Show $\operatorname{Var}(X)=E(\operatorname{Var}(X\vert \mathcal{F}))+\operatorname{Var}(E(X\vert \mathcal{F}))$  I think the fact that:   $\operatorname{Var}(X\vert \mathcal{F})=E[X^2\vert \mathcal{F}]-E[X\vert \mathcal{F}]^2(*)$  may help me:  using $(*)$  $E(E[X^2\vert \mathcal{F}]+E[X\vert \mathcal{F}]^2)+E[E(X\vert \mathcal{F})^2\vert \mathcal{F}]-E[E(X\vert \mathcal{F})\vert \mathcal{F}]^2$  I know that via the tower property $E[E[X\vert \mathcal{F}]]=E[X]$ BUT does this also hold for $E[E[X\vert \mathcal{F}]^2]$, i.e. is $E[E[X\vert \mathcal{F}]^2]=E[X]?$ Any why?  Any ideas on how to solve the underlying problem

Same as . Let $X$ be a square integrable random variable on $(\Omega,\mathcal{F},P)$. Let $\mathcal{G}$ be a sub-$\sigma$-algebra of $\mathcal{F}$. Define the conditional variance of $X$ given $\mathcal{G}$ by $$\operatorname{var}(X\mid\mathcal{G})=\Bbb{E}[(X-\Bbb{E}[X\mid\mathcal{G}])^2\mid\mathcal{G}]$$ Prove the formula  $$\operatorname{var}(X)=\operatorname{var}(\Bbb{E}[X\mid\mathcal{G}])+\Bbb{E}[\operatorname{var}(X\mid\mathcal{G})]$$  1 I don't understand part of the presented solution.  2 Is my attempt also correct?  3 Alternate solutions?  1 I don't understand this part of the solution wherein  $$\operatorname{var}(X\mid \mathcal{G})=\Bbb{E}[(X-\Bbb{E}[X\mid\mathcal{G}])^2 \mid \mathcal{G}]$$  $ =\mathbb E[ X^2 \mid \mathcal G] - \mathbb E [X \mid \mathcal G]^2 $. I think it is making use of the fact that $\mathbb E [X \mid \mathcal G]$ is $\mathcal G$-measurable in saying:  $\mathbb E[XE[X\mid\mathcal G]\mid\mathcal G] = \mathbb E[X\mid\mathcal G] \ E[X\mid\mathcal G] = E[X\mid\mathcal G]^2$, but isn't $E[X\mid\mathcal G]$ supposed to be bounded? How to show this?  My attempt:  $E(X^2) < \infty$  $\to E(X) < \infty$  $\to E(X\mid\mathcal G) < \infty$, but I don't think .  2 My own attempt: I tried evaluating $$E(\operatorname{var}(X\mid\mathcal{G}))=E(\Bbb{E}[(X-\Bbb{E}[X\mid\mathcal{G}])^2\mid\mathcal{G}])$$  Is it correct to say that $E(\Bbb{E}[(X-\Bbb{E}[X\mid\mathcal{G}])^2\mid\mathcal{G}]) = E([(X-\Bbb{E}[X\mid\mathcal{G}])^2])$?  After expanding the square I encounter $E[XE[X\mid\mathcal G]]$ and rewrite  $= E[E[XE[X\mid\mathcal G]]\mid\mathcal G]$  $ = E[E[X\mid\mathcal G] \ E[X\mid\mathcal G]]$ (*)  $ = E[E[X\mid\mathcal G]^2]$  (*) Assuming this is all correct, I am still unsure about this part. Is it really bounded?  3 Is there a way to go about this without saying $E[X\mid\mathcal G]$ is bounded?  4 Is this wrong? It's from Stochastic Calculus class notes, though the problem is for an Advanced Probability class (and the notes don't say anything about bounded weirdly).


I just got told that if you search for recent games, your games are organized into skill brackets.  Since all my solo matches are in "very high" and I dont consider myself very skilled, and i do a lot of dicking around i wonder how big the "very high" skill bracket is, it must be pretty big.  Are there any Stats from Replay parser/ api sites how many players/matches are in what bracket?

Supposedly DOTA 2 matchmaking is divided into brackets.  I want to know which difficulty bracket I'm in. How can I find this information?


Is there any function $f:\mathbb{R}\to\mathbb{R}$, other than the identity, such that   $$f\circ f\circ f=Id.?$$   That is a pretty simple question, but surprisingly I am not able to say anything about it. If we require only $$f\circ f=Id.,$$ then, there are some answers, like $f(x)=1/x$ and $f(x)=-x$, for example. And if we allow $f$ to be over $\mathbb{C}$, then the original question also has some answers, like $f(x)=e^{2\pi i/3}x$. But none of these generalize to $f:\mathbb{R}\to\mathbb{R}$ such that $f^3=Id.$. Do you have any idea?

Let $f:\mathbb R \to \mathbb R$ be a continuous function such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , then is it true that $f(x)=x , \forall x \in \mathbb R$ ? I can see that $f$ is bijective , hence strictly monotone . But I cannot progress further . Please help. Thanks in advance


I want to get a list of all commands from the ZSH history in ~/.zsh_history.  The file is formatted like so:  : 1467892191:0;cd /usr/share : 1467892276:0;lsrc : 1467892743:0;logout : 1467892751:0;reload : 1484284548:0;echo 'multiple \ line \ test'   Commands may span multiple lines.  The initial format is the same for every command, e.g the regex ^: \d{10}:\d;.  Here's the desired output  cd /usr/share lsrc logout reload echo 'multiple \n line \n test'   Any standard Unix command is fair game.  The purpose of this is so I can pass the list of commands to my $EDITOR to for easy selection for documentation or write-ups.  Here's as far as I got with awk, which prints mostly empty lines.  awk -F': [0-9]{10}:[0-9];' '{ print $1 }' ~/.zsh_history

Often I have complicated installation procedures to follow, like having to build dependencies for buildtools, to build dependencies for the application I wish to install from source.  Once I have done this once, I don't really want to do have to try and remember all the steps I have done.  The command-history in zsh (and other shells) already records what I have done. Is it possible to export the last 100 (for example) commands executed in to a .sh script?    I could then edit this script, remove commands that are from before I started installing, and remove commands that were me making mistake, and be left with a install script I can give to someone else in a similar environment. (Or use myself on another machine.).  I suspect, that my command history is already stored in one of the dot-files in my home directory.


I want to create list view in alert dialog. I pass not empty strings to ArrayAdapter but i receive error "java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.ListView.setAdapter(android.widget.ListAdapter)' on a null object reference"  @Override protected void onListItemClick(ListView l, View v, int position, long id) {     super.onListItemClick(l, v, position, id);     PackageManager pm = getPackageManager();     ApplicationInfo app = applist.get(position);     ArrayAdapter arrayAdapter = null;      try{         AlertDialog.Builder builder = new AlertDialog.Builder(ViewAppsPermissions.this);         final View mView = getLayoutInflater().inflate(R.layout.popup_layout,null);         AlertDialog dialog = builder.create();         builder.setView(mView);         Button button = (Button) mView.findViewById(R.id.button7);         ListView listView = (ListView) mView.findViewById(R.id.textView);         try {              PackageInfo packageInfo = pm.getPackageInfo(app.packageName, PackageManager.GET_PERMISSIONS);             String[] requestedPermissions = packageInfo.requestedPermissions;             System.out.println("lenght :" + requestedPermissions.length);             arrayAdapter = new ArrayAdapter<String>(this, android.R.layout.simple_list_item_1, requestedPermissions);          } catch (PackageManager.NameNotFoundException e) {             e.printStackTrace();         }           listView.setAdapter(arrayAdapter);         dialog.show();     } catch(ActivityNotFoundException e) {         e.printStackTrace();     } catch(Exception e) {         e.printStackTrace();     } }   XML:  <LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"     android:layout_width="match_parent"     android:layout_height="match_parent"     android:orientation="vertical" >       <ListView         android:id="@+id/listView"         android:layout_width="match_parent"         android:layout_height="match_parent" />      <Button         android:id="@+id/button7"         android:layout_width="match_parent"         android:layout_height="wrap_content"         android:text="Close" />  </LinearLayout>   Stack Trace :  W/System.err: java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.ListView.setAdapter(android.widget.ListAdapter)' on a null object reference W/System.err:     at com.example.admin.sap.displayScreens.ViewAppsPermissions.onListItemClick(ViewAppsPermissions.java:75) W/System.err:     at android.app.ListActivity$2.onItemClick(ListActivity.java:319) W/System.err:     at android.widget.AdapterView.performItemClick(AdapterView.java:334) W/System.err:     at android.widget.AbsListView.performItemClick(AbsListView.java:1531) W/System.err:     at android.widget.AbsListView$PerformClick.run(AbsListView.java:3667) W/System.err:     at android.widget.AbsListView$3.run(AbsListView.java:5590) W/System.err:     at android.os.Handler.handleCallback(Handler.java:739) W/System.err:     at android.os.Handler.dispatchMessage(Handler.java:95) W/System.err:     at android.os.Looper.loop(Looper.java:145) W/System.err:     at android.app.ActivityThread.main(ActivityThread.java:5942) W/System.err:     at java.lang.reflect.Method.invoke(Native Method) W/System.err:     at java.lang.reflect.Method.invoke(Method.java:372) W/System.err:     at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:1400) W/System.err:     at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:1195) V/ActivityThread: updateVisibility : ActivityRecord{75ac80f token=android.os.BinderProxy@239ba43c {com.example.admin.sap/com.example.admin.sap.displayScreens.ViewAppsPermissions}} show : true

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 own an Android device with a removable MicroSD card. The card uses either FAT32 or ExFAT technology. These are "non-journaling filesystem" technologies, so the data on the cards can become corrupted in certain cases.  Perhaps I should run a consistency check (e.g. fsck / Chkdsk / ScanDisk) every so often.  How can I run a consistency check on my MicroSD card, without having to plug the card into a PC?

Sometimes my SD card gets "corrupted" and this leads to many read/write errors. Usually, connecting the SD card to the windows 7 and selecting the "Error Checking" (Right click the drive > Tools > Error Checking) option finds the corruption and fixes it.  Is there any tool or app for checking SD cards for drive errors and fixing the same from within the android itself?  I'd also like to mention that I'm on rooted froyo with busybox installed.


I have one post with 3 downvote and to receive Peer Pressure badge I've deleted it, but after I've got what I wanted, I've restored it.  Is this legal?   Can I use this technique in the future?

Lets be honest with ourselves does it really matter that people are gaming badges/rep?  Surely if someone is so obsessed with rep that they are willing to go to any length to get it, that's their problem?  I use SO to get questions I can't find the answer to answered, I don't care if the person who answers it has 1 rep or 100,000 rep. If the answer is correct thats all that matters.  If it's wrong I'll vote it down, if it's correct or kind of correct I'll vote it up and maybe comment on it.  Most of the badges could be gamed, but some person some where having "all teh badgezors" is no skin off my backnose. I don't care so long as when I have a question someone is willing to answer it.  I'm all for the community, I answer questions when I can and when it's not already been answered, I up/down vote things as I think is appropriate. Usually I'm motivated by making the community a better place, sometimes I'm motivated by making my rep a round number (I was so chuffed when my rep hit 1337) but I really don't care about who has what badges, sure I feel a little fuzzy inside when I (legitimately) get a badge, because I can see that I have benefited the community in some way, I'm not worried about the penis measuring that seems to make so many people go off the rocker. Who cares if people have more rep than you or don't legitimately have badges?  Fair enough more rep leads to higher levels of privilege but badges don't mean squat, if someone has low enough self esteem that the only way they can get their kicks is by getting virtual badges to put on their virtual sash well they have bigger problems that badge gaming. And why should we care?


