at) should be reachable via NAT as mail.bgschwechat.ac.at WSUS Server (dc2.bgs.ac.at) - only for internal clients   My question: What kind of SSL-Certificate would we need to secure eg. both domains (bgschwechat.ac.at AND bgs.ac.at) so that they appear secured from outside when NATTING for example mail.bgschwechat.ac.at to xch.bgs.ac.at ?  Or do we need to rename the interior domain to the official domain name?  ...recommandations where to purchase such certificate? how can I add an overlapped anchor in both overlapped paths automatically If parsing the output of ls is dangerous because it can break on some funky characters (spaces, \n, ... ), what's the best way to know the number of files in a directory?  I usualy rely on find to avoid this parsing, but similarly, find mydir | wc -l will break for the same reasons.  I'm working on Solaris right now, but I'm looking for a answer as portable across different unices and different shells as possible. Can't move files to trash without any permission issues This is not like one of the cases addressed before - I've checked them all.  I've suddenly begun getting that message "... can't be put in the trash. Do you want to delete it immediately?" this morning in my Home directory only.  I have a Home partition (ext4, mounted properly) with symlinks for user folders like Downloads, Documents, etc. to folders with the same names in a Data partition (ntfs, mounted properly).  For example, I cannot move a file in Downloads folder to Trash when I try via Home, but no problem if I try via Data partition, although the file in question has the same ownership and permissions at both locations.  Also no problem at all with files in my Home folder, including sub-folders like Public that are not symlinked to my Data partition.  Interesting puzzle for me...  PS: Just upgraded to 15.04 but I don't think it matters... On second thought, it might perhaps be something to do with upgrading from Nautilus 3.10 to 3.14?  PPS: This bug has been finally resolved some time later in version 16.10, and no longer exists under Ubuntu 17.04. I'm trying to convert some strings that are in French Canadian and basically, I'd like to be able to take out the French accent marks in the letters while keeping the letter. (E.g. convert é to e, so crème brûlée would become creme brulee)  What is the best method for achieving this? Java ReentrantReadWriteLocks - how to safely acquire write lock? I am using in my code at the moment a  to synchronize access over a tree-like structure.  This structure is large, and read by many threads at once with occasional modifications to small parts of it - so it seems to fit the read-write idiom well.  I understand that with this particular class, one cannot elevate a read lock to a write lock, so as per the Javadocs one must release the read lock before obtaining the write lock.  I've used this pattern successfully in non-reentrant contexts before.  What I'm finding however is that I cannot reliably acquire the write lock without blocking forever.  Since the read lock is reentrant and I am actually using it as such, the simple code  lock.getReadLock().unlock(); lock.getWriteLock().lock()  can block if I have acquired the readlock reentrantly.  Each call to unlock just reduces the hold count, and the lock is only actually released when the hold count hits zero.    EDIT to clarify this, as I don't think I explained it too well initially - I am aware that there is no built-in lock escalation in this class, and that I have to simply release the read lock and obtain the write lock.  My problem is/was that regardless of what other threads are doing, calling getReadLock().unlock() may not actually release this thread's hold on the lock if it acquired it reentrantly, in which case the call to getWriteLock().lock() will block forever as this thread still has a hold on the read lock and thus blocks itself.  For example, this code snippet will never reach the println statement, even when run singlethreaded with no other threads accessing the lock:  final ReadWriteLock lock = new ReentrantReadWriteLock(); lock.getReadLock().lock();  // In real code we would go call other methods that end up calling back and // thus locking again lock.getReadLock().lock();  // Now we do some stuff and realise we need to write so try to escalate the // lock as per the Javadocs and the above description lock.getReadLock().unlock(); // Does not actually release the lock lock.getWriteLock().lock();  // Blocks as some thread (this one!) holds read lock  System.out.println("Will never get here");   So I ask, is there a nice idiom to handle this situation?  Specifically, when a thread that holds a read lock (possibly reentrantly) discovers that it needs to do some writing, and thus wants to "suspend" its own read lock in order to pick up the write lock (blocking as required on other threads to release their holds on the read lock), and then "pick up" its hold on the read lock in the same state afterwards?  Since this ReadWriteLock implementation was specifically designed to be reentrant, surely there is some sensible way to elevate a read lock to a write lock when the locks may be acquired reentrantly?  This is the critical part that means the naive approach does not work. How to enable crash reports/core dumps/stack trace logging globally? Crashing bugs can be the most annoying ones, leading to data loss, downtime and frustrated users. It would be good if applications crashed less.  Because of the complexity of the machine context, crashes often can't be reproduced in reasonable time for an ordinary user. That doesn't mean that the bug is rare - It could simply mean that the thing that triggers it occurs rarely for each user (for example DST changes). Such bugs are unlikely to be fixed unless a lot of users report them. It would be good if more crashes were reported.  To debug crashes, the developers need as much unambiguous context as possible. Generated crash reports are good, because they're usually detailed and accurate. Users can't be expected to zealously observe and report all the context manually, so they often submit sparse and wrong information.  