Let $H$ a Hilbert space.   Q1) Does $H$ has an orthogonal/orthonormal basis ? I know that it's true if $H$ has finite dimension, but what happens in infinite dimension ? Because Gramm-Schmidt is not applicable anymore...   Q2) If the answer to my previous question is yes, does it still hold if we suppose $H$ being only an inner space (with infinite dimension) ?

The problem is to prove that every Hilbert space has a orthonormal basis. We are given Zorn's Lemma, which is taken as an axiom of set theory:  Lemma If X is a nonempty  with the property that every  of X has an upper bound in X, then X has a maximal element.   Given a orthonormal set $E$ in a Hilbert space $H$, it is apparently possible to show that $H$ has an orthonormal basis containing $E$.   I tried to reason as follows: Suppose $E$ is a finite set of $n$ elements. Then one can number the elements of $E$ to create a totally ordered set of orthonormal elements. Then the span $<E>$ can be identified with $R^n$, where each element $v = v_1 e_1 + v_2 e_2 + ... + v_n e_n$ is identified with the vector $(v_1, v_2, ..., v_n)$. On $R^n$ we have a total order, namely the "lexigraphical order" $(x_1,x_2,...,x_n) \leq (y_1,y_2,...,y_n)$ if $x_1 < y_1$ or if $x_1 = y_1$ and $x_2 < y_2$ or if $x_1 = y_1$, $x_2 = y_2$ and $x_3 < y_3$ and so on. Hence $E$ is a totally ordered subset of $H$ and $H$ is a partially ordered set. However, this set doesn't seem to have an upper bound. The set $E$ does have an upper bound. If we define a total order on $E$ only, then X is a partially ordered set satisfying the criteria so X has a maximal element?   This is as far as I got, and I am not sure the entire argument is correct. I don't see how what kind of maximal element I am seeking, since the orthonormal basis of a Hilbert space can have countably infinity number of elements.


Problem : Suppose that $f$ is continuous on $\mathbb{R}$. Show that $f$ and $\hat f$ cannot both be compactly supported unless $f=0$.  Hint : Assume $f$ is supported in [0,1/2]. Expand $f$ in a Fourier series in the interval [-,1], and note that as a result, f is a trigonometric polynomial.  I proved that f is trigonometric polynomial by using hint. But, I don't know how to prove function's fourier transform cannot compactly supported function.  Can I get some hints?

I am stuck on the following problem from Stein and Shakarchi's third book.   I can't figure out how to use the hint productively. Once I know $f$ is a trigonometric polynomial, I see how to finish the problem, but I don't know how to conclude that $f$ is a trigonometric polynomial.  I tried substituting in the Fourier transform in the formula for Fourier coefficients and switching the order of integration, but I couldn't get that to work. I can't think of any more ideas.  Problem: Suppose $f$ is continuous on $\mathbb{R}$. Prove $f$ and $\hat f$ cannot both be compactly supported unless $f=0$.  Hint: Suppose $f$ is supported in $[0, 1/2]$ and expand it in a Fourier series in $[0,1]$. Show $f$ must be a trigonometric polynomial.  This question was asked before, but with different hypotheses and in the context of complex analysis. Please do not close as a duplicate.


I installed Firefox on my Mac. The problem is that upon launching it, the title bar of the window appears stuck below the macOS Menu bar and hence is inaccessible.    I tried to zoom in and out, but it only zoom's the content. I'm unable to resize the window. Any ideas how can I fix this?

I encountered a strange problem today. I downloaded FileZilla and on first launch the title bar was above my mouse pointer's reach. Making the window unmovable.  Here is a screenshot of my situation.    Is there a way to fix this? I've tried reopening the application and rebooting.


When I open terminal, the start text like:  maryam@laptop: $   doesn't appear in the first line of terminal. Also any command like cd or ls doesn't work. I can't do anything in my terminal.  How can I fix it?

I've closed the terminal killing a process, after that when opening a new terminal the prompt wasn't there.  After searching online other questions, with CTRL-C y get the prompt back. However, when opening a new terminal the prompt is gone again.  I've tried the following code:  ^Cmartin@martin-N550JV:~$  martin@martin-N550JV:~$ ps   PID TTY          TIME CMD 17626 pts/0    00:00:02 bash 20957 pts/0    00:00:00 ps martin@martin-N550JV:~$ sudo kill 20957 [sudo] password for martin:  martin@martin-N550JV:~$ sudo kill 17626 martin@martin-N550JV:~$    Taken from this   I've also uninstalled and then re-installed the terminal, with no success.  Is there a solution for this?


I must write a class Person with 3 attributes (Name,Surname,Age) in all his instances. How can i set it that it cant be possible to add more attributes? class Person:    def __init__(self,name,surname,age):         self.name=name         self.surname=surname         self.age=age

What is the purpose of  in Python — especially with respect to when I would want to use it, and when not?


If a there's a new user with less than 50 reputation Stack Overflow must hide the "add comment" option instead of displaying a popup saying: "You need 50 reputation to comment". And then if the user reaches 50 reputation it must show a notification saying something like: "You have been enabled to comment".  So the "add comment" option will only show if the user has 50 reputation.

On Drupal Answers, there are many 1-reputation users with an unregistered account who write a comment, or a different question as answer. The fact they don't see an "add comment" link, and they see a text area where they can start to write, doesn't probably help.  I understand that not showing immediately a text area where to write an answer could probably be a wall for new users (although I think it would be clear what the purpose of an "Add your answer" button is), and I am not going to suggest that. I think that showing an "add comment" link that shows a dialog box explaining why the user cannot add a comment, and that comments written as answers are going to be deleted could probably help.   The link could also be disabled, and show a tooltip explaining to the users why it is disabled. That is what is done on meta sites when users cannot edit (or suggest edits for) posts written by other users:


I am getting this error on using a custom font. I have tried using the code in MainActivity and the Respective xml activity(Enquiry) too ( in this case there's no error but the font wont apply).  MainActivity  public class MainActivity extends AppCompatActivity         implements NavigationView.OnNavigationItemSelectedListener {     WebView webView;    TextView tv_appname;     Typeface typeface;      @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_main);         String fontpath="font/batman.ttf";         tv_appname=(TextView)findViewById(R.id.tv_appname);         typeface= Typeface.createFromAsset(getAssets(),fontpath);         tv_appname.setTypeface(typeface);   Acitivity Enquiry(In which the text is placed whose font I want to change)  <LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"     xmlns:app="http://schemas.android.com/apk/res-auto"     xmlns:tools="http://schemas.android.com/tools"     android:layout_width="match_parent"     android:layout_height="match_parent"     android:background="@drawable/bg"     tools:context="mayank2511.galgotiasuniversity.EnquiryActivity"     android:id="@+id/nav_enq"     android:paddingLeft="20dp"     android:orientation="vertical">     <TextView         android:layout_width="match_parent"         android:layout_height="wrap_content"         android:text="Enquiry Form"         android:textSize="34sp"         android:textColor="#fff"         android:id="@+id/tv_appname"         android:layout_marginTop="10dp"         android:gravity="center"/>   Enquiry Activity (incase it helps- it's commented rn)  public class EnquiryActivity extends AppCompatActivity {    /* TextView tv_appname;     Typeface typeface; */     @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_enquiry);         /*String fontpath="font/batman.ttf";         tv_appname=(TextView)findViewById(R.id.tv_appname);         typeface= Typeface.createFromAsset(getAssets(),fontpath);         tv_appname.setTypeface(typeface);         getSupportActionBar().hide();*/         getWindow().setFlags(WindowManager.LayoutParams.FLAG_FULLSCREEN,WindowManager.LayoutParams.FLAG_FULLSCREEN);     } }

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?


I'm trying to return the file selected by the user. That works fine. I can check fileToOpen in openFile and it is 100% correct, but when I sysout it in the main method I just get null. I want the path that the user has selected.   This is the main class:      public class Main {      public static void main(String[] args) {          File fileToOpen = null;          ReadIn openLog = new ReadIn();          openLog.openFile(fileToOpen);          System.out.println(fileToOpen);      } }   This is the ReadIn class:  public class ReadIn extends JFrame{       public File openFile(File fileToOpen){          final JFileChooser fileChooser = new JFileChooser();         int modalToComponent=fileChooser.showOpenDialog(this);         if (modalToComponent == JFileChooser.APPROVE_OPTION) {             fileToOpen = fileChooser.getSelectedFile();                  }          return fileToOpen;      }  }

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


Consider this simple debian package:  (to inspect you'll have to click the download link for Linux). After unpacking, it has the following file structure:  ├── opt │   └── Wolfram │       └── WolframScript │           └── bin │               └── wolframscript └── usr     ├── local     │   └── share     │       └── man     │           └── man1     │               └── wolframscript.1     └── share         ├── icons         │   └── hicolor         │       ├── 128x128         │       │   └── mimetypes         │       │       └── application-vnd.wolfram.wls.png         │       ├── 32x32         │       │   └── mimetypes         │       │       └── application-vnd.wolfram.wls.png         │       └── 64x64         │           └── mimetypes         │               └── application-vnd.wolfram.wls.png         └── mime             └── packages                 └── application-vnd.wolfram.wls.xml   The only relevant file is the opt/Wolfram/WolframScript/bin/wolframscript binary (I think). I tried executing this plainly but I get a bash: ./wolframscript: No such file or directory error. How do I make this binary/package usable in NixOS?  EDIT: To answer @muru's question:  $ file opt/Wolfram/WolframScript/bin/wolframscript opt/Wolfram/WolframScript/bin/wolframscript: ELF 64-bit LSB executable, x86-64, version 1 (GNU/Linux), dynamically linked, interpreter /lib   $ ldd opt/Wolfram/WolframScript/bin/wolframscript         linux-vdso.so.1 (0x00007fff767c9000)         libpthread.so.0 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib/libpthread.so.0 (0x00007f55b8525000)         librt.so.1 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib/librt.so.1 (0x00007f55b831d000)         libdl.so.2 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib/libdl.so.2 (0x00007f55b8119000)         libstdc++.so.6 => not found         libm.so.6 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib/libm.so.6 (0x00007f55b7d84000)         libgcc_s.so.1 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib/libgcc_s.so.1 (0x00007f55b7b6e000)         libc.so.6 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib/libc.so.6 (0x00007f55b77ba000)         /lib64/ld-linux-x86-64.so.2 => /nix/store/7gx4kiv5m0i7d7qkixq2cwzbr10lvxwc-glibc-2.27/lib64/ld-linux-x86-64.so.2 (0x00007f55b874400

What are the different methods to run a non-nixos executable on NixOs? I'd like to see also the manual methods.


