While I was writing one of my first papers in LaTeX, I used the reference/citing style that was used in the example provided by the professor. For referencing or citing, he uses ~\ref{} or ~\cite{}, but I noticed that in my document \ref{} and \cite{} gave the same result. Can anyone explain me difference and notation and when to use which if there is a difference?

gained a reputation of painting red the draft dissertations of his students, taking particular note of incidents when they omitted a non-breaking space that should have been included.  I have this list of places where you have to place non-breaking space:   before \cite before \ref before inlined equation   But, I am not sure if I got the rules right; is a non-breaking space mandatory  before all inline equations? How about numbers which occur in the text? And what if I refer to a program variable, or to program text, for example,  The 371 programmers who read, on 11 different occasions, the Java program in Figure~\ref{Program:Example}  noticed that it is peculiar since parameter \texttt{i} is never read by functions \texttt{f()} and \texttt{thisLongFuncgtionName()}...   Do I have to write The 371 programmers or The~371 programmers? on 11 different occasions or on~11 different occasions?  Do I need to write parameter~\texttt{i}? I think I should. What about functions~\texttt{f()}? And should I write and~\texttt{thisLongFuncgtionName()}? How about citations that use author, year convention?  In short, I think have an idea, but no exact definition of when you should add non-breaking space.


I'm trying to prepare a document based the American Chemical Society manuscript sample files, available  under the 'Standard submission option'. However, when I compile the unmodified achemso-demo.tex file, I get warnings that each of the citations is undefined, and they don't show up in the document. I have achemso-demo.tex in the same directory as achemso.bib.   I'm new to LaTeX and don't really know where to start troubleshooting. I'm working in Texmaker using the LaTeX build option.

I've browsed the forums and found a number of posts that have addressed this issue, but none of the solutions seem to work for me. I have the following script that I just copied from the bibtex home page to get familiar with it. Instead of the citation number I get a question mark. I compile using Latex+Bibtex+Latex+Latex+PDFLatex+ViewPDF just as has been previously suggested and the problem persists.   \documentclass[11pt]{article} \usepackage{cite}  \begin{document}  \title{My Article} \author{Nobody Jr.} \date{Today} \maketitle  Blablabla said Nobody ~\cite{Nobody06}.  \bibliography{mybib} \bibliographystyle{plain} \end{document}   My bibliography (Bib.bbl)  @misc{ Nobody06, author = "Nobody Jr", title = "My Article", year = "2006" }    Looking at previous posts one thing that is concerning is that my .bbl looks empty as shown below. Further, I don't have a .blg  \begin{thebibliography}{}  \end{thebibliography}


I am wondering how to turn the following into a question     "Narendra Modi is the 18th Prime Minister of India"   How to ask this as question, so that answer will be  18th  I have tried searching these links but couldn't match my needs.        Some body could help me.. Sorry If I'm vague and dont lambast at me since this is my first post here.

Possible Duplicates:             Given that I want to know Barack Obama is the 44th President of U.S.A, how can I frame a question like:     The how manyeth president is Barack Obama?


I often surf the terraria wiki to look for more interesting things to do or make. So when I found out about the truffle it (the last NPC I need) it sounded like a great thing to get. The truffle had been moaning at me for AGES now (named muscaria) even though I didn't know of its existence. Now I have made a surface mushroom biome and filled all the boxes; but alas, still no joy.  What am I doing wrong?

I currently find myself in a pickle because even after I've built the mushroom biome and met all other requirements, the Truffle NPC won't move in.   I've defeated not only the Wall of Flesh but Ocram already. Created a surface mushroom biome. Built a house made out of mushrooms with mushroom furniture.   I have no idea how long it takes for the NPC to move in or if I'm wrong in any of the steps.


I recently installed lampp and apache is unable to start because there is another web server already running. How do I disable whatever default server might be running in Ubuntu 12.04?

How do I stop Apache2 from automatically starting on boot? I can't seem to find an option that disables the automatic start-up when I turn on the machine.


By definition, the center of G is the set:  $Z(G)$ = {$g\in G|g^{-1}xg=x$ for all $x\in G$}  We need to show that:   The identity element exists It is closed under the operation For every element $g$, there exists in $G$ the inverse element $g^-1$   My attempt:   Since it is defined that:   $g^{-1}xg=x$  Thus implying that $g^{-1}\in G$.   For the identity element $e$ and any element $x\in G$, since the identity element is its own inverse, it then implies:   $e^{-1}xe=x$  Hence $e\in G$.   Now by multiplying by $g$ on both sides, we get:   $g(g^{-1}xg)=gx$  $(gg^{-1})xg=gx$  $(e)xg=gx$  $xg=gx$  Thus, it is closed under the operation, hence implying that $Z(G)$ is a subgroup of $G$. Your help and feedback would be really appreciated.

Question: Let $G$ be a group. Prove that $Z(G)$ is a subgroup of $G$.   If I want to show that $Z(G)$ is a subgroup of $G$ that means I have to show that it is closed under group operation?  Here is my attempt.   Let $a,b$ be elements in $Z(G)$ and $x$ be an element in $G$. Then $ax=xa$ which is under group multiplication commutative and under inverse $(a^{-1}) x=x(a^{-1})$. And hence $(a^{-1})bx= (a^{-1})xb=x (a^{-1})b$ which is under group operation so $(a^{-1}),b$ are elements in $Z(G)$ thus a subgroup of $G$.  Really appreciate if anyone can help me by directing me if my attempt is not good. Thanks in advance.


I'm using Firefox for my browsing needs, and I want to make switching tabs a bit more intuitive. In my  I can use Ctrl+← and Ctrl+→ to switch a tab to the left or right. This works totally intuitive.  In Firefox however, I have to use Cmd+Tab and Cmd+Shift+Tab to switch a tab right or left respectively, which totally annoys me. Does anybody know whether and how I can customize Firefox so that I can use Ctrl+← and Ctrl+→?   All tips are welcome!

How do I reassign the keyboard shortcuts for Firefox? I want to use ctrl+right/left to switch tabs. Is there a plugin for this, if Firefox doesn’t natively support this?


We will be arriving at the domestic Terminal 1B and need to transfer to the International Terminal 2.  We are a family of 4 with 8 pieces of checked luggage and four carry-on bags. Will there be big enough vans available?   We will be arriving around 4:30pm and our connecting international flight is at 10:20 PM. I haven't traveled through Mumbai airport in the last 10 yrs, so not sure about the current amenities.