The target audience for a lot of applications is not developers or sysadmins, but rather the general public, at home or at work. Such users can't be expected to know how to collect crash information manually, or to install -dbg packages, but generated reports from such users can still be usable. Some applications have their own crash reporting tools, but in my experience these rarely work, and when they report that they failed to report the error there doesn't seem to be any information on how to do it manually (I've observed this for recent versions of both Firefox and Flash). System-wide generation of crash reports would be good.  Is there any sort of crash report generation* which can be enabled globally** without installing a ton of -dbg packages, reading the documentation of each and every application, or slowing a normal machine down to a crawl?  * Logs, core dumps, stack traces, whatever  ** Not necessarily for init, but at least for a significant subset of the applications running on a typical desktop Linux installation. In my experience GUI applications crash 100+ times more frequently than shell applications, so GUI applications would naturally be the focus. TypeError: Element-wise multiplication: not supported between 'Matrix' and 'Vector' is $\sqrt{x}$ always positive? Recovering user files with a Live CD What is the difference between the GNU Makefile variable assignments =, ?=, := and +=? Can anybody give a clear explanation of how variable assignment really works in Makefiles.   What is the difference between :   VARIABLE = value  VARIABLE ?= value  VARIABLE := value  VARIABLE += value   I have read the  in GNU Make's manual, but it still doesn't make sense to me. My friend and I were discussing this and we couldn't figure out how to prove it one way or another.  The only rational values I can figure out for $\sin(x)$ (or $\cos(x)$, etc...) come about when $x$ is some product of a fraction of $\pi$.  Is $\sin(x) $ (or other trigonometric function) necessarily irrational if $ x $ is rational?  Edit: Excluding the trivial solution of 0. Weird display on screen before swipe lock Samsung Galaxy s6 edge plus How to write 1, 2, ... as a subscript to a letter? How do you sort du -sh /dir/* by size? I read one site that said use | sort -n but that's obviously not right. Here's an example that is wrong.  [~]# du -sh /var/* | sort -n 0       /var/mail 1.2M    /var/www 1.8M    /var/tmp 1.9G    /var/named 2.9M    /var/run 4.1G    /var/log 8.0K    /var/account 8.0K    /var/crash 8.0K    /var/cvs 8.0K    /var/games 8.0K    /var/local 8.0K    /var/nis 8.0K    /var/opt 8.0K    /var/preserve 8.0K    /var/racoon 12K     /var/aquota.user 12K     /var/portsentry 16K     /var/ftp 16K     /var/quota.user 20K     /var/yp 24K     /var/db 28K     /var/empty 32K     /var/lock 84K     /var/profiles 224M    /var/netenberg 235M    /var/cpanel 245M    /var/cache 620M    /var/lib 748K    /var/spool Darth Vader threw Emperor Palpatine to a pit. Well, , but unlike other times, Palpatine wasn't injured or unconscious when he was thrown.  Why didn't he simply prevent his fall using his lightsaber (I have seen such action in Star Wars: The Clone Wars TV series lots of time) and make his way out? Remove duplicate rows in MySQL Octal number literals: When? Why? Ever? I have never used octal numbers in my code nor come across any code that used it (hexadecimal and bit twiddling notwithstanding).  I started programming in C/C++ about 1994 so maybe I'm too young for this? Does older code use octal? C includes support for these by prepending a 0, but where is the code that uses these base 8 number literals? Are there any rules related to the creation of a ?   I am aware of the creation method for the amulet. But I'm asking about creating the actual construct. In my preamble, you'll find:  \renewcommand{\baselinestretch}{1} \renewcommand{\familydefault}{\sfdefault} \usepackage[sfmath]{kpfonts} \usepackage[mathrmOrig]{sfmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{animate} \usepackage{anysize} \usepackage{arcs} \usepackage{array} \usepackage[scale=0]{background} \usepackage{blindtext} \usepackage{calc} \usepackage{cancel} \usepackage{chngcntr} \usepackage{CJK} \usepackage{CJKspace} \usepackage{CJKpunct} \usepackage{colortbl} \usepackage{enumitem} \usepackage{epstopdf} \usepackage{etoolbox} \usepackage{fancybox} \usepackage{fancyhdr} \usepackage{float} \usepackage{framed} \usepackage{graphicx} \usepackage{hyphenat} \usepackage{ifthen} \usepackage{latexsym} \usepackage{lmodern} \usepackage{multicol} \usepackage{multirow} \usepackage{mwe} \usepackage{pgffor} \usepackage{rotating} \usepackage{tabularx} \usepackage{textcomp} \usepackage{tgheros,tgtermes,tgcursor} \usepackage{tikz} \usepackage{times} \usepackage{tipa} \usepackage{varwidth} \usepackage{wasysym} \usepackage{wboiboites} \usepackage[abs]{overpic} \usepackage[breaklinks,colorlinks=true,linkcolor=red,citecolor=red, urlcolor=blue]{hyperref} \usepackage[framemethod=TikZ]{mdframed} \usepackage[breakable, theorems, skins]{tcolorbox,empheq} \usepackage[default]{gillius} \usepackage[document]{ragged2e} \usepackage[latin1]{inputenc} \usepackage[spanish]{babel} \usepackage[T1]{fontenc} \usepackage[total={18.59cm,26.5cm},left=1.5cm,top=2.5cm]{geometry} \usetikzlibrary{matrix,arrows, positioning,shadows,shadings,backgrounds,calc, shapes, tikzmark} \usetikzlibrary{shadows.blur} \usetikzlibrary{shapes.symbols} \usetikzlibrary{patterns,fadings} \tcbuselibrary{skins,breakable,listings,theorems}    I'm trying to draw an arrow for X axis and Y axis.   \begin{tikzpicture} \draw[yellow!10, fill=blue!5](-1, -1) rectangle (7, 5); \draw[dotted] (-0.75,-0.75) grid (6.75,4.75); \node[below] at (-0.25,0){$O$}; \draw[-&gt;,black, thick] (-0.75,0)--(6.75,0); \end{tikzpicture}   But I get this error:    Additionally, if I remove -> from the options of \draw the tikz picture compiles normally.