I'm trying to call a command from a variable in a script with a specific locale, example :  $ myYTDL="LANG=C.UTF-8 youtube-dl --get-filename"   but each time I try and call it in the script, I get :  $ $myYTDL $url LANG=C.UTF-8: command not found   How can I do that ?

$ ls -l /tmp/test/my\ dir/ total 0   I was wondering why the following ways to run the above command fail or succeed?  $ abc='ls -l "/tmp/test/my dir"'  $ $abc ls: cannot access '"/tmp/test/my': No such file or directory ls: cannot access 'dir"': No such file or directory  $ "$abc" bash: ls -l "/tmp/test/my dir": No such file or directory  $ bash -c $abc 'my dir'  $ bash -c "$abc" total 0  $ eval $abc total 0  $ eval "$abc" total 0


I've seen the behavior on occasion and are a bit curious of the ruling. How can a post be marked as a duplicate of post which wasn't there at the time of the original post? The most recent example I've seen is this:    Posted February 12 and marked as a duplicate of    Posted March 14.  I'm told its because the second post had better answers. I'm curious if this is correct. Shouldn't the answers on the later question be merged to the first one, which is the original one?

I have seen this many times, a question is being asked because a previous, duplicate question was asked and answered a few years ago and has no longer relevant answers.  The  is to edit the old question, or add new answers to it, but it is not always happening.  I was wondering, should I still mark it as duplicate and vote to close it? Or just leave it as is?


Here is the percentage of normal forms among fertile mens according to the centile (Source: Cooper et al. 2010):   2.5: 3%  5 (below this is Teratozoospermia): 4% 10: 5.5% 25: 9% 50 (median): 15% 75: 24.5% 90: 36% 95: 44% 97.5: 48%   Men who have less than 4% of their sperm that have normal morphology are diagnosticated with Teratozoospermia (also called Teratospermia) and are likely to be infertile, though technically 5% of fertile men have Teratozoospermia.  I read on the internet that abnormally-shaped sperms are bad and useless because their abnormal shape prevents transport through the cervix and/or prevents them from adhering to the ovum.  But I think that if they were really that bad, Mother Nature would not have engineered the average men with 85% of their sperm abnormally-shaped.  And I also heard that even animals have a big fraction of their sperm that are abnormally-shaped.  So, in men, why do over 80% of sperm have abnormal form?

If a trait would be advantageous to an organism then why hasn't it evolved yet?  Conversely, if a trait is not advantageous or mildly disadvantageous, why does it exist?  In other words why does evolution not make the organism more "perfect"?    This is a general question that would be applicable for any kind of trait. Please keep the answers precise and scientific.   Read this meta post for more information:


In any SE site, from my account page, I can see things I flagged. But in Area51, I can't see such option in my account page. How can I see the history of my flags or what action were taken etc.?

Why is there not a flag count for Area 51? As a user that likes to help out on SO as much as possible, I enjoy to see my flag count on the different sites, so that I can see what I need to improve on, and so that I can also see how accurate I am at flagging questions/answers. So can the flag count be implemented on Area 51, like it is on every other Stack Exchange site?


I am relatively new to the Java Swing library and I am attempting to write a program that detects a mouse hover event and shows a popup. I am using the mouseEntered event, however it is only being triggered when the mouse enters from outside the entire frame, as opposed to hovering over different components within the frame. Is there anyway I can fix this?

I have a JComponent that's painting various shapes on itself.  I'm detecting whenever the mouse enters one of these shapes and changing the tooltip accordingly.  The problems I'm having are:   The tooltip doesn't follow the mouse as the user tracks the mouse across the shape. It  stays where it was first set and then only jumps whenever another shape changes the tooltip. It takes about a second for the tooltip to appear, but I'd like it to appear immediately.   Can someone suggest a way of getting these behaviours without writing a custom tooltip mechanism?


As I understand, magnetic materials (ferromagnets, paramagnets and diamagnets) appear due to the polarization of it atoms or molecules. In other words, they exist because their atoms or molecules are polarized. This means that every magnet is just a consequence of the existence of electric dipoles.   From this statement it seems obvious that there cannot exist a magnetic monopole, since the very definition of magnetic field needs a dipole to be there. My question is, why then postulate the existence of a magnetic monopole? How would a magnetic monopole be different to a single electric charge?

One thing I've heard stated many times is that "most" or "many" physicists believe that, despite the fact that they have not been observed, there are such things as magnetic monopoles.  However, I've never really heard a good argument for why this should be the case. The explanations I've heard tend to limit themselves to saying that "it would create a beautiful symmetry within Maxwell's equations" or similar. But I don't see how the fact that "it would be beautiful" is any kind of reason for why they should exist! That doesn't sound like good science to me.  So obviously there must be at least another reason apart from this to believe in the existence of natural magnetic monopoles. (I'm aware that recent research has shown that metamaterials (or something similar) can emulate magnetic monopole behaviour, but that's surely not the same thing.) Can anyone provide me with some insight?


I need to login to a user that I've created on a remote host running Ubuntu. I can't use an ssh key because the ssh login will happen from a bash script ran within a server that I won't have access to (think continuous integration server like Bamboo).   I understand this isn't an ideal practice, but I want to either set the remote host to not ask for the password or be able to login with something like ssh --passsword foobar user@host, kind of like MySQL allows you to do for logins.   I'm not finding this in man ssh and  I'm open to any alternatives to getting around this issue.

I tried writing a shell script which can do automatic login into a ssh server using password which is mentioned in the script. I have written the following code:  set timeout 30 /usr/bin/ssh -p 8484 root@172.31.72.103 expect  {    "root@172.31.72.103's password"     {       send "password\r"     } }   This code is not running properly, still it is asking for the password. Can somebody please help me in solving this


The following MCE points out that it is possible to make the listings' line numbers non selectable (thanks to the accsupp package) in case of the beamer class.  But, in case of the standard classes (e.g. article) and if hyperref is used, the following error is thrown:  ! TeX capacity exceeded, sorry [input stack size=5000]. \normalfont  ...ault \seriesdefault \shapedefault                                                    \relax  l.18 Foo   Do you know why and how to circumvent this limitation?  \documentclass{beamer} % \documentclass{article} \usepackage{listings} \usepackage{accsupp} \usepackage{hyperref} % \DeclareRobustCommand\nonselectable[1]{%   \BeginAccSupp{method=plain,ActualText={}}#1\EndAccSupp{}% } \renewcommand*\thelstnumber{%   \nonselectable{\the\value{lstnumber}}% } % \begin{document} \begin{lstlisting}[numbers=left] Foo \end{lstlisting} \end{document}

This question is related to the answer to the question   Unless you turn hyperref off, the following MWE   \documentclass{article}  \usepackage{listings} \usepackage{accsupp} \renewcommand*{\thelstnumber}{\protect\BeginAccSupp{ActualText={}}\arabic{lstnumber}\protect\EndAccSupp{}}  \lstset {     language={[LaTeX]TeX},     numbers=left,     columns=flexible, }  \usepackage{hyperref}  \begin{document}  \begin{lstlisting} Hello\\ Universe! \end{lstlisting}  \end{document}   cannot be compiled with the following error message:    How do I prevent conflicts between accsupp and hyperref?


Consider this simple function I am trying to add in my .aliases (dnf is Fedoras newest replacement of Yum):  function abc() {     dnf search something }   It works well on Bash but I get the following problem on zsh:  dnf:1: maximum nested function level reached   What can be the cause of this problem?    $ type -a dnf dnf is /usr/bin/dnf dnf is /bin/dnf

How can I write a function in zsh that invokes an existing command with the same name as the function itself? For example, I've tried this to illustrate my question:  function ls  {     ls -l $1 $2 $3 }   When I execute it with ls * I get the following:  ls:1: maximum nested function level reached   I assume this is because the function is being called recursively. How I can avoid that?  This is a crude example, and in this case an alias would do the job, but I have a more complex example where an alias isn't suitable and so I would need to write a function.


So we know that in the Potterverse they celebrate Christmas. Hopefully most people on here know the original reason for Christmas is the supposed birth of Jesus.   What is Jesus considered to be when taken from a in-universe point of view? Is Jesus considered a wizard by the wizarding community or the author/narrator?   (It seems plausible seeing as most of his miracles would not be too difficult for a wizard such as Dumbledore, and other mystical/magical figures like Morgan le Fey or Merlin were shown to be wizards in-universe).

Every winter, Hogwarts students return home and celebrate Christmas with their families. However, given their extensive use of magic, it does not seem likely they'd understand Christianity the way muggles would.  How and why do wizards observe Christmas?


In hex calculations it's true that: 0x000000010e257a92 + 0x30 + 0x3E8 = 0x000000010e257eaa  you can try it on:  But In my program when I do the calculation I get different result which is x = 0x000000010e263f12 Why is this happening and how to fix? My code: MallocMetadata *next_node = node->next; MallocMetadata *prev_node = node->prev; MallocMetadata *x; if (prev_node)     x=prev_node + sizeof(MallocMetadata) + prev_node->size;  Please Note, In the example I test prev_node->size = 1000 and  sizeof(MallocMetadata)=48 where MallocMetadata is a class.

Does anyone have any good articles or explanations (blogs, examples) for pointer arithmetic?  Figure the audience is a bunch of Java programmers learning C and C++.


I want to save some typing when I use a comon style for my tables.   But because \caption and \label have to be used inside the float, I want to pass the values for these macros via arguments into my envrionment.  I want to keep these inside the end code of my environment, to easily keep the caption at the bottom of the table.  Here is the MWE to my problem:  \documentclass[     fontsize=12pt,     a4paper ]{scrreprt}   \newenvironment{bordertab}[2]     {         \begin{table}             \centering             \begin{tabular}{| l c r |}                 \hline     }     {                 \hline             \end{tabular}             \caption{#1}             \label{tab:b:#2}         \end{table}     }   \begin{document}     \begin{bordertab}{A table with a border}{ex1}         1 & 2 & 3 \\         4 & 5 & 6 \\         7 & 8 & 9 \\     \end{bordertab} \end{document}   and the errors which LaTeX throws at me when using it:  ! Illegal parameter number in definition of \reserved@a. <to be read again>                     1 l.28 ^^I\end{bordertab}  You meant to type ## instead of #, right? Or maybe a } was forgotten somewhere earlier, and things are all screwed up? I'm going to assume that you meant ##.  ! You can't use `macro parameter character #' in restricted horizontal mode. <argument> \ignorespaces ##                            1 l.28 ^^I\end{bordertab}  Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'.  ! You can't use `macro parameter character #' in restricted horizontal mode. <argument> \ignorespaces ##                            1 l.28 ^^I\end{bordertab}  Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'.  ! Illegal parameter number in definition of \reserved@a. <to be read again>                     2 l.28 ^^I\end{bordertab}  You meant to type ## instead of #, right? Or maybe a } was forgotten somewhere earlier, and things are all screwed up? I'm going to assume that you meant ##.