I am travelling from Chandigarh to Mumbai (T1) and 90 minutes later I need to catch another flight from Mumbai (T2) to Shirdi.  It seems that T1 is domestic and T2 is international. What is the best way to reach to T2 airport so that I catch my flight in 90 minutes?


Sometimes my Ubuntu 16.04 is not shutting down when I am trying to shutdown from the task menu. I am forcing shutdown by pressing the power button. I want to know the reason and solution for this.

My Ubuntu 16.04 hangs on shutdown/restart requiring me to press and hold the power key to turn the machine off... I don't know how to report this as a bug and what commands to run to show the necessary hardware/sys log info? Any help would be hugely appreciated!


I have a webshop with many queries on the different modules. Now I want to change MySQL to one of the two newer versions.  What's the best type to convert my existing MySQL to?

In our place we're split between using mysqli and PDO for stuff like prepared statements and transaction support. Some projects use one, some the other. There is little realistic likelihood of us ever moving to another RDBMS.  I prefer PDO for the single reason that it allows named parameters for prepared statements, and as far as I am aware mysqli does not.  Are there any other pros and cons to choosing one over the other as a standard as we consolidate our projects to use just one approach?


Why this code returns 43 as the result, I expect it to result 42. The code is as follows:  function say667() {   // Local variable that ends up within closure   var num = 42;   var say = function() { console.log(num); }   num++;   return say; } var sayNumber = say667(); sayNumber();

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


Consider this code  \documentclass{report} \usepackage{graphicx} \begin{document} \begin{figure}[htp] \includegraphics[width=0.4\textwidth]{imageA.png} %\includegraphics[width=0.4\textwidth]{imageB.png}                                                                                \end{figure} \end{document}   Compilation works fine with pdflatex. With xelatex however imageA.png is displayed blank while imageB.png appears normally.   I don't see any warnings what might be wrong with imageA.png nor anything specific in the .log files. Nor do I see any warnings referred to in   Any clues?

MWE  Please use the image linked to below.  \documentclass{article} \usepackage{graphicx}  \begin{document} \includegraphics{dank} \end{document}   Oddly enough, only this picture fails and only when compiling with XeTeX (as opposed to pdfTeX or LuaTeX):  ERROR: Dimension too large.  --- TeX said --- <to be read again>                     b l.5 \includegraphics{dank}  --- HELP --- From the .log file...  I can't work with sizes bigger than about 19 feet. Continue and I'll use the largest value I can.    is a bit of an eyesore, so I'm not displaying it inline.  Please check the shasum to make sure it's still the same file when you download it.  $ shasum dank.jpg b889bc28b2ccd079073267159db0562f45b58e4d  dank.jpg   What's special about this image?  Why does it fail?  Its natural setting (as seen with LuaTeX or pdfTeX) is well under 19 feet.


I am curious how to calculate the infinite product  $$ \prod_{k=1}^\infty \left( 1 + \frac{a}{k^2} \right). $$  WolframAlpha  that it is equal to approximately  $$ \prod_{k=1}^\infty \left( 1 + \frac{a}{k^2} \right) \approx \frac{0.31831 \sinh (3.14159 \sqrt{a})}{\sqrt{a}} $$  which I suspect might be given by  $$ \frac{\sinh (\pi \sqrt{a})}{\pi \sqrt{a}}. $$  This in turn suggests that  $$ \sinh a = a \prod_{k=1}^\infty \left( 1 + \frac{a^2}{\pi^2 k^2} \right), $$  which is confirmed by WolframAlpha.  However, I don't know how this is derived.

How do I find:  $$\prod_{n=1}^\infty\; \left(1+ \frac{1}{\pi ^2n^2}\right) \quad$$  I am pretty sure that the infinite product converges, but if it doesn't please let me know if I have made an error. Also, could I have a nice explanation as to how would someone arrive to the answer.  Thanks alot.


I often hear people say things like “That's the reason why I....”  As far as I know, “That's the reason I...” would still be grammatically correct, but I can't find anything stating one way or the other.  Can someone please tell me whether I'm right or wrong?

Can the "why" be removed from the phrase "have some reason why you?"  Example:     Do you have some reason you ____?   vs.     Do you have some reason why you ____?   Are these both grammatically correct? What's the difference, if any? Googling I find a lot of both, but I'm still wondering about this.


Sometimes (perhaps once a month) my system stops responding so bad that it won't react to magic SysRq combinations (which are allowed and do work properly at all other times). I'm quite sure this is due to a resource starvation rather than due to a deadlock, because this happens progressively and the signs are the same every time:  some demanding process takes up 100% CPU and starts allocating large amounts of memory (this is intentional: typically a calculation of some sort), memory allocation goes out of hand (I have a widget to watch resource usage in the toolbar), process switches become laggy, I can't issue the command to cancel the task fast enough, mouse stops moving and keyboard input does not go through, if any music was playing, it goes into a ~3-second loop and then stops.  In several hopeless seconds, everything is completely frozen. This is when every guide tells you to use SysRq, but that does not react either. Allow me to say again, I am absolutely sure I am using the right key combination for the machine and under any other condition I could to S+U+B, or launch the OOM killer, or anything else, but after the first two steps happen my system seems to be beyond the point of no return. Surely enough, the keyboard will still send interrupts to the processor, so the fault is on the kernel's side for not processing them with enough priority (I would expect absolute priority over everything else and unconditional immediate execution of these requests). Is it somehow possible to request reserving some minimal resources in the kernel, in terms of guaranteed CPU time and memory, so that my SysRqs always go through? I'm currently running 5.8.5 kernel in an Arch Linux distribution, if this makes any difference. I have a feeling that the swapping mechanism may be involved, but haven't been able to diagnose this hypothesis properly. I have 12GB of RAM + 4GB swap. Edit: I'm not interested in workarounds like identifying the offending process(es) and limiting its resources in advance. I'm leaving that for the last resort.

I'm running a linux box(ubuntu) and every few months it freezes and I'm left with no choice(SysRq-F and other keyboard shortcuts are not working) but to reboot it losing all the data.   I'm wondering why the kernel is not killing the processe(s) that eats the memory or CPU?   What's the point keeping the system in a frozen/unresponsive state?


