I submitted a paper to a computer science conference, and the reviewer mentioned that I should correct grammar/writing issues throughout the paper. Some of the things he/she mentioned: don't -> do not can't -> cannot it's hard -> it is hard So are abbreviations not welcomed in academic writing? If yes, then should I also change all aren't/isn't to are not/is not?

How compelled should I feel to use non-contracted forms (do not rather than don't and so on) when writing in a rather formal text, say an academic paper? In one case I am afraid to seem too stilted, in the other, too casual. Are there good guidelines?  And are there differences in this regard between British and American English?  (In this  there was not much more than "Contractions are more frequent in informal than formal contexts".)


As question title states, I'm interesting in Bayesian update of normally distributed data with known variance. I compared three sources and they seems to contradict each other. I use some kind of unified notation:  1)   $$\mu_{post} = \frac{n\times\sigma_{prior}^2}{\sigma_{known}^2+n \times\sigma_{prior}^2}\times \bar x+\frac{\sigma_{known}^2}{\sigma_{known}^2+n\times\sigma_{prior}^2}\times \mu_{prior}$$  $$\sigma_{post}^2=(\frac{1}{\sigma_{prior}^2}+\frac{n}{\sigma_{known}^2})^{-1}$$  2)   $$\mu_{post} = \frac{\sigma_{prior}^2}{\frac{\sigma_{known}^2}{n}+\sigma_{prior}^2}\times \bar x+\frac{\sigma_{known}^2}{\frac{\sigma_{known}^2}{n}+\sigma_{prior}^2}\times \mu_{prior}$$  $$\sigma_{post}^2=(\frac{1}{\sigma_{prior}^2}+\frac{n}{\sigma_{known}^2})^{-1}$$  3)   $$\mu_{post} = \frac{\frac{n}{\sigma_{known}^2}}{\frac{n}{\sigma_{known}^2}+\sigma_{prior}^2}\times \bar x+\frac{\sigma_{prior}^2}{\frac{n}{\sigma_{known}^2}+\sigma_{prior}^2}\times \mu_{prior}$$  $$\sigma_{post}^2=(\sigma_{prior}^2+\frac{n}{\sigma_{known}^2})^{-1}$$  I'm asking for two things:  1) verification of my notation changes from original sources  2) if they are correct, explanation of the difference between them

Given a random variable $X$ which follows a normal distribution $X \sim (\mu,\sigma^2)$ with unknown mean and known variance. Say we have $n$ observations $y_i$ where $1\le i \le n$ and each $y_i$ is sampled from a normal distribution $Y_i \sim N(x,\sigma_i^2)$ (not i.i.d.) where $x$ is sampled from $X$ and it is the same for all $\{Y_i\}$, but $\sigma_i$ is different for different $Y_i$.  The question is: how to compute the posterior distribution $X$ given the observations p(X|{y_i})? The question is different from the answer listed in  because $y_i$ is not sampled from i.i.d. distribution.


I am a programmer and I want to build a web application that includes online payment, but I am not sure which payment solution is the right choice.   I want to build a mobile topup website, and certainly, the payments needs to be collected, with instant response of the payment status. I thought to use 2chceckout, but they say they cannot provide such solution.  Now, what I want to know is that, whether my question fits at all to stackexchange.com or not, if yes, which site should I ask it at?

I want to ask about payment processors for use in a website. The one I found on Stack Overflow was closed because it's off-topic. None of the others automatically lend themselves to this question. Any ideas?


The problem states: Let $X$ be a completely regular space such that $|X|<c=|\mathbb{R}|$. Prove that there exists a basis $\mathcal{B}$ for the topology on $X$ such that for all $B\in\mathcal{B}$, $B$ is both open and closed.  I let $\mathcal{B}$ be the collection of all clopen sets since any other choice for $\mathcal{B}$ would yield a coarser topology. It is easy to verify that $\mathcal{B}$ forms a valid basis. Let $\tau$ be the topology on $X$ and let $\tau_\mathcal{B}$ be the topology generated by $\mathcal{B}$. Then clearly $\tau_\mathcal{B}\subset\tau$. I couldn't figure out how to show that $\tau_\mathcal{B}=\tau$, so I assumed it wasn't and tried coming to a contradiction. If $\tau_\mathcal{B}\neq\tau$, then that means there must exist an open set $U\in\tau$ and a point $x\in U$ such that every clopen set containing $x$ must intersect $X\setminus U$. I thought that maybe using this along with the completely regular condition, I could prove the existence of some surjective function $f:X\to[0,1]$, thus contradicting the cardinality restriction, but I couldn't find any way of doing that. Any ideas?

I have $X$ as a countable, Tychonoff space, and I want to show that the collection of clopen subset of $X$ form a base for the topology on $X$.  Can I first just define a base $\mathscr{B}$ of X, let $x\in X$ and $E \subset X$ is closed such that $x\notin E$. So $x\in X-E$, which is open.   I also noticed that the interval $[0,1]$ is uncountable. Can I define a function $f: X\to [0,1]$, then f is onto. Do I need to show that $f$ continuous next?


This works in 16.04 but not in 18.04.  Is there a fix?   amixer -D pulse sset Master 30%

is there a way to adjust the system volume via commandline so that the default volume popup (the one that pops up when pressing the media keys on notebooks) is still shown.  I need this for my remote control. It'll be run using a lircrc file and irexec.


I am currently trying to use texstudio as the default application for opening *.tex files, but I cannot change the default application associated with that file type.   I tried to change it by right-clicking on the .TEX file, then Properties, Open with, Show other applications. However, neither texmaker nor texstudio will appear in the programs list and oddly enough, there is no "add application" button anymore.  I tried to make an entry in my /home/user/.local/share/applications/mimeapps/mimeapps.list but nothing happened.  Is there no way to change the list of "other applications" or add an default application program manually?

gedit is set by default to open about any source file. I've gone through the file properties and changed default application to VIM for C and C++ files.  I'd need to do this for any source file I open now, for python files, for text files, for ruby, any, since gedit is set to open all of them.  How can I change this to open with VIM without going the hassle of setting "open with" one by one?


What should it say on a label: Is it "ladies' beer" or "ladies beer?"

I’ve been looking over what has been posted regarding the use of ’s.   I used to be a Technical Writer (years ago). The title of one of our training documents was Users’ Guide.  Once, a coworker said every time he saw that title he expected users to start coming.    Never made any sense to me, but I have to admit that the majority of us didn't understand the use of s’ in place of ’s.  What is the difference?


As the Ancient One explains to Bruce Banner:     The Infinity Stones create what you experience as the flow of time. Remove one stone and that flow splits.   She asks Banner to return them to their respective locations correctly.  Won't the destruction of the 6 Stones impact the universe in the current timeline?

The Ancient One explains:      "The Infinity Stones create what you experience as the flow of time, remove one of the stones and that flow splits."   As we know, post Avengers: Endgame,       (all instances of) the Infinity Stones are destroyed (see this question: )   What does this mean for the flow of time? In particular,       does this mean the rules of time travel are different in the MCU depending on whether you travel to before the destruction of the stones in 2018, or after?


If I save layer files in ArcGIS 9.3, can they be opened and modified in ArcGIS 10.1?  When I try to open the layer file in 10.1, it does not work and gives me an error message: "the imported layer is in an invalid format."

If I save layer files in ArcGIS 10, can they be opened and modified in ArcGIS 9.3?


I am a freelance graphic designer, but also a full time student with a full time retail job. In my regular job I do no design work. The freelance has not been very often, because of how busy I am.   I was recently recruited to design a logo and entire interface for a new app that's being developed. I'm not sure what I should charge, because I haven't designed an app interface before. I was offered what seems like an obnoxiously low payment for the entire job.   Is it unreasonable to require hourly payment, or is it better to be payed by the job? What would be a reasonable amount to charge by the job (in an L.A. suburban area)? I am very skilled but like I said, don't do this very often.

I was hoping I would find some people in the industry that could help me decide what's the best price to charge to design (in this case) business cards.  What are standard prices for professional designers?  From a firm point of view? From a freelancer?  I don't want to overcharge clients but I don't want to ruin the industry by underselling my services.


I want to open multiple terminal windows (20 to be specific) through a bash script. Can someone help ?

How do I execute a program X times in the terminal?  I read that I have to do a bin/bash txt, but I don't know how to execute this X times.


I was trying to download cmatrix and it has malformed lines i went to a bunch of different forums and i couldn't find out how to identify a malformed line how do i identify malformed lines in the text editor im using ubuntu 18.04.2 LTS the text editor with the malformed lines

I have unistalled and reinstalled the Ubuntu Software Center as per info I found in a similar thread and I got the same response about line 91 or something like that.  I just tried to upload a screen shot but since I'm new it won't allow me to.  I also can not figure out how to cut and paste anything so I have to hand type what the error screen says, both when I attempt to open the software center and nothing happens, when I try to enter commands into the terminal to uninstall, reinstall, whatever I get the same following:  COULD NOT INTITIALIZE THE PACKAGE INFORMATION An unresolvable problem occured while initializing the package information Please report t:his bug against the 'update-manager' package and include the following error message: 'E: Malformed line 91 in source list/etc/apt/sources.list (dist parse)  E: The list of sources could not be read.,  E: The package list of status file could not be parsed or opened.   How do I report bugs?  What can be done about this.  I have searched and everything everyone says to do leads me back to the same line error message.  So, I don't know how to get to line 91 in the source list; to tell you what it says. Sorry, I'm really new to this. That is what I need is to find out how to get there and fix what it says. I would really like to NOT have to re partition my hard drive and start from scratch, so I'm really looking forward to getting this problem solved. I need to be able to install new software.


vs.:     In the "old" times Ubuntu had a separated "ncurses-based" installer when people wanted to use Full Disc Encryption when installing. It was named: Alternate installer.   Question: What happened to the alternate install CD? Are there any

I would like to download the alternate installation ISO for the current release, Ubuntu 13.10 Saucy Salamander, but I can't find it on the releases.ubuntu.com website. Aren't alternate ISOs provided anymore?  I need the alternate ISO because Xorg crashes on recent versions of Ubuntu when using old SIS on board graphics.  In fact, I just patched Ubuntu sources and generated a custom package for the xserver-xorg-video-sis driver on my PPA to try fix this problem, after installing with the minimal ISO.


I am copying this .img file to my USB flash drive using dd command. How can I check its progress ?