Environments are allowed to have arguments, but reference to those arguments can only appear in the opening code of the environment, and not the closing code.  What is the reason for this, and are there preferred ways around it?  e.g.  \newenvironment{foo}[1]% {some code #1} % allowed {some code #1} % not allowed


I need to obtain today's date but instead of current time I need the first time of the date.   WRONG WAY:   '4/7/2017 4:50:13 PM'    as result of getdate() function  RIGHT WAY:   '4/7/2017 00:00:00 AM'   Thanks for your help

SELECT GETDATE()   Returns: 2008-09-22 15:24:13.790  I want that date part without the time part: 2008-09-22 00:00:00.000  How can I get that?


Prove the estimate $$\binom{n}{k} \le \left(\frac{en}{k}\right)^k$$ directly from $$e\left(\frac{n}{e}\right)^n \le n! \le en\left(\frac{n}{e}\right)^n.$$

This is from page 3 of  ().  Copying the relevant segment:     Stirling’s approximation tells us $\sqrt{2\pi n} (n/e)^n \leq n! \leq e^{1/12n} \sqrt{2\pi n} (n/e)^n$. In particular we can use this to say that   $$ {n \choose k} \leq \left(\frac{en}{ k}\right)^k$$   I tried the tactic of combining bounds from $n!$, $k!$ and $(n-k)!$ and it didn't work. How does this bound follow from stirling's approximation?


Can you help me to calculate this limit?  $$\lim_{x\to \infty}\Big[\sin(\sqrt{x+1}) - \sin(\sqrt{x}) \Big]= \:?$$  I don't have idea how to calculate it.

I want to compute $$\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}.$$  Is it OK how I want to do?    $$\sin{\sqrt{x+1}}-\sin{\sqrt{x}}=2\sin{\frac{\sqrt{x+1}-\sqrt{x}}{2}}\cos{\frac{\sqrt{x+1}+\sqrt{x}}{2}}=2\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}}\cos{\frac{\sqrt{x+1}+\sqrt{x}}{2}}$$  I'm not surem but I want to say that $$|\cos \frac{\sqrt{x+1}-\sqrt{x}}{2}| \leq 1$$ $$\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}} \to 0 \mbox{ when } x \to \infty$$ So the limit is $0$ ?  I thinks is not because  if I say that $ \displaystyle|\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}}| \leq 1$ I will obtain that another limit than $0$.   Thanks :)


I have seen several questions that discuss using your "Favorite" tags to construct a newsletter.   I'm looking for a similar request - but for ignored tags.  I figure it might make sense to split this request from the "favorite" requests because it has different implementation.  Can we exclude questions on the "ignore" tags lists in the newsletter?   For example, I subscribe to the Board and Card Games newsletter.   Currently (and frequently) 6 of the 7 questions are about magic-the-gathering, a tag I have in my ignored list.     I now get a newsletter where at best 1/7 questions is interesting and worth clicking on.  Related questions about using "Favorites":

Stack Overflow is huge and varied. Wouldn't it be great if I could just subscribe to a newsletter with a list of my favorite tags? If I love dealing with , I think it would make sense for my version of the newsletter to focus more on Android questions.  Or, if I sign up for the  newsletter, but don't own a Mac, it would be nice if I my newsletter would focus on the part of the site I do follow (i.e., iOS).  So I would like to suggest that the newsletters for each site (optionally) take into account the user's favorited and ignored tags for that site.  I know that you can receive emails about specific filters, but I don't think that's a good solution for users who already receive the newsletter. Most of the questions it highlights cover topics that I have no interest in. It would be much better if I could filter out all the noise and get down to my likely favorites.


From a little research done it seems as though they would create subatomic particles (maybe electrons?)If so, would photon collisions technically create matter? Is this a widely thought of theory?

Could someone explain to me what the collision of two photons would look like? Will they behave like,   Electromagnetic waves: they will interfere with each other and keep their wave nature Particles: they will bounce like classical balls   I assume that energy of that system is too small to make creation of pairs possible.


If a multiclass spellcaster has access to a certain level of spells from one class, can they cast at that level in other classes, too?  Eg, if you have a wizard 5/cleric 2, can they cast 2nd and 3rd level cleric spells? Or could a wizard 17/cleric 3 cast 9th level spells from either class, or only wizard?  Not a duplicate because the question flagged doesn't address what happens if one class has reached a certain level of spells and the other hasn't.

If I multiclass into 2 or more classes/subclasses that can cast spells, how do I determine what spells I know or can prepare?  For instance, if I am playing a multiclassed character with 1 level in warlock, 2 levels in bard, and 3 levels in paladin, how do I determine which spells I know/have prepared?    Related:


Is it normal practice to write code (JS/PHP) in feature?  I was thinking that feature should contains ONLY settings, however I've read that some developers write code there and they believe it's fine.  the reason why I ask I found a video on  where they write code in feature so I'm in doubt now.  Any pros and cons to that?

Does anyone have experience with using a feature as a module? The usage I am talking about is strictly placing hooks inside the .module file. Can that trigger any sort of bug?


I have a interntal fat32 partition, shared with windows. In Ubuntu I don't have write access.  The fstab file looks like this:  /dev/disk/by-label/SHAREDI /media/SHAREDI auto, users,nosuid,nodev,nofail,x-gvfs-show 0 0  When I open up the partition in Nautilus its owner is "root".   Any ideas? I've spent quite a lot of time reading the fstab options and can't see what's wrong.   Help me askubuntu you're my only hope.

I have Ubuntu 18.04 installed on a SSD with a larger separate HDD with 1 partition that contains Windows 10 and another NTFS partition that I use for storing all sorts of data. I have added the NTFS data partition to mount at startup using the Disks Utility in Ubuntu, it auto mounts just fine but only has read access. I would like to have this partition also have write access from Ubuntu. But I cant figure out how. (Fast Startup in Windows 10 is disabled)  Heres my fstab file (The last entry, dev/sdb4, is the NTFS data partition):  # /etc/fstab: static file system information. # # Use 'blkid' to print the universally unique identifier for a # device; this may be used with UUID= as a more robust way to name devices # that works even if disks are added and removed. See fstab(5). # # <file system> <mount point>   <type>  <options>       <dump>  <pass> # / was on /dev/sda3 during installation UUID=0e4a3e97-171f-4c96-9260-e2eb217f4302 /               ext4    errors=remount-ro 0       1 # /boot/efi was on /dev/sda2 during installation #UUID=1022-A48D  /boot/efi       vfat    umask=0077      0       1 # swap was on /dev/sda1 during installation UUID=c59f57b3-26c6-4fb1-82ae-29e676a973b1 none            swap    sw              0       0 UUID=1022-A48D  /boot/efi   vfat    defaults    0   1 /dev/sdb4 /mnt/sdb4 auto defaults,x-gvfs-show 0 0   These are the permissions for this partition    Also please explain how this drive can be added to the Favorites (the side bar which shows the running apps or apps that you have marked as favorite) in 18.04?


I am getting java.lang.NullPointerException can anyone please help me out? I am a beginner in java.  public class HelloComplex {      public static String[] vehicles = {"Car","Bus","Auto"};      public static String[][] drivers = {         {"Richa","Preeti","Bhawna","Vishakha"},         {"Rishabh","Shahrukh","Shubham"},         {"Antriksh","Ashwani","Navneet"}         };      public static void main(String[] args) {          Map<String, Set<String>> map = new HashMap<String, Set<String>>();          for(int i =0 ; i<vehicles.length; i++){              String vehicle = vehicles[i];             String[] driversList = drivers[i];              Set<String> driverSet = new LinkedHashSet<String>();              for( String driver : driversList){                 driverSet.add(driver);             }              map.put(vehicle, driverSet);         }              Set<String> driversList = map.get("helicopter");// here i am getting              for(String driver : driversList){                 System.out.println(driver);             }     }  }

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?


PROG=${0##*/} seems to parse out the shell script name, but it's unclear how that works. ${0} I understand is the first or 0th variable.

I'm quite confused about the following regular expressions I found in a shell script:  ${0##*/} ${0%/*}   How do they work?


I am using Ubuntu 16.04 LTS, 64 bit.  I have a folder full of 44 jpeg files with the following naming format—  0094-001.png.jpeg 0094-002.png.jpeg … 0094-044.png.jpeg   I want to change them all into files with the following naming format—  0094-001.jpeg 0094-002.jpeg … 0094-044.jpeg   I attempt the following command in the terminal—  mv ./*.png.jpeg ./*.jpeg   I get the following error—  mv: target './0094-044.png.jpeg' is not a directory   Why?

I realized I had named a bunch of files in an off-by-one fashion so I wanted to rename any file starting with "1" to the same thing except starting with 2.  For example mv 1.4.5.txt 2.4.5.txt or mv 1-chart.jpg 2-chart.jpg etc.  I tried mv 1* 2* but this was not accepted because it interprets 2* as a directory.


Suppose $Q$ is orthogonal $n$ by $n$ matrix and $v,u$ are vectors in $\mathbb R^n$. Show that   $$Qu \cdot Qv = u \cdot v$$   My attempt:  We will denote arbitrary element of $Q$ as $q_{ij}$  So   $$Qv =  \begin{pmatrix} \sum_{i}^{n}q_{1i}v_i\\  \cdots\\  \sum_{i}^{n}q_{ni}v_i \end{pmatrix} $$  and  $$Qu =  \begin{pmatrix} \sum_{i}^{n}q_{1i}u_i\\  \cdots\\  \sum_{i}^{n}q_{ni}u_i \end{pmatrix} $$   Hence  $$\begin{align}Qu \cdot Qv & = \sum_{j=1}^{n}\biggr(\sum_{i=1}^{n}q_{ji}u_i \sum_{i=1}^{n}q_{ji}v_i\biggl ) \\ & = \sum_{j=1}^{n}\sum_{i=1}^{n}q_{ji}^2v_iu_i \\  & = \sum_{i=1}^{n}\sum_{j=1}^{n}q_{ji}^2v_iu_i = \sum_{i=1}^{n}\underbrace{\sum_{j=1}^{n}q_{ji}^2}_{= 1}v_iu_i = u \cdot v \\  \end{align}$$  $\blacksquare$   Is it correct? Is there a better way to prove it?