Lets say I have a class called Dog. It's a public class. I don't have any access modifier before the bark method. Is that bark method public, default, or something else? Where can I access that method from? I'm assuming only from the object instantiated from the Dog class, but couldn't hurt to ask. Thanks!     public class Dog {     private String name;     private String breed;      //Constructor     Dog(String name, String breed)     {         this.name = name;         this.breed = breed;     }      void bark()     {         System.out.println("ROOF!");     }      String getName()     {         return name;     }      String getBreed()     {         return breed;     } }

In Java, are there clear rules on when to use each of access modifiers, namely the default (package private), public, protected and private, while making class and interface and dealing with inheritance?


Triangle ABC is isosceles with BC as base, AB=AC and Angle A=20 degrees. Points D and E lie on sides AB and AC respectively, such that D lies between A and B, E lies between A and C, angle BCD=50 degrees, angle CBE=60 degrees. Determine Angle ADE.  Edit: I have tried to solve this question with simple additions/subtractions of angles with and without additional geometric constructions to achieve the goal but in vain. Is there a solution that does not involve trigonometry?

The following is a geometry puzzle from a math school book. Even though it has been a long time since I finished school, I remember this puzzle quite well, and I don't have a nice solution to it.  So here is the puzzle:    The triangle $ABC$ is known to be isosceles, that is, $AC=BC$. The labelled angles are known to be $\alpha=\gamma=20°$, $\beta=30°$. The task is to find the angle labelled "?".  The only solution that I know of is to use the sine formula and cosine formula several times. From this one can obtain a numerical solution. Moreover this number can be algebraically shown to be correct (all sines and cosines are contained in the real subfield of the 36th cyclotomic field). So in this sense I solved the problem, but the solution is kind of a brute force attack (for example, some of the polynomials that show up in the computation have coefficients > 1000000). Since the puzzle originates from a book that deals only with elemetary geometry (and not even trigonometry if I remember correctly) there has to be a more elegant solution.


I have a file, /home/user/important.txt. To find it, I use:  find /home/user -type f -name 'important'   Then, I want to open the file in the  editor using a pipe.  How can I do this?  Something like   find /home/user -type f -name 'important' | vi

Is there a way that I can pipe the output of this command (assuming there is only one file found) to vi.  I want to find this command, and then call it up in vi.  Thanks.  find . -name 'id.properties'


After following the instructions in other posts, I am still getting the same error when I try to mount my Windows 8 drive in Ubuntu 14.04 on a dual boot system. I have disabled fast start after shutdown, hybrid hibernation, and the preinstalled Asus Instant On service. I have tried restarting Windows rather than shutting down. In all cases I get the same error message:     Error mounting /dev/sda4 at /media/jesse/OS: Command-line mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda4" "/media/jesse/OS" exited with non-zero exit status 14: Windows is hibernated, refused to mount.   Failed to mount '/dev/sda4': Operation not permitted   The NTFS partition is in an unsafe state. Please resume and shutdown   Windows fully (no hibernation or fast restarting), or mount the volume   read-only with the 'ro' mount option.   I did not have the same issue before upgrading from Ubuntu 12 to 14.   For what it's worth my computer is supposedly a "hybrid" with an SSD drive installed, although I can't see that the SSD drive is being used at all with my present settings. Any thoughts?

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


if I have more than one posts that publish in the same day, the_date() function does not print publish date.  How can I fix it?  thanks  I solve this by: "the_time(get_option('date_format'));"

I am using wordpress 3.2 and I did a query post like this:  <?php query_posts("posts_per_page=1post=type&page=post_parent=10");?>   Then I try to echo out the date of this post I queried like this.  <?php echo the_date(); ?>   It gives me the title of the post and the excerpt and the permalink but no date. What do you think the problem is. I'm sure it's something quite embarrassing.  Here is the code in my template file for the video page:      <?php query_posts("posts_per_page=1post=type&page=post_parent=10");?>
Recent Video

<?php echo the_date(); ?>

<?php echo the_title(); ?><?php echo the_excerpt(); ?>

<a href="<?php echo the_permalink(); ?>" class="more2">Watch Now
   Here I try to put the query in a loop:  <?php query_posts("posts_per_page=1post=type&page=post_parent=10");?> <?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
Recent Video

<?php echo the_date(); ?>

<?php echo the_title(); ?><?php echo the_excerpt(); ?>

<a href="<?php echo the_permalink(); ?>" class="more2">Watch Now
 <?php endwhile; else: ?>
<?php _e('Sorry, no posts matched your criteria.'); ?>
 <?php endif; ?>   the_date() did not work but the the_title() and other functions worked. By the way this changed my query to the_post() which is not what I'm wanting. I want to query the latest video like I did above the loop.  By the way I used the_date function earlier in the page and it worked. Could that be the problem? Here is it before the code that I had a problem with.
     <iframe id="video" src="http://www.youtube.com/embed/videoseries?list=<?php print get_post_meta($post->ID,"playlist_id", true); ?>" width='560' height='350' frameborder="0">

<?php echo get_post_meta($post->ID,"speaker", true); ?>

<?php echo the_date(); ?>


People have been suggesting to use Int32.TryParse but I found out that in case of any string such as "4e",it would give me output 0(i would directly print my input),whereas Int32.Parse would give an Exception. Is  there a  side to using TryParse which I am not able to see? Any help would be much appreciated

What is the difference between Parse() and TryParse()?  int number = int.Parse(textBoxNumber.Text);  // The Try-Parse Method int.TryParse(textBoxNumber.Text, out number);   Is there some form of error-checking like a Try-Catch Block?


Definition: An exotic $\mathbb{R}^4$ is a smooth open 4-manifold $R^4$ that is homeomorphic to $\mathbb{R}^4$ but not diffeomorphic to it. Definition: An exotic $R^4$ is called small if it can be smoothly embedded as an open subset of the standard $\mathbb{R}^4$. We can assume that $R^4$ is an open inside of $\mathbb{R}^4$. Question: Does there exist a small exotic $R^4\subset \mathbb{R}^4$ which is a star-convex subset of $\mathbb{R}^{4}$?

After googling this fact (which is used in Bott and Tu to show the existence of good covers of manifolds) I've gotten the impression this is somewhat difficult to prove.  But I also came across this homework problem (problem 0) with a hint:    which gives me the impression that it is maybe not so difficult as I thought.  If anyone has any thoughts about how to prove this result I'd be very appreciative. Thanks for your time.