I've not used dd all that much, but so far it's not failed me yet. Right now, I've had a dd going for over 12 hours - I'm writing an image back to the disk it came from - and I'm getting a little worried, as I was able to dd from the disk to the image in about 7 hours.   I'm running OSX 10.6.6 on a MacBook with a Core 2 Duo at 2.1ghz/core with 4gb RAM. I'm reading from a .dmg on a 7200rpm hard drive (the boot drive), and I'm writing to a 7200rpm drive connected over a SATA-to-USB connector. I left the blocksize at default, and the image is about 160gb.  EDIT: And, after 14 hours of pure stress, the dd worked perfectly after all. Next time, though, I'm going to run it through pv and track it with strace. Thanks to everyone for all your help.


How can I track the coordinates of an object while animating in real time?     public void MoveTo(FrameworkElement fe, double pathlength, double x)     {         double speed = 250;          double X = Math.Abs(pathlength + x);         double quart = Math.Sqrt(X * X);          double time = quart / speed;          var left = new DoubleAnimation         {             From = x,             To = pathlength,             Duration = new Duration(TimeSpan.FromSeconds(time))         };          fe.BeginAnimation(Canvas.LeftProperty, left);     }

Does anybody knows, if there is a way to use a property that is animated as source for a binding? As far as I found out, is that an animation doesn't "really" set the value on the property, and therefore doesn't fire the changed events, which is needed to trigger the binding.  tia Martin


I'm new to c#, But have I can code in Lua, and I'm trying to use some of my skills where necessary so I am trying to Concatenate the operator of the players choice to get them a result.  I've tried searching google for a solution, and I have tried to print it with out concatenating it in different ways, but I just cant figure out what to do.  using System;  namespace FirstConsoleProject {     class Program     {          static void Main(string[] args) //This is a Method, named "Main". It's called when the program starts         {             int numberOne;             int numberTwo;             string method;              Console.WriteLine("What would you like to do? <+, -, *, />");             method = Console.ReadLine();             Console.Write("Please type the first number: ");             numberOne = Convert.ToInt32(Console.ReadLine());             Console.Write("Please type the second number: ");             numberTwo = Convert.ToInt32(Console.ReadLine());             Console.WriteLine(numberOne + method + numberTwo + " = " + numberOne + method + numberTwo);             Console.ReadKey();          }     } }   I expect the out put to say "numberOne+numberTwo= ANSWER", not "numberOne+numberOne = numberOne + numberTwo".

I would like to do the equivalent of:  object result = Eval("1 + 3"); string now    = Eval("System.DateTime.Now().ToString()") as string   Following Biri s , I got this snippet (modified to remove obsolete method ICodeCompiler.CreateCompiler():  private object Eval(string sExpression) {     CSharpCodeProvider c = new CSharpCodeProvider();     CompilerParameters cp = new CompilerParameters();      cp.ReferencedAssemblies.Add("system.dll");      cp.CompilerOptions = "/t:library";     cp.GenerateInMemory = true;      StringBuilder sb = new StringBuilder("");     sb.Append("using System;\n");      sb.Append("namespace CSCodeEvaler{ \n");     sb.Append("public class CSCodeEvaler{ \n");     sb.Append("public object EvalCode(){\n");     sb.Append("return " + sExpression + "; \n");     sb.Append("} \n");     sb.Append("} \n");     sb.Append("}\n");      CompilerResults cr = c.CompileAssemblyFromSource(cp, sb.ToString());     if (cr.Errors.Count > 0)     {         throw new InvalidExpressionException(             string.Format("Error ({0}) evaluating: {1}",              cr.Errors[0].ErrorText, sExpression));     }      System.Reflection.Assembly a = cr.CompiledAssembly;     object o = a.CreateInstance("CSCodeEvaler.CSCodeEvaler");      Type t = o.GetType();     MethodInfo mi = t.GetMethod("EvalCode");      object s = mi.Invoke(o, null);     return s;  }


I have no programming knowledge whatsoever. I accidentally bought a laptop that only has FreeDOS on it. I have decided to have a go at installing Ubuntu on this.   I have looked at video and written tutorials, but it seems that I am missing something. On a different computer, I downloaded Ubuntu ISO file (as a FAT32) on to the desktop, then transferred it  along with the file folder across to the pen drive along with the universal file installer 1.9.8.0.  Next I turned on my HP laptop, pressing Esc repeatedly during boot. This now gave me the option of booting the computer from the pen drive, but this is where it goes wrong. Unlike the videos and blogs, Ubuntu does not show up, it reverts back to dos.  Anyone help a novice please?

This is the third time I've tried to install Ubuntu Server 14.04.03 64-bit on the same laptop, and each time it caused different problems.  Each time I wrote the same iso image to a USB flash drive by using a different application and OS.   Universal USB Installer (pendrivelinux.com) from Windows WinImage writer from Windows built-in image writer from Linux Mint 17.2    The iso image is the same in all three cases, the USB flash drive is the same, and the laptop is the same. However each time the installation of Ubuntu gave me different installation options. For example, the last time I installed Ubuntu, it didn't show all the packages to choose while installing (Basic Ubuntu server, etc.).


Lets assume the following in C or C99:  typedef struct {    int x;    double y; } MY_S;  MY_S a[666] = {333, 666.6};   Does this initialize the first object of the array only? If yes, is there a way to initialize ALL elements of the array to all the same values using that syntax (without calling a function/loop and without repeating the initializer)?

I have a large array in C (not C++ if that makes a difference). I want to initialize all members of the same value.  I could swear I once knew a simple way to do this. I could use memset() in my case, but isn't there a way to do this that is built right into the C syntax?


After a set time period I'd like to have my computer lock. I do not want the computer to go into any kind of power saving mode, I'd just like it to lock the screen.  Which setting must I configure?

I know you can automatically Sleep and Hibernate your computer with a timer. But these affect running programs and stop downloads ... so I was wondering if there is a way to automatically Lock your computer with a timer?


Double double;     int integer = (int) Math.round(double);     String string = Integer.toString(integer);      System.out.println(string);     findTxtField().setText(string);   I am using the above code as An EXAMPLE- I have coded my mobile application using CodeNameOne. The variables are initialized.   I am receiving an error message when running the mobile application and hitting the button that executed similar code(above), unfortunately, after troubleshooting I figured out it was the outputting to the text-field that was causing the crash.  My Mobile application has 5 UI sections. The section for user "registration" will take the data, calculate it and then output the data using a text-field on another UI section "Results".  Any Idea why I am having this issue?  Error:  java.lang.NullPointerException at userclasses.StateMachine.onMain_BtnInfoAction(StateMachine.java:171) at generated.StateMachineBase.handleComponentAction(StateMachineBase.java:2251) at com.codename1.ui.util.UIBuilder$FormListener.actionPerformed(UIBuilder.java:2831) at com.codename1.ui.util.EventDispatcher.fireActionEvent(EventDispatcher.java:345) at com.codename1.ui.Button.fireActionEvent(Button.java:397) at com.codename1.ui.Button.released(Button.java:428) at com.codename1.ui.Button.pointerReleased(Button.java:516) at com.codename1.ui.Form.pointerReleased(Form.java:2560) at com.codename1.ui.Form.pointerReleased(Form.java:2496) at com.codename1.ui.Component.pointerReleased(Component.java:3108) at com.codename1.ui.Display.handleEvent(Display.java:2017) at com.codename1.ui.Display.edtLoopImpl(Display.java:1065) at com.codename1.ui.Display.mainEDTLoop(Display.java:994) at com.codename1.ui.RunnableWrapper.run(RunnableWrapper.java:120) at com.codename1.impl.CodenameOneThread.run(CodenameOneThread.java:176)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Im using c++. Does anyone know how i can fix this? Undefined symbols for architecture x86_64: "Template::Template(std::__1::basic_string<char, std::__1::char_traits, std::__1::allocator >, int)", referenced from: _main in main.cpp.o ld: symbol(s) not found for architecture x86_64 clang: error: linker command failed with exit code 1 (use -v to see invocation) basically writing a merge sort algorithm main: int main() {   int SORT_MAX_SIZE = 16;   int userNumInput;   std::string userDataType;   std::cout << "What type of data would you like to enter options: int, string "                "or Dollar objects" << std::endl;   std::cin >> userDataType;   std::cout << "Please enter the number of elements you would like to enter"             << std::endl;   std::cin >> userNumInput;   if (userNumInput > SORT_MAX_SIZE) {     std::cout << "Please enter the number of elements less then 16"<< std::endl;     std::cin >> userNumInput;   }   Template createTemp = Template(userDataType, userNumInput);   int userData; //todo:how to change this to a different data type   for(int i = 0; i < userNumInput; i++) {     std::cout << "Please enter an element for the spot " + std::to_string(i) <<               std::endl;     std::cin >> userData;     createTemp.userArray[i] = userData;   }   RecurMergeSort(createTemp.userArray, userNumInput);   std::cout << "Sorted Array:" << std::endl;   print(createTemp.userArray, userNumInput);   return 0; }  template class: #include "Template.h" #include "Dollar.h"  Template::Template(const std::string d, int a) {   dataType = d;   numInput = a; }  void Template::createTemplate() {   //create an array based on the information provided above   if (dataType == "int") {     int userArray[numInput];   } else if (dataType == "Dollar objects") {     Dollar userArray[numInput];   } else if (dataType == "string") {     std::string userArray[numInput];   } }

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


EDIT:I'm just confused how to properly use the term. I understand that each alternate universes have it's own designation numbers but just wondering whether the term 'Marvel Universe' simply just mean the main universe which is 616 or it could be use to referred to the whole multiverse(main universe + all the alternate universes) as well?

I know that there are at least 3 Marvel Universes:  Marvel Cinematic Universe -    Has all of the main ongoing Marvel movies    (1, 2)  (1, 2, 3)  (1, Age of Ultron) etc    Marvel's Ultimate Universe -    Has the other Marvel movies    (1, 2, 3, Origins: Wolverine, First Class, The Wolverine, Days of Future Past)  (1, 2)  etc       Main comic book continuity This is the big one, it contains         etc     Then there are apparently off-shoot Earths, continuities which deviate from the main continuity (Earth 616). How many Marvel Earths (Universes) are there?   Further Reading:


Ubuntu Desktop version 16.04 AMDGPU-PRO version 17.10-414273 GPU: RX 480 UEFI with secure-boot disabled   On a fresh installation of Ubuntu, I installed AMDGPU-PRO by following . Commands repeated here in case the link goes dead:  apt update apt dist-upgrade cd /tmp tar -Jxvf amdgpu-pro-17.10-414273.tar.xz cd amdgpu-pro-17.10-414273 ./amdgpu-pro-install -y   After restarting, Ubuntu gets stuck booting indefinitely with the following text displayed in tty7:  /dev/sdb5: clean 414434/8847360 files, 8735918/35384576 _   At this point, I can switch to a different tty and login, etc.  Logging in and running amdgpu-pro-uninstall and restarting fixes the hang on boot...but then I don't have drivers.  It might be important to note that I'm dual-booting Windows and Ubuntu from different partitions on the same disk.