I have a URL that looks like:  url.com/show.php?id=abc  url.com/show.php?id=xxx  How would I go about converting that URL to url.com/abc url.com/xxx  How do I go about making friendly URLs in PHP?

The actually URL which my app uses is:  http://site.com/search.php?search=iPhone    but I would like it to be possible to achieve the same with   http://site.com/iPhone   I have no experience of rewrite rules, how can I set this up?  The solution has worked but the new URL is displayed in the address bar. I thought it would have been possible to set this up so that it appears as though the page location is   http://site.com/iPhone   without changing to display   http://site.com/search.php?search=iPhone    Is this possible? Thanks.


Nautilus has some bookmarks in the left-hand bar by default. I do not store any music or videos on my computer, and would like those book marks to disappear. How can I make this happen? The linked question has not been updated to include 16.04 and the answers there do not include the fact that the file in ~/.config/ gets re-written upon log-in.

I want to remove Videos and Music from the left side panel. But, I can't seem to find the option to do so. How do you do that?


Since I've never run into this kind of problem before with an error message, this broken count<0.  Left clicking on package manager is no different than right clicking. (what error message says to do)  What this site says to do is put in command sudo apt-get install-f. Where do I put that command as I have tried different places without anything happening.  I'm just into basic computer use so this is a problem for me.

I am a new user, who has just been told to run / execute a command. The answer has some text with a grey background like this text here or  sometimes this text here.   However, I don't know what "run" or "command" means in relation to Ubuntu.  How do I do this?    This is intended for use as a Q&A you can link to when you tell someone to run a command.


What is the proper way to use the DateTime.TryParse() method to convert the string to a DateTime object, and then use the DateTime.ToShortDateString() to reformat the data into the the string?Output:5/26/2016 12:00:00 AMDesired: 5/26/2016 To get current date and time:  DateTime CurrentDateTime = DateTime.Now;  To Convert today's DateTime to short date:  string CurrentDate=CurrentDateTime.ToShortDateString(); To Convert today's DateTime to short time: string CurrentTime= CurrentDateTime.ToShortTimeString()  Resources:

How can I format a date as dd/mm/yyyy or mm/dd/yy ?   Like in VB format("dd/mm/yy",now)  How can I do this in C#?


I am not fluent in English, so I will explain using 2 searches contained in the images below with Breaking Bad tv series as an example ...  Search 1:     Search 2:     If  someone searches Google or any other search engine this phrase (-torrent-download-watch) should be automatically and invisibly added.  Are there any MITM proxy Gurus around here that can help me? If creating the script is hard, I can (please tell me if this is against the rules) hire someone.

I know its a silly question,but i want the search results to be intentionally inaccurate.  Sorry, i am not fluent in english,so i will explain using the  images below with Breaking Bad tv series as an example :      Using (-) sign I can exclude unwanted results,but dont want the other users become aware of it  Any script and software that can help me achieve this?   Edit- I am leaning more towards Fiddler,Are there any Fiddler Gurus around here that can help me,perphaps i can(please tell me if this is against the rules) hire someone.  @krowe - I think the Fiddler way  is more suitable for me,but really really thank you for helping me.


I use 2 monitors on Ubuntu 20.04, let's call them "Old" and "New". Sometimes I only need "New". They seem to work well with following exception: Problem:  When the computer is starting, no matter what option I use, the login screen always appears on the "Old", even if I select "New" in the "single display option". How can this be fixed?  Facts:  Just did a fresh install of Ubuntu 20.04. My monitors are both iiama. "New" is identified by the system as being monitor n°1 and "Old" as monitor n°2. Already tried setting one and then the other as the Primary Display. Already re-arranged monitors position (this was an issue on ubuntu 14.04 which was what I had) and put "New" both to the left and to the right.  Thanks to the links suggested by PRATAP I was able to solve this problem. There were several solutions but the only one that worked for me was  (quoting from the solution):  sudo cp ~/.config/monitors.xml ~gdm/.config/monitors.xml   sudo chown gdm:gdm ~gdm/.config/monitors.xml  And in the /etc/gdm3/custom.conf uncomment WaylandEnable=false (basically remove the # before Wayland)  sudo gedit /etc/gdm3/custom.conf  IMPORTANT!: some of the users referred they had to go into recovery mode to revert this situation because they only got a blank screen and were unable to login. This was not my case as everything worked fine for me. For more information look at the links mentioned by PRATAP, specially the second one, there are other solutions proposed but they didn't work in my case.

On Ubuntu 18.04, I have connected my laptop to an external display and I am able to set the external display as primary and external display only mode. But when I turn on my laptop or log out from my session the display login screen is displayed only on my(internal) laptop screen. But once I login the display switches to external only and my laptop screen turns off as expected. Is there a way I can make the login screen appear only on the external screen on bootup or on logout as in 16.04? Also the login screen does not follow my cursor as in 16.04.


$$\sum_{i=k}^n\binom ik=\binom{n+1}{k+1}$$ $$n,k\in N^+;n\ge k$$  Or it can be expressed as:  $$\sum_{i=k}^ni(i-1)\cdots(i-k+1)=\frac{n+1}{k+1}n(n-1)\cdots(n-k+1)$$ $$n,k\in N^+;n\ge k$$

After reading , the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$  What's the name of this identity? Is it the identity of the  modified.  How can we prove it? I tried by induction, but without success. Can we also prove it algebraically?  Thanks for your help.    EDIT 01 : This identity is known as the  because, on Pascal's triangle, when the addends represented in the summation and the sum itself are highlighted, a hockey-stick shape is revealed.


If I am addressing a card to multiple family members with the last name Thomas, is the correct spelling Thomas's or Thomas'?

When pluralizing family (last) names that also happen to be common English words, does the pluralization follow the same rules as the common word?  For example, "the Smith family" can be pluralized as "the Smiths", but what if the family name is "Wolf" or "Fish"?  Would the correct pluralization be "the Wolfs" or "the Wolves"?


$ax^2+bx+c=0$ is a quadratic equation with integer roots $\alpha,\beta$ and the positive coefficients are in AP.Find $\alpha+\beta +\alpha\beta$.  My attempt:  $\alpha+\beta +\alpha\beta=\frac {-b}{a}+\frac {c}{a}$ and we know $\frac{a+c}{2}=b$.  But I cannot eliminate the $a,b,c$ terms to get the answer $7$ given.  How to do it?Any quick,short,simple solutions?

The terms $a,b,c$ of quadratic equation $ax^{2}+bx+c=0$ are in A.P. and positive. Let this equation have integral root $\alpha,\ \beta$. Then find the value of $\alpha+ \beta + \alpha \cdot \beta$ ?   please point where I'm wrong:  Let common difference be $d$  $\implies \alpha+ \beta + \alpha \cdot \beta=\dfrac{c-b}{a}=\dfrac{d}{a} \implies a|d \ \ \ \ \longrightarrow  \ \ \ \ \              \because (b=a+d$, $c=a+2d)$  Also , $ax^{2}+(a+d)x+(a+2d)=0$.   $\implies$ $\alpha,\ \beta=\dfrac{-(a+d) \pm \sqrt{(a+d)^{2}-4\cdot a \cdot (a+2d)}}{2a}$.   For this to be integer $\sqrt{(a+d)^{2}-4\cdot a \cdot (a+2d)}$ must be perfect square.  $\implies$ ${(a+d)^{2}-4\cdot a \cdot (a+2d)}=p^{2}$ for some $p$.  $\implies -3a^{2}+d^{2}-6ad=p^{2}$  $\implies -3a^{2}+a^{2}q^{2}-6a^{2}q=p^{2}$ $\because$ $a|d \implies aq=d$ for some $q$.  $\implies a^{2}(-3+q^{2}-6q)=p^{2}$   $\implies -3+q^{2}-6q\ $  has to be perfect square. By trial $q=7$  But I need to get this without trial, please help.


I replaced Windows 10 with Ubuntu 16.04 (now Ubuntu is the only OS installed), but every time I turn on my laptop, I still have to choose which OS to use in GRUB. It's not automatically loading Ubuntu, although when I choose Ubuntu it works fine. Is there any way I can make it automatically load Ubuntu? My laptop uses UEFI.

Recently I decided to use only Ubuntu and there is no Windows in my laptop. When I turn on my laptop the GRUB menu is showing but I don't need to choose OS anymore.   How can I remove or hide this? And after removing this how could I access to recovery mode?


My machine is unable to play any video format. Error is:  Videos requires to install plugins to play files of the followings  types:MPEG-1 Layer 3(MP3) decoders, MPEG-4 Video decoder.

How can I install the most used plugins like flash player and mp3 in Ubuntu?


Context  Many writing and referencing styles, as you know, require certain specific guidelines when cross-referencing images, tables, equations, sections etc...  Per example, in the APA style you would adopt the following examples when cross referencing tables and images:  "As shown in Table 2 ..." or "As illustrated in Figure 3 ..."  For the MLA style: you would use: "As illustrated in Fig. 1"  For the IEEE style: "Fig. 4. Intercomplex crosstalk characteristics"  etc...  I am writing a thesis and I want to know kindly what package(s) & what cross-referencing commands should I use in order to make cross-referencing very easy to change between different styles in the future (following exact styles' guidelines), surely the \ref{XYZ} won't do it as this would mean I had to go and change all the instances of figures, tables, equations etc...  I want kindly a very easy way to switch between APA, MLA, Chicago, Harvard, IEEE etc.. at least not more difficult that adding a couple of lines in the preamble of the thesis. I would be hopeful of not doing the whole thing manually.  Kindly can I know how to do that in APA (Figure 3, Table 4) and in MLA (Fig. 1). What lines of LaTeX code can do that?  I apologize if this seems like a neophyte question, I do not know what is the best approach that would lead to the least headache in the future.   The question has some similarities in terms of pros and cons of cross-referencing packages to the question:  but is not duplicate since non of the answers explain how to transform automatically a Figure 1 to Fig. 1 or Table 1 and Tab. 1 or Chapter 1 and Chap. 1 or vice versa depending on specific styles (referencing/Writing styles) such as IEEE, APA, Chicago, Harvard etc...  In other words, is there a package which allow me to plug in something like APA and then all cross-referencing of figures, tables, equations and chapters are changed accordingly to the style? Then later I might decide to switch to MLA, can I easily do that?   Or at least if no package exist that takes into consideration styles: and let us say cleveref is the best option for customization, can anyone kindly tell me how to "marry" [if we can say that :-) ] cleverref package with the APA or with MLA or with IEEE.   There are many who are interested in such answers which this question provide an opportunity to elucidate these solutions.   So you use BibLaTeX APA style, you definitely want to follow also the same exact style in cross-references.  Any suggestions are greatly appreciated.

Inspired by my earlier question , here is another similar question.  There are many different packages for making cross references. Among them , , , , … The  package defines its own cross-referencing command for theorems…  Which collection of packages provides which kind of functionality, and which packages cause conflicts with each other?