The below code results in a NullPointerException. The error is shown at the line linearLayout.addView(listView).  What's wrong?  public class SettingsActivity extends AppCompatActivity{ protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     ListView listView = new ListView(this);     listView.setAdapter(new ArrayAdapter<String>(this,R.layout.settings_list_items_layout,R.id.settings_text_view_id,settingsItem));      LinearLayout linearLayout = findViewById(R.id.settings_linear_layout);     linearLayout.addView(listView);      setContentView(linearLayout);     } }   The error code shown is below  05-10 11:58:37.920 5131-5131/com.example.malai_pt1882.economictimesdemo E/AndroidRuntime: FATAL EXCEPTION: main Process: com.example.malai_pt1882.economictimesdemo, PID: 5131 java.lang.RuntimeException: Unable to start activity ComponentInfo{com.example.malai_pt1882.economictimesdemo/com.example.malai_pt1882.economictimesdemo.SettingsActivity}: java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.LinearLayout.addView(android.view.View)' on a null object reference     at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2778)     at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:2856)     at android.app.ActivityThread.-wrap11(Unknown Source:0)     at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1589)     at android.os.Handler.dispatchMessage(Handler.java:106)     at android.os.Looper.loop(Looper.java:164)     at android.app.ActivityThread.main(ActivityThread.java:6494)     at java.lang.reflect.Method.invoke(Native Method)     at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run(RuntimeInit.java:438)     at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:807)  Caused by: java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.LinearLayout.addView(android.view.View)' on a null object reference     at com.example.malai_pt1882.economictimesdemo.SettingsActivity.onCreate(SettingsActivity.java:34)     at android.app.Activity.performCreate(Activity.java:7009)     at android.app.Activity.performCreate(Activity.java:7000)     at android.app.Instrumentation.callActivityOnCreate(Instrumentation.java:1214)     at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2731)     at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:2856)      at android.app.ActivityThread.-wrap11(Unknown Source:0)      at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1589)      at android.os.Handler.dispatchMessage(Handler.java:106)      at android.os.Looper.loop(Looper.java:164)      at android.app.ActivityThread.main(ActivityThread.java:6494)      at java.lang.reflect.Method.invoke(Native Method)      at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run(RuntimeInit.java:438)      at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:807)   It shows the error in addView() method.

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 arriving at Heathrow Airport Terminal 3 (Air Canada) and departing from Terminal 1 on SAA to SA (layover is 11 hours).  Are there any showers for connecting passengers anywhere (money is no problem), or do I have to leave the airport on a Hoppa Bus and get a day room at one of the local hotels? I don't really want to leave the airport environment! Cheers!

Reading the  questions here, I am not too hopeful, but this is the perfect site to find the answer if it does exist:  Facts:   I arrive at T5 (British Airways) at 08:30, depart at 11:40 from T5 (British Airways) to another country. No time once I reach final destination to shower, Leave straight from work to catch the first leg. US citizen + passport, only final destination visa (currently)   Desire:  I want to shower - 10 mins is plenty.  Assume money is no object (pay for lounge access, cabs etc), but I'd rather not buy full ticket if I can avoid it.  P.S. It's a wedding, so I REALLY want to shower before haha.  EDIT: My plan so far (which doesn't work because it's after Security):   Travel from  Use    UPDATE:  I followed G & Doc's advice and walked over to the Sofitel Hotel (Immigration + walk ~20-25 min total) showered there for £25 and walked back through Security with plenty of time to spare.  Thank you all for your help!


How can I show that  $(n!)^2$ divides $(2n)!$, where $n$ is a natural number?  So far I've noticed that we can rewrite $\dfrac{(2n)!}{(n)!^2}$ as a combination and we know that combinations are always natural, but is there an elegant way that makes more use of divisibility?

Prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer.      For clarity: the denominator is the only part being squared.   My thought process:   The numerator is the product of the first $n$ even numbers and the product of the first $n$ odd numbers.   That is, $(2n!) = (2n)(2n-2)(2n-4)\cdots(2n-1)(2n-3)(2n-5).$ In effect, the product of even numbers can be cancelled out with $n!$ resulting in the following quotient:  $$ \frac{(2^n)(2n-1)(2n-3)}{(n!)}\;.$$  To me this looks even thanks to the powers of $2$. But I am not convinced for some reason.   Was this approach to naive?   Sorry for the poor notation, I don't know any coding languages, my apologies.


As part of a larger proof, I must show that:  $$\sum_{n=1}^{N-1}\cos(2\pi\frac{n}{N})=-1$$  I have thought about this but can't figure out how to get my hands on the value since I don't know any relations between sums of sinusoids and other stuff.  My gut feeling is that this is fairly obvious.    I can't use exponents because the proof this is a part of is showing that $1+\sum_{n=1}^{N-1}z^n=0$ for $z$ on the unit circle, and this argument would require the assumption.  I was thinking of using an argument similar to this:      Consider $\sum_{n=1}^{N}\cos(2\pi\frac{n}{N})$. Notice that $\cos(2\pi\frac{n}{N})=-\cos(\pi-2\pi\frac{n}{N})=-\cos(2\pi\frac{N/2-n}{N})=-\cos(2\pi\frac{3N/2-n}{N})$ so all the terms on the first half of the sum cancel (due to the 2nd-to-last identity), and all the terms on the second half cancel (due to the last identity).   However, formalizing this gets hairy when considering $\floor{\frac{N}{2}}$ that are odd. Is there a simple way to fix my argument?

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series:  $$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \cos \biggl( \frac{ 2 a + (n-1)\cdot d}{2}\biggr)$$  There is a slight difference in case of $\sin$, which is: $$\sum_{k=0}^{n-1}\sin (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \sin\biggl( \frac{2  a + (n-1)\cdot d}{2}\biggr)$$   How do we prove the above two identities?


I used the following    \usepackage[a4paper,width=150mm,top=25mm,bottom=25mm,bindingoffset=6mm]{geometry} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhead{} \fancyhead[RO,LE]{Systemic Crisis: Visualizing Vulnerability} \fancyfoot{} \fancyfoot[LE,RO]{\thepage} \fancyfoot[LO,CE]{chapter \thechapter} \fancyfoot[CO,RE]{Raisul Islam} \renewcommand{\headrulewidth}{0.4pt} \renewcommand{\footrulewidth}{0.4pt}    I am writing my thesis. i have the warning     Package Fancyhdr Warning: \headheight is too small (12.0pt): Make it   at least 14.49998pt. We now make it that large for the rest of the   document. This may cause the page layout to be inconsistent, however.   Please help

My LaTeX file compiles fine. However, in reading my .log file, I see many repeated instances of  Package Fancyhdr Warning: \headheight is too small   Looking for it in google, I found some 'fixes', but first I'd like to know what the error is about.  What is fancyhdr? What is \headheight? What does the error mean?