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I'm facing problem logging in. Actually I typed "sudo startx" command to run x server that was not working with "startx". But after then login window appeared and after entering my password it is not showing anything. After few seconds again that login window appears. Even guest account option is also not coming.  OS: ubuntu 18.04 LTS

I was reading some blog and I found that I can manually start GUI by issuing this command sudo startx, so I did that. I did it in the terminal with the GUI already running. Now I'm unable to login to my user account.  Before that my PC used to boot straight into my account without asking for the password (without even showing the GRUB menu since I have only Ubuntu 12.04 installed on my PC). But now it boots and lands in a screen (without showing the GRUB menu) which displays my user account along with the Guest account. When I choose my account, it asks for the password. I entered the password but it comes back again to the same screen without any response. I am damn sure that the password that I entered was right. When I choose the Guest account, everything goes well. Now I have access only to the Guest account.  I have read the answer in  and run the command rm ~/.Xauthority but it says there is no such file. Can anyone help me. Thanks very much!!


I would like to fix the horizontal math spacings, when any math expression is shown inside a block of text, without acting on the text itself.  The maths spacings should be exactly the same as in a normal displayed equation (when it is shown between paragraphs).  See for example the following MWE : \documentclass[11pt,letterpaper,twoside]{book} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry} \usepackage{microtype} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{mathtools} \usepackage{tensor} \everymath{\displaystyle} %\thinmuskip=1\thinmuskip % Solution from another question %\medmuskip=1\medmuskip  % Solution from another question %\thickmuskip=1\thickmuskip  % Solution from another question  \begin{document}  Bla bla bla $r(t) = | \, c \, \Delta t + a \, |$, blabla bla.  Blabla bla bla $t < \tensor{t}{_{\mathcal{P}}} - t_0$ Blabla $\mathcal{P}$, bla bla blablabla blabla bla $t > \tensor{t}{_{\mathcal{P}}}$ bla bla bla blabla blabla $\mathcal{P}$.  Blabla bla $t = \tensor{t}{_{\mathcal{P}}}$ Blabla bla blablabla blabla.  Bla bla bla ${r(t) = | \, c \, \Delta t + a \, |}$, blabla bla.  Blabla bla bla ${t < \tensor{t}{_{\mathcal{P}}} - t_0}$ Blabla $\mathcal{P}$, bla bla blablabla blabla bla ${t > \tensor{t}{_{\mathcal{P}}}}$ bla bla bla blabla blabla $\mathcal{P}$.  Blabla bla ${t = \tensor{t}{_{\mathcal{P}}}}$ Blabla bla blablabla blabla.  \end{document}  I need a global command at the preamble level, not individual ${...}$ (local level).  Using the commands from the answer  appears to fix the issue.  But I'm wondering if there's another way, from a specific command to fix the inline math horizontal spacings, in a similar way to \everymath{\displaystyle}.  Also, I don't want to affect the normal displayed equations between any block of text. So is the commented out solution the only one available at the preamble level?

Sometimes it's annoying that LaTeX stretches and shrinks formulas in math mode. I know that one can prevent that with ${ ... }$, but I have a big document (~100 pages) and I don't want to check every formula and fix it (not to mention complication of the code). So, is there a way to just fix spacing for every formula? I don't think that overall result will be so bad as long as I use microtype package.


Let $G$ be a group, and let $H$ be a subgroup of finite index in $G$, and let $N \colon = \cap_{x \in G} \ xHx^{-1}$. Then $N$ is clearly a subgroup of $G$ which is contained in $H$ and such that $aNa^{-1} = N$ for all $a$ in $G$.   Is $N$ of finite index in $G$? And If so, what can we say about an upper bound for the index of $N$? If not, then can we find a subgroup $N^\prime$ of finite index in  $G$, contained in $H$, and such that $aN^\prime a^{-1} = N^\prime$ for all $a$ in $G$? And what can we say about the index of $N^\prime$ in $G$?

Let $G$ be a group and $H<G$ such that $[G:H]<\infty$. There exists a subgroup $N\triangleleft G$ such that $[G:N]<\infty$.  I have to show this fact (that according to my book is due to Poincaré), but I think that the statement, written in this way, is trivial: for every group $G$, I can take $N=G$, in fact $G\triangleleft G$ and $[G:G]=1$.  Where am I wrong?  If I'm not wrong, do you know a similar statement?


Are there any major differences in performance between http and https?  I seem to recall reading that HTTPS can be a fifth as fast as HTTP.  Is this valid with the current generation webservers/browsers?  If so, are there any whitepapers to support it?


Given a triangle $\Delta$ABC, how to draw any inscribed equilateral triangle whose vertices lie on different sides of $\Delta$ABC?

Consider triangle ABC. Point D is on AC, E is on BC and F is on AB. Given that triangle DEF is equilateral and that segments CD, BE and AF are equal in length, prove that triangle ABC must also be equilateral. I've played with this one for long enough using circles, sine law, cosine law, etc., and have almost reached the point of capitulation. Any hints would be appreciated. I'm not actually sure if the statement is true, but I haven't been able to find a counterexample, either, so I'm stuck both ways.


Envelopes are on sale for Rs. 30 each. Each envelope contains exactly one coupon, which can be one of four types with equal probability. Suppose you keep on buying envelopes and stop when you collect all the four types of coupons. What will be your expected expenditure?  I tried finding a pattern in the probabilities for each of the mass points taking $X$ as the number of trials required. But as I proceeded, it took an ugly structure with little noticeable pattern. Certainly I am not on the right track. Can someone please help me solving the problem?

I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided die wins.  I won, eventually, and the others finished 1-2 turns later. Now I'm wondering: what is the expectation of the length of the game?  I know that the expectation of the number of rolls till you hit a specific number is  $\sum_{n=1}^\infty n\frac{1}{6}(\frac{5}{6})^{n-1}=6$.  However, I have two questions:   How many times to you have to roll a six-sided die until you get every number at least once?  Among four independent trials (i.e. with four players), what is the expectation of the maximum number of rolls needed? [note: it's maximum, not minimum, because at their age, it's more about finishing than about getting there first for my kids]   I can simulate the result, but I wonder how I would go about calculating it analytically.    Here's a Monte Carlo simulation in Matlab  mx=zeros(1000000,1); for i=1:1000000,    %# assume it's never going to take us >100 rolls    r=randi(6,100,1);    %# since R2013a, unique returns the first occurrence    %# for earlier versions, take the minimum of x    %# and subtract it from the total array length    [~,x]=unique(r);     mx(i,1)=max(x); end  %# make sure we haven't violated an assumption assert(numel(x)==6)  %# find the expected value for the coupon collector problem expectationForOneRun = mean(mx)  %# find the expected number of rolls as a maximum of four independent players maxExpectationForFourRuns = mean( max( reshape( mx, 4, []), [], 1) )  expectationForOneRun =    14.7014 (SEM 0.006)  maxExpectationForFourRuns =    21.4815 (SEM 0.01)


i recently installed ubuntu 16.04,(dual boot with windows 10 using usb drive) i did the disk partition and all and now it is present in my hard disk. but when i restarted after installation, i was not asked to choose ubuntu or windows 10, it directly took me to windows, their was no GRUB bootloader.  and i tried this in windows cmd(admin):  "bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi" . it said successful, but when i restarted again, i was back into windows. now i dont know what to do, and that GRUB loader... should that be installed or something???

I went ahead and installed windows 10 on my windows 8 and Ubuntu dual boot PC. All went smooth and Windows 10 works perfectly however the computer automatically boots to Windows and the grub launcher is missing. The partitions are still there I just need some help getting Ubuntu back. Thank you in advance!   Edit: I found a way around it. I don't know of this works for everyone but I went in to the control panel and went to update and recovery. Then I went to recovery and booted into uefi.  Then I selected boot from device and my Ubuntu partition was there and I could boot into it.  Feel free to post other solutions though!


I have problems doing this exercise:     Let $G$ be a group and $Z(G)$ the center of $G$.      Prove: If $G/Z(G)$ is cyclic, then $G$ is an abelian group.   My attempt:  I think that I have to show $G/Z(G) = \{G\}$, since from this it follows $Z(G) = G$, and so $G$ is abelian. Maybe one way of proving that $G/Z(G) = \{G\}$ is by showing $|G/Z(G)|=1$.   $G/Z(G) \neq \emptyset$ should be clear. Now let's take $g_1Z(G), g_2Z(G) \in G/Z(G)$ aribtrary, and show that they are equal.   Since $G/Z(G)$ is cyclic, I know that there is a $k \in \mathbb{N}$ so that $g_1Z(G) = (g_2Z(G))^k = g_2^kZ(G)$. Since $Z(G)$ is the center, I think I should use that the elements of $Z(G)$ commutate with the elements of $G$. But I have no idea, how I can continue now.  Tank you for your help.  Regards,  S. M. Roch

Let $G$ be a group and let $G'$ denotes its commutator subgroup, that is the group generated by all elements of the form $g^{-1}h^{-1}gh$.  Is the following true:      If $G/G'$ is cyclic, then G is abelian.   Recall that the claim is true for the $G$ modulo the center of $G$.  See


I am taking an exam tomorrow on Complex Analysis, and this is a problem I have come across multiple times on old exams and I've been stumped.  "Show that there is no function f analytic on the punctured plane $\mathbb{C}-\{0\}$ that satisfies $$|f(z)| \ge \frac{1}{\sqrt{|z|}} \,\,\, \forall z \neq 0."$$  I probably tried a number of things back in June when I first saw it, but can't find my work on that right now. When I was going through again today, my initial approach was to assume by contradiction that there is such an f. I set $g(z)=f(1/z)$. Then g would have a pole at infinity. Bringing that information back to f, there's a pole at 0. Which I probably should have seen before doing that.  Then there's an entire function h and some integer n such that $f(z)=\frac{h(z)}{z^n}$. Right? So I was playing with h. From the inequality, $|h(z)| \ge |z|^{n-1/2}$. That doesn't look like a contradiction to me, but maybe I'm missing something.  I asked somebody who has passed this exam before, and they suggested setting $g(z)=\frac{1}{f(z)}$. That gives the inequality $|g(z)| \le \sqrt{|z|}$. Again, I look at singularities. Here, the only singularity is at infinity, the same as my other g. I feel like it's just giving the same information as my first attempt, and I am still seeing no contradiction.  I attempted to search for this on here, but couldn't find a way to formulate it that got me any relevant results through the search bar. If this is a repeat, just point me to the old one and trash mine.