My MWE:  \documentclass[12pt]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.9} \usepackage{amsmath} \usepackage{mathspec} \setmainfont[Ligatures=TeX]{Times New Roman} \setmathsfont(Digits,Latin,Greek){Times New Roman}  \begin{document} \pgfplotsset{every axis/.append style={     line width=.1 pt,     tick style={line width=.6pt}},     major grid style={gray!15} } \begin{tikzpicture} \begin{axis}[grid=major, clip mode=individual, height=8cm, width=10cm, %xmin=0, %xmax=0.32, %ymax=7000, enlarge x limits=.1, enlarge y limits=.1, ylabel={Stokes shifts, cm$^{-1}$}, xlabel={$\Delta$f}, minor x tick num=4, minor y tick num=4, every node near coord/.append style={anchor=west,font=\tiny,fill=blue!10,rounded corners=3pt,inner sep=1.5pt,xshift=1mm}, ]   \addplot+[nodes near coords,only marks,point meta=explicit symbolic,black,font=\tiny] table[meta=label] { x   y   label 0.30515 6571.54357  ACN 0.20957 5442.03427  THF 0.26329 6764.93214  DMSO 0.30859 6338.69055  MeOH 0.28869 6125.2616   EtOH 0.24969 5878.82326  n-PenOH 0.20519 5635.74187  n-DecOH 0.00579 5619.78163  Toluene -0.00165    5415.76404  Cyclohexane 0.21467 6038.64734  DME 0.26116 5854.44675  Triton X-100 %0.28679    8886.51915  PC };  \end{axis} \end{tikzpicture} \end{document}     As you can see labels near value 0.25 of x-axis overlap.  Is there a way to adjust position of one of those labels manually or automatically to make graph look better?

Sometimes, it's hard to avoid "colliding" marker labels in scatter plots, by which I mean labels that overlap each other. If I don't want to remove data points to avoid the overlap, is it possible to shift individual labels (as with TikZ nodes)? The following MWE illustrates the problem:  \documentclass{article} \usepackage{tikz} \usepackage{pgfplots} \usepackage[active,tightpage]{preview} \PreviewEnvironment{tikzpicture} \begin{document} \begin{tikzpicture}  \begin{axis}[     xlabel=$a$,     ylabel=$b$ ] \addplot[blue,mark=*,mark options={fill=blue},nodes near coords,only marks,    point meta=explicit symbolic] table[meta=label] { x y label 100 152 {Long label 1} 200 180 {Long label 2} 110 150 {Long label 3} }; \end{axis} \end{tikzpicture} \end{document}   Ideally, I would like to be able to adjust selected labels left/right/up/down. Thanks!


I'm studying about the field of Galois (Finite Fields) and I'm going through a proof that tries to show that if a finite set $F_p$ is a field, then $p$ must be a prime. *note: I cannot link the materials since they're in foreign language    I don't understand the last reasoning of the proof, so I will write all of it out.    Let's assume $p$ is not a prime i.e. $p = qs$. Since we assumed that $F_p$ is a field, than each element different from $0$ has a multiplicative inverse, i.e. $ql=1(mod p)$. From here, we can deduce that $p$ is divisor of $ql-1$. From here, we can deduce that $q$ also has to be divisor of $ql-1$.   I understand everything until the following point: "The last statement is possible only if $q=1$." This means that $p$ must be a prime.  Why is it that if $q|ql-1$, then $q=1$?

I know little about group theory, and the concept of a field characteristic is new to me. Although there are some posts on this website that explain it very well.  "In layman's terms, it's the amount of times we can keep adding 1 to itself without looping back to 0. The characteristic being $p$ means that $\underbrace{1+1+\dots+1}_p=0$."  I think I can get my head around the idea, but there is still something I don't understand.    "We can see quickly using a zero divisor argument that the characteristic of any field with positive characteristic must be prime."  Why is it that it has to be prime? Why can't it be something else?


I have some AMPscript that is working when I preview it against data in a Data Extension. No errors.  However, when I make an edit to the Ampscript content block, even if it's just a HTML TXT change to a word and nothing to do with the Ampscript, I get the below error.  ERROR:     An error occurred when attempting to evaluate an Trim function call. See inner exception for details.   Invalid index (parameter 2) passed to Row function. Index must be less than or equal to the row count.    Index Value: 1    Row Count: 0    Function: Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_PRODUCT_NAME", 0), 1)   Content Block:  Snack Club order details:   %%[   var @XML, @nodes, @rowCount  SET @XML = AttributeValue("XML") SET @productRows = BuildRowSetFromXML(@XML, "/root/ITEM", 0) ]%%   %%[   for @j = 1 to RowCount(@productRows) do      SET @productXML = Concat("<item>", Field(Row(@productRows, @j), "XML"), "</item>")     SET @ITEMPRODUCTNAME = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_PRODUCT_NAME", 0), 1), "Value"))      SET @ITEMPRODUCTSKU = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_PRODUCT_SKU", 0), 1), "Value"))      SET @ITEMPRODUCTURL = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_PRODUCT_URL", 0), 1), "Value"))      SET @ITEMPRODUCTIMGURL = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_PRODUCT_IMG_URL", 0), 1), "Value"))      SET @ITEMQTY = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_QTY", 0), 1), "Value"))      SET @ITEMSUBSCRIPTIONPRICE = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_SUBSCRIPTION_PRICE", 0), 1), "Value"))      SET @ITEMTOTAL = Trim(Field(Row(BuildRowSetFromXML(@productXML, "ITEM/ITEM_TOTAL", 0), 1), "Value"))      SET @rowColor = Iif(Mod(@j,2) == 0, "#ffffff", "#efefef")   ]%%   %%[next @j]%%

                      Product         	                      Quantity         	                      Price         	                      Item Total

                      %%=v(@ITEMPRODUCTNAME)=%%         	                      %%=v(@ITEMQTY)=%%	             $%%=v(@ITEMSUBSCRIPTIONPRICE)=%% Each	             $%%=v(@ITEMTOTAL)=%%

                      Shipping Address         	                      Order Subtotal*             $%%ORDER_SUBTOTAL%%

                      %%SHIPPING_ADDRESS_1%% %%SHIPPING_ADDRESS_2%%         	                      Order Shipping             $%%ORDER_SHIPPING%%

                      %%SHIPPING_ADDRESS_TOWN%%, %%SHIPPING_ADDRESS_STATE%%

                      %%SHIPPING_ADDRESS_ZIP%%

I have a Partner sending some data to a Triggered Email/Data Extension which includes a column for XML data.   The trigger is erroring and not allowing the data to get to the Data Extension.   Below is what they are sending over. Is the formatting of the XML incorrect?  XML data that I've used in the past in Data Extensions starts with....   <?xml version="1.0" encoding="UTF-8" standalone="yes"?>   This version of XML starts with... {"XML":  Could that be it?  {"To": {"SubscriberKey": "test@acme.com", "ContactAttributes": {"SubscriberAttributes": **{"XML":** "<root><ITEM><ITEM_PRODUCT_NAME>dark chocolate nuts & sea salt</ITEM_PRODUCT_NAME><ITEM_PRODUCT_SKU>15127</ITEM_PRODUCT_SKU><ITEM_PRODUCT_URL>https://www.test.com/15127.html</ITEM_PRODUCT_URL><ITEM_PRODUCT_IMG_URL>https://www.test.com/images/nuts.png</ITEM_PRODUCT_IMG_URL><ITEM_QTY>1</ITEM_QTY><ITEM_SUBSCRIPTION_PRICE>12.59</ITEM_SUBSCRIPTION_PRICE><ITEM_TOTAL>12.59</ITEM_TOTAL></ITEM><ITEM><ITEM_PRODUCT_NAME>crunchy peanut butter</ITEM_PRODUCT_NAME><ITEM_PRODUCT_SKU>41800</ITEM_PRODUCT_SKU><ITEM_PRODUCT_URL>https://www.test.com/images/butter.png</ITEM_PRODUCT_IMG_URL><ITEM_QTY>1</ITEM_QTY><ITEM_SUBSCRIPTION_PRICE>11.37</ITEM_SUBSCRIPTION_PRICE><ITEM_TOTAL>9.55</ITEM_TOTAL></ITEM><ITEM><ITEM_PRODUCT_NAME>pear cinnamon & pecan</ITEM_PRODUCT_NAME><ITEM_PRODUCT_SKU>17227</ITEM_PRODUCT_SKU><ITEM_PRODUCT_URL>https://www.test.com</ITEM_PRODUCT_URL><ITEM_PRODUCT_IMG_URL>https://www.test.com/images/apples.png</ITEM_PRODUCT_IMG_URL><ITEM_QTY>1</ITEM_QTY><ITEM_SUBSCRIPTION_PRICE>12.59</ITEM_SUBSCRIPTION_PRICE><ITEM_TOTAL>12.59</ITEM_TOTAL></ITEM></root>", "SHIPPING_LNAME": "Tester", "FIRST_NAME": "Test", "LAST_NAME": "Tester", "ORDER_TOTAL_SAVINGS": -5.97, "MERCHANT_ORDER_ID": "1810002352", "SHIPPING_ADDRESS_STATE": "NY", "ORDER_PLACE_DATE_LONG": "Fri 11 January 2019", "SHIPPING_ADDRESS_ZIP": "10004", "ORDER_SHIPPING": 0.00, "CARD_TYPE": "Visa", "ORDER_SUBTOTAL": 47.32, "ORDER_PLACE_DATE_SHORT": "01/11/2019", "SHIPPING_FNAME": "Test", "SHIPPING_ADDRESS_TOWN": "new york", "ORDER_TOTAL": 47.32, "CARD_EXPIRE": "12/2027", "CARD_HOLDER": "Test Tester", "SHIPPING_ADDRESS_1": "75 broad st", "SHIPPING_ADDRESS_2": "fl 23"}}, "Address": "acme@test.com"}}   AMPSCRIPT IN EMAIL Calling the XML....  %%[   var @LOOPINGAPPENDIX  set @LOOPINGAPPENDIX = AttributeValue("LOOPINGAPPENDIX")  set @productRows = BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM", 0)  ]%%   %%[   for @j = 1 to RowCount(@productRows) do       set @productXML = Concat("", Field(Row(@productRows, @j), "XML"), "")      set @ITEMPRODUCTNAME = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_NAME", 0), 1), "Value"))      set @ITEMPRODUCTSKU = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_SKU", 0), 1), "Value"))      set @ITEMPRODUCTURL = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_URL", 0), 1), "Value"))      set @ITEMPRODUCTIMGURL = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_IMG_URL", 0), 1), "Value"))      set @ITEMQTY = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_QTY", 0), 1), "Value"))      set @ITEMSUBSCRIPTIONPRICE = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_SUBSCRIPTION_PRICE", 0), 1), "Value"))      set @ITEMTOTAL = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_TOTAL", 0), 1), "Value"))      set @rowColor = Iif(Mod(@j,2) == 0, "#efefef", "#ffffff")   ]%%   %%[endif]%%   %%[next @j]%%


I'd like to run Supermicro IPMI console which requires JRE but each time I get this error in Firefox:  You need the latest Java(TM) Runtime Environment. Would you like to update now?   I've downloaded and installed java on /usr/local/java/jre1.8.0_261 and in terminal I get # java -version java version "14.0.2" 2020-07-14 Java(TM) SE Runtime Environment (build 14.0.2+12-46) Java HotSpot(TM) 64-Bit Server VM (build 14.0.2+12-46, mixed mode, sharing)  But after restarted firefox I still can not access JRE. There are some old similar questions  which suggested installing icetea plugin. I did that sudo apt-get install icedtea-8-plugin, but the problem persists. I have also followed  old instructions but it did not work The  says: Starting with Firefox Version 52 (released in March 2017), Firefox has limited support for plug-ins, and therefore will not run Java. Use the Java Control Panel to find the installed Java version. How to find the installed Java version  So I suppose a lot have been changed since Firefox 52 and we need a new instruction if such integration is possible at all. My current firefox is 80.0.1 (64-bit) Really appreciate your hints to resolve this annoying problem.