Is there a way using c# or arcpy to use a polygon to cut a  hole in a database through lines, points, and polygons, like a reverse cookie cutter?  This is without having to import and export the whole database. Just cut the hole in place in the database.

Is there a way to perform a 'reverse' of the clip function in ArcMap?  I am not exactly sure how to explain this so here is a diagram:


I'm really wondering if the Axiom of Choice is essential in this proof.

In Abbott's Proof of the Bolzano-Weierstrass Theorem, does Abbott use any form of the Axiom of Choice ?   I think he is since he chooses an $a_{n_k} \in I_k$ where there are multiple such $a_{n_k}$.


Hello I am trying to prove that given a prime $p$ and a natural $n$ then the highest power of $p$ that divides $n!$ is:  $V(p)=$ $\sum_{i=1}^{\infty}$ $[n/p^i]$   being []: $ℝ→ℤ$ the function that given any number $x$, returns the largest interger $≤x$.  So I figured I could prove that $p^{V(p)}$ divides $n!$ then prove that there is no greater power $m$ such that $p^m$ divides $n!$. The thing is... I cant seem to prove that $p^{V(p)}$ divides $n!$ , tried by induction, tried to divide it and doing it directly, but in every try there's always a bump I cannot seem to get past.  Appreciate any help.

How does one find the highest power of a prime $p$ that divides $N!$ and other related products?  Related question: How many zeros are there at the end of $N!$?    This is being done to reduce abstract duplicates. See   and  for more details.


The question states: "Assume A,B,C,D are pairwise independent events. Decide if A ∩ B and B ∩ D are independent events. Then repeat this assuming the four events are mutually independent." I am not sure how to go about doing this proof and could use some insight on how to do it.

Assume A,B,C,D, are pairwise independent events. Decide if $(A \cap B)$ and $(B \cap D)$ are independent events? Then repeat this assuming the four events are mutually independent.  Well, what I'm thinking is  $P(A \cap B) = P(A) \cdot P(B) \\P(A \cap C) = P(A) \cdot P(C) \\P(A \cap D) = P(A) \cdot P(D) \\P(B \cap C) = P(B) \cdot P(C) $...and soo on , which is what makes it pairwise independent, so assuming this is pairwise,  then that means $(A \cap B)$ and $(B \cap D)$ are also independent because   $P(A \cap B) = P(A) \cdot P(B) \\P(B \cap D) = P(B) \cdot P(D) $......this is correct to say they are independent??  then I dont understand to assume the 4 events are mutually exclusive?  does that mean   $P[(A \cap B) \cap (B \cap D)] = P(A) \cdot P(B) \cdot P(D)$??  Which does not make them independent because of B?  I am not too sure. I am confused and clarification is much appreciated. Any help IS MUCH APPRECIATED TOO.


I came across this sentence on the ACT:  It was adopted by the Akkadians, Hittites, Persians, and others, and used for over 3,000 years.  I can see that the comma in "and others, and used" is helpful for a reader to parse the sentence, but I don't see that the comma is necessary or, frankly, even allowable. My understanding is that you should put a comma and conjunction in between two independent clauses, and you should not put a comma in between a subject and a verb, as in "I went to town, and saw the circus." Yet, that is precisely the sort of comma that I see in the sentence. As far as I know, this is the way the comma should work:  I lost at cards and regret it. (no comma) I lost at cards and checkers and regret it. (no comma) I lost at cards, checkers, and even our drinking game and regret it. (commas for the list)  The structure of the ACT sentence is similar to 3. What am I missing?

I apologize in advance for any and all wrong use of terminology.  Consider a sentence of the form      The project was created to practice X and learn Y.   I believe the "practice X and learn Y" is a compound predicate and so there should be no comma before the "and". However, I get confused if X is a list. If I simply replace the X by "V, W, and X", I get      The project was created to practice V, W, and X and learn Y.   Is this correct? It looks strange to me, and I'm not so sure since the "X and learn Y" could be read as a single item? I was going to write a similar sentence, and I wrote it as     The project was created to practice V, W, and X, as well as to learn Y.   However, if the "as well as" is just a placeholder for "and", then isn't the comma before "as well as" wrong, since it "splits a compound predicate"?  Any help is appreciated. Thank you for your time and have a great day.


I was always told that the former order is the only grammatical one, however, in one of the videos on Youtube () I encountered the latter order:  "The only winning move is to not play"  instead of  "The only winning move is not to play"  Can this order be used in some instances? When can you do this? What is the meaning of such order?

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


In ArcMap, is it possible to automatically (through a tool) snap points in one point layer (A), to points in another point layer (B)?  I do not wish to snap the points to a line, nor do I wish to merge the points - I would like the end result to be a new layer (C) containing points from layer A that have been moved to match the nearest point in layer B.  If a separate layer cannot be created, but layer A is altered to match the locations of layer B, that is also fine.  I don't think a spatial join works for me, as far as I understand it, as I want the physical location of one of the point layers to move.    I also do not wish to merge the two sets of points, but keep them separate.

I have two point shapefiles: Red and Blue.  Each point shapefile has a z value which represents a radius (i.e. represented as buffers in the example).  A duplicate point is defined as a point that lies within Z distance of another point, which can range from 2 - 10 m.  In this example there are ten pairs of duplicate points--seven pairs overlap perfectly, while three pairs overlap by falling within another point's Z value.  I would like to keep only one of each duplicate within Z and merge the two shapefiles together in ArcGIS Desktop.    How can I find and merge duplicate points?


Let $Z_n$ be the set of all $n \times n$ matrices that commute with all $n \times n $ matrices. Show that $$Z_n = \{\lambda I_n \ | \  \lambda \in \mathbb R\}$$  ($I_n$ is the $n \times n$ identity matrix)  I don't know how to use $E_{ij}$ (matrix with $1$ in $(i,j)$ and $0$ elsewhere) and the elementary matrix $P_{ij}$ to prove this question. Can anyone explain it please?

The question is from Axler's "Linear Algebra Done Right", which I'm using for self-study.  We are given a linear operator $T$ over a finite dimensional vector space $V$. We have to show that $T$ is a scalar multiple of the identity iff $\forall S \in {\cal L}(V), TS = ST$. Here, ${\cal L}(V)$ denotes the set of all linear operators over $V$.  One direction is easy to prove. If $T$ is a scalar multiple of the identity, then there exists a scalar $a$ such that $Tv = av$, $\forall v \in V$. Hence, given an arbitrary vector $w$, $$TS(w) = T(Sw) = a(Sw) = S(aw) = S(Tw) = ST(w)$$ where the third equality is possible because $S$ is a linear operator. Then, it follows that $TS = ST$, as required.  I am, however, at a loss as to how to tackle the other direction. I thought that a proof by contradiction,  ultimately constructing a linear operator $S$ for which $TS \neq ST$, might be the way to go, but haven't made much progress.   Thanks in advance!