I have some trouble solving this problem: Does there exist a holomorphic function $f$ on $\mathbb C\setminus \{0\}$ such that $$|f(z)|\geq \frac{1}{\sqrt{|z|}}$$ for all $z\in\mathbb C \setminus \{0\}$? I don't know where to start. My intuition is that you would get a problem with the singularity near $0$, but I am not sure how to prove it. Any help would be appreciated! Thanks!


I am planning to virtualise 50 desktops as thin clients(concurrent users). Well i will need 5 servers where 3 will be used for server virtualisation and 2 for desktop virtualsiation.All the servers will be Hexa Core with 2 CPU's.I want to know the number of licenses i will be requiring for Vmware vSphere 5 Enterprise Plus ,Vmware vCenter Server 5 Standard,Vmware Horizon Advanced edition.I am purchasing 50 TSA licenses separately.

This is a  about Licensing.    Questions on licensing are off-topic on Server Fault.  If your question has been closed as a duplicate of this question, then this is because we want to help you understand why licence questions are off topic rather than just telling you "it just is". In all likelihood, this question will not address your question directly, it was not meant to.    I have a question regarding software licensing. Can the Server Fault community please help with the following:   How many licenses do I need? Is this licensing configuration valid? What CALs do I need to be properly licensed? Can I run this product in a virtual environment? Can I downgrade this product to an earlier version? Am I entitled to feature X with license Y?


I can't click on anything in Minecraft. I am not in adventure mode, I can place blocks and torches and stuff, but I can't break anything or use any items. When I go to the menu, I can't click and save the game either. I was looking at my coordinates when I accidently hit escape and I was confused and then I hit escape again and that it when I couldn't hit or break blocks or anything. Then I tried doing it again to see if it would fix the problem, but it didn't. If anyone can help or send advice, it is greatly appreciated.

I'm playing on a Survival world with cheats on, "easy" difficulty, and at night in-game. I didn't have a sword or anything to make a sword with, and I was starving, so I switched to Creative to give myself a stack of food and a bed to set my spawn point. When I switched back to Survival, I couldn't destroy or place blocks. I'm on single player, and my Internet is fine, and I can destroy blocks still if I switch to creative. I've tried resetting the button one, and reloading the map, and it still doesn't work. I've even tried deleting everything I gave myself in Creative. This happened before on a different world and I ended up deleting it.  This only happens on this world. How do I fix it?  If I know I'm in the correct game mode, what else can cause this?  Are there different causes in multiplayer?


There is something that i couldn't actually understand about GLMs. In wikipedia it says "(GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution". Does this mean logistic regression has a normal distribution as its error distribution ? I think it should have a binomial one. I couldn't even completely understand what an error distribution is... The thing is, what i understand with the GLM is that it helps to deal with data that has non-linear relations by using linear models. But the function uses residuals so the distribution shouldn't change much about its responses, so i think the link function is what makes the difference. Can somebody suggest me some sources for learning these models or clerify the misconception on my head ?

I have been discussing with several lab members about this one, and we have gone to several sources but still don't quite have the answer:  When we say a GLM has a family of poisson let's say are we talking about the distribution of the residuals or the response variable?  Points of contention   Reading  article it states that the assumptions of the GLM are The statistical independence of observations, the correct specification of the link and variance function (which makes me think about the residuals, not the response variable), the correct scale of measurement for response variable and lack of undue influence of single points  question has two answers with two points each, the one that appears first talks about the residuals, and the second one about the response variable, which is it? In this , when talking about assumptions, they state "The distribution of the residuals can be other, eg, binomial" At the beginning of  chapter they say that the structure of the errors has to be Poisson, but the residuals will surely have positive and negative values, how can that be Poisson?  question, which often is cited in questions such as this one to make them duplicated does not have an accepted answer  question the answers talk about response and not residuals In  course description from the University of Pensilvania they talk about the response variable in the assumptions, not  the residuals


I am self studying Abstract Algebra. At the beginning I picked Herstein's algebra book as my first introductory text but I wasn't able to solve half of the problems in the exercises so I decided to first go through an "easier" text and so I decided to study from J. Gallian's Contemporary Abstract Algebra .      Now I have finished reading this book and have solved 80-90% of the exercises from it. I believe I understand all the basic concepts now and can solve most of the standard exercises. I am now looking for a more advanced text (to strengthen my concepts) that covers the same material and the one I can go through on my own with a good collection of problems.       I have already checked out Herstein- and after understanding the theory well enough from Gallian and solving loads of problems from it, its problems do not scare me anymore.       I am thinking of Dummit foote. What do you guys think about it? Is this book alone sufficient to suit my needs?       Any other suggestions would be welcome.      Also please don't suggest more than two books- not only it make me confused over which one to read first, it is not possible for me to go through 3-4 or more books as I have to revise and study other subjects too but maybe later I can check them out.  Edit: It would be great if someone could tell me what do they think about Hungerford's algebra and P.Cohn's Basic Algebra? Would they satisfy all the conditions I stated above like having a nice collection of problems and good for self study and not too elementary. How do these two compare to Dummit foote?

Does anyone have any suggestions for abstract algebra books particularly suited to self-study?     Here is some background and motivation, if it's helpful.  I'm currently a junior in high school, but I have some familiarity with groups, rings, polynomials and fields, as I went through Fraleigh's book. I liked its writing style, but many of the problems were not helpful. I would like to get better at algebra with some other book, particularly one that's aimed at someone who already has a little familiarity with the objects, but is by no means completely comfortable.  One of my longer-term goals is to learn a bit of algebraic number theory, as I've only been studying elementary number theory. That's why I feel it  good to learn more algebra first. (I'd also be interested in suggestions of other good subjects to learn prior to tackling algebraic number theory.)  I was considering using one of Lang's books, since they seem pretty universal, but I've heard rumors that they are very terse and not good for self-learning.


Why are axions considered cold dark matter? They have a very low mass and if I'm not wrong they decouple before BBN, and in some models even earlier than neutrinos, they they should definitely be relativistic at the moment of decoupling and therefore Hot dark matter. So why aren't they cold dark matter?

Numerical simulations of observed large-scale structure formation work best with Cold Dark Matter (CDM; see the answer ). Neutrinos are candidates for Hot Dark Matter (HDM), and hence they cannot account for the total dark matter abundance of the Universe. By the same token, axions are also relativistic because they have very tiny masses. Aren't they also candidates of HDM like neutrinos? Shouldn't they also be disfavoured for the same reason?


I believe bipartite means you can split the vertices of a graph into 2 groups, where each vertex in the first is connected to all in the second (correct me if Im wrong) Does that mean every 2-colorable graph is bipartite? If not, what are some counterexamples, and an explanation why?

I've been stuck on this question for some time, can anyone please help me out with it...  Definition: A graph $G = (V, E)$ can be coloured with $k$ colours if $\forall v \in V$, $v$ is assigned exactly one of $k$ colours and $\forall e = (u, v) \in E$, $u$ and $v$ are coloured with different colours. Prove that a graph $G = (V, E)$ is bipartite if and only if $G$ can be coloured with 2 colours.


I have two macs, and at some point one of them stopped being able to log into Messages ( just the apple account ) and FaceTime.  The other mac worked fine, but was not using iCloud keychain ( at the time I did not realize this was the issue ).  Later, I activated iCloud keychain on the working mac and FaceTime stopped working there as well so I think this is related. De-activating iCloud keychain does not fix it.  Making a new account does, but this is a pain.  This started I think on Mavericks, and upgrading to Yosemite Beta hasn't fixed it.  My hunch is there is some keychain confusion going on, but I erasing any keychains related to apple hasn't helped either.  This apple discussion shows I'm not the only one, but nobody has a solution.    Any ideas?  Thanks!

On my OSX laptop (10.8.5) I've recently been unable to sign into iMessage. By recently I mean approximately a week. I've not done any updates that I recall lately.  Coworkers are able to send me messages and my phone gets the messages directly over iMessage, so my account is working on this network (wifi and wired go through the same set of equipment out to the internet, so it's not a port blocking issue, and we're a small network of about 50 users) and my account is working in general.  I can login to  just fine from my computer. I'm logging into the computer and my phone with the same gmail address and password in both places.  Next steps?  One solution on the internet was "do you have a serial number in "About This Mac" and I do.


I have this line of HTML:  <li class="col-xs-6 col-sm-6 col-md-2 filter active" data-filter=".office">   And i want to check if the  ".filter" has class ".active", if it has active class then i need to get its data attribute. I tried like this, but it alerts undefined  if($(".filter").hasClass("active")) {      var activeFilter = $(this).attr("data-filter");     alert(activeFilter); }   What I'm doing wrong?

I'm working with jQuery and looking to see if there is an easy way to determine if the element has a specific CSS class associated with it.  I have the id of the element, and the CSS class that I'm looking for.  I just need to be able to, in an if statement, do a comparison based on the existence of that class on the element.


Do I need a dweller in the storage room(s), or can I use the dweller elsewhere?

I've played Fallout Shelter for a while now and normally use dwellers with appropriate SPECIAL stats for each room (Strength in the reactor, Perception in the water supply, etc).  However, I have a question regarding Endurance. The only room which uses this is the storage room. It doesn't produce anything; it has no cooldown; it just does nothing...  Even if I just build and upgrade the warehouse, my stock capacity is increased. Is there any good reason for me to waste my dwellers by assigning them to storage rooms?


What is color?  “The property possessed by an object of producing different sensations on the eye as a result of the way the object reflects or emits light”…. You might say.  So take a white object and paint it “red”. What property of the paint now makes the object appear red?  “Pigmentation!” … you might say.  Good. Now that I’ve got you thinking in line with what I’m thinking, please help me understand what pigmentation actually is. I’m looking for an explanation that goes down to the microscopic level. What is it about the elemental structure of different pigmentation that alters the way that pigmentation (color) is seen by our eyes when applied over an object?

I understand that light (color) is part of the electromagnetic spectrum, and that it depends on what wavelengths are reflected/absorbed. Though what property of an individual atom gives it its color? Do electrons, neutrons, and other subatomic particles have color?  Basically: What intrinsic property causes the differences between how the varying wavelengths of light are reflected at the atomic scale? Also, how do photons factor into this?