In the following question we regard vectors in $\Bbb R^n$ as columns and define the dot product in the usual way which means that $x · y$ = $x^{t}y$  a) If A is an n × n matrix show that $A_{ij}$ = $e_i \cdot A e_j$ where $e_i$, $i =1, \dots , n$ are the standard basis vectors in $\Bbb R^n$  b) Show that a matrix $P$ is orthogonal if and only if ($Px$) · ($Py$) =$x · y$ for all $x, y$ ∈ $\Bbb R^n$  Working -   I got part (a) alright but have no idea of where to start with part (b) except to use the information that an n x n matrix $P$ is orthogonal if $P^{-1}$= $P^{t}$ and that $P^{t}$$P$=$I$, $P$$P^{t}$=$I$, where $I$ is the identity matrix. Any suggests are gracefully appreciated. Feel free to edit my question for clarity. Thank you


This is an example to illustrate the following theorem:  Let $a,b$ be integers and let $m,n$ be positive integers. The system \begin{eqnarray*} x&\equiv & a\pmod{m}\\ x&\equiv & b\pmod{n}\\ \end{eqnarray*} has solution if and only if $(m,n)\mid (a-b).$ In this case, the solution can be uniquely expressed modulo $[m,n]$  Determine the solutions to the following linear system of equations \begin{eqnarray*} x&\equiv & 5\pmod{6}\\ x&\equiv & 8\pmod{15}\\ \end{eqnarray*} The system will have a solution if $(15,6)\mid (5-8)$, wich is true, since $3\mid-3$. I have found that the solution of this system is $x\equiv 23\pmod{30}$, Which they argue as follows:  Since there is a solution, we express $-3$ as a linear combination of $6$ and $15$: $5-8= -3 = (-3)\cdot 6 + 1\cdot 15$, thus $x=8+15=23$.  In this step I am stuck, Is there another way to get to that 23?, if someone could explain in detail what was done in this step I would be very grateful.

We want to find the solution $x$ to the congruence system  $$\begin{align} x &\equiv r_1 \!\!\!\pmod{\!m_1}\\ x &\equiv r_2 \!\!\!\pmod{\!m_2}\end{align},\ \ {\rm where}\ \  \gcd(m_1, m_2) = 1$$  These can be rewritten as  $$\begin{align} x &= r_1 + m_1 j\\ x &= r_2 - m_2k\end{align}$$  for unknown integers $j, k$. So we set those two equations as equal and rearrange them to  $$m_1j + m_2k = r_2 - r_1$$  Now assume we perform $\text{egcd}(m_1, m_2)$, which gives us the solution to  $$m_1u + m_2v = \gcd(m_1, m_2)$$  Let the integer $\,h\,$ make $\,h \gcd(m_1, m_2) = r_2 - r_1$.  Then $\qquad hm_1u + hm_2v = h\gcd(m_1, m_2) =  r_2 - r_1 = m_1j + m_2k$  At this point I am lost because I don't think we can just assume  $hm_1u = m_1j$ and extract $j = hu$.   How do I get the values of $j$ or $k$ so I can get the value of $x$?


I just installed Ubuntu 16.04 on a Gigabyte PC. Installation went without any issues. This OS is fantastic. I just have one problem, it freezes often usually while browsing the Internet.Can someone please steer me in the right direction?

I am fairly new to Ubuntu and I was wonder what a good way is to debug when something crashes?   For example: I installed 11.04 and the default media player banshee makes my laptop crash after a few minutes of playing music. Since the system completely freezes and there is not error message it's hard to find out what is wrong.  Second problem I have is that sometimes the system crashes to login. I am suspecting it to be a Chromium or Flash but I am not 100% sure.  So anybody got some tips on how to debug stuff like this?


A chapter in my book ends with an odd-numbered page. The next page is an empty page with an even number.   How to remove the numbering and header on the empty page?

To ensure that a new chapter starts on a right-hand page, the book class (and the report class with the options twoside and openright) will insert blank pages between chapters if necessary. However, these pages still contain the headers and footers as defined by the class. How can I remove those?  Note: I know that I can manually add \clearpage\thispagestyle{empty} at the appropriate points of my document. However, this seems awkward and is prone to fail if I change my document later. I'm looking for automatic solutions.


I wanted to try the latest SE iOS app beta on iOS 9 (13A4325c).  After downloading v 1.3.2.229 via mobile safari, this modal dialog casts shade upon stack developers:    Have I missed a certificate to install?

Given the , I'm following  and going mainstream using Apple's TestFlight beta testing product.  To enroll in the iOS app beta program, .  Existing testers will need to reenroll.  After you register (but not immediately) you will receive instructions from Apple for installing the app on your phone. The invitations will be sent out in waves, so if you don’t get an invite immediately, be patient.  Crash reports will be automatically reported back to us using . Bugs or feature requests should be reported here on meta and tagged .  The easiest way to report a bug/feature request is in the About page at the bottom of the menu.  These options include relevant build and device information in your post.  As always, we welcome your feedback and are committed to building the best mobile app possible for browsing the Stack Exchange sites.  How is this different from the existing beta program?  For testers:   All updates are done through the Test Flight app, meaning there's no secret link to lose. You can get optional email or push notifications from Test Flight alerting you to the updated build and what's changed. The app isn't installed separately from the production app. It appears and behaves exactly like the App Store build app except that it has new features and an orange dot before its name:     For us:   The beta precisely emulates the behavior of the App Store build. It significantly lowers the gap between releasing to the beta channel and releasing to the App Store, making it much easier to ship new releases. It makes shipping a beta harder. (You win some, you lose some.)


I am trying to install Ubuntu into the VirtualBox in my iMac/OS 10.12.1 Sierra. I have the Ubuntu in the VirtualBox window informing it is running but the Ubuntu window shows a message:FATAL, No bootable media found? This where my effort stopped. Next I would like to install the Firefox into Ubuntu from the dmg file on my iMac desktop. How to do that?

I would like to know if anyone can help me with installing Ubuntu on VirtualBox


This method is more easy to understand.  This method is easier to understand.   Which one is correct sentence and why?

Is "more easy" a correct grammatical way of saying "easier"? What other ways can you express the word "easier"?


I use LaTeX for keeping a lab/coding notebook, and often I want to refer to variable names containing underscores, like force_compute.  Most of the time I don't want to bother using \verb for this, because it's just a lab notebook, I'm the only one likely to ever read it, and that's several extra characters to type.  But for some reason LaTeX as usually configured doesn't allow one to use the underscore character in text mode.  You have to use \_, which is fine, but, well, twice as many characters as I want to type.  Is there any way to make a single underscore character in text mode output a single underscore glyph in the output, but work as usual in math mode?  (I.e. denote subscript in math mode.)

I use _ character often in text mode, so I changed category of underscore: \catcode\_=12, but that applies also to mathmode and now I'm unable to make subscripts with underscore in mathmode. Is there a way to make latex interpret underscore in text mode as the underscore character, and in mathmode as subscript?


The only examples of simple rings I know that are not division rings a matrices over simple rings, but matrix rings always have zero divisors.  Are there simple rings that are not division rings but have no zero divisors? Else is having no zero divisors a sufficient condition for simple rings to be division rings

I need a simple Noetherian domain which is not a division ring.    I do know that this ring must not be Artinian, since otherwise it would be a division ring. Thanks in advance!


So there's something that's bugging me on Ubuntu, never figured out how to fix it. On Windows 10, if I have multiple files in a folder and I type the first letters, it just automatically selects the folder starting with the same few letters. On Ubuntu, it lists matching items, like this:  As you can see, it does a search of "goo" instead of highlighting the google-chrome folder without searching. Is there any way to fix this? Thank you!

Until now I was using a "traditional" version of Nautilus: that that comes with Ubuntu 10.10. Now I'm using 3.6.3, included with Ubuntu 13.04 (most likely any recent version is equivalent for the scope of my question, anyway).  One major difference between the two is the search-as-you-type behavior: in classic versions of Nautilus, when you typed an input, the file with the closest alphabetical match would become the selected one, the eligible files/folders being restricted to the current directory.  The new behavior is to perform an optionally-global search instead.  Can one configure Nautilus to provide the previous functionality ?


I'm relatively new to Stack Overflow and already have experience with getting both a question and an answer deleted.  I understand why  was closed, but the closing happened too fast. The first time I looked at my question after posting it, it was already closed; I didn't get the chance to respond.  The deletion of  was done by mistake. The deleter wrote that I should have deleted the answer by myself to avoid bothering the moderators. That was offensive, IMO.  I suggest implementing a time period, e.g. one day, during which questions cannot be closed. That way, authors would have the chance to explain the causes of their answers.

Since it's currently impossible to delete a "vote to close",* when I see a poorly asked question, should I immediately vote to close, or should I comment, and give the OP a chance to improve his question?  Waiting increases the chance that I'll forget, and never vote to close, potentially leading to a cluttered site.  Voting to close immediately increases the chance that the question will be closed, and the author will be forced to re-post his (hopefully improved) question, which leads to a cluttered site. :)  *It is now possible to , but that doesn't change the fundamental nature of this question.


import javafx.application.*; import javafx.geometry.*; import javafx.scene.*; import javafx.scene.layout.*; import javafx.scene.text.*; import javafx.stage.*;  public class Drawing extends Application{ private BorderPane mainPane; private HBox statusBox; private Text statusText;  public void start(Stage primaryStage) {      statusText = new Text("OFF");     statusBox = new HBox(statusText);     statusBox.setAlignment(Pos.CENTER);     mainPane.setTop(statusBox);          //nullPointerException here      Scene scene = new Scene(mainPane, 1000, 1000);     primaryStage.setTitle("Draw Something");     primaryStage.setScene(scene);     primaryStage.setResizable(false);     primaryStage.show(); }  public static void main(String args[]) {     launch(args); } }   I want to create a BorderPane and set the top portion for some text. I created an HBox to put inside. I don't know why this error occurs.

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?


How can I prove by induction the following statement:  $1+2+2^{2}+...+2^{n-1} =2^{n}-1; \forall n \geqslant 1$

I have this summation and I was attempting to prove it by induction however I have gotten stuck and not sure how to carry on further, if anyone could help point me in the right way that would be much appreciated! $$\sum_{k=0}^{N-1} 2^k = 2^N-1$$  So first I have the base case: $n=2$:  $$\sum_{k=0}^{1} 2^k = 3, \iff 2^2-1=3$$  Then I assumed true for $n=r$ so: $$\sum_{k=0}^{r-1} 2^k = 2^r-1$$  Then I considered $n=r+1$ so I want to show: $$\sum_{k=0}^{r} 2^k = 2^{r+1}-1$$  $$\sum_{k=0}^{r} 2^k = \sum_{k=0}^{r-1} 2^k + (r+1)^\mathrm{th}\text{ term}$$ $$\sum_{k=0}^{r} 2^k = 2^r -1+ (2^{r+1}-1)$$  But now I'm not sure how to go further or whether I got the "$(r+1)^{th}$" term correct or if I can even do this? If anyone can help me complete it and give me tips on induction as I always fail on the inductive step!