I'm trying to learn Scala and I'm confused when to use currying functions over partially applied functions.  I'm pretty sure those concepts were not made to be redundant, but I can't see the real purpose of the different approaches.  I was experimenting with this code:  Solution uses currying:  object CurryTest extends App {    def filter(xs: List[Int], p: Int => Boolean): List[Int] =     if (xs.isEmpty) xs     else if (p(xs.head)) xs.head :: filter(xs.tail, p)     else filter(xs.tail, p)    def modN(n: Int)(x: Int) = ((x % n) == 0)    val nums = List(1, 2, 3, 4, 5, 6, 7, 8)    println(filter(nums, modN(2)))   println(filter(nums, modN(3))) }   Solution uses partially applied function:  object PartialFunctionTest extends App {    def filter(xs: List[Int], p: Int => Boolean): List[Int] =     if (xs.isEmpty) xs     else if (p(xs.head)) xs.head :: filter(xs.tail, p)     else filter(xs.tail, p)    def modN(n: Int, x: Int) = ((x % n) == 0)    val nums = List(1, 2, 3, 4, 5, 6, 7, 8)    println(filter(nums, modN(2,_)))   println(filter(nums, modN(3,_))) }   Both give the same result:  List(2, 4, 6, 8) List(3, 6)   Are those different approaches equivalent?  Could somebody enlighten me, what is the best use case for each?

I quite often see on the Internet various complaints that other peoples examples of currying are not currying, but are actually just partial application.  I've not found a decent explanation of what partial application is, or how it differs from currying. There seems to be a general confusion, with equivalent examples being described as currying in some places, and partial application in others.  Could someone provide me with a definition of both terms, and details of how they differ?


I'm firmly of the belief that the stack concept is badly designed but haven't known why until I read this article:    The display of a score to others as a core design point is deeply flawed for the reasons pointed out in the article:     simply holding meritocracy as a value seems to promote discriminatory behavior   Almost every argument about the stack exchange concept invokes the idea that it is a meritocracy and at the same time users of stack sites are continuously complaining about 'noobs' not understanding the system.  I propose that scores for individuals should be made private and only be displayed to that individual. Helping people in order to increase an epeen score is a bad form of incentive.

Coming from Stack Overflow here.  I understand that a point system is a must when you have experienced and inexperienced users all mixed together in the same boat. However, I don't understand the point of being able to see each other reputation. In fact, on Stack Overflow, the only thing that users gain with reputation are privileges, which is okay. However, these privileges are only meta tools that has nothing to do with their actual knowledge (to some extent). That being said, if these personal privileges were private (unknown to other users), it would change absolutely nothing for the other users, and the user itself.  Now, some of you will say that being able to see a user's reputation is a good overall measure of its actual capacity to answer. So when you see two answers which seem valid, but one from a 200 reputation user and one from a 20000 reputation user, our subconscious makes the biased assumption that the latter must be the best one. Even if it's usually the case, there is already a point system that takes care of that. In fact, if the latter is really a better answer, we vote the question up. If one's bad, we vote it down. As simple as that; no need for reputation.  Also, like stated in this , this makes users worry about reputation, just like if it was a form of RPG where some are better than others. However, the reality is that old users benefit from that, and new users will never be able to come as close in terms of reputation. It's not like boxing where you can prove you can knock your opponent. It's a system where only time can push you up, even if you are extremely knowledgeable but unfortunately new to the platform. Most importantly, I think that a platform like Stack Overflow, which is suppose to promote community assistance and development, is bringing down the majority by exposing the minority, when the main reason why we are all here is to learn.  I do think that a system where everyone is equally exposed on the website would be better. The reputation system would remain, but it would be private, just like the money in your bank account. There would be no bias, and the point system would still work as intended (good = +1, neutral = 0, bad = -1). In fact, it would be similar to the Reddit approach (to some extent), which is in my opinion a way more friendly one.  Any toughts?


I wrote a script to backup a database. When I execute it directly, it works. I tried to make it a cron job and while it runs (I checked with service status cron) it seems that it silently fails.  Here is the script:  #!/bin/bash echo "Starting mongo backup" mkdir /home/ubuntu/backups docker exec -it mongodb mongodump --archive=/root/mongodump.gz --gzip docker cp mongodb:/root/mongodump.gz /home/ubuntu/backups/mongodump_$(date +%Y-%m-%d_%H-%M-%S).gz echo "Mongo dump complete" printf "[default]\naccess_key=\nsecret_key=\nsecurity_token=\n" > ~/.s3cfg s3cmd put /home/ubuntu/backups/* s3://my-backup-bucket/ echo "Copy to S3 complete" rm /home/ubuntu/backups/* -r echo "Files cleaned"   I used only absolute paths (EDIT: yeah actually I didn't), no environment variable, no un-escaped %. I don't know what I missed.

Often, crontab scripts are not executed on schedule or as expected. There are numerous reasons for that:   wrong crontab notation permissions problem environment variables   This community wiki aims to aggregate the top reasons for crontab scripts not being executed as expected. Write each reason in a separate answer.  Please include one reason per answer - details about why it's not executed - and fix(es) for that one reason.  Please write only cron-specific issues, e.g. commands that execute as expected from the shell but execute erroneously by cron.


I did not found many results when searching in Google and the items that I found did not help me very much.  How can I add a label "New" to posts that are not older than 24 hours?  Is there a function I can add in my functions.php I can use to manage this?

Every time i publish a new post i want to display an icon like a badge (NEW) and after a specific time it will disappear.  Lets say i publish a new post and i want to display that it is a new post. So i want to insert an icon that for example a star, in each new post in the blog list view into the metadata of the posts. Also i want to be removed after a specific time will pass. Lets say in one day or 24 hours the icon should be removed automatically.  How can i do this?