I am wondering why the follow does not work:  template<typename Derived> struct Base0 {     const auto& derived() { return static_cast<const Derived& >(*this);} }  template<typename Derived> struct Base1: Base0<Base1<Derived>> {     auto foo () { return derived().foo_impl();} }  struct Foo: Base1<Foo>> {     auto foo_impl () { return "foo";} }   It complains  that derived() is not a member. Changing derived()  to this->derived() works, but I guess this will get Base1<Base0<Foo>>& instead of Foo& (which is not desired), right?  Alternatively, we can do the follow:  template<typename Derived> struct Base0 {     const auto& derived() { return static_cast<const Derived& >(*this);} }  template<typename Derived> struct Base1: Base0<Derived> {     // for some reason, "this->" is still needed here, why???      auto foo () { return this->derived().foo_impl();} }  struct Foo: Base1<Foo>> {     auto foo_impl () { return "foo";} }   But I am not sure if this is the conventional way of doing multilevel inheritance using CRTP. Any comments?

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I'm encountering what I'm sure is an encoding error but I can't seem to find the weak link in my logic.  In particular, when trying to insert a Greek lambda into my database, the cell is blank after the lambda.  The process:  Before any html is printed, I'm doing:  header('Content-Type: text/html; charset=utf-8');   Next, I'm connecting using PDO:  $dsn = 'mysql:host=' . $config['host'] . ';dbname=' . $config['dbname'] . ';charset=utf8';  $options = array(             PDO::ATTR_EMULATE_PREPARES => false,              PDO::ATTR_ERRMODE => PDO::ERRMODE_EXCEPTION         );         try {             $dbh = new PDO($dsn, $config['username'], $config['password'], $options);             $dbh->exec("SET NAMES utf8");             $dbh->exec("SET FOREIGN_KEY_CHECKS = 1");   When I do      SHOW FULL COLUMNS FROM my_table   I can see that the collation is utf8_general_ci. When I do:     echo mb_detect_encoding($data_to_be_entered);   I get UTF-8  When I echo out $data_to_be_entered into the console right before I insert it into the database, I see: (𝜆=23)  However, in my database, I just see ( as the entry.

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I want to create a link that takes me to the address' Google Street View. I found this:   The solution for the question above was:  Pennsylvania Ave SE, Washington, District of Columbia, 20003  Is there a parameter I can add to the link to make it automatically go to Street View?  I am currently using the arcgis World Geocoder in my application, so I will try to pass the address entered into the link to google Street View.      function locate() {       map.graphics.clear();       var address = {         "SingleLine": dom.byId("address").value       };       locator.outSpatialReference = map.spatialReference;       var options = {         address: address       }       locator.addressToLocations(options);     }   Thank you!

Hi I have the address of a property and my application can launch a browser to go to . If a good match is found it will take it directly there. Is there any thing I can append to the url to make it switch to streetview without having the exact coordinates? I dont't want to code any javascript or flash.


I am a java developer for three years but never thought about the underlying performance costs between different implementations of lists. That s why I make a benchmark like  :  private static int N = 10000000; public static void main(String args[]){     doSt(new ArrayList<String>());     doSt(new ArrayList<String>(N));     doSt(new LinkedList<String>()); }  private static List<String> doSt(List<String> fizzbuzz) {     long l = System.currentTimeMillis();     int counter = 1;     while(counter <= N){         fizzbuzz.add("aa");         counter++;     }     long l2 = System.currentTimeMillis();     System.out.println("time spent " + (l2-l)); }   and I see  time spent 148,  time spent 33,  time spent 198,   meaning that   time performance(ArrayList with initial capacity) > time performance(ArrayList) > time performance(LinkedList).   LinkedList and ArrayList is pretty close, since insertion is O(1) in both implementations, I am not bothered by the small difference.   BUT, if I change the implementation like :  private static int N = 10000000; public static void main(String args[]){     doStWithIfElse(new ArrayList<String>());     doStWithIfElse(new ArrayList<String>(N));     doStWithIfElse(new LinkedList<String>()); }  private static List<String> doStWithIfElse(List<String> fizzbuzz) {     long l = System.currentTimeMillis();     int counter = 1;     while(counter <= N){         if (counter %3 == 0 && counter %5 == 0){             fizzbuzz.add("FizzBuzz");         }         else if (counter %3 == 0){             fizzbuzz.add("Fizz");         }         else if (counter %5 == 0){             fizzbuzz.add("Buzz");         }         else{             fizzbuzz.add(Integer.toString(counter));         }            counter++;     }     long l2 = System.currentTimeMillis();     System.out.println("time spent " + (l2-l)); }   then,   time spent 516,   time spent 8452,   time spent 6808,  Then All of a sudden, ArrayList with the initial capacity becomes the poorest performer and ArrayList without the initial capacity beats them all with a big margin.   That really confused me a lot. What is the reason of performance changes when I introduce the if else statements?

How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related:


i'm trying to create a partition where it'd store an image of the OS with all the necessary software installed(i still need to find out how to do it) and an active VHD attached  something like this  +----------------------+--------------------+ | VHD file + image | SYSTEM (8.1)    | +----------------------+--------------------+ 　　| +-------+ | VHD     | +-------+ where the image and the VHD file would be hidden to the user so that they wouldn't be able to accidentally delete them  is there a way to do it?   it would cretaintly seem easy to just remove the partition path, and it'd be inaccessible, but upon reboot, the VHD drive would disappear

I am creating a system based on VHD. The partition is like this:  +----------+-----------+ | VHD file | User Data | +----------+-----------+ 　　| +------------+ |   SYSTEM   | +------------+  The system volume has a default drive letter C. Windows 7 automatically assign letter D for "VHD file" volume and E for "User Data" The "VHD file" volume also contains bootmgr and page file.   My purpose is to hide "VHD file" volume so that no page file will be located in it and user cannot see vhd file and boot directory in it.  Windows 7 doesn't allow to remove letter after OOBE because the page file is in it. (Thus, we have to relocate page file, restart, and remove letter).  So my guess is do it during OOBE or specialize pass.  The result should be like "SYSTEM RESERVED" 100MB partition -- no drive letter, no page file, but with key files in it.  Any ideas are welcome!


I have encountered this function while trying to construct a function that is discontinuous everywhere but has IVP.But the function is not clear to me.I need a proper explanation about the definition and graph of the function

Can you give a definition of the Conway base-$13$ function better than the one actually presented on , which isn't clear? Maybe with some examples?


I am a Linux/Ubuntu Noob and I have Saucy Salamander. Lately I installed the Android tablet emulator for Ubuntu using VirtualBox from the software center. I followed all the steps listed  but when I got down to the section where it says  "AndroVMplayer  The AndroVMplayer is a software used to display the VM content and manage its events. It won’t work if the VM is not running ! Open a command line interpreter, get to the AndroVMplayer directory, and type : AndroVMplayer [width] [height] [density]"  I have no clue how to navigate directories. Every place I go, it seems they expect people to just know this. I would like a step-by-step guide explaining each step to navigating to that particular directory. Somebody please help?

I am new to Linux and Ubuntu and have tried changing to folders/directories with some difficulty.  Could someone explain why the following commands failed to change to the desired target folder/directory?  sharon@sharon:~$ cd Home  bash: cd: Home: No such file or directory  sharon@sharon:~$ cd /Home  bash: cd: /Home: No such file or directory  sharon@sharon:~$ cd Documents  sharon@sharon:~/Documents$ cd Downloads  bash: cd: Downloads: No such file or directory  sharon@sharon:~/Documents$ cd /Downloads  bash: cd: /Downloads: No such file or directory  sharon@sharon:~/Documents$


I live in Resistencia, about 350Km away from Asuncion, the capital of Paraguay. And about 1000Km away from Buenos Aires, the capital of Argentina, my own country.  Let's assume I want  to go to Miami.  If I search flights originating from my city, most travel websites (Google Flights, Despegar, etc) will try to sell me tickets from Resistencia to Buenos Aires, and then to Miami. This will end up costing me 27.000 Argentine pesos. Usually this includes flights from Aerolinas Argentinas only, as it seems to be the lowest priced airline. The trip to Buenos Aires is usually 2000-2500 pesos for both tickets. So the bulk of the pricing is the international flight.  Instead, if I search for flights to Miami from Asuncion, Paraguay, I also get two flights (usually stopping in Lima or Panama), but the price is actually as low as 12.000 Pesos. There are no flights to Asuncion but it's a 5-6 hour bus ride.   Why is this difference so HUGE? I think maybe because the Aerolineas flight is a direct flight, and the others make a stop somewhere else.  Edit: this is, I think, a diffrent question from  because that one explains about "fine" pricing by airlines, simulations, etc. I don't think this is related, because that fine pricing is usually a few % points. This is a whooping 50% difference. There must be something different going on.

Based on the question , I got curious. Is there a guide or resource that describes how the price of a ticket is determined?  When you search you often see curious effects like cheaper tickets for a flight from A to B with a layover compared to a direct flight. This seems counter-intuitive from an outsider's perspective since you fly twice. Also one way tickets more expensive than 2 ways.  It can be a short set of rules. Something that helps someone to get started with finding good prices. I know these can be very complex and they probably change over time and over airline interests but there is probably a simplified set of rules that can be enunciated.


Often times there are multiple good comments on a question and you want to upvote them all. However, you can only do one every 5 seconds. I presume this is to prevent spam (especially from bots). However, based on how the rest of the site works, restrictions such as these are suppose to go away as the user gains more rep and becomes more trusted. So why not just have a point where the site says 'you are trusted enough to not upvote spam, so upvote as fast as you want`, though still have the limit of 30 per day?  Edit: Yeah, chaning the coment system to x every y seconds is an alternative answer, but Im something different - removal entirely based on rep. I think it would work better.

I quite often will read a thread of comments, and want to vote up a few of them. I vote one up, read the next few comments, vote up another and get a *giant red box*.  I've seen that "You can only submit a comment vote every 5 seconds" box far too often. Can I vote for 12 comments per minute, rather than 1 comment every 5 seconds?


I have this limit (derived from an improper integral in the larger problem) that WolframAlpha says equals zero. But it doesn't have the steps to get there. How indeed do I show this instead of waving my hands that we can apply l'Hospital's rule to infinity and the denominator will eventually win and the limit will approach zero.  Check form ($\infty * 0$): $$\lim_{t \to \infty} -t^{x}e^{-t}$$ Rearrange into $\frac\infty\infty$: $$= \lim_{t \to \infty} \frac{-t^x}{e^t}$$ Apply l'Hospital's Rule: $$= \lim_{t \to \infty} \frac{-xt^{x-1}}{e^t}$$ I don't see a clear way of showing this goes to zero, but zero is the correct answer.

Let $x>0$ be a constant. Show that $\lim_{z \rightarrow \infty} -z^xe^{-z} = 0$.  Do I apply L'hopital's rule here? It doesn't seem to help, for example, after one round of differentiating the numerator and denominator, I get $\frac{d}{dz} z^x = xz^{x-1}$ and $\frac{d}{dz}e^z = e^z$. I am unsure on how to proceed.