Mozilla announced that NPAPI will not be supported since the released version 52. This means that Java will not be supported either.  Chromium based browsers do not support java for some time already.  At java.com they suggest using Internet Explorer or Safari.  I am using a Java app to sign banking documents. Is there any way to use Java in Ubuntu?


I'm investigating if two of our processes are producing products with the same or different average measurements.   The first process has been used for a very long time and thus I have a sample size of 430 measurements for it.   The second process is very new and only has a sample size of 15 measurements for it.   I've done an F-test to compare the sample variances for what I have now, and I have no evidence to suggest the variances of the samples are different.   When I perform a t-test for the differences of averages, I get results that indicate a very significant difference between the two processes' measurements.   Is there any test out there that will achieve the goal as the t-test, but will also control for or take into account the very large sample size differences?

I have two independent groups: from one I have drawn a sample of size less than 30 due to its small population, while the second group has sample size 100.  Is it appropriate to use an independent samples t-test in this case?


Find Galois group of $Q=\mathbb{Q}\sqrt{(2+\sqrt2)(3+\sqrt3)}$.   I know the minimal polynomial is $f(x)=x^8 -24x^6+144x^4-288x^2+144$. It's irreducible over $\mathbb{Q}$, hence, $[Q:\mathbb Q]=8$.  Let $g(x^2)=f(x)$. It's splitting field is $K=\mathbb Q(2+\sqrt2)(3+\sqrt3)$. One can show that $K\simeq\mathbb{Q}(\sqrt2,\sqrt3)$. Obviously, $[K:\mathbb{Q}]=4$ and, since $K$ contains $\mathbb Q(\sqrt 2)$ and $\mathbb Q(\sqrt 3)$, $Gal(K,\mathbb Q)\simeq \mathbb Z_2^2$.  Since $[Q:K]=2$, $Gal(Q,K)\simeq \mathbb Z_2$.  I suppose that $Gal(Q,\mathbb Q)\simeq \mathbb Z_2^3$ but I don't really know how to prove that (and not 100% sure if it's true).  Could you please help me?

I aim to prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\Bbb Q$. To do this, I aim to show that it is the splitting field of the minimal polynomial of $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$.  Thee minimal polynomial is $144-288 x^2+144 x^4-24 x^6+x^8$. And all its roots are:$\pm \sqrt{(2\pm \sqrt{2})(3\pm \sqrt{3})}$  I do  notice this post:   But I cannot fully understand how I can do that. My questions are:   Call $\sqrt{(2+ \sqrt{2})(3+ \sqrt{3})}=\alpha$. How can we show that $\pm \sqrt{(2\pm \sqrt{2})(3\pm \sqrt{3})}\in\Bbb Q(\alpha)$? There is a comment which mentioned a trick to check if we have found all the roots.     Part 3 is not tedious at all, just apply the automorphism $\sqrt{2}\rightarrow -\sqrt{2}$ to the polynomial evaluated at $α$ to see that it remains zero. Repeat for $\sqrt{3}$.    I would like to learn about the trick mentioned in the comment but I cannot fully understand it. S ocould someone please show me how to do that?  And now I need to determine the Galois group of $\Bbb Q$. Is there any rather simple way to see what the Galois group is?   Thanks for any help!  EDIT: Now I had stucked on it for some time and I think I do need help...  We know that the automorphism is uniquely determined by where it sent the generater to. So we only need to determine its effect on $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$.   As $(\sigma(\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})))^2=\sigma((\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})}))^2)=\sigma(\mathbb{Q}((2+\sqrt{2})(3+\sqrt{3})))=6+2\sigma(\sqrt{3})+3\sigma(\sqrt{2})+\sigma(\sqrt{6})$. I need to determine where to send $\sqrt{2},\sqrt{3},\sqrt{6}$.   But I only know that I can send $\sqrt{2}\mapsto\pm\sqrt{2}$, same to $\sqrt{3},\sqrt{6}$. But there are then too many possiblities. So what should I do now to rule out some possiblities?  Now I realize that maybe I need not determine where to send $\sqrt{6}$ to because once we determine $\sqrt{2},\sqrt{3}$ we have already know that where to send $\sqrt{6}$...  Is that correct?


I have just started using QGIS 3.4 and want to split a polygon with a line from another layer. I can do this in 2.18 but there is no option in 3.4  Is this correct, is the tool not available

I am trying to split a selected polygon ("regions") with a selected line from another layer ("streets") in QGIS 3.8.3. In the example below, I want to split the selected polygon coloured in yellow with the street pointed at by the blue arrow.    After reading the post , I realized I can't find it either. I installed the plugin, but the tool seems to be missing from my toolbar:


Determine the fourth roots of -16 in the form $x +iy$ where $x$ and $y$ are not trigonometric functions.  I do not even know what they really want from me in this question.  My initial thought wass: $\sqrt[4]{-16} = 0 + 2i = 2i$  but that seems overly simplistic for a problem that counts as 8 points in an exam.

Probably dumb question, but I would like to ask it anyway.  I was to solve this equation:  $z^4 = -16$  At first glance, the way to solve it would be (as any other equation):  $z^2 = \sqrt{-1} * 4 \lor z^2 = -\sqrt{-1} * 4$  $z^2 = 4i \lor z^2 = -4i$  $z = 2\sqrt{i} \lor z = -2\sqrt{i} \lor z = 2i\sqrt{i} \lor z = -2i\sqrt{i}$  However, in suggested answers, there are $z_1, z_2, z_3$ and $z_4$ found using trigonometric formulas. Is there something particulary wrong in my solution and the only proper one uses trigonometric form of complex number?


I've seen a lot of times in c++ libraries tones of objects whose names start with underscores.  I know some cases when this is useful for example:      class Person {     private:         unsigned int age;        //...     public:        Person(unsigned int _age): age(_age) {}     };   here it's useful to distinguish logically same objects _age, age.  But there are also cases when global functions names (not from a class) also have single or multiple underscores. So I would like to understand this in general and more ideologically.  So:  What are the benefits for this kind of naming ?  When it's need to use single and when multiple underscores at the start ?

It's common in C++ to name member variables with some kind of prefix to denote the fact that they're member variables, rather than local variables or parameters. If you've come from an MFC background, you'll probably use m_foo. I've also seen myFoo occasionally.  C# (or possibly just .NET) seems to recommend using just an underscore, as in _foo. Is this allowed by the C++ standard?


The New Image modal dialog in the Disk Utility application (on OS X 10.10.5) opens up with the Cancel button off the bottom of my MacBook Air 11's built-in display.  The green resize button, option resize, and option Window : Zoom don't bring it back on-screen.  How can I get the Cancel where I can see it to close the modal dialog, and/or do something else if another readable button appears to so allow?  Note that the answer to this question:  does not work with the Disk Utility New Image dialog on an MBA 11 (which appears to behave differently from a plain file-picker dialog).  ESC will close the window, but not allow you to actually see the Close button or any other useful buttons nearby for other operations.  Shift-drag-resize by mouse will expand but not shrink the New Image modal sheet enough on an MBA 11.  Making the Disk Utility window full-screen beforehand will not resize the New Image sheet to fit the MBA 11 display.  Any other ideas?

My chooser (file-picker dialog) goes under the dock so I can't see buttons. What can I do?


I am looking for good resources or books on Simple Harmonic Motion and Wave that doesn't require any prior knowledge of those topics. Books that consist    even the derivation of even the very basic equation would be nice.

I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better book. We cover:    coupled oscillators, forced oscillators,  Fourier analysis,  traveling waves,    and some other topics. Any help with the topic would be appreciated.


How do one show $\lim_{n\to \infty} \frac{\tan(n)}{2^n}=0 $ But, I didn't compute $\lim_{n\to \infty} \frac{\tan(n)}{2^n} $, as $\lim_{n\to\infty} \tan(n) $ doesn't exist even in extended real line. So, I am unable to use L'Hospital's rule. What should I do? My other question is what is the limit of $\lim_{n\to\infty} |\tan(n)| $, is it $\infty$ or doesn't exist infinitely? Sorry to everyone for edit, i am now curious about this limit. That's why I edit it. I knew, I asked a different question before in this post, but please don't do vote for closing it, I didn't know much about this $\lim_{n\to \infty} \frac{\tan(n)}{2^n}$ because of the tan(n) term, so , please help me how should I deal with it?

Determine this series converge or diverge, and if it converges, find its value.  $$\sum_{n=1}^{\infty}\frac{\tan{n}}{2^{n}}$$  This was too hard for me, as unboundedness of $\tan{x}$ at infinite number of poles make harder to guess the behavior of value of tangent function at positive integers.  Thanks.


I have been trying to achieve a system which can scale a number down and in between two ranges. I have been stuck with the mathematical part of it.  What im thinking is lets say number 200 to be normalized so it falls between a range lets say  0 to 0.66 or 0.66 to 1 or 1 to 1.66. The range being variable as well.  Any help would be appreciated.  Thanks

I am lost in normalizing, could anyone guide me please.  I have a minimum and maximum values, say -23.89 and 7.54990767, respectively.  If I get a value of 5.6878 how can I scale this value on a scale of 0 to 1.


I am planning to travel to Iran (I am Iranian also) from the U.S. (and I have a permanent residency card i.e. Green card holder) ... do I need a transit visa at Vienna airport?

I found many related questions on this site but I am still not sure about the rules. How can I decide if I need a visa to transit? Schengen members as of May 2021 are as follows:  Austria Belgium Czech Republic Denmark (excluding Greenland and the Faroe Islands - but an open border with the Schengen Area is maintained) Estonia Finland France (excluding overseas departments and collectivities) Germany Greece Hungary Iceland Italy Latvia Liechtenstein Lithuania Luxembourg Malta Netherlands (excluding Aruba, Curaçao, Sint Maarten and the Caribbean Netherlands) Norway (excluding Svalbard) Poland Portugal Slovakia Slovenia Spain (except Ceuta and Melilla) Sweden Switzerland


Can anyone explain how to install it?  This is the error I get while trying to install netbeans:

I'm new to Ubuntu, using 18.04 and trying to install Netbeans or Eclipse but neither of them works.  At first my java was version 10. Searching for solutions I found many suggestions to install version 8 so I installed that and changed my default java to 8, but I'm getting new errors.  Here is the error of eclipse which is in its configuration folder (after running eclipse from terminal, eclipse guided me there to see the error):  !SESSION Sat Jun 09 15:21:19 CEST 2018 ----------------------------------------- !ENTRY org.eclipse.equinox.launcher 4 0 2018-06-09 15:21:19.382 !MESSAGE Exception launching the Eclipse Platform: !STACK java.lang.ClassNotFoundException: org.eclipse.core.runtime.adaptor.EclipseStarter     at java.net.URLClassLoader.findClass(URLClassLoader.java:381)     at java.lang.ClassLoader.loadClass(ClassLoader.java:424)     at java.lang.ClassLoader.loadClass(ClassLoader.java:357)     at org.eclipse.equinox.launcher.Main.invokeFramework(Main.java:626)     at org.eclipse.equinox.launcher.Main.basicRun(Main.java:584)     at org.eclipse.equinox.launcher.Main.run(Main.java:1438)     at org.eclipse.equinox.launcher.Main.main(Main.java:1414)   Netbeans doesn't even give error messages - it just can't load.  Again I searched to see what is wrong it seems these applications even need older versions of java but I can't find any older version. (java doesn't support them)  Can someone please help?