For a ceiling and floor function, the number is taken to 0 decimal places. Does this process mean that 0.9 recurring inside a floor function would go to 0? Or would the mathematician take 0.9 recurring to be equal to 1, thus making the answer 1?  And if 0.9 recurring does equal 1, does that mean (by definition) that ⌊1⌋ = 0?

Are the floor functions of $0.999\cdots$ and 1 equal?  It is true that $0.999\cdots=1$ but how does one justifies the integer part of $0.999\cdots$ being 1 , where it is not, or alternatively without using $0.999\cdots=1$ how can we show that  $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$ ?


I know the addition theorem for binomial coefficients:  $\binom{x^*+y^*}{n}=\sum_{k=0}^n \binom{x^*}{n-k} \binom{y^*}{k}$  for $x^*,y^*\in \mathbb{R}$ and $n \in \mathbb{N}$.  Using this theorem i can prove identities such  $\binom{2n}{n}=\sum_{k=0}^n \binom{n}{k}^2$ easily by applying $x^*=y^*=n$.  But what about the identity:  $\binom{x+y+n-1}{n}=\sum_{k=0}^n \binom{x+n-k-1}{n-k} \binom{y+k-1}{k}$  Of course we see that it results from the Theorem but is it a problem that $k$ is "part of $x^*$ and $y^*$ here?

How can I prove that $${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $$  I tried the following:  We use the :  $$y^{\underline k}=\underbrace{y(y-1)(y-2)\ldots(y-k+1)}_{k\text{ factors}},$$ so that $\binom{y}k=\frac{y^{\underline k}}{k!} .$   Then  $${x +y+n- 1 \choose n} = \frac{(x +y+n- 1)!}{n! ((x +y+n- 1) - n)!} =  \frac{1}{n!}. (x +y+n \color{#f00}{-1})^{\underline n} $$  And  $$ {x+n-k-1 \choose n-k}{y+k-1 \choose k}$$ $$\frac{1}{(n-k)!}.(x+n-k-1)^{\underline{n-k}}.\frac{1}{k!}.(y+k-1)^{\underline{k}}$$ $$\frac{1}{k!.(n-k)!}.(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$ $$\sum_{k=0}^n{n \choose k}(x+n-k-1)^{\underline{n-k}}.(y+k-1)^{\underline{k}}$$  According to the Binomial-coefficients:  $$ ((x+n-k-1) + (y+k-1))^{\underline{n}}$$ $$ (x+y+n\color{#f00}{- 2})^{\underline{n}}$$  What is wrong ? und How can I continue?  :/


Dealing with a string === "1$$$2!@!@3!@!@4!@!@5". I want to be able to split it at both $$$ and !@!@ which are custom delimiters that have been passed in. Since I have to be able to take in any custom delimiter I can't simply use a regex that only pulls out the numbers b/c I could deal with a custom delimiter such as [r9r] which I need to split by.  delimiter = delimiter.substring(0, delimiter.length - 1); console.log(delimiter) // => "$$$|!@!@"   const regex = new RegExp(`(,|\\n|\\${delimiter})`,'g');   const finalStr = str.substring(str.indexOf('\n'), str.length)   console.log(finalStr); // => "1$$$2!@!@3!@!@45"   let arr = finalStr.split(regex).filter(Boolean);   console.log(arr); // => ["1$$$2", "!@!@", "3", "!@!@", "4", "!@!@", "5"], why does '$$$' stay attached to the 1 and 2?   const finalArr = [];   for (let char of arr) {     if (parseInt(char)) {       finalArr.push(char);     }   }   console.log(finalArr) // => ["1$$$2", "3", "4", "5"]   return finalArr;   I want my final array to be: ["1", "2", "3", "4", "5"] but for some reason the '$$$' doesn't get split like the '!@!@' delimiter does. When I used '!!!' instead of '$$$' it worked so I assume its a special character but still couldn't find a way to accept it.

I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps?


I just downloaded Ubuntu 20.04 LTS and cannot find "workspaces" on the right of the desktop display. If I go to Appearance settings, there is no menu for Workspaces. If I use the Super Key there are no workspaces shown. How can I turn on to have workspaces that are supposed to be in this version of the OS?

Any idea how to have more than 2 workspaces on Ubuntu 18.04.1?


I think the issue is in someway related with GTK, any Ideas ?

I don't know what I did wrong in my Ubuntu 18.04 OS. For some reason some of my apps look like this:    This also happens to other gnome apps like pdf-reviewer and Logs. Window title, menu bar etc. are all blank, display only squares.  *Problem solved: I downloaded Google Fonts, saved them in a new folder, they can be applied system-wide, but after I did some font settings using Google Fonts it didn't work. I changed the font of Interface with Tweaks-Tool, that was what causing the problem.


As long as there is an open file descriptor pointing to a file, I can bring it back with cp like this:  # Open for reading exec 3< file # Delete rm file # Bring it back cp /proc/self/fd/3 file   This solution is okay with small files, but it's really slow with larger ones (like >5GiB). So I wonder, is there a way of bringing it back without copying the content? I mean, the data lies there untouched unless the descriptor is closed, so why shouldn't it be possible to link a filename to the memory area the data resides?  Please enlighten me on this. A hackish command line solution, a platform/filesystem dependent C API etc. everything is welcome; I just want to know if this is possible somehow somewhere, and if not, I want to know why.  Googling didn't help at all, all I could find is copy-of-copy articles about how to restore files with lsof and cp.

If I know the index node (inode) of a file, but I don't know its path (or any of its paths), is it possible to create a hard link to that inode directly?  I could find the file using sudo find / -inum 123546 and then create a hardlink, but that would be way too slow for my application.  N.B. I'm using an ext4 filesystem.


A similar question has been asked here: , and I've used the advice that was posted.   However, I still can't figure out which of the partitions is Ubuntu.  Here's a screenshot after I run diskmgmt.msc    I need a fresh install of Ubuntu since my current one has suddenly stopped working. I had used .iso image by mounting the image and installing it on a thumb drive when I partitioned it.  To do the above, do I need to remove the partition first from diskmgmt.msc and then go about partitioning it again from the image like I did the first time around?   Update. I get "Boot error" when I try to run the Ubuntu installer by booting from USB. When I press enter, it takes me to the grub screen. Do I need to use Windows recovery disk to repair so that grub is no longer there? (This problem was resolved)  I have now attached the screenshot that I get when I choose "Something else" when the installer asks me how I want to partition my disk. It seems the 52.64 GB was the one with Ubuntu on it. I was confused because according to the diskmgmt.msc it's 100% free. . I have deleted ext4 and swap, restarted the install, selected "Install Ubuntu alongside them" and that seems to have worked.  Thanks everyone for the advice!

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


I've  that it's OK to ignore the image title, but not the alt field from a SEO perspective.  However, the SEO expert in the company insist it's highly required for SEO.  Who is right?  Is there any reference or documentation for it?

The title attribute is an HTML standard element available across most tags.  e.g.
by Function
   I've used this attribute on some sites for usability;  many browsers pop up a "tooltip" over the link with the more detailed description of what is on the other side.  I've been wondering if doing so is having a negative effect on my rankings (hidden text?) or if it has any effect at all on onsite or offsite keyword relevance calculations.  Does anyone know of any research done on this?


what would be best for SEO?   force all website page to SSL using 301 force just some page like login and registration page and make it optional for other pages.

Google just announced that SSL will affect site ranking positively:   I have an Easter Island tourist agency called Easter Island Traveling for which I had planned doing a subdomain (secure.*) for doing sales, logins etc.  Now, does Google want my SSL to be on for all of my site to have this SEO benefit? This would be quite radical by Google, since it would affect my site speed negatively. Or is it enough that I have SSL on a part of the site only? Thoughts?


With a prime number p and a not equal to 0, how can I prove that there exists an integer b such that ab is congruent to 1 (mod p)?  What I have done so far is I know that the GCD(p,a) is either 1 if p does not divide a or it is p if p does divide a. I am able to take GCD(p,a) = 1 to the end by using the fact that ab + pk = 1 and manipulating that to show that ab is congruent to 1 (mod p), but am stuck on how to move forward if the GCD(p,a) = p and p divides a.

Isn't finding the inverse of $a$, that is, $a'$ in $aa'\equiv1\pmod{m}$ equivalent to solving the diophantine equation $aa'-mb=1$, where the unknowns are $a'$ and $b$? I have seem some answers on this site (where the extended Euclidean Algorithm is mentioned mainly) as well as looked up some books but there is no mention of this. Am I going wrong somewhere or is this a correct method of finding modular inverses? Also can't we find the Bézout's coefficients by solving the corresponding diophantine equation instead of using the extended Euclidean Algorithm?


I'm solving some cryptographic problem,  I need the  cube root of 4.157786362549383e+37, which gives me 3464341716380.1113  using  x = x ** (1. / 3)   I thought it was weird at first, so I did try:  x=1000 print(x) x= pow(x,1/3) print(x)   but got 9.99999998  I have even tried somewhere . But i got the same result. Is there something wrong? How can I calculate the true cube root?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


When I try to install any application or update, it shows unmet dependencies- Try apt-get -f install.  How to solve this ?

Occasionally, when I'm installing stuff, I get an error like the following:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  package1 : Depends: package2 (>= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this?


Let $C \subset X$ be a connected space and $A \subset X$ s.t. $C\cap A \neq \emptyset$ and $C\cap (X-A) \neq \emptyset$. Prove that $C\cap \partial A \neq \emptyset$.  I don't know how to prove this since I fail to see how I can use the fact that C is connected. Any hint would be appreciated.

Let $X$ be topological space and $A\subseteq X$.   If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$.  Assume that $E\cap\partial A=\emptyset$.  If $E\cap\partial A=\varnothing$ then $E=(E\cap\text{int}(A))\cup(E\cap\text{ext}(A))$, i.e. a union of disjoint sets open in $E$.   Also the sets are nonempty because: $E\cap\text{int}(A)=E\cap A\neq\varnothing$ and $E\cap\text{ext}(A)=E\cap A^c\neq\varnothing$.  This contradicts that $E$ is connected.  Fixed.


Consider $$f(z)=\frac{1}{e^z-1}$$ I want to expand it over $z_0=0$ in a Laurent series.  We know that $$e^z=1+z+\frac{z^2}{2!}+\frac{z^3}{3!}+\cdots$$ And I know that $$\frac{1}{x-1}=-1-x-x^2-x^3-x^4-x^5+\cdots$$ But I can't get the correct answer for my desired series which is, $$\frac{1}{x}-\frac{1}{2}+\frac{x}{12}-\frac{x^3}{720}+\frac{x^5}{30240}+O(x^6)$$ Any help?