Upgraded to 19.04 today and have run into a problem:  I am able to access my flash drive from my username folder on my desktop and copy and paste back and forth to my Documents, etc. BUT, when I am in Inkscape, Gimp, Scribus, or any other software, I am not able to access at all - It says that I do not have permissions.  I have tried sudo chown user:user media/user/device with no change.  The strangest part is that I can access it and copy and paste when accessing through the user folder on my desktop - I just can't open it from within applications. Anyone know how to fix?

I have Ubuntu 18.04 LTS installed. I inserted USB-flash to my laptop. It was automounted to /media/username/DISKLABEL and opened in Nautilus. I can read and write objects to it. How can I access it from the application, which is installed as Snap? I tried snaps of the following applications such as gedit, arduino-mhall119, organize-my-files. All them show me errors if I navigate to /media folder:    Could not read the contents of Media Error opening the directory of '/media': permission denied  Output of active Snap  is below: $ snap interfaces  | grep -v ".*-$" Slot                             Plug :browser-support                 organize-my-files :core-support                    core:core-support-plug :cups-control                    gedit :desktop                         gedit,organize-my-files :desktop-legacy                  gedit,organize-my-files :gsettings                       gedit,organize-my-files :home                            arduino-mhall119,gedit,organize-my-files :network                         arduino-mhall119,gedit,organize-my-files,pulsemixer :opengl                          organize-my-files :pulseaudio                      organize-my-files,pulsemixer :unity7                          arduino-mhall119,gedit,organize-my-files :wayland                         gedit :x11                             arduino-mhall119,organize-my-files,pulsemixer gnome-3-26-1604:gnome-3-26-1604  gedit gtk-common-themes:gtk3-themes    gedit gtk-common-themes:icon-themes    gedit gtk-common-themes:sound-themes   gedit -                                arduino-mhall119:serial-port -                                gedit:avahi-observe -                                gedit:mount-observe  Updates:  connecting mount-observe to Gedit with snap connect gedit:mount-observe does not help. it seems that we need special Snap with support of  interface.


If I believe a fact, is that fact also my opinion? I'd always thought that opinion and fact are mutually exclusive. To me, 1+1=2 cannot be considered an opinion, as it is a fact.  Merriam-Webster has a few definitions of the word opinion, including one that seems to suggest that facts could also be considered opinions:     a view, judgment, or appraisal formed in the mind about a particular matter   and one that seems to support the idea that fact and opinion are mutually exclusive:     belief stronger than impression and less strong than positive knowledge

I've seen this so many times and it drives me crazy. The latest was the actor Paul Giamatti setting some story straight in the press about him: "It's unfortunately an incorrect fact about me and it's all over the place."  I've seen this written so many times, in magazines, books, but surely a fact is, by definition, true. So there cannot be any such thing as a "false" fact. Right?


$$\lim_{x\to \ 0}\frac{{(1+x)}^\frac{1}{x}-e+ex}{x^2}$$  Using Taylor Expansion, $(1+x)^{1/x}=e(1- \frac{x}{2} + \frac{11x^2}{24} + ...)$. Finally, I found that $$\lim_{x\to \ 0}\frac{{(1+x)}^\frac{1}{x}-e+ex}{x^2}=\lim_{x\to \ 0}\frac{\frac{ex}{2}+\frac{11ex^2}{24}+...}{x^2}$$  $$=\lim_{x\to \ 0}\frac{\frac{e}{2}+\frac{11ex}{12}+...}{x}$$  Now, It seems limit doesn't exist, but options are given for this question as  1) $\frac{11e}{12}$  2)$-\frac{11e}{12}$  3)$\frac{11e}{24}$  4)$-\frac{11e}{24}$. So How to proceed further?  Thank you.

$$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $$   (can this be duplicate? I think not) I tried it using many methods  $1.$ Solve this conventionally taking $1^\infty$ form in no luck  $2.$ Did this, expand $ {(1+x)^{\frac1x}}$ using binomial theorem got $\frac13$ then grouped coefficients of $x^0$ and it cancelled with $e$ then took coefficient of $x$ cancelled with $\frac{ex}{2}$ and so on   very messy right ? at last I got $\frac13$ but that's not the expected answer!  I must have went wrong somewhere can anyone help me with this.


Prove that if W is a subspace of V, then $dim(W)+dim(W^0)=dim(V)$, where $S^0$ is the annihilator defined by $S^0={f \in V^* |f(x)=0 \text{for all} x \in S}$    So for this problem, we are going to construct basis for W and $W^0$ such that $W \bigcup W^0$ generates V right?

Let $V$ be a finite dimensional real vector space with inner product $\langle \, , \rangle$ and let $W$ be a subspace of $V$. The orthogonal complement of $W$ is defined as   $$ W^\perp= \left\{ v \in V \,:\, \langle v,w \rangle = 0 \text{ for all } w \in W \right\}. $$   Prove the following: $\dim W + \dim W^\perp= \dim V$.   I'm not sure how to find the relationship between number of basis vectors in $W$ and $W^\perp$.


I am learning photography and looking to buy a flash. I learned the basics of the flash, and as far as I saw everywhere, the Guide Number had a feet unit with the ISO number; e.g. 160' at 100 ISO.  I came across this format and I don't know how to interpret it — it displays the feet, ISO and another distance. See for example   I don't understand what it means by 196.85' (60 m) ISO100 at 200 mm position or 190.29' (58 m) ISO100 at 105 mm position. Can someone please help me interpret this?

From this , I understand that the flash guide number (GN) is given by the following formula:  Guide Number = Shooting Distance × f-number ÷ ISO factor   I'm assuming that the GN calculated via the equation above will be based on a flash that is firing at full power. Am I correct to assume that if I set the flash to fire at half power, that the guide number is effectively halved? i.e. the equation will now be:  Guide Number = Shooting Distance × f-number ÷ ISO factor * Power Level   where power level can be the following 1, 1/2, 1/4, 1/8, ... 1/64, etc?


#include <stdio.h> void func1(char *a); int main() {         char *mStat="welcome home";         printf("Text before: (%s)\n",mStat);         func1(mStat);         printf("Text after: (%s)\n",mStat);         return 0; }   void func1(char *a) {         printf("Input: (%s)\n",a);         a[1]='a'; }   This program crashes with a segfault all the time in the line where I am modifying the character in the string. What is wrong with it ? What is the correct way of doing it ?

The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC.


I am trying to send the user to the mail app from my native app. I would like the embed a  tag into the body of the message. I know this is possible because the 'LOL Cats' app does it. I have been trying without success:      NSString *url1 = [NSString stringWithFormat:@"mailto:email@email.com?subject=Check%20Out%20This%20Faux%20Screen&body=<img%20src=\"http://www.sample.com/FauxFoneServer/screenShot/getScreenByID?cur=%@\"/>The%20awesome%20person%20who%20sent%20you%20this%20email%20thinks%20you%20should%20visit%20http://www.fauxscreen.com"                          ,[ScreenShotsAppDelegate sharedDelegate].viewController.curImage.imageID]; [[UIApplication sharedApplication] openURL:[NSURL URLWithString:url1]];

What's the best way of sending an email with an image from the application to the Mail.app for someone to send to any contact they like?  For example, in my app (iMood), you can select a 'mood', I'd like the user to be able to email this to a friend for example, by using a button in the navigation bar.  I can easily create the button etc. but just need to know a way to enable the user to send the image (ie. image.png) from the project to Mail.app as maybe an attachment or a picture in the email.  Thanks in advance.


I am 16 years old and I don't have any documents except my birth certificate and my students identity card is also expired. I am going to Kolkata to Imphal to apply for my adhar card. So how can I fly? Is there any way to fly?

I am travelling from Delhi to Indore, a domestic flight. I forgot to take ID proof. Can I still fly?


Before I begin let me preface this with the following: I understand that mechanically speaking the barbarian and Monk armor classes are calculated 10 + Dex mod + Wis/Con depending on the class played. My conundrum is this: One of my players is playing a Dragon Born Monk who just got to level 4, He has decided on  taking the racial feat Dragon Hide. The feat reads as:  You manifest scales and claws reminiscent of your draconic ancestors. You gain the following benefits: Your scales harden. While you aren't wearing armor, you can calculate your AC as 13 + your Dexterity modifier. You can use a shield and still gain this benefit.  Now the question: As monk uses Wisdom and Dexterity to calculate AC and as they don't wear armor or use shields anyway, is this just adding a +3 Natural Armor bonus to his base AC? I have seen some debate go back and forth saying that this would be legal while others are claiming that by taking the feat he is actually changing how his AC is calculated. Rather than the feat adding Natural Armor to his base AC. So the second part of the question is: If this is something doesn't work Would this be game breaking in someway? As it stands right now from my perspective I would have to say I am leaning slightly on the side of allowing it due to the nature of how he got the bonus. First he had to take the feat at 4th instead of an attribute increase, Second it does not clash with the concept of the monk who uses insight and agility to deflect/dodge incoming attacks, adding scales doesn't make one less insightful or less dexterous. But I am posting this because I am still on the fence. Please and than you for your insights.

In D&D 5E, does natural armor stack with Unarmored Defense? We have a level 2 player character who wild shaped into an animal. The player said they could stack its natural armor with Unarmored Defense, getting effectively 10 + natural armor + WIS + DEX = a super high AC. Does this work?


If I'm going to create video delivery site for big country (Russia), should I use CDN for video? I believe, that store video in two places, Tokyo (for East part of country) and Frankfurt (for West part of country) for example much cheaper than load videos to CDN. However, I'm a bit worry about video load speed, but should I? UPD. Sorry I'm not really good in this kind of questions. So, as for the tecnical details. I suppose that, it's will be quite big service. Most part of users based in one country. Our own servers output speed about 220Gb/s. From answer below, I understand that most likely I'll need cdn, but what parameters should I keep in mind while choosing?

This is a  about capacity planning for web sites. Related:      What are some recommended tools and methods of capacity planning for web sites and web-applications? Please feel free to describe different tools and techniques for different web-servers, frameworks, etc., as well as best-practices that apply to web servers in general.


If  $n = { \dfrac{a}{b} }$ , with $n$ ${ \in }{ \mathbb{N} }$, $a$ ${ \in }$ ${ \mathbb{N} }$, and $b$ ${ \in }$ ${ \mathbb{N^*} }$ , and if $a$ and $b$ are coprime, then does $b$ $=$ $1$ ? I can only see that as an option, but I'm not enirely sure. A little help ? Thanks.