Given the fact that Dursleys were cruel towards Harry and didn't ever want him to know that he is a wizard. If they were somehow successful in keeping him away from Hogwarts, I wonder would it be possible that Harry's magical powers if continuously suppressed by Dursleys turned him into an obscurus?

In the movie, Newt reveals that the beast attacking New York was actually an Obscurus, which he explains is      a burst of dark power that manifests in witch or wizard that represses their magical power.   Now, he goes on to explain that      The oldest known Obscurial was 10 years old, but they're usually younger.   If this is true, why then      did Harry Potter or Hermione Granger not develop an Obscurus? They were not even aware magic existed until they were 11. My only thought would be that they didn't actively repress their magic, just didn't know what it was.   I don't know if there was any more detail given in a companion novel, Pottermore or the book itself, but on the wiki it made no mention of details other than was given in the movie. Are there any additional rules that would explain why this doesn't happen more often?


For example, would you say: "There were carrots and gravy in the fridge." You wouldn't say, "There were gravy." So does this make sense? Another example: "There are radio parts and a radio in the car." You wouldn't say, "There are a radio in the car." So, again, how does this make sense? Any ideas on how to fix this? Thanks.

It seems I put a   Bounty assigned by outside party, two lengthy, reference-citing answers, one "-1" (awarded the bounty), one "-2", two others scored "0" and "-2" respectively, the answers suggesting one or the other is correct, 73 comments and no consensus so far - and me, as the asker, lost without a clue what to think of the answers anymore -  this is no longer "Learners' Level" question, so I thought I'd bring it here and hear what the experts have to say.    Original question:  Plurality of verb depending on plurality of list elements  An edit was suggested to my sentence.     There was were an orange, some grapes, two apples and a small pile of cherries on the plate.   In my native language plurality of the verb always follows plurality of the first element on the list. There were an orange,... sounds awkward to me, no matter what follows up. My simple solution was reordering:     There were some grapes, an orange, two apples and a small pile of cherries on the plate.   But that's not the first time I faced this situation and I'd like to know what the rules of grammar say about that - was my editor overzealous or am I trying to copy rules of my language that don't apply in English?    Someone linked a  for negatives, where the situation is more clear-cut ("There is no..."). Same applies to connection with "or" apparently, per accepted answer there. Still, nothing for "and".  It seems there is a consensus that in that if the verb goes after the list, it will be plural.     an orange, some grapes, two apples and a small pile of cherries were on the plate.   There doesn't seem to be clear consensus for:     On the plate { was | were } an orange, some grapes, two apples and a small pile of cherries   Adding more to the confusion is the abbreviated form: "There's"     One last note. In North America, at least, there is a widespread use of using a singular form like "there is" and "there was", without regard for the subject item or items, and this "there is" is often shortened to "there's":           There's three apples on the table!      Could you please clarify this mess?


I am not sure what I did, but the run dialogue keeps clearing itself after execution. Before, if I typed "cmd" and opened a second time, it would stay there, now it always opens a with an empty entry field. How can I make it so that it remembers the last command I executed?

When opening Run via +R in Windows Server 2019, there are no items in its history or Registry key: (I believe the situation is the same in Windows 10) HKCU\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\RunMRU   I think it's because I deleted a folder in one of the Windows system directories, and while I can't think of the exact name of that folder, I remember its name contains history  Is there a way to fix this?


Let $\alpha,\beta$ be fixed complex numbers and $z$ is a variable complex number such that $|z-\alpha|^2+|z-\beta|^2=k.$Find out the condition for $k$ such that the locus of $z$ is a circle.    I think,if i take $\alpha,\beta$ as diametrically opposite points and $z$ on the circumference,then the $\alpha,\beta$ subtend right angle on $z$.But i cannot figure out the condition.The answer given is $k>\frac{1}{2}|\alpha-\beta|^2$

If $z_1$ and $z_2$ are fixed and satisfies $|z-z_1|^2+|z-z_2|^2=k$   what are the possible values of k so that this equation represents a   circle?   I tried using pythagoras theorem,that the equation of circle should be $z-z_1|^2+|z-z_2|^2=|z_1-z_2|^2$.  So k should be $|z_1-z_2|^2$.But the answer is given is $k>\frac{1}{2}|z_1-z_2|^2$.Where am I going wrong?How to approach the problem (preferably geometrically) ?


I just setup a VPS and I installed everything I needed and it runs well. Problem is that I want it to be able to update automatically and allow me to install plugins without ftp. This is my setup:   I created a new user and group named: "wordpress" Nginx and PHP-FPM both uses "wordpress" as the user and group. I added my own ssh account to the group "wordpress". Lets say my username is "user". I changed the ownership of the files to the user "user" and the group "wordpress" including the right permissions (775 for folders and 664 for files, I will try 755/644 later). Changed folder group (chgrp -R) to "wordpress". I also performed "chmod g+s" on the folder so new files belong to the "wordpress" group.   With all of the above I still can't install new plugin (and probably themes or update), but if I change the files owner to "wordpress" all is fine. Is it not possible to have the "user" own the files so incase I upload my files with sftp I don't have to chown.  TL;DR Is it possible to have WordPress files owned by a user thats in the same group as the group that runs nginx/php-fpm and still be able to install plugins?  edit: More info: nginx.conf at the top contains user wordpress wordpress and pool.d/www.conf contains 2 lines with user = ilyesnl group = ilyesnl. I also confirmed both processes being run by user wordpress.

I'm upgrading multisite to 3.5.1 and it did not allow me to do automatic upgrading I see this message:     "To perform the requested action, WordPress needs to access your web   server. Please enter your FTP credentials to proceed. If you do not   remember your credentials, you should contact your web host."   So I add the FTP credentials in wp-config.php but still does not work. I investigate and found out that Wordpress core files are owned by the root and not by my ssh username. Example of these files are the files in the wp-includes and wp-admin.  Is there a way to perform automatic upgrade of Wordpress multisite without having a root access?


I have a computer with an Ubuntu OEM installation running on it. I want to reinstall Ubuntu on this computer without the OEM installation and do a custom installation instead, but I'm at a dead end. Someone help please.

I would like to see a full how-to guide on how to install Ubuntu.


I added labels to the arrows in an example of the tikz-cd manual:  \begin{tikzcd}   A \arrow[r, bend left=50, ""{name=U, below, draw=red}]   \arrow[r, bend right=50, ""{name=D, draw=red}]   & B   \arrow[Rightarrow, from=U, to=D] \end{tikzcd}   Which gives this:     Now simply setting A and B to lower case results in the following diagram, where the label of the upper arrow is off:    The reason seems to be that the upper-case letters A and B have the same height, whereas a is smaller than b. Anyone has an idea how to fix this?

I need to draw a graph where some nodes have the same y-coordinate. I want the text within the nodes on the same y-coordinate to be baseline-aligned. However, the text seems to be aligned by the bottom lines, not the baseline.   Here's what I tried to do:  \documentclass[final,t]{beamer} \mode<presentation> \usepackage{tikz} \usepackage{pgfplots} \tikzstyle{gate2} = [circle,fill=white,draw=black,minimum size=1cm] \begin{document}     \begin{tikzpicture}         \node[gate2] (mu_0) at (0, 0) {$\mu_0$};         \node[gate2, baseline = (mu_0.base)] (Lambda_0) at (2,  0) {$\Lambda_0  $};     \end{tikzpicture} \end{document}   What I see is that the shapes are at the same y-coordinate (as expected), but mu is higher than Lambda. How do I specify that mu and Lambda should be on the baseline?


When I use the documentclass book, I notice that it will align even numbered pages to the right and odd numbered pages to the left, so that when printed, the text of my document will be closer to the center.  Is there a typographical reason for this, or even a logical one? I would have assumed the opposite alignment so that you would never have the problem that text would become hard to read in the center (oddly worded, sorry) when printed.

Shouldn't the twoside option produce a wider margin at the binding/spine edge, rather than the other way around? I'm using \documentclass[twoside]{report}.


public MultiplicationTable() {     JLabel jl;     JTextField tf;     JButton btn[];     Container c;     JPanel p1, p2, p3;     int a;     String value;      super ("Multiplication Table");     c = getContentPane();     p3 = new JPanel (new FlowLayout());     btn = new JButton[1];     btn[0] = new JButton ("Show Times Table");     jl = new JLabel ("Enter a Number:");     tf = new JTextField(5);     p3 = new JPanel (new BorderLayout(5,5));     p3.add (jl, BorderLayout.NORTH);     p3.add (tf, BorderLayout.CENTER);     p3.add (btn[0], BorderLayout.SOUTH);      btn[0].addActionListener(         new ActionListener()          {             public void actionPerformed(ActionEvent e)              {                 String Value;                 Value = tf.getText();                 if (Value == "1")                 {                     System.out.print ("asd");                 }             }         }     );  }   I would like to make the action listener for the button as I enter "1" in the text field. I really need to work on these codes. I wish you could help. Thanks!

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


I want to inform other that one of the team require additional time to close a task. which one is appropriate  Team needs more time   or  Team need more time

I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved?


Define the sequence of Fibonacci numbers as: $F_1$ = $F_2$ = 1 and $F_n$ = $F_{n−1}$ + $F_{n−2}$ for every n > 2. Prove that, for any positive integer $k$, there is a Fibonacci number ending with $k$ zeroes I am able to figure out that this problem is a application of PigeonHole Principle. I can't figure out how to approach it or what will be the reasoning. Can someone help me out? A little bit wordy and rigorous proof/hint is appreciable.

Let $F_0, F_1, F_2, \ldots$ be the Fibonacci numbers, defined by $F_0 = 0$, $F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for all $n\geq 2$.  In  question Oleg567 conjectured the following interesting fact about Fibonacci numbers: $$ k\mid F_n\quad\Longrightarrow\quad k^d\mid F_{k^{d-1}n} $$ where $k \in \mathbb{N}$ and $n \in \mathbb{N}$. This can be regarded as an analogue of Hensel's lifting lemma.  I would be glad to give a proof (following the share your knowledge, Q&A-style), based on a simple combinatorial identity, and see if others come out with more elegant ones.


I have a network of roads and I would like to obtain a graph made by edges, each of them delimited by a origin node and a end node, such as the picture shows.    I would like to obtain a table made of rows like this      "edge_id, origin_node_id, end_node_id, origin_node_X, origin_node_Y, end_node_X, end_node_Y"    for example, for the a12 edge: "a12, 48.1234, 50.0000, 48.1335, 49.1111", where the origin node 1 coordinates are (48.1234,50.0000) and the end node 2 coordinates are (48.1335,49.1111).  I used the field calculator with these expressions:     x_at(0),y_at(0),x_at(1),y_at(1)    to get "origin_node_X,origin_node_Y,end_node_X,end_node_Y".  Now I am searching for a way to obtain the id of nodes which obviously are in another layer.   So I think that I could need a field calculator expression or python code to relate nodes' layer with edges' layer. I think that "get_feature" could be useful but at the moment I did not find the right way to use it. Another option is to make a text output file with python.