Trying to compute the first five coefficients of the Laurent series for $$\frac{1}{e^z-1}$$ centered at the point $0$. I'm not seeing a way to use the geometric series due to the exponential. Any ideas?


I am trying to connect to a database with phpMyadmin but I get an nullpointer in properties  Here is my code:   public Connection getConnection() throws SQLException {         final String ip = prop.getProperty("database_ip");         final String dir = prop.getProperty("database_dir");         final String username = prop.getProperty("database_username");         final String password = prop.getProperty("database_password");          try {             Class.forName("com.mysql.jdbc.Driver");         } catch (ClassNotFoundException e) {             throw new IllegalStateException("No suitable driver found");         }         return DriverManager.getConnection("jdbc:mysql://" + ip + "/" + dir, username, password);     }   and here is where the nullpointer happens:  private Properties getPropertyFile(String path) {         Properties prop = new Properties();         try {             prop.load(getClass().getClassLoader().getResourceAsStream(path));         } catch (IOException e) {             e.printStackTrace();         }         return prop;     }   and here is my map structure:

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?


The real risk of cbdcs to the financial system may be that they eventually precipitate a new kind of run: on the idea that banks need to exist "at all". What does 'at all' refer to here? Does it give the sentence a negative meaning?

Without which, we would be able to act at all.   I’m hearing this in my own head as, “Without which, we would not be able to act at all.”   So I'm wondering, is the former just a cleaner and less hectoring version of the second, with both meaning the same thing?


I've got several email accounts, but I always set them up to be auto forwarded to the main one, so I always check just one inbox. This is awesome, but sometimes I need labels to organize and categorize work, promos, academic, etc...  Lets suppose main account is julian@gmail.com, academic is julian@university.edu, and work is julian@company.com, What I have now is academic and company forwarding everything automatically to Gmail, and it's working, and some labels are working as well, but there are some groups such as math@university.edu that is a list to all of the students in that class, or project@company.com that has same behavior.  I set up a label called "academic" to everything in Gmail that matches To:julian@university.edu, and in this scenario is working:  From: martin@university.edu To: julian@university.edu (julian@university.edu forwards everything to julian@gmail.com) So in inbox, I see "To: julian@university.edu", and that conversation gets the label!   But, let's suppose this scenario:  From: martin@university.edu To: math@university.edu (It's forwarded auto to all students, so julian@university.edu receives it) (julian@university.edu forwards everything to julian@gmail.com) So in inbox, I see "To: math@university.edu", and that conversation does not get the label!   I don't want to modify the label so it consider julian@university.edu AND math@university.edu, it's just not practical, there are like 15 groups among university, familiar and work, so filters would be a bit confuse.  Is there a way that Gmail detects that email is being forwarded FROM academic, without taking into account the TO and FROM fields, so it puts the correct label on it?  The deliveredto field was quite useful for admin by google accounts, but that field seems to stop working when secondary accounts are not Google, such as Gmail or a simple cpanel email account. How do I get same effect with different accounts?

EDIT:  You cand find additional information in   I have two email accounts, one is my main Gmail account which I check regularly (for simplicity I name it mygmail@gmail.com), and the other one is from university mail service where I currently study (and I name it myunimail@mail.uni.com).  As the disk quota of university mail server is too low and there are lots of daily announcements from university staff which contain huge attachments, after about 5-7 days all disk quota is used and afterwards no emails will be delivered to my inbox.  So I created a filter in the university mail service (which uses Zimbra) to forward all received messages to email alias mygmail+UNIFWD@gmail.com and then delete the message.  Now the main problem is: I want to create a filter in Gmail to mark these forwarded messages with a custom label, but the information included in message header, specially FROM and TO fields, is not enough to distinguish these messages from other ones (as shown below)    As you can see, there is no sign of alias I used in the Forwarding Address in Zimbra's filter settings. Even I can't rely on TO field (which contains myunimail@mail.uni.com) because there are messages which are sent to both of my email addresses, so some mistakes will occur if I use this field.  By the way, these forwarded messages are marked by Gmail as being sent via mail.uni.com  Is there any way I can use this to filter messages?  Did I miss something while setting up the filter in Zimbra?


whenever I run the main class as shown below,    package gardeningmania;   import processing.core.PApplet;  import java.io.File;   public class GardeningMania {   public static void main(String[] args) {     PApplet.main(new String[]{/*"--present",*/ "gardeningmania.Game"});    Game.main("null"/*"gardeningmania.Game"*/);     File currentDir = new File("."); getAllFilse(currentDir); } }   I get this error:  ERROR CODE  Exception in thread "main" java.lang.StackOverflowError  at java.util.Hashtable.put(Hashtable.java:437) at sun.java2d.Disposer.add(Disposer.java:139) at sun.java2d.Disposer.addRecord(Disposer.java:107) at sun.awt.image.BufImgSurfaceData.initRaster(Native Method) at sun.awt.image.BufImgSurfaceData.createDataIC(BufImgSurfaceData.java:256) at sun.awt.image.BufImgSurfaceData.createData(BufImgSurfaceData.java:86) at sun.awt.image.BufImgSurfaceManager.<init>(BufImgSurfaceManager.java:55) at sun.awt.image.SurfaceManager.getManager(SurfaceManager.java:78) at sun.java2d.SurfaceData.getPrimarySurfaceData(SurfaceData.java:273) at sun.java2d.SunGraphicsEnvironment.createGraphics(SunGraphicsEnvironment.java:180) at java.awt.image.BufferedImage.createGraphics(BufferedImage.java:1154) at java.awt.image.BufferedImage.getGraphics(BufferedImage.java:1142) at processing.core.PFont.<init>(PFont.java:227) at processing.core.PFont.<init>(PFont.java:328) at processing.core.PApplet.createFont(PApplet.java:6560) at processing.core.PApplet.createFont(PApplet.java:6488) at gardeningmania.Game.<init>(Game.java:497) at gardeningmania.ImageLoader.<init>(ImageLoader.java:12) at gardeningmania.Game.<init>(Game.java:524) at gardeningmania.ImageLoader.<init>(ImageLoader.java:12)   Can anyone explain what this error message means?

What is a StackOverflowError, what causes it, and how should I deal with them?


There is no Times New Roman Font present in LibreOffice Writer. I looked upon the question . But I have the fonts installed on my system already, but is it not showing up on Libreoffice Writer?  My system specs  $ libreoffice --version LibreOffice 5.1.2.2 10m0(Build:2)

I don't have these fonts:  times new roman, arial and calibri..., like in microsoft office? What can I do?


I know that the difference between two musical notes is given by the sound frequency, and the difference in volume is given by the amplitude.  What I am wondering is why does the same note sound different on different musical instruments?  What in the wave makes the difference between the sound of a harmonica and the sound of a violin singing the same note?

What are those characteristics by which every sound can identified uniquely?  For example, pitch is one of the characteristics of sound, but let’s say a note C# can also be played on a guitar and piano with same pitch but the resulting sound that we hear is different so what are those characteristics which defines every sound.


This is a homework problem in my graph theory class and I wanted tips on how to solve it. Any tips would be appreciated..   Show that any doubly stochastic matrix is a convex combination of permutation matrices, i.e. any double stochastic A can be written as A=t1P1 +t2 +⋯tlPl, where each Pi is a permutation matrix, and the numbers ti  satisfy t1, . . . , tl ≥ 0 and ∑li=1 ti = 1.

According to Birkhoff, $n$-by-$n$ stochastic matrices form a convex polytope whose extreme points are precisely the permutation matrices. It implies that any doubly stochastic matrix can be written as a convex sum of finitely many permutation matrices. But for a specified such matrix, is there a algorithm to compute the coefficients of a combination? For example, given that: $$A=\left[\begin{matrix}0.5&0.2&0.3\\0.1&0.6&0.3\\0.4&0.2&0.4\end{matrix}\right],$$  How do you know that: $$A=0.4\left[\begin{matrix}1&0&0\\0&1&0\\0&0&1\end{matrix}\right]+0.2\left[\begin{matrix}0&1&0\\0&0&1\\1&0&0\end{matrix}\right]+0.1\left[\begin{matrix}0&0&1\\1&0&0\\0&1&0\end{matrix}\right]+0.1\left[\begin{matrix}1&0&0\\0&0&1\\0&1&0\end{matrix}\right]+0.2\left[\begin{matrix}0&0&1\\0&1&0\\1&0&0\end{matrix}\right]$$  And please briefly prove the correctness of the algorithm.


I would like to know if this ECS motherboard is compatible with Linux. The model is ECS A320AM4-M3D RYZEN AM4. With what version of Ubuntu it is compatible?

I have a device on which I would like to install Ubuntu. How do I find out if Ubuntu will work on it?


In cricket playing countries like Australia, South Africa and England, pitches often are thought to support fast and swing bowling. But in the Asian subcontinent and other countries, pitches are typically not too bouncy.  How do cricket pitches vary? Will the weather conditions play a role in affecting cricket pitches?

I've heard some pitches will support only fast bowlers and some pitches only spin bowlers. What is the mechanism behind this? How can a pitch support either one? What will be difference between these two pitches?


I want to make an Ubuntu desktop app that will display my website, kind of like the Amazon app that comes in the default installation.  I am not trying to make an app for Ubuntu Touch, nor setting up my website so it will have Unity integration when users visit it with Mozilla Firefox.   I want mine to be just like the Amazon app. It will have an icon, and won't let users navigate away from my site. (If people click a link on my site to say, facebook.com, I don't want it to let them go there.)  Is there an easy way to make one of these?

I'm trying to create some webapps to use with Firefox. I got an tutorial from Canonical () and I didn't understand one thing, maybe someone could help me.  I have to run the following script in Web Console:  // ==UserScript== // @name          tumblr-unity-integration // @include       https://tumblr.com/dashboard // @version       @VERSION@ // @author        WebApps Team // @require       utils.js // ==/UserScript==  window.Unity = external.getUnityObject(1.0);  Unity.init({ name: "Tumblr",             iconUrl: "icon://Tumblr",             onInit: null });   Everything is fine, it created the icon launcher and work with alt+tab. That enough for me by now, but, if I close the windows, the launcher icon that I created before stop working (I mean, it open the site, but doesn't work like other webapp and doesn't show in alt+tab too). Maybe I have to run this script automatically every time I enter on that site (In this example, Tumblr). How can I do that?  Thanks,


I wanted to know why "negative energy" of a two particle system implies  that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason for that and simply state it. I tried looking on Wikipedia but it offers the "principle of minimum potential energy" as a reason. Is there any other reason for this?