I am trying to find a sufficient and complete statistics function for $0<\theta<1$ of a sample $X = X_1, \dots, X_n$ from the Geometric Distribution.  We have $f(x;\theta) = (1-\theta)^{x-1}\theta $. Thus :  $$p(x;\theta)=\prod_{i=1}^n(1-\theta)^{x_i-1}\theta=\theta^n\prod_{i=1}^n (1-\theta)^{x_i-1}$$  $$=$$  $$\theta^n(1-\theta)^{\sum_i^n (x_i-1)} = \theta^n\exp\bigg\{(1-\theta)\ln\bigg(\sum_{i=1}^n(x_i-1)\bigg)\bigg\}$$  $$=$$  $$\theta^n\exp\bigg\{(1-\theta)\sum_{i=1}^n\ln(x_i-1)\bigg\}$$  This is an expression of the form of the Exponential Distribution Family and since the support does not depend on $\theta$, we can conclude that it belongs in the exponential distribution family. Thus, a sufficient and complete statistics function for $\theta$, is :  $$\sum_{i=1}^n\ln(x_i-1) \longrightarrow T(x) = \sum_{i=1}^n\ln x_i$$  Question : Is my approach and my conclusion correct ? Thanks in advance for your time.

Let$ X_1, ...,X_n$ be a random sample feom a distribution $Geometric(\theta)$ for $0<\theta<1$. I.e,  $$p_{\theta}(x)=\theta(1-\theta)^{x-1} I_{\{1,2,...\}}(x)$$  Find the unbiased estimator with minimum variance for $g(\theta)=\frac{1}{\theta}$  My attempt:  Since the geometric distribution is from the exponential family, the statistics $$\sum X_i $$ is complete and sufficient for $ \theta$. Also, if $$T(X)=X_1$$ is an estimator for $g(\theta)$, it is unbiased. Therefore, by the Rao-Blackwell theorem and Lehmann-Scheffé Theorem, $$W(X) = E[X_1|\sum X_i]$$ is the estimator we are looking for.  We have the following:  $W(X) = \sum_{i=1}^t i\, P(X_1=i|\sum X_i =t) = \sum_{i=1}^t i\, \frac{P(\sum_{i \geq 2} X_i  =t-i)P(X_1=i)}{P(\sum_{i \geq 1}X_i =t)}$  Since the variables are iid geometric, the sums distributions are both negative binomials. But i am having troubles tosimplify the binomial coefficients and give a final answer with a better form, if it is possible.I wpuld be glad if I could get some help.  Thanks!  Edit: I dont think you guys understand my doubt: Ithink I made all the correct steps, maybe only forgot some indicator function. Here is what I did:  $$...=\sum_{i=1}^ti\frac{\binom{t-i-1}{n-2}\theta^{n-i}(1-\theta)^{t-i-n+1} \theta(1-\theta)^{i-1}}{\binom{t-1}{n-1}\theta^n(1-\theta)^{t-n}}=\sum_{i=1}^t i \frac{\binom{t-i-1}{n-2}}{\binom{t-1}{n-1}}$$  As i said, I am having troubles to simplify this and with the somatory index


TL;DR: How to unregister a camera from Windows?  Windows 7 Professional  I've (stupidly) installed some drivers that would allow my smartphone to appear as a webcam in Windows. I have since removed the associated application  However, things like Skype and Chrome still think I have a webcam. And they try to launch it, which results in "Critical Error: Could not start iWebcamera App."    I see the same error popup periodically in Chrome too.  Neither Skype nor Chrome offer any way to "remove" a camera, so I suppose it is upto Windows to unregister the camera, but I can't seem to find out how.  I tried looking under Device Manager, but couldn't find anything there either.  Question is: How do I unregister a camera from Windows? How can I tell Windows I don't have such a camera that it thinks I do. Where does Windows store it's information about available cameras?

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


I'm trying to figure out how to find the remainder of large numbers not in mod 10 by doing different examples.  Something that I'm working on is $98765 ^ {54321}$ (mod 7).   Can anyone help me find a general way to do these types of problems?

How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and .


I am updating computer stored a couple of years.  It is running Ubuntu 11.10 and I want to upgrade to 13.10. With only 3.9 gigs of ram, it appears the store may have been saying that is highest I can use. Is there anything like a tutorial somewhere?  I am new here. Thanks in advance!

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I do not know where to start, any hints are welcome.

How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$


If $x$ is in radians, then we know that $$\lim_{x \to 0} \frac{\sin x}{x} = 1.$$  An elementary "proof" involving a geometric construction is often found in calculus texts.   And, one can also supply a rigorous proof of this using the machinary of uniformly convergent series of functions. Am I right?  Now I'm wondering if it is possible to give an $\varepsilon$-$\delta$ proof of this statement but using only the trigonometric or circular definition of the sine function.  If so, then can anybody in the valued Math SE community please supply such a proof in a detailed anough answer? Thanks in advance!!

It is well known that   $$\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$$  I know several proofs of this: the geometric proof shows that $\cos(\theta)\leq\frac {\sin(\theta)}{\theta}\leq1$ and using the Squeeze Theorem I conclude that $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$, other proof uses the Maclaurin series of $\sin(x)$. My question is: is there a demonstration of this limit using the epsilon-delta definition of limit?


Let $(X,\mathscr T)$ be a metrizable space such that every metric that   generates $\mathscr T$ is bounded. Prove that $X$ is compact.   My attempt:-  We know that $(X,\mathscr T)$ is metrizable. So there is a metric on $x$ such that collection of all open sets with respect to the metric is the $\mathscr T$. Let $\{d_\alpha\}_{\alpha \in \Lambda}$ be the collection of metric that generates $\mathscr T$. We know that $\forall \alpha \in \Lambda, (X,d_\alpha)$ is bounded.  Suppose on contrary $X$ is not compact. So  $(X,d_\alpha)$ is not sequantially compact. So, there is a $\{x_n\}$ be a sequence in $X$ such that none of its subsequence converges. How do I make contradiction with our assumption?

The title is a claim my classmate made during our summer vacation :D  He showed me a TeX file describing a proof of his claim, and it contains a fairly short but elegant proof. He says that the motivation was to see if the converse of the statement '$(X, d)$ is compact $\Rightarrow$ All metrics homeomorphic to $X$ is bounded.  I was surprised by his work, and wanted to know if it's already discovered and/or published.  So the question is,    Is the claim my classmate made is already discovered? If it is, any references?  How about more general one? like, can we remove/reduce the condition of the claim more weaker?  Are there any underlying theorems or theories in it? If it is not yet discovered, where should I recommend him to publish his work? (LOL) I think it is worth sharing the proof.