Does anyone have a simple work-flow for drawing cross sections of earth features in QGIS?   My thing is that QGIS is being used to present the plan view, but we have a little interest in some elevations as well. All the data is one set and is simply an elevation value in the attribute table, I don't want to have to move all that to CAD.  One logical workaround is to present the z value as the y.  I am a dunce in paper space in CAD, and would be more comfortable with the QGIS Composer.


Material is wood, I confirmed I can set my spawn using a bed in it, and there's a chair and table along with light sources. I did this in the old patch of terraria as well and it worked fine, but now it doesn't?

I read on the wiki that people will move in under the following conditions:   You do something to please them An empty house is available with a light source, table, and chair (also with walls).   I have a house which is about 7x8, then a roof space above that; about half the area. I could put furniture up there too, but will anyone move in?


How do I prove this if I am given the information that: $p \ge 2$ and is a prime and $g$ is an element of order $p − 1$ in $\Bbb Z_p$. I know I am supposed to use Fermat's little theorem and do a contradiction proof but I am not quite sure on how to do it.

How can I show that the order of an element modulo $n$ divides $\phi(n)$?  I know that if $a$ and $n$ are relatively prime, then the least positive integer $x$ such that $a^x\equiv1\pmod n$ is its order modulo $n$. I also know that, by Euler's theorem, $a^{\phi(n)}\equiv1\pmod n$. Therefore, it must be the case that $x\leq\phi(n)$.  However, all that I am left to do is to show that $kx=\phi(n)$, for some integer $k$. Do you guys have an idea on how to do this? Thanks in advance!


Let $X=(X_1,X_2,...,X_n)$ be an independent multivariate random variable, i.e. $$ F_X(x_1, x_2,...,x_n)=\prod_{i=1}^{n}F_{X_i}(x_i) $$ This implies that if we take 2 components $X_i, X_j$, these are independent as well: $$ F_{(X_i, X_j)}(x,y)=F_{X_i}(x) \cdot F_{X_j}(y) $$ I need to prove that the reverse statement is not true, i.e this is false: $$ F_{(X_i, X_j)}(x,y)=F_{X_i}(x) \cdot F_{X_j}(y) \implies F_X(x_1, x_2,...,x_n)=\prod_{i=1}^{n}F_{X_i}(x_i) $$  A theoretical proof or a counter-example are both acceptable. Thanks, András

Show by a counterexample that for a family $(X_i)_{i\in I}$ of random variables the independence of all pairs $(X_i,X_j)$ with $i,j\in I, i\neq j$ does not imply the independence of the family (It is enough to consider $\mbox{card}(I)=3$.).      Hello, I am searching for a simple example. The professor gave the hint that one might consider random variables which only can take two different values, but I do not know exactly what is meant.  By the way:  We call the family $(X_i)_{i\in I}$ of random variables independent, if $(\sigma(X_i))_{i\in I}$ is independent, whereat we call a family $(\mathcal{E}_i)_{i\in I}$ with $\mathcal{E}_i\subset\mathcal{A}$ independent, if for any finite subset $I_0\subset I$ and any choice $E_i\in\mathcal{E}_i, i\in I_0$, it is $$ \mathbb{P}(\bigcap_{i\in I_0}E_i)=\prod_{i\in I_0}\mathbb{P}(E_i). $$


I have installed Ubuntu 14.04 along with the existing windows 8 ....  I have made three partitions of / , /boot and swap, but seems as it is not visible on windows neither on Ubuntu. What can do for visibility of these drives?

This is not a question on  or  but is a question on access rights and how not to let them bite you in the lower abdomen...  ;-) This question will not help you how to make partitions on your disk, but will tell you what to do in , depending on your personal use case, so choose one of the following:      Note: The above questions can also be used with multiple disks, but the examples in the answers are given for one disk.


Let $X$ be a matrix $2000x2000$ and $Y=adj(X)$. What are the possibilities the rank of $Y$ to be? I can't seem to understand how that size of the matrix is helping in solving the problem. Any hints?  Edit: I forget to tell that $X$ is singluar matrix.

Let $A$ be a square and singular matrix of order $n$.  Is $\operatorname{adj}(A)$ necessarily singular? What would be the rank of $\operatorname{adj}(A)$?


I have developed an automatic train system using minecarts and redstone circuits to let the minecarts travel between stations. It worked so far for lines in the near environment. But I noticed that it fails for longer distances, because the chunks are not loaded - therefore the minecart will stop and never come back, until the chunks were loaded by a passing player.    I am using a 1.9 Vanilla server, and I have full access to the server.  The Chunks don't need to be loaded when no player is on the server. But if there are players, the chunks containing the stations and the line should always be loaded when players are online.  How can I achieve this?  I am willing to install server mods, if necessary, but I only found a mod for MC 1.7. For some tutorials, I am confused about "Lazy Load chunks" and "entity chunks", and I do not know which type I need for my scenario. I also read that it might be possible using command block chains, but I do not know exactly how this works (and if it actually works for this scenario).    I do not understand why you think it is a duplicate. Once again, if the end station is set to a spawn point, then the whole track in the middle (the powered rail) won't work. So the linked question doesn't fit the problem situation.

I have command blocks on my adventure map, the map is partially parkour and has no ground just floating islands, I don't want people too see the command blocks so I put them 200 blocks away and they're supposed to have low render distance but if they have low render distance it won't load and the commands won't be executed, what do i do?


We can do with ease:  myalias='command param1 param2'   then myalias param3 runs   command param1 param2 param3   I need an alias which will run the same, but without the last 'space':  command param1 param2param3   For example I have many servers in /24 subnet and need to run the same command using the ip. So I want alias like command param1 192.168.0. then just run myalias 103 and the command will be applied to 192.168.0.103.  I tried to add $1 at the end of the alias but no luck.

For bash script, I can use "$@" to access arguments. What's the equivalent when I use an alias?


Consider the following expression $$\sqrt[4]{1296}=6$$  To find the 4th root of $1296$, first we write $1296$ as product of prime factors $$1296=3^4 \times 2^4$$  Now, $$\sqrt[4]{1296}=\sqrt[4]{3^4 \times 2^4}=3\times 2=6$$  But, I find it confusing when we have a decimal, say find $\sqrt[4.5]{1296}$  What does it really mean? How do we calculate it? I assume there is some real meaning for this because all the calculators calculates these.  Note: I know $\sqrt[4.5]{1296}=4.91688$ and $4.91688^{4.5}=1296$. This is not what I am asking. Actually, $4.5$th root or $4.5$th power, all are confusing statements to me and I was trying to understand if this has a real meaning.

Say you have a number $x^{\sqrt 2}$.  Is there any way to represent this number so that there's no root (or irrational) as the exponent (so that it's easier to understand for me)? I just can't wrap my head around this.  I was thinking something like $$x^{2^{1/2}}$$ and extending on that idea, but I don't know how.  Also, what about for $x^{\sqrt 3}$? Or $x^{\sqrt n}$?


According the  $3D$  $\in$ $SO(3)$ corresponding to a rotation by an angle $\theta$ about a fixed axis specified by the unit vector $\hat{\omega}=(\omega_x,\omega_y,\omega_z) \in R^3$ defined as follows  \begin{bmatrix} \cos \theta +\omega_x^2 \left(1-\cos \theta\right) & \omega_x \omega_y \left(1-\cos \theta\right) - \omega_z \sin \theta & \omega_x \omega_z \left(1-\cos \theta\right) + \omega_y \sin \theta \\ \omega_y \omega_x \left(1-\cos \theta\right) + \omega_z \sin \theta & \cos \theta + \omega_y^2\left(1-\cos \theta\right) & \omega_y \omega_z \left(1-\cos \theta\right) - \omega_x \sin \theta \\ \omega_z \omega_x \left(1-\cos \theta\right) - \omega_y \sin \theta & \omega_z \omega_y \left(1-\cos \theta\right) + \omega_x \sin \theta & \cos \theta + \omega_z^2\left(1-\cos \theta\right)  \end{bmatrix}  does there exist $n$-dimensional analogue of this formula?  How to find $n$ dimensional rotation matrix which corresponds rotation of an angle $\theta$ around the $(n-2)$-dimensional subspace?

There is a 2d rotation matrix around point $(0, 0)$ with angle $\theta$.  $$ \left[ \begin{array}{ccc} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{array} \right] $$  Next, there is a 3d rotation matrix around point $(0, 0, 0)$ and unit axis $(u_x, u_y, u_z)$ with angle $\theta$ ().  \begin{bmatrix} \cos \theta +u_x^2 \left(1-\cos \theta\right) & u_x u_y \left(1-\cos \theta\right) - u_z \sin \theta & u_x u_z \left(1-\cos \theta\right) + u_y \sin \theta \\ u_y u_x \left(1-\cos \theta\right) + u_z \sin \theta & \cos \theta + u_y^2\left(1-\cos \theta\right) & u_y u_z \left(1-\cos \theta\right) - u_x \sin \theta \\ u_z u_x \left(1-\cos \theta\right) - u_y \sin \theta & u_z u_y \left(1-\cos \theta\right) + u_x \sin \theta & \cos \theta + u_z^2\left(1-\cos \theta\right)  \end{bmatrix}  How it is possible to generalize rotation matrix on $N$ dimension around zero point and $N-2$ dimensional unit axis with angle $\theta$?


I am relatively new to Java and am using it with VS Code. I have downloaded the JAR file for GSON and I would like to use it in order to parse through a JSON structured string and assign it to string variables.   The only issue I am having is actually using the GSON api with the java class that reads through the JSON string and parses it. After downloading the JAR file, how do I import it into my java class that contains the readString method?   I am using VS Code as the IDE and am unable to find any documentation for VS Code  Any advice would be amazing!

I read the Java tutorials on Sun for JAR files, but I still can't find a solution for my problem. I need to use a class from a jar file called jtwitter.jar, I downloaded the file, and tried executing it (I found out yesterday that .jar files can be executed by double clicking on them) and Vista gave me an error saying "Failed to load Main-Class Manifest attribute from [path]/jtwitter.jar".  The guy who coded the .jar file wants me to import it, but where do I store the .jar file to import it in my code? I tried putting both the .jar file and my .java file in the same directory, didn't work.  The file I'm trying to work for is here:   I'm using JCreator LE.


I am facing a problem with Minecraft. It is actually crashing every time I start playing it. I am running Windows 10 64-bit on PC with an Intel Core i5 Processor (2nd Gen). .  My graphics card broke, and this problem appeared afterward. So, is it happening because of the absence of a graphics card?  Thanks! :D

When I try to launch Minecraft 1.7.4 or newer, the game crashes on startup, and the game output screen says this:  #  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=*, pid=*, tid=* # # JRE version: Java™ SE Runtime Environment (7.0_51-b13) (build 1.7.0_51-b13) # Java VM: Java HotSpot™ Client VM (* mixed mode, sharing windows-* ) # Problematic frame: # C  [ig4dev32.dll+0x3e88] OR # C  [ig4dev64.dll+0x55ec] OR # C  [ig4icd32.dll+0x104a77] OR  # C  [ig4icd64.dll+0x84930a]   This happens with both Java 7 and 8.  What causes this error, and what can I do to fix the issue?