Could you give me an idea of what  mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)?  Why, when a stable bound state exists, the energies of the related stationary wavefunctions are negative?  I figured it out, mathematically (for instance in the case of a potential described by a Delta function), but what is the physical meaning?


I would like to be able to see all the steps my Minecraft is going through when it loads, through CMD or another Windows program. Is this possible?

The Minecraft console disappears and the Minecraft Java game loads after the game output is loaded. Is it possible for it to stay? I would like to see the game output.


I am so confused what is @class ? What does it when i am using this directive? when to use this directive and why? I did not get any link proper that tells why,what and when to use? Please tell me with an example?

It is to my understanding that one should use a forward-class declaration in the event ClassA needs to include a ClassB header, and ClassB needs to include a ClassA header to avoid any circular inclusions. I also understand that an #import is a simple ifndef so that an include only happens once.  My inquiry is this: When does one use #import and when does one use @class? Sometimes if I use a @class declaration, I see a common compiler warning such as the following:     warning: receiver 'FooController' is a forward class and corresponding @interface may not exist.   Would really love to understand this, versus just removing the @class forward-declaration and throwing an #import in to silence the warnings the compiler is giving me.


I created a shortcode that is displaying the results as intended, but outside of the div or table cell where I placed the shortcode within my site. Is there a cleaner way to write this that will generate the code in the expected location?   <?php function minisocialvar( $atts ) {   $s = shortcode_atts( array(         'id' => '',         'fb' => '',         'tw' => '',         'ig' => '',         'yt' => '',         'in' => '',         'fk' => '',         'align' => 'left',         'size' => '',     ), $atts ); ?>      <div id="<?php echo $s['id']; ?>" style="text-align: <?php echo $s['align']; ?>;">     <?php if (!empty($s['fb'])) { ?>         <a href="<?php echo $s['fb']; ?>" title="Follow Us On Facebook" target="_blank" class="fb-socialicon">             <span class="fa-stack <?php echo $s['size']; ?>">                                                              <?php } ?>      <?php if (!empty($s['tw'])) { ?>         <a href="<?php echo $s['tw']; ?>" title="Follow Us On Twitter" target="_blank" class="tw-socialicon">             <span class="fa-stack <?php echo $s['size']; ?>">                                                              <?php } ?>      <?php if (!empty($s['ig'])) { ?>          <a href="<?php echo $s['ig']; ?>" title="Follow Us On Instagram" target="_blank" class="ig-socialicon">              <span class="fa-stack <?php echo $s['size']; ?>">                                                                  <?php } ?>      <?php if (!empty($s['yt'])) { ?>          <a href="<?php echo $s['yt']; ?>" title="Watch Us On YouTube" target="_blank" class="yt-socialicon">               <span class="fa-stack <?php echo $s['size']; ?>">                                                                   <?php } ?>       <?php if (!empty($s['in'])) { ?>          <a href="<?php echo $s['in']; ?>" title="Join Us On LinkedIn" target="_blank" class="in-socialicon">             <span class="fa-stack <?php echo $s['size']; ?>">                                                               <?php } ?>      <?php if (!empty($s['fk'])) { ?>          <a href="<?php echo $s['fk']; ?>" title="View Us On Flickr" target="_blank" class="fk-socialicon">             <span class="fa-stack <?php echo $s['size']; ?>">                                                               <?php } ?>
 <?php } ?>  <?php add_shortcode( 'minisocial', 'minisocialvar' );

I'm using a shortcode to pull in different loops via the loops-name.php. For some reason it is always at the top of the page. I googled it and using echo instead of return causes that problem but with my code I am not using echo. Here's the shortcode:  // setup the shortcode for use function friendly_loop_shortcode( $atts, $content = null ) { extract( shortcode_atts( array( 'category' => '', 'module' => '' ), $atts ) );  include(locate_template('loop-'.$module.'.php'));  }   Any idea why this is happening?


Is there any way to recover the messages that I accidentally deleted on my cellphone. I am not using Google backup or any other backup service and have never synced with any other device.

I deleted an entire SMS thread by mistake from my HTC Wildfire. Is there any way I can retrieve that thread ?


I'm a beginner in C programming, but I was wondering what's the difference between using typedef when defining a structure versus not using typedef. It seems to me like there's really no difference, they accomplish the same goal.  struct myStruct{     int one;     int two; };   vs.  typedef struct{     int one;     int two; }myStruct;

I have seen many programs consisting of structures like the one below  typedef struct  {     int i;     char k; } elem;  elem user;   Why is it needed so often? Any specific reason or applicable area?


I have seen at many places that $A=\mathbb{R}^n-\{a\}$ for some $a\in \mathbb{R}^n$ is path connected. But how do we prove it? I understand that we have to show that there is a continuous map $\gamma:I\rightarrow A$ between any 2 points of $a_1, a_2\in A$ such that $\gamma(0)=a_1$ and $\gamma(1)=a_2$. $(I=[0,1])$ But I have no idea on finding such $\gamma$. Any hints?

The question is:     Show that if $A⊆\Bbb R^n$ is finite and $n≥2$, then the set $\Bbb R^n\backslash A$ is connected in $(\Bbb R^n,τ_d)$ where $τ_d$ is the topology induced by the Euclidean distance in $\Bbb R^n$.   My attempt:  Denote $A^C=\Bbb R^n\backslash A$ and suppose $A=\{a_1,…,a_n\}$. Assume by contradiction that $A^C$ is not connected, then there exists $O_1,O_2∈τ_{A^C }$ st. $A^C=O_1⋃O_2,O_1⋂O_2=∅$. Here $\tau_{A^C}$ is a subspace topology.  Intuitively, part of $A$, denoted by $A_1$ is "enclosed" in $O_1$ and the rest, denoted by $A_2$ are "enclosed" in $O_2$. Then $G_1=O_1\bigcup A_1$ is an open set in $\tau_d$, and $G_2=O_2\bigcup A_2$ is also an open set in $\tau_d$, and $\Bbb R^n=G_1\bigcup G_2$. However, $G_1, G_2$are disjoint, contradicting with the fact that $\Bbb R^n$ is connected.  However I got stuck when trying to implement this idea. Can anyone provide some help? Thank you!


Does MySQL have any functions like SUM but then do the MULTIPLICATION of a collumn?  Example: I have an table like this, and I want to multiply the entire collumn  +--------------+ | combinations | +--------------+ |            3 | |            5 | |            4 | |            6 | |            1 | |            3 | |            4 | +--------------+   expected result:  +----------------------------+ | product_total_combinations | +----------------------------+ |                       4320 | +----------------------------+   I cannnot find anywhere how to achieve this. Any help is appreciated.

I need an aggregate function that MySQL doesn't provide.  I would like it to be in MySQL's flavor of SQL (that is, not in C).  How do I do this?  What I'm stuck on is creating an aggregate function -- the  don't seem to mention how this is done.  Examples of desired usage of a product function:  mysql> select product(col) as a from `table`; +------+ | a    | +------+ |  144 | +------+ 1 row in set (0.00 sec)  mysql> select col, product(col) as a from `table` group by col; +-----+------+ | col | a    | +-----+------+ |   6 |   36 | |   4 |    4 | +-----+------+ 2 rows in set (0.01 sec)


When I type $\varprojlim_n$ in the common inline math environment I get the picture as below.     However I want to be rendered as .  The same thing happens with summations. I understand that if I use the paragraph math mode it will solve my problem. Unfortunately, that is not an option. Is there any way to do this?

I want the limits of the sum sign to be placed where I placed the red lines in the photo. This is the line of script I used:  $Result = p + \sum_{i=0}^{n} f(x)$    This is what I get and the red lines is what I want.


I'm using Ubuntu 17.10 and I'm considering switching to Lubuntu since my machine is pretty old for this heavy OS. I read it uses the same repositories as Ubuntu, but when trying Lubuntu from a disk on key the "shop" (app market) did not show GIMP or OpenShot in search.  I noticed Lubuntu has a built in tool similar to GIMP but I would like to use those two I mentioned.  So will I have a problem if I switch?

What different Ubuntu derivatives are there? And what is special with them?


I get struggled in choosing to put or not to put a preposition at the end of the sentence. I feel like it's optionally, but I'm not sure, so I'm asking. The question is, should I put prepositions in these sentences and why?  What am I guilty of? It's nothing compared to what I could be asking for. Whom are you talking to?  It seems a big theme (prepositions at the end or the start of a sentence), that is why I would like to thank you even if you explain to me at least these cases.

Like many others, I commonly find myself ending a sentence with a preposition.  Yes, it makes me cringe.  I usually rewrite the sentence, but sometimes (in emails) I just live with it.  To, with... you know who you are.  Should I keep fighting myself on this one, or is it okay in some circumstances?


Occasionally I come across great answers that aren't marked as accepted. They are commonly accompanied by the comment:     "This should really be marked as accepted."   ()  In my opinion, the upvotes on the answer itself indicate the quality of the answer, and any commenting to the effect of...     "This should be accepted"      "This is the better answer"      "This works better than the accepted answer"   ... is no better than a longer way of adding this comment:     "+1"   Which makes upvotes on said comment even more ridiculous, does it not?    In most cases, a highly upvoted comment indicates extra information relevant to the answer. This expectation makes comments like those above rather distracting and, dare I say, detract from the quality of the presented answer.  Can you provide a counter-discussion exploring the positive value of such comments? Or should they be flagged "not constructive" without reservation?

New users already have a reminder to accept an answer on their question. So I don't see the need in general for this post-answer badgering, even if it is intended to be genuine constructive help (which it almost always isn't). To me it seems like little more than rep greed, especially on a site like StackOverflow where such a reminder comes within 10-20 minutes of posting the answer, and when the comment is clearly intended for the OP to accept the commenter's answer. To me it feels like pressuring the OP to accept their answer before a better answer has a chance to come along (or, as others have put it, rep-whoring).  I know we've talked in the past about , but that deals with the behavior itself. I'm asking about how we should treat the comments after they've come - I'm not sure whether I should send the commenter to the meta question I just linked, flag the comment, or ignore it. Ignoring it doesn't feel right, but saying something in the open might not seem genuine in cases where I have a competing answer.  EDIT I'd like to add something to consider here: the case where a user makes it seem like further discussion or clarification of an answer hinges on an up-vote/accept first. A couple of examples I culled recently, but I don't want to call out the user here (they're both from the same user, on different posts, in response to questions trying to clarify their answer):     consider up-voting my answer if you found it useful first.      up-vote my answer if you found it helpful first.


I'm trying to check a string for a specific number but it doesn't seem to find it.  string = sc.next();  if(string != "-1")  return 0;   So when I enter -1 into the input, it just continues on without breaking the program. Am I doing something wrong here?