Show that if $fd'=f'd $ and the pair $f, d $ are coprime, that is gcd($d,f $)=1, as is the pair $f',d' $, then $f=f' $ and $d=d' $.  This should be simple, but I couldn't verify it. Thanks in advance!


I am a citizen of the United States but next year I am going on exchange in Spain. My student visa will expire in the end of June but I want to travel around to visit friends and family I have in other countries within the Schengen Zone (ex. Denmark, Norway, Germany etc). I have tried reading other forums and questions with nearly the same type of question, but I still don't understand the answer. I know that under normal circumstances I can enter the Schengen Zone without a visa and travel within it for 90 days as a tourist. So after my visa expires, let's say I leave and go to Germany. Would that be okay or not? Because I didn't enter Spain/the Schengen Zone as a tourist until I leave Spain as a student. Is that logic correct?

I am an Australian currently on a Netherlands working holiday visa that ends in May next year. I would like to know if when my visa ends I then get another 90 days just as a regular tourist visa as I would like to do some more travel within Europe when my visa ends before going home to Australia.


What is the difference between "I did play " and "I played" according to the British English?

The two sentences here both indicate that, at some point in the past, I performed some work:   I did work I worked   What is the difference between these two sentences? Does constructing one with did and the other with a simple past change the meaning?


I'm new to CSS. I want to use the Helvetica Neue font in my little project. I have downloaded the .ttf file and I tried to insert it through the @font-face rule:  @font-face{     font-family:"Helvetica Neue Light";     src:url("contenuti/HelveticaNeue-Light.ttf"); /*That's where I put it*/ }   To apply it I used:  .xyz{     font-family:"Helvetica Neue Light";     /*...other things...*/ }   The problem is that neither Safari or Chrome display it  What could I do?

Is there a way to add some custom font on a website without using images,  or some other graphics?  For example, I was working on a wedding website, and I found a lot of nice fonts for that subject. But I can't find the right way to add that font on the server. And how do I include that font with CSS into the HTML? Is this possible to do without graphics?


I know that current is same in a series circuit becuase the current only has one path to flow but I'm confused on how resistors work in series. From what I've read is that current is the same before and after a resistor (Eg. if 500ma flow into a resistor 500ma flow out of the resistor) so what is the resistor actually limiting?

We know that when a resistor is connected in series , the current flowing through that resistor will be constant.But how do we use a resistor to limit the current flowing through a circuit ,when resistor is connected in series with the circuit ?


First I'd like to thank everyone in advance for helping me - communities like this are exactly what amatuers like myself need when faced with perplexing issues.  I've recently begun virtualizing servers - on of which is a dns server running bind9 on debian 7.  My dhcp server correctly issues it as the primary dns for the network, but I just can't seem to get head or tail of why it isn't working.  Feel free to ask me for more info  Zone file (the email has been changed to hide my personal info)  ; BIND data file for kilraine zone ; $TTL    604800 @       IN      SOA     kilraine.lan. myaddress.myemail.com. (                      2014060303         ; Serial                          604800         ; Refresh                           86400         ; Retry                         2419200         ; Expire                          604800 )       ; Negative Cache TTL          IN      A       192.168.1.2 ; @       IN      NS      dns.kilraine.lan @       IN      A       192.168.1.2  dns2    IN      A       192.168.1.1 dns     IN      A       192.168.1.2 dhcp    IN      A       192.168.1.3 main    IN     A      192.168.1.10   Reverse zone file  ; ; BIND reverse data file for kilraine.lan ; $TTL    604800 @       IN      SOA     kilraine.lan. myaddress.myemail.com. (                      3006201401         ; Serial                          604800         ; Refresh                           86400         ; Retry                         2419200         ; Expire                          604800 )       ; Negative Cache TTL ; @       IN      NS      dns. 1       IN      PTR     dns2.kilraine.lan 2       IN      PTR     dns.kilraine.lan 3       IN      PTR     dhcp.kilraine.lan 10      IN      PTR     main.kilraine.lan   And lastly my named.conf.local file.    // // Do any local configuration here //  // Consider adding the 1918 zones here, if they are not used in your // organization // include "/etc/bind/zones.rfc1918";  zone "kilraine.lan" {         type master;         file "/etc/bind/db.kilraine.lan"; };  zone "1.168.192.in-addr.arpa" {         type master;         file "/etc/bind/db.192"; };   I have restarted bind9 numerous times, and I have always gotten "OK".  I used the dnsutils tool 'dig' on both the server and a client, each return the following      ; <<>> DiG 9.8.4-rpz2+rl005.12-P1 <<>> kilraine.lan ;; global options: +cmd ;; Got answer: ;; ->>HEADER<<- opcode: QUERY, status: SERVFAIL, id: 46467 ;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 0, ADDITIONAL: 0  ;; QUESTION SECTION: ;kilraine.lan.          IN  A  ;; Query time: 2 msec ;; SERVER: 192.168.1.2#53(192.168.1.2) ;; WHEN: Mon Jun 30 21:53:41 2014 ;; MSG SIZE  rcvd: 30   I get the following error if I try to use dig kilraine.lan @dns.kilraine.lan  couldn't get address for 'dns.kilraine.lan': not found   Though I get the original dig output from "dig kilraine.lan @192.168.1.2"  Thanks - I REALLY appreciate any help!  Please, don't hesitate for more info!!!

I've recently begun virtualizing servers - one of which is a DNS server running BIND 9 on Debian 7.  My DHCP server correctly issues it as the primary DNS for the network, but I get the following error if I try to use dig kilraine.lan @dns.kilraine.lan  couldn't get address for 'dns.kilraine.lan': not found   Though I get the original dig output from dig kilraine.lan @192.168.1.2.  Details:  BIND 9 on Debian 7; Virtualized CT through Proxmox.  Zone file (the email has been changed to hide my personal info)  ; BIND data file for kilraine zone ; $TTL    604800 @       IN      SOA     kilraine.lan. myaddress.myemail.com. (                      2014060303         ; Serial                          604800         ; Refresh                           86400         ; Retry                         2419200         ; Expire                          604800 )       ; Negative Cache TTL          IN      A       192.168.1.2 ; @       IN      NS      dns.kilraine.lan @       IN      A       192.168.1.2  dns2    IN      A       192.168.1.1 dns     IN      A       192.168.1.2 dhcp    IN      A       192.168.1.3 main    IN     A      192.168.1.10   Reverse zone file  ; ; BIND reverse data file for kilraine.lan ; $TTL    604800 @       IN      SOA     kilraine.lan. myaddress.myemail.com. (                      3006201401         ; Serial                          604800         ; Refresh                           86400         ; Retry                         2419200         ; Expire                          604800 )       ; Negative Cache TTL ; @       IN      NS      dns. 1       IN      PTR     dns2.kilraine.lan 2       IN      PTR     dns.kilraine.lan 3       IN      PTR     dhcp.kilraine.lan 10      IN      PTR     main.kilraine.lan   And lastly my named.conf.local file.    // // Do any local configuration here //  // Consider adding the 1918 zones here, if they are not used in your // organization // include "/etc/bind/zones.rfc1918";  zone "kilraine.lan" {         type master;         file "/etc/bind/db.kilraine.lan"; };  zone "1.168.192.in-addr.arpa" {         type master;         file "/etc/bind/db.192"; };   I have restarted BIND 9 numerous times, and I have always gotten "OK".  I used the dnsutils tool 'dig' on both the server and a client, each return the following      ; <<>> DiG 9.8.4-rpz2+rl005.12-P1 <<>> kilraine.lan ;; global options: +cmd ;; Got answer: ;; ->>HEADER<<- opcode: QUERY, status: SERVFAIL, id: 46467 ;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 0, ADDITIONAL: 0  ;; QUESTION SECTION: ;kilraine.lan.          IN  A  ;; Query time: 2 msec ;; SERVER: 192.168.1.2#53(192.168.1.2) ;; WHEN: Mon Jun 30 21:53:41 2014 ;; MSG SIZE  rcvd: 30


I'll probably be scolded for this, but I couldn't find an appropriate answer here nor by seraching the internet (perhaps I need another way of phrasing the question). I use TeXLive 2020 on Debian Testing; I write primarily in Spanish and so I have need of the inputenc package to typeset accented characters, as in my name: Óscar. However, upon composing an introduction to LaTeX I accidentally forgot that I hadn't loaded this package and typed as if it had been loaded, and both the DVI and PDF outputs show accents! I compiled the following: \documentclass{article}  \begin{document} \title{Introducción a \LaTeX} \author{Óscar Guajardo} \date{} \maketitle  ¡Hola mundo! Esto es \LaTeX, un sistema de composición de documentos; estas páginas son parte de un DVI.   Ça va? È posto! Weierstraß. Łódź. \end{document}  I attach the output below; as you can see, it shows all the "special characters" without having loaded inputenc; I wrote the above code on a Bash terminal using nano, but the output is reproducible with TeXstudio and TeXmaker. I am not complaining nor I want a "solution" (since there's no problem, quite the contrary). I'm just so used to loading inputenc to write in Spanish that I'd really like to know if it is now unnecessary. Thanks!

I am used to the fact that LaTeX will only know letters like ä, ö, ü, or ß if I use packages like  \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc}   Today, I tried LaTeX on a Mac for the first time, using the MacTeX distribution and texmaker. Without writing down any packages, all umlauts and ß were accepted correctly from scratch. Why is that and will the usage of special letters without using the packages cause any problems?


I know that there is no increasing function $f: \aleph_1 \to \mathbb{R}$, so it seems like for $\alpha < \aleph_1$, there should exists a function $f: \alpha \rightarrow \mathbb{R}$ that is strictly increasing.   I can't think of how this could be shown/constructed. Any ideas?