Here is the code, changes Section format in document body.  1 Intro 2 Market Study 3 Stakeholder Opinions   to:  1. Intro 2. Market Study 3. Stakeholder Opinions   From .  Code for this is.  % Put period after section numbers. \makeatletter % we use \prefix@<level> only if it is defined \renewcommand{\@seccntformat}[1]{%   \ifcsname prefix@#1\endcsname     \csname prefix@#1\endcsname   \else     \csname the#1\endcsname\quad   \fi} % define \prefix@section \newcommand\prefix@section{\thesection. }% \makeatother    How to perform action, for TOC to match?   But, what do I write, to redefine style in \tableofcontents command? Using the article class.

Here is the code, changes Section format in document body.  1 Start 2 Market Study 3 Stakeholder Opinions   to:  1. Start 2. Market Study 3. Stakeholder Opinions   From [this StackExchange TeX post].   How to perform action, for TOC to match?   But, what do I write, to redefine style in \tableofcontents command? Using the article class.


I'm trying to figure out if for any polynomial $f$,  $f(\cos(t),\sin(t))=\sum_{i,j}a_{i,j}\cos(t)^i\sin(t)^j=0$ implies $x^2+y^2-1$ divides $f$.   Trigonometric identities are not exactly central to the class I am taking, so I believe the question simply wants me to assume this, but I'm still curious as to why it is true.  In trying to prove this, I know that through polynomial division one can get $f=qg+r$ where the degree of $x$ in $r$ is 1 or 0 and $r(\cos(t),\sin(t))=0$.   If the degree of $x$ in $r$ is zero we simply have a polynomial in $\sin(t)$, and a polynomial only has finitely many roots whereas $\sin(t)$ can take infinitely many values, so $r=0$.  If the degree of $x$ in $r$ is one, and there is only an $x$ term, one can argue that we can choose $t$ to make all the $\sin$ terms arbitrarily small and the $\cos$ term close to 1, and if the constant term is equal to -1 just stop close to 1, and if it is close to -1 stop at 1.  However, I don't know how to proceed when there are terms like $xy$ in $r$. I was thinking of looking at it as $x$ times a polynomial in $y$ plus a polynomial in $y$, but I'm not sure if that helps.  I'm sure there is a more simple way to do this that I'm not seeing, any hints?

Pythagoras says that $\cos^2 \theta + \mathrm{sin}^2\theta = 1$ for all real $\theta$.  (Vague) Question. Is this the only relationship between the functions $\cos$ and $\sin$?  More precisely:  Let $\langle \cos,\sin\rangle$ denote the intersection of all subalgebras of the $\mathbb{R}$-algebra of all functions $\mathbb{R} \rightarrow \mathbb{R}$ containing $\{\cos,\sin\}$. (By default, all my algebras are unital, associative and commutative.) Let $A$ denote the $\mathbb{R}$-algebra presented by the generators $\{c,s\}$ and the relation $c^2+s^2=1$. There is a unique $\mathbb{R}$-algebra homomorphism $\varphi : A \rightarrow \langle \cos,\sin\rangle$ given as follows. $$\varphi(c) = \cos, \,\,\varphi(s) = \sin$$  We know that $\varphi$ is surjective.     Question. Is $\varphi$ injective?   So consider $f \in A$. Then $f = \sum_{i,j : \mathbb{N}}a_{ij}s^ic^i$ for certain choices of $a_{ij} : \mathbb{R}$. Now suppose $\varphi(f)=0$. We want to show that $f=0$. Ideas, anyone?


I often get confused by the rules for using hyphens. According to  from the Oxford Dictionaries web site, I must always use a hyphen in these cases:        Hyphens are used in many compound words to show that the component words have a combined meaning.    Hyphens can be used to join a prefix to another word, especially if the prefix ends in a vowel and the other word also begins with one (e.g. pre-eminent or co-own).   Hyphens can also be used to divide words that are not usually hyphenated.      Ok, with these three rules in mind, I suppose I should write living-room: after all, these two words have a combined meaning. To support this argument, I may say we write bedroom — one word only — which means we’ve combined bed and room to refer to one thing, the bedroom. So living room should either be hyphenated or written together as only one single word.   Equally, food handling department should be written as food-handling department even though as with living-room, I have never actually seen it written with a hyphen.   I am a bit confused. Isn’t hyphenating these words arguably a grammatical error,  or does hyphen usage vary from one country to another?  (I mean, for example, that perhaps in England they write living room, in Australia livingroom, and in Canada  perhaps living-room.)    As tchrist pointed out in the comment section, hyphen usage has nothing to do with grammar. It's only a ortographic convention.   The reason I'm asking this question is: I once took an IELTS preparing course and there was a question whose answer was food-handling department but I wrote food handling department. My answer was considered to be wrong - according to the entity behind the course, food-handling department was the only acceptable answer.    Given hypen usage is only convention and not grammar, can we really say I got that question wrong?

Some compound words are written without hyphens (nonaggression, nonbeliever), some with hyphens (well-intentioned), and others with spaces (post office).  Is there a rule or good guide as to which option should be used?


I have tuples, $\{(X_i,Y_i)\}_{i=1}^n$, which are iid.  Suppose I introduce a new variable, $T_i = g(X_i)$, where the function $g$ is arbitrary. Is it true that $\{(T_i, Y_i)\}_{i=1}^n$ are iid as well? Is the following argument correct?    My reasoning:  for $i \neq j$:  \begin{align*} P(T_i \in A, Y_i \in B, T_j \in C, Y_j \in D) &= P(g(X_i) \in A, Y_i \in B, g(X_j) \in C, Y_j \in D) \\ &= P(X_i \in g^{-1}(A), Y_i \in B, X_j \in g^{-1}(C), Y_j \in D) \\ &= P(X_i \in g^{-1}(A), Y_i \in B) P(X_j \in g^{-1}(C), Y_j \in D) \\ \end{align*}  where $g^{-1}(A) = \{ x: g(x) \in A \}$.

Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case.


There are complex $\mathbb C$, quaternions $\mathbb H$ and octonions $\mathbb O$. Is there any higher dimensional generalization of them, such in the $\mathbb R^{16}$? Or why do we just study three kinds of numbers in Mathematics?  Any advice is helpful. Thank you.

In the construction of types of numbers, we have the following sequence:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S}$$  or:  $$2^0 \mathrm{-ions} \subset 2^1 \mathrm{-ions} \subset 2^2 \mathrm{-ions} \subset 2^3 \mathrm{-ions} \subset 2^4 \mathrm{-ions} $$  or:  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions"  With the following "properties":   From $\mathbb{R}$ to $\mathbb{C}$ you gain "algebraic-closure"-ness (but you throw away ordering). From $\mathbb{C}$ to $\mathbb{H}$ we throw away commutativity. From $\mathbb{H}$ to $\mathbb{O}$ we throw away associativity. From $\mathbb{O}$ to $\mathbb{S}$ we throw away multiplicative normedness.   The question is, what lies on the right side of $\mathbb{S}$, and what do you lose when you go from $\mathbb{S}$ to one of these objects ?


I had read that the fabricate a custom IC is very expensive (>10000$) but why?  For example an 555 timer cost <1$. If I design and 555 timer with an inverter at the output in some program (don't include that the license is also expensive) and then I want to fabricate that why will cost so much? What the 555 timer don't have but my IC have which makes the price >10000 times more expensive?  EDIT: I am asking the reason that the price is different between the two ICs!

I have browsed several ASIC manufacturer's webs, but I haven't found an actual number. I assume there would be a fixed cost associated with creating masks and such and then there will be a cost per unit.     Note: that I don't actually want to have an ASIC made, I'm just curious.


I get a null pointer exception. Why? I tried and debugged the code...Java says the String array is filled. But when i start the program without debugging mode, Java says nullpointerexception...  BufferedReader quelle = new BufferedReader(new FileReader(file));     String auftrag = quelle.readLine();     String[] daten = auftrag.split(";"); //... String test;      for(int i = 3;i<=daten.length-1;i+=3)     {          test = daten[i-3] + " " + daten[i-2] + " " + daten[i-1];         g.drawString(daten[i-3] + " " + daten[i-2] + " " + daten[i-1],x,y);         y += 16;     }

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 am finding it difficult to ride a Mountain bike, I feel that it may be more comfortable to change the tyre to that of a road bike, which are thinner in size.  Please advise if I can do so.

I'm an occasional biker. I bought a mountain bike (nothing fancy) with the idea that I might use it off-road or on mountain trails (of which there are many here in Calgary). However, since I've bought it I've done nothing but bike in the city on streets and paved bike trails.  Is there anything worth doing to my bike to convert it to something more suited to urban biking? In particular, the tires have me wondering; they have large rubber off-roading lugs that surely aren't doing me any favors on pavement. I'm not looking to spend a tons of money on a retrofit, but will do so if its worthwhile.


I used to procrastinate on SE by reading recent popular question, which were available from top bar. I can't find them any more. Where are they now?

Before today, I would visit Stack Overflow every day and click somewhere in the upper-left corner (I've forgotten what it said, and it's gone now!) and if I didn't have any notifications I would see a list of interesting questions from various sites in the Stack Exchange network which - I believe - were classified as "hot".  Now this new top bar has appeared, and I have no idea how to get this list any more. I'm not really sure what it was called so my searches have been useless as well.


I solved the equation $\sqrt{6-5x}=x$ as follows: $$(\sqrt{6-5x})^2=x^2$$ $$6-5x=x^2$$ $$0=x^2+5x-6=(x+6)(x-1)$$ $$x=-6 \quad \text{or} \quad x=1$$  If I plug in $x=-6$ into the original equation, I get $\sqrt{6+30}=\sqrt{36}=\pm 6$ and if I plug in $x=1$, I get $\sqrt{6-5}=\sqrt{1}=\pm 1$.  To me it seems that both values satisfy the original equation. I am using an online education system for my class called MyMathLab and the solution is only $x=1$. Why is that?  Thank you in advance.

Last year in Pre-Algebra we learned about square roots. I was taught then that $\sqrt{64}=8$ and $\sqrt{100}=10$, which I understood and accepted. I was also taught that $\pm\sqrt{64} = 8,-8$ because both of those numbers squared is 64, which I also get. But this year, with a new school and teacher in a different state, our teacher is telling us that: $\sqrt{64}=8,-8$ and $\pm\sqrt{64}$ also is $8,-8$. The way to get the positive root of something is: $+\sqrt{64}=8$ And these seem to contradict each other. I was always taught that a regular square root returned a positive number and only a positive number, but now my teacher is saying a regular square root gives two numbers, and considering the square root of a number $n$ is defined as $y^2=n$ I see where he is coming from. Upon researching this Wikipedia says:  For example, $4$ and $−4$ are square roots of $16$ because $4^{2} = (−4)^{2} = 16$  And Wolfram MathWorld says:  Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of $9$ are $-3$ and $+3$  But on the other side, Wolfram Alpha, when given "The square root of 9" gives only 3.  So, which is right? Is $\sqrt{64}$ considered $8$? or is it $8,-8$?