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?


So, for example, we have the planet, a spaceship (cylinder shaped) and a ball in it (spaceship is like transparent so we can see the ball). We are on the planet looking at the ship. The spaceship moves the speed of light and the ball with it. But what if the ball was moving, for example, 50000 km/h in the ship? It should still be moving the speed of light to us, but would it go through the ship?

Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.)


I learned "not to go" is right but sometimes I could find "to not go" what's correct? ex) She said not to go there. ex) She said to not go there.

This is one thing that keeps bugging me, and maybe there's a direct answer. Grammatically, which one is more correct of these two?  Does it make a difference?  I tried not to do that. I tried to not do that.


i'm tring to insert into my database the following string: "è" but each time i try in the database nothing is added. This is the code that i use to insert.  $string = mysql_real_escape_string($_REQUEST['string_passed']); $query = "UPDATE my_table SET my_field = '$string' WHERE id = '$id'";   In my connection.inc.php file i have following code.  mysql_connect("localhost", "root", "") or die("Problem: ".mysql_error()); mysql_select_db("my_db") or die("Poblem: ".mysql_error()); mysql_query('SET NAMES utf8');   I know, i can insert $string using htmlentities but there is any other solution?

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've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of the two operators can be measured with certainty simultaneously.  But what is the physical significance when two operators do not commute such as to give a certain value? For example the position and momentum operator do not commute and give a value of $i\hbar$. What is the significance of the $i\hbar$?

I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?   E.g. an operator $A$ with the Hamiltonian $H$?


Hello I stuck with this character encoding problem, please help.  What I did:   I created a database with UTF-8 Encoding. I created a database connection with charset, names etc set to UTF-8. I try to set paypal button encoding both UTF-8 and ISO-8859-9. Added header('Content-Type: charset=utf-8'); to my postback php file. Added setlocale(LC_ALL, "tr_TR"); to my postback php file. I set hidden charset input to paypal button code. Also set "lc" tr_TR. Tried to change encoding with "iconv" both latin5 to utf-8 and iso-8859-9 to utf-8 Double checked if the files i am working on are UTF-8 Without BOM   But no luck...  After I sent the form, on paypal page, it shows "options" correctly but the values are not inserting to my database as shown instead there are only question marks.  Please help, thanks.  Edit: I'm trying to get Turkish characters correctly: üğİışŞöÖçÇÜĞ


I have many problems. First of all, I had dual booted Windows with Ubuntu 19.04, then I lost my Windows. I had checked partitions with GParted, but there is nothing related to Windows.   I had checked GRUB error also. I confirmed that I had lost my Windows. But there is another issue, total space of my hard disk is 1 TB, I gave Ubuntu with 10 GB space. And there is 910 GB unallocated space in the disk partitions. I don't know where is the remaining 90 GB space.

I just used boot and nuke to wipe my hard drive and reinstall my OS systems. When selecting the hard drive I noticed that there were only 931gb free in my hard drive.  Is this normal? It sees like a strange number as I though terabyte drives held 1024gb.  Is some of the hard drive hidden? Are there any programs that can check?  Thanks in advanced for any help with this!  df -h returns the following:  Filesystem           Size  Used Avail Use% Mounted on udev                 3.9G     0  3.9G   0% /dev tmpfs                786M   18M  768M   3% /run /dev/sda5            437G  5.7G  409G   2% / tmpfs                3.9G   31M  3.9G   1% /dev/shm tmpfs                5.0M  4.0K  5.0M   1% /run/lock tmpfs                3.9G     0  3.9G   0% /sys/fs/cgroup tmpfs                786M   20K  786M   1% /run/user/124 /home/*/.Private     437G  5.7G  409G   2% /home/* tmpfs                786M  2.0M  784M   1% /run/user/1000   lsblk returns the following:  NAME           MAJ:MIN RM   SIZE RO TYPE  MOUNTPOINT sda              8:0    0 931.5G  0 disk   ├─sda1           8:1    0   500M  0 part   ├─sda2           8:2    0 478.8G  0 part   ├─sda3           8:3    0   496M  0 part   ├─sda4           8:4    0     1K  0 part   ├─sda5           8:5    0 443.9G  0 part  / └─sda6           8:6    0   7.9G  0 part   └─cryptswap1   253:0    0   7.9G  0 crypt [SWAP] sr0             11:0    1  1024M  0 rom      EDIT: I am literally installing the dual boot system as we speak. Windows first, here is a breakdown of what Windows 10 sees:   So total size is 931.51GB. That is a very strange number.


I understand how to prove it... but without any kind of rigorous mathematical proof, how could it be explained to a layman who understands countable sets that $\mathbb{Q}$ is in fact countable? I have seen from other posts on this site vague ideas, but none are as fulfilling as I would have hoped.   e.g. My closest idea was that if a rational number can be expressed as $\frac{p_i}{q_i}$, then do:   Set $q_j=j$. For $i\in \mathbb{N}$,  then do $\frac{\sum p_i}{q_j}$.  Set $q_j=j+1$ do $\frac{\sum p_i}{q_{j+1}}$   etc .... although i'm not sure this quite works?  I think the above can be shown with examples to a layman quite easily, are there any other (simpler) ideas?

I want to prove that $\mathbb{Q}$ is countable. So basically, I could find a bijection from $\mathbb{Q}$ to $\mathbb{N}$. But I have also recently proved that $\mathbb{Z}$ is countable, so is it equivalent to find a bijection from $\mathbb{Q}$ to $\mathbb{Z}$?


I finished building my new gaming PC today. Since my phone's (Galaxy S9) internet is usually much faster than my house's internet, I tethered it to my new computer. However, I'm experiencing much, much slower internet speeds than on my last PC. So, I ran a few speed tests. On my phone, I got around ~20Mbps download speeds. On my PC, I got around ~0.80Mbps download speeds. This seems to make no sense, as I even have USB 3.0 ports that I can plug into instead of the 2.0 ports I used to have. I tried , but to no avail. I did recently buy a new USB-C cable for my phone, maybe that's the cause?  My phone's tethering speeds have never been this slow, and it's really starting to sour my new computer's freshness.  What could possibly be happening?  Other info:  Completely fresh install of Windows 10 Home.  Asus Prime X470-Pro motherboard.  Android Pie installed on my phone.  EDIT: I am already running RNDIS6. This is not my problem...

I have two Android smartphones that can provide their internet connection to a computer over USB via the RNDIS (Remote Network Device Interface Specification) protocol. I also have two computers dual-booting Windows 7 Ultimate and some flavor of Linux (one of them has Fedora 17, the other has Ubuntu 12.04).  When I connect either smartphone to either computer and the computer is running Windows, I have to wait about 90 seconds before I can use my internet connection after enabling tethering from the phone.  When I connect either smartphone to either computer and the computer is running Linux, I have to wait about 2.5 seconds before I can use my Internet connection.  My question is, why is there such a ridiculously long delay on Windows?  On Windows, it says "Identifying..." on the adapter for about 60 seconds, then says "Limited Or No Access", then if I keep refreshing my browser, EVENTUALLY it will let me browse. After that it's OK.  On Linux, it connects instantly, just like plugging in an ethernet cable. Boom, done.  I don't think it's hardware related because I have two phones from different manufacturers (Motorola and HTC) running two different versions of Android (2.3.6 and 4.0.4). On the computer side, I have a Lenovo ThinkPad T530 and a hand-made desktop. I've actually tried it on two separate hand-built desktops; one a Nehalem system and one Ivy Bridge. As far as I can tell, they have absolutely nothing to do with one another.  Things I've tried to improve the performance on Windows:   CLEAN install of Windows. Absolutely nothing except base drivers, SP1 and critical updates. No VPN software, no security software, no virtualization software, no custom netfilt drivers whatsoever except those drivers absolutely required to tether to the phone. Unchecking all but TCP/IPv4 in the network connection properties (so unchecking QoS, Client for Microsoft Networks, Link-Layer Topology, etc. Setting static IP and static DNS servers.   None of this helps at all. I simply cannot navigate anywhere on the computer until about 90 seconds after enabling tethering on the phone, and the problem ONLY occurs on Windows. On Linux it's fine.  Pretty stumped about this. For what it's worth my RNDIS driver is version 6.1.7600.16385 and the name is "Remote NDIS based Internet Sharing Device" followed usually by a number like #2, #9, etc. I'm using a genuine copy of Windows in all cases and I've tried both an OEM buildout of Windows from Lenovo (on the ThinkPad) as well as a clean Microsoft install from the retail CD on my desktops.


One of our stored procedure was using Cursor to update rows. Total rows to be updated varies from 1000 to 2000. In our scenario, this stored procedure was taking 50 minutes to complete the update.  I replaced the Cursor and used Table Variable. At any point of time, the Table Variable will also contain 1000 to 3000 rows. When executed the update finished in 2 minutes.  Server is Windows Server 2012 64-bit with 64GB RAM. SQL Server 2008  I want to know whether to replace Table Variable with #TempTable? In the scenario mentioned above, Table Variable is working fine.   I checked few posts on Table Variable. One post says SQL Server decides when to keep Table Variable in memory and when to move it to TempDB.  For the above configuration mentioned, when will Table Variable be moved to TempDB?

This seems to be an area with quite a few myths and conflicting views.  So what is the difference between a table variable and a local temporary table in SQL Server?


These examples i am taking from a grammar book. I want to know why we use past particle from in this instead verb first foam and also mention which type of sentences is it.  1)the garden is filled with men, women and children in the evening. 2)New York is the busiest city in USA. it is always crowded with people.

Can you guys help me with my problem here. I"m confused between these two sentences:     My hand breaks   and      My hand is broken   As far as I'm concerned, for the first sentence "breaks" is a verb. Conversely, for the second sentence "broken" is an adjective. But is the first sentence grammatically correct? If it is, do both sentences indicate the same meaning?


Today while searching I voted on a question and suddenly got a hat so out of curiosity I checked it and it said I received a "Mmmm Bacon" hat, as shown below.     Now the question is how a hat that is to be awarded on 30th of December is awarded on 29th of December? Is this a bug or something else that I failed to understand?

I just got the  hat which states "post or vote on December 21".  Does SE have a time machine now?


Installed 20.04 on 4/23 and can't drag and drop. I've had this issue with previous LTS installs and fixed it by toggling "experimental views" on/off through gsettings. That's not working this time.

If I insert a flash drive and try to drag any files onto desktop - nothing happens.  Or from any other folder.  Drag 'n copy only works if you open desktop in nautilus ("show desktop in files").  I already ran the command:  gsettings set org.gnome.nautilus.preferences use-experimental-views false   It didn't help. How to fix this?