All countable ordinals are embeddable in $\mathbb{Q}$.  For "small" countable ordinals, it is simple to do this explicitly.  $\omega$ is trivial, $\omega+1$ can be e.g. done as $\{\frac{n}{n+1}:n\in \mathbb{N}\} \cup \{1\}$.   $\omega*2$ can be done as $\{\frac{n}{n+1}:n\in \mathbb{N}\} \cup \{1+\frac{n}{n+1}:n\in \mathbb{N}\}$, and $\omega*n$ as $\bigcup_{i\le n} \{i+\frac{n}{n+1}:n\in \mathbb{N}\}$  That immediately also gives $\omega^2$ as  $\bigcup_{i \in \mathbb{N}} \{i+\frac{n}{n+1}:n\in \mathbb{N}\}$  And going further is still relatively easy: We can biject the above embedding of $\omega^2$ onto a single interval $(0,1)$, e.g. through $f(x)=1-\frac{1}{x+1}$ since this is an order preserving bijection from $\mathbb{Q}^+$ to $(0,1)$, allowing us to get $\omega^2+n$, $\omega^2*n$ etc. And by iterating that process, we can get any ordinal below $\omega^\omega$.   But this sort of embedding fails at $\omega^\omega$ as the iteration of $f$ doesn't seem compatible with taking the infinite union - figuratively speaking, we'd squish things to $0$. So what would an explicit embedding of $\omega^\omega$ look like? And the question, then, is if it is possible to give an explicit embedding of $\epsilon_0$? Is the fact that Peano arithmetic cannot prove well-foundedness of $\epsilon_0$ an indication that it cannot be embedded by such elementary functions and their iterations?  And what about even bigger countable ordinals such as the Veblen ordinals, Feferman-Schütte, Bachmann-Howard? From its definition, even if the above all are possible, I assume that the definitive bound of where one can define an effective procedure for the embedding must be Church–Kleene - is that a correct conclusion?  Lastly, does the situation change when we use $\mathbb{R}$ instead of $\mathbb{Q}$, which would allow us to use, perhaps, more easily understood yet inherently complex functions?  Edited because $\omega^2 \neq \omega^\omega$


I'm working on a little text adventure, and when I try to have the player input a number to advance to a different part of the game, it only displays the last else statement. I'm having the number they input stored as a string so that the code works even if the player inputs letters. Here's the code I have for it //first question given to player, acts as tutorial     System.out.println("Type 1: Start Game");     System.out.println("Type 2: End Game");     String game = input.nextLine();      if(game == "1")     {         floorOne.enterMansion();     }     else if(game == "2")     {         System.exit(0);     }     else     {         variables.invalidAnswer();         menu();     }  Any help would be great, thanks!

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Do I partition Windows 7 hard disk before I install Ubuntu using disk utility in Windows 7? Or do I do it with my Ubuntu ISO CD after booting? And can I choose the size of the partition using Ubuntu ISO CD?

Following is the layout of the current partitions of my single hard drive viewed from Windows 7:   C: has Windows 7 system files and my personal data; Q: for Lenovo recovery; SYSTEM_DRV: for Windows boot files;   My goals are:   to create another partition D: for my personal data, and dedicate C: for Windows system files and applications only. to install Ubuntu alongside Windows. D: will be shared between the two OSes.   My questions are:   Is it correct that the free space generated from shrinking C: will only be able to create an extended partition, since there are already 3 primary partitions? So must D: be one logical partition on the extended partition, just as the partitions for Ubuntu will be? Will this be bad sometime? If yes, other better solutions? What are the good utilities to accomplish the partition tasks? Can Ubuntu installer solely handle them? Or better to have some of the jobs done in Windows with some recommended softwares?   Thanks and regards!


I have two HDDs: the first of 150gb (/dev/sdc) with 30gb in use, the second of 100gb (/dev/sdd). There are sdc1 and sdd1 partitions with the same format.  I want to clone the 30gb from the first disk to the second with differences sizes. What is the best way? Clone it with dd or with cat?  Two possibilities:  From the sdc disk:  dd if=/dev/sdc of=/dev/sdd cat /dev/sdc >/dev/sdd   From the sdc1 partition:  dd if=/dev/sdc1 of=/dev/sdd1 cat /dev/sdc1 >/dev/sdd1     Other questions:   Assuming that /dev/sdd1 already exists with data, could I overwrite it?  Could it cause an error in a sector of the hdd /dev/sdd?

How to clone a harddisk to a smaller sized one.   Clonezilla is great but it doesn't support such functionality. Also dd and PartImage don't support this demand. rsync will not copy the MBR since an MBR is not a file.   I need to clone a HDD not to take a backup, so rsync is not an acceptable answer.  Any suggestions?


From Statistical Inference of Casella, a conditional pdf is obtained through the joint pdf by the following equation, (1) $$ p_a(x_a | x_b) = \frac {p(x_a, x_b)}{p_b(x_b)} $$ In section 2.1.3 of PRML, the author did not mention explicitly the equation, but I guess he using the same approach. The author obtain the conditional mean and covariant matrix by directly manipulating the quadratic form of the exponent of the joint pdf. I understand how he obtain the conditional mean and covariant matrix, but since he does not explain how to obtain the corresponding Gaussian pdf, I have no idea if that pdf is equal to (1). This are the derived conditional mean and covariant matrix derived from the joint pdf, and other relevant vectors and matrices The result conditional mean of $x_a$, given $x_b$ $$ \mu_{a|b} = \mu_a - \Lambda_{aa}^{-1} \Lambda_{ab} (x_b - \mu_b) \\ $$ The resulted conditional covariant matrix $$ \Sigma_{a|b} = \Lambda_{aa}^{-1} \\ $$ The random vector $$ x = \binom{x_a}{x_b} \\ $$ The joint mean $$ \mu = \binom{\mu_a}{\mu_b} \\ $$ The joint covariant matrix and its inverse $$ \Sigma = \begin{bmatrix} \Sigma_{aa} & \Sigma_{ab}\\  \Sigma_{ba} & \Sigma_{bb} \\ \end{bmatrix} \\ \Lambda = \Sigma^{-1} = \begin{bmatrix} \Lambda _{aa} & \Lambda _{ab}\\  \Lambda _{ba} & \Lambda _{bb} \\ \end{bmatrix} \\ $$ The quadratic form of the exponent of the joint pdf $$ (x - \mu)^T \Sigma (x - \mu) $$ (2) The general multivariate Gaussian pdf on a random vector $X \in R^D$ $$ N(x | \mu, \Sigma) = \frac{1}{(2\pi)^{0.5D}} \frac{1}{|\Sigma|^{0.5}} \exp\big(-0.5(x-\mu)^T \Sigma^{-1} (x-\mu) \big) $$

I've been reading over this , trying to make sense of how the mean and variance of a gaussian conditional was derived. I've come to accept that unless I allocate a dozen or so hours to refreshing my linear algebra knowledge, it's out of my reach for the time being. that being said, I'm looking for a conceptual explanation for that these equations represent: $$\mu_{1|2} = \mu_1 + \Sigma_{1,2} * \Sigma^{-1}_{2,2}(x_2 - \mu_2)$$ I read the first as "Take $\mu1$ and augment it by some factor, which is the covariance scaled by the precision (measure of how closely $X_2$ is clustered about $\mu_2$, maybe?) and projected onto the distance of the specific $x_2$ from $mu_2$." $$\Sigma_{1|2} = \Sigma_{1,1} - \Sigma_{1,2} * \Sigma^{-1}_{2,2} * \Sigma_{1,2}$$ I read the second as, "take the variance about $\mu_1$ and subtract some factor, which is covariance squared scaled by the precision about $x_2$." In either case, the precision $\Sigma^{-1}_{2,2}$ seems to be playing a really important role. A few questions:  Am I right to treat precision as a measure of how closely observations are clustered about the expectation? Why is the covariance squared in the latter equation? (Is there a geometric interpretation?) So far, I've been treating $\Sigma_{1,2} * \Sigma^{-1}_{2,2}$ as a ratio, (a/b), and so this ratio acts to scale the (second) $\Sigma_{1,2}$, essentially accounting for/damping the effect of the covariance; I don't know if this is valid. Anything else you'd like to add/clarify?


I am new to the DBA Part.  I had an 110 GB Database from which I deleted records from a 95GB sized table. Since the SQL Server Stores memory for the future, it still had 110 GB on the disc.  I ran the Shrink Database through GUI, but it was taking a lot of time. So, I cancelled it, but it remained in the greyed state. When shown from sys.sysprocesses, it shows the last batch time some 3 hours ago and is in runnable state. Can I kill the SPID?  To make it worse, Database is in multi-user mode.  Update: After three long hours, the process got rolled back on its own.

I have only 2GB left, so I need to remove this history table. This table now is empty but the database disk space not released. And the database file is 320GB.


I want to install the class found at this git repository:   I see some questions asked in the past on installing packages in LaTeX but this sounds like a different kind of file than a .cls file.  My impression is that packages come in either a .ins or a .dtx file which I would assume you don't use the same way as a .cls file.  I believe I'm using TeXlive, and although I often compile through Sublime Text 2 I also have TeXWorks which can often be simpler to install packages I don't already have.  A couple months ago I installed the latest version of TeXlive, though in my local directories (C:/users/Me/...) I have no folder for texlive2015.  I have a folder, /.texlive2013 and another one, /TeXWorks.  In my shared directories (C:/texlive/...) I do have a folder, 2015.  My operating system is Windows 10.  In trying to figure this out on my own I've seen reference to a "texmf" structure, and I've tried googling and learning about it but I'm still not getting a very clear picture of it since my directories don't seem to make a lot of what I see in those pages.  What I do have are things like C:/texlive/2015/texmf-dist/ and C:/users/Me/.texlive2013/texmf-config.    So anyway, back to my question, can anyone tell me how I go about installing the class file?  [Update: Due to a recommendation in the comments I followed another question and made the directory C:/Users/Me/texlive/texmf/tex/latex/commonstuff/ and put the .cls file in there.  Then I made the minimal example .tex file as follows  \documentclass{homework} \begin{document} Text \end{document}   and in Sublime Text 2 it gave me the error 4: LaTeX Error: Missing \begin{document}. [<].  In TeXWorks it gave basically the same error.]

I know how to define a package or a class, but how do I make it available (to myself) at all times?  Say I have the package file commonstuff.sty (or myprettyclass.cls), that I want to be able to include in any .tex file I create on my computer. Where do I put it? Do I need to run some installer on it, or is it enough to keep it in a certain folder?  Note: I know I can just place it in the same folder as the .tex file, but that's not what I'm after here. I'm looking for a way to "install" the package centrally on my computer.


So I just ordered a new phone (Honor 5x) I need to know can I install an early version of Nougat & when its released will it operate on my phone? Thanks!

Android Nougat .  It adds features such as multi-window support.  You can review the high-level changes at .  Of course, not all devices will get this update right away, even at release; others won't get it at all. Manufacturers and carriers often choose to add their own custom modifications, which tend to delay the official release.  When will each device get Nougat, either officially or unofficially, if ever?  See also:


I posted this question earlier, and was wondering if somebody could help me answer it:    Thanks in advance!

Let $F$ be a field and $u\in F$. Further, let $F\subset G$ be a finite extension and $v\in G$ such that $v^n=u$ for $n>0$.     How would I show that there exists a $\tilde{u}\in F$ such that $u^{[G:F]}=(\tilde{u})^n$?   My first thought was to use the norm map $N_{G/F}(x)=\Pi_{\sigma\in X(G/F)}\sigma(x)$, where $X(G/F)$ is the fundamental set for $F\subset G$. However, I wouldn't know how to continue on this path.