I'd like to create a reference sheet of common distributions for my statistical theory class, but I'm having some issues understanding R's implementation of the negative binomial distribution in the stats package. Here's the code I've been using to visualize the distribution.  ggplot(data.frame(x=c(0:30)), aes(x)) + stat_function(geom="point", n=16, fun=dnbinom,                 # Arguments to pass to dnbinom()               args = c(p = 0.2, size = 2))   By my understanding of the NBD, p = 0.2 should be the probability of success (or failure, depending on your framing), and size = 2 should be the number of successes we are looking to observe. However, the output of the plot is .  I'm having trouble understanding how it's possible to have any probability mass at 0, before we've run any trials at all. I've read the documentation for dnbinom(), but I'm still not sure why this is the result, and the docs don't offer details on the exact equation that was implemented, or a sufficiently basic example that would show how the function works. Any advice/input would be much appreciated. Thanks!

I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of R gives me Negative Binomial as the best-fit. Now from the  page, the definition is given as:     NegBin(r,p) distribution describes the probability of k failures and r   successes in k+r Bernoulli(p) trials   with success on the last trial.   Using R to perform model fitting gives me two parameters mean and dispersion parameter. I am not understanding how to interpret these because I cannot see these parameters on the wiki page. All I can see is the following formula:    where k is the number of observations and r=0...n. Now how do I relate these with the parameters given by R? The help file does not provide much information either.   Also, just to say a few words about my experiment: In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment.   Now, if the model fits the Negative Binomial, I can blindly say that it follows that distribution but I really want to understand the intuitive meaning behind this. What does it mean to say that the number of people contacted by my test subjects follows a negative binomial distribution? Can someone please help clarify this?


I am applying for some postdoc programs and have come across a requirement called "motivated letter of application" which I assume is essentially similar to what many here refer to as statement of purpose.   Since I never had to write such a letter before I am not quite sure what it should contain. I couldn't find any specific instructions regarding the letter so I wonder whether or not there are general (subject-agnostic) guidelines or expectations regarding this type of personal letter.   Is it essentially about:   who I am, or  what I have done so far, or what I want to do in the future, or why I am applying to this specific position?   (1) is essentially answered by the CV, so it would be mostly re-iterating the same stuff in a less verbatim/list format.  (2) is again answered partially by the CV and partially by the list of publications and thesis.  That leaves (3) and (4), where the first one is dependent on what resources I can get. I mean, coming from a cross-disciplinary field I can imagine developing towards a number of different fields. I don't feel like there is one very specific thing/project I want to do. Finally, (4) is also a bit tricky to answer, since the truth would be as simple as, "it's a cool position". The more elaborate answer would be something like "I like the project description and consider myself fulfilling the requirements"  Those of you who do read such letters of motivation, what do you actually look for in specific terms? Things like "suitability of the candidate" doesn't help much in terms of structuring the letter, I think.

I am putting together my application for a postdoctoral position in theoretical condensed matter physics. The position is not a fellowship and is a regular postdoc position. If you have gone through the process of applying for such positions a number of times, or, even better, if you have reviewed such research statement letters, what are the main points that are sought/you seek in such letters? Specifically, should I put more emphasize on my PhD research to demonstrate my "depth of knowledge" on projects I have worked on (past research), or dwell more on things that I want/am capable to do (future research)?


I am running ubuntu 13.04 and I want to set it up so that all the web traffic in the LAN  must go through my machine .

Few years ago I have configured proxy server on freebsd by IT guys. it's functions   register computers by MAC address. filter web sites, messengers, downloads set few computers without internet access set some computers with limited internet access. set some computers with full internet access /using exception by ip/. save and review internet usage of people.   i have manual how to add computer by mac, add ban list website and restrict or exception a computer. but now it's not working and i can't find it guys to fix it  So I want to try it myself on Ubuntu. Please again please tell me how to configure proxy server on Ubuntu STEP BY STEP? It's very important for me. Please help me. Or if you have already documented manual please share with me.  Thank you for your help


I'm doing some experiments with \hypertarget and \hyperlink (from hyperref) used inside some TikZ nodes and I noticed an unexpected behaviour.  Please consider the following example code:  \documentclass{article} \usepackage{tikz} \usepackage{graphicx} \usepackage{hyperref}  \begin{document}  \hypertarget{test}{This is the target}  \begin{tikzpicture}   \node[rotate=90]      at (0,0)      {\hyperlink{test}{This is the link?}};   \node      at (4cm,0)      {\rotatebox{90}{\hyperlink{test}{This is the link}}}; \end{tikzpicture}%  \end{document}   The output:    As you can see, when the rotate option is used to rotate a node and its contents, the hyperlink doesn't get affected; the text rotates but the clickable area remains unaffected. If the rotation is performed using a \rotatebox applied to the node contents, the hyperlink gets transformed appropriately.  I know that this behaviour has been noticed before and some alternatives (included the use of \rotatebox, \adjustbox or making the whole tikzpicture the contents of the hyperlink) have been suggested in the answers to , but I am not interested here in known workarounds; I want to know the reason behind the behaviour and whether or not it is possible to to get the hyperlinks to obey the rotate option for nodes.

I have a TikZ picture with a node containing a minipage with an itemize environment; each item is a hyperref to other sections of the document.   When scaling the image (for example with \begin{tikzpicture}[scale=.7, transform shape] I've a strange behavior: links in itemize are not in the right place: they present a somewhat vertical offset, as if they don't scale as the rest of image.   Here the MWE:  \documentclass[a4paper]{article} \usepackage{tikz} \usepackage[pdftex]{hyperref} \begin{document}  Here something interesting\label{text:interesting-one} \newpage  Here something interesting, too\label{text:interesting-two} \newpage  and here there are very very interesting stuff\label{text:interesting-three} \newpage  \newpage Now the problem: links rectangles have some offset, making links unusable in case of long itemize  \begin{figure}[htb] \begin{tikzpicture}[scale=.7, transform shape] \node at (0,0) (mynode) { \begin{minipage}{4cm} \begin{itemize} \item \hyperref[text:interesting-one]{First link} \item \hyperref[text:interesting-two]{Second link} \item \hyperref[text:interesting-three]{Third link} \item \hyperref[text:interesting-one]{First link again} \item \hyperref[text:interesting-two]{Second link again} \item \hyperref[text:interesting-three]{Third link again} \end{itemize} \end{minipage} }; \end{tikzpicture} \end{figure} \end{document}   And here a snapshot of the problem    Note: This is evident using the default settings of hyperref package, which draws the red rectangle around links, but it took me some time to found it when only the text is coloured, i.e. when using \usepackage[linkcolor=blue,colorlinks=true]{hyperref}


This is Problem 22-17 in Spivak's Calculus (3rd edition). It says to use the previous problem, which is if $\lim_{n\to\infty}a_n=l$, then $$\lim_{n\to\infty}\frac{\sum_{i=1}^n a_n}{n}=l.$$ I think I'm supposed to let $a_n=f(n)-f(n-1)$ and then $\sum_{i=1}^n a_n=f(n)-f(0)$, so $$\frac{\sum_{i=1}^n a_n}{n}=\frac{f(n)-f(0)}{n}$$ which has the same limiting behavior as $\frac{f(n)}{n}$. But I can't figure out how to use the continuity of $f$, as something like a rescaled version of $\tan$ is periodic and so $f(n+1)-f(n)=0$, but $\lim_{x\to\infty}\frac{\tan(x)}{x}\neq 0$.

Let $f:[0,+\infty)\to\Bbb R$ be a function bounded on each finite interval. I want to show that if $\lim\limits_{x\to+\infty}[f(x+1)-f(x)]= L,$ then also $\lim\limits_{x\to+\infty}\dfrac{f(x)}x = L$


I have some serious suspition that my boss installed some kind of spy software. Maybe a keylogger, screen capture or something to know what I do when he's not at the office.  I have nothing to hide so I don't know if he doesn't tell me anything because he didn't find anything out of place or because I'm being paranoid and he's not spying me.  Either way I want to be sure if I'm being spied because:   I don't want to work for someone he doesn't trust me me It's illegal and I won't allow anyone to store my passwords (I do access my personal email, homebanking and Facebook account during lunch breaks) and personal information.   So... how can I detect spy software in a iMac running OS X 10.6.8? I have full admin permissions know it.  I tried scanning all folders in my user's and system Library but nothing rang any bell but since I think any of this software would hide the folder (either by location or name)  I don't think I'll find a folder named Employeee Spy Data  I also looked all the processes running at different moments with Activity Monitor but again... it's not like the process would be called SpyAgent Helper  Is there a list of known possible folders / processes to look for?  Any other way to detect?

I'm looking at buying a second-hand Mac, probably one that does not include an OS installation disk.  How can I scan it to make sure that it has not had security threats installed on it?  Is there a CD or DVD image I can boot it up with to perform this scan offline?  Edit: prospective machine would be a 2011- or 2012-vintage MacBook Pro.  Also note that I don't have reliable access to high-speed internet, so solutions that involve downloading 5GB over the Internet are not ideal.  For others, though,  may be helpful.


I am looking for a elementary (and possibly short) prove that  $$y^2=x^3+23$$ has no solutions $(x,y)\in \mathbb Z^2$.  Reducing the equation modulo $p$ didn't help.  Thanks in advance:).  Edit: I want to see a solution without using the theory of elliptic curves. This question appeared in our last exam of "introduction to number theory". We only know basic facts like the legendre symbol, hensels lemma, Chinese Remainder Theorem etc..

As the title stated, I am wondering the integers $x,y$ that satisfy the equation $x^2-y^3 = 23$.


I'm a total newbie, so sorry if this is a stupid question.  I was wondering if I could make a version of Ubuntu I could run straight from the USB stick. Not like the installer, but I'd plug it in and it would be a full version of Linux that saves my stuff and all of that.  At first I tried plugging in 2 USB sticks into my computer. One empty one, one with the installer, and install from one onto the other. The installation took a few hours but went fine. However, once it said it was going to reboot, the whole computer crashed. I let it sit for about ten minutes before turning off the PC. When I turned it back on, it seemed fine, but I couldn't boot the USB stick I just installed Ubuntu onto. I can still boot the installer USB fine (I'm actually using the "Try Ubuntu" feature on it to write this), but the installed one doesn't work.  Now I just want to know if there's a straight-forward, newbie-friendly guide on how to make a bootable Ubuntu stick. All the official ones I could find were just for putting the installer on a USB.  Thanks in advance!

If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly.


I need to write a script to test if a service inside of an Android emulator is ready for apk installation or not using this command adb -s emulator-5554 shell pm list package | grep package:com.android.  If the command does not output any one of these substrings in the first line, then the avd is not ready for apk installation  Is the system running? Can't find service online  This is my script if [ $(adb -s emulator-5554 shell pm list package | grep package:com.android. | head -n 1) = *"Is the system running?"* ] ||    [ $(adb -s emulator-5554 shell pm list package | grep package:com.android. | head -n 1) = *"Can't find service"* ] ||    [ $(adb -s emulator-5554 shell pm list package | grep package:com.android. | head -n 1) = *"online"* ] ; then   echo "could not find package service" else   echo "found package service"     fi    but I get this error ./script.sh: line 4: [: =: unary operator expected ./script.sh: line 5: [: =: unary operator expected ./script.sh: line 6: [: =: unary operator expected

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?