Let $f(z)=z^{n}+a_{n-1}z^{n-1}+\cdot\cdot\cdot+a_{0}$ be a complex polynomial such that $|f(z)|\leq 1$ for $|z|\leq 1.$ I have to prove that $f(z)=z^{n}.$   I tried it as   As $|f(z)|\leq 1$ for $|z|\leq 1$ we must have coefficient $a_{0},a_{1}\cdot\cdot\cdot a_{n}$ to be zero because by triangular inequality $$|z^{n}+a_{n-1}z^{n-1}+\cdot\cdot\cdot+a_{0}|\leq 1+|a_{n-1}|+\cdot\cdot\cdot+|a_{0}|$$ so all of the coefficient $a_{0},a_{1}\cdot\cdot\cdot a_{n}$ to be zero. But it is not exact proof. Please suggest me further improvement. Thanks

Let $p(z)=z^{n}+a_{n-1}z^{n-1}+...+a_{0}$ be a polynomial of degree $n\geq1$.  How can you prove that either $p(z)=z^{n}$ or there exists $z'$ with $|z'|=1$ such that $|p(z')|>1$.  Maybe we can use the maximum modulus principle and consider $q(z)=z^{n}p(1/z)$.


I have now asked my "real" question (one whose answer effectively answers this question) here ("").  The  spell's description states:  On a hit, the target takes 1d8 lightning damage, and it can't take reactions until the start of its next turn.  It is unclear to me when the reaction prevention actually occurs (on being hit or on taking damage). I have found this Q/A ("") where a comment from @DavidCoffron says:  [shocking grasp] interrupts the damage taking (which is the trigger), not the hit (which causes the reaction-block)  And then there is this Q/A ("") where the following sentence exists in @chaoticgeek's answer:  In addition you take damage and can't take reactions together so if you can prevent the first you have to prevent the other since it is a chain linked by 'and' in this situation... [T]he reaction prevention only comes with the damage that is dealt  Does the 'and' in shocking grasp really link the clauses enough to make them simultaneous? Are the hit and the damage happening at the same time? Does shocking grasp prevents the target from taking reactions once the spell hits them or once the spell damages them?  I do not believe that this Q/A ("") is a duplicate of mine because I am specifically wondering when you are prevented from taking reactions, which (as the quotes above show) does not seem to be entirely agreed upon.

A few attacks, such as the Shocking Grasp cantrip, can prevent reactions on a target when they hit it.  A few "defensive reactions", such as the Shield spell (+5 to AC including against attack roll), can prevent an attack from succeeding.  I have recently faced the following scenario : I had an AC of 18, and an opponent attacked me with an equivalent of Shocking Grasp, touching with, I believe, a 21. At that moment, I was not sure if I could use my reaction to cast a Shield to jump my AC to 23 (therefore blocking the attack), or if the attack already prevented me from using Shield.  As far as I know, an attack has three phases (make the roll, determine if it hits, then apply the damage and effects). I would believe that the Shield reaction occurs between phase 2 and phase 3, therefore potentially protecting from an attack like Shocking Grasp, but I could be wrong.


I am about halfway through a 3 month summer internship in Bellevue, WA. My pre-tax bi-monthly paychecks are ~$3000 (6k/mo). However, I pay ~$815 in taxes each paycheck. This comes to about 27% in taxes, which makes sense since I am being paid hourly what would equate to about 80k/yr salary. However since this is only a 3-month gig I will only be walking away with ~$18,000 pre-tax (~$10,800 post-tax) at the end of the internship.  I am a Utah resident and I plan to do my final year of my degree at my local university following the internship. The following 9 months I want to be minimally employed, focus on school, and live off the money earned. So, my yearly earnings will likely be well below $35k.  From each paycheck my taxes are broken down as:   ~$190 : OASDI ~$45 : Medicare ~$580 : Federal Withholding   It seems that a 27% tax for <30k/yr of earning is pretty steep. I understand that in ~9 months I can file a tax return and will probably get a large return, but I need every penny I can get now since I am planning to live off it when I return to Utah. I am not a dependent of my parents.   So:  a) Can I somehow lower my taxes since I wont end up making very much money this year? (I think I only put 1 exemption on my W4)  b) Can I get money I was already taxed back before "tax season"?  c) Are all these tax percentages correct and am I not actually being overtaxed?  d) Will I owe the state of Utah a ton of income tax when I return?  FYI: I don't know much about the tax system at all. I just confusingly fill out boxes on the W4 and 1040 and such and am usually taxed appropriately.

I just got out of college, still live with the parents (saving up money) been employed for a year in the industry, and got a not bad starting salary. First check I received was shocking, to see 28.5% cut off for Federal + MA State + SS Employee. And this is prior to enrolling in the 401k.  Is that normal?


If "it" is a noun, what is it? If instead, "it is" is the 3rd person present verb to-be, what is the subject of the sentence? (How is it grammatical to have a sentence consisting only of two verbs in that case?)

Could you please remind me what term linguists and the grammar people use to call it when it's used as a subject pronoun, but the funky thing is that it doesn't really refer back to anything in particular like he, she or we usually do which do refer back to a person or an animal that they stand for.  In grammar-speak, when it is used like that they say that it has no antecedent. I think I knew the term, but I unfortunately forgot it. I did a Google search, but the only thing I could find was empty subject. But the truth is that I don't think that's what they actually use in linguistics. Would you please refresh my memory?  Examples:        It's quite cold today outside. So, I don't really wanna go out.   Did I solve that math problem? Yes. Actually, it was very easy to get it cracked. There was really nothing to it!   Don't mention it! It's nothing. I really like to help people who are in need.


I'm working on this problem:  Let $K=Z/pZ$ where p is a prime. For $n\in Z_+ $, use induction on n to show that for $f=a_0+a_1x+a_2x^2+...+a_nx^n \in K[x]$, it is the case that $f^p=a_0+a_1x^p+a_2x^{2p}+...+a_nt^{np}$  So far I think I have a rough idea of how the base case works, using the fact that $a^p=a$ for any element of K: Let $n=1$. Then $f=a_0+a_1x$ and so $f^p=(a_0+a_1x)...(a_0+a_1x)$. Using the binomial expansion I know that for a prime p, the coefficients of everything except powers of $a_0$ and $a_1x$ are multiples of that prime, and so these elements are cancelled out. This leaves $f^p=a_0^p+a_1^px^p=a_0+a_1x^p$. What I don't understand is the induction step. Suppose it is true for $n=k$. Let $n=k+1$. Then $f=a_0+a_1x+...+a_kx^k+a_{k+1}x^{k+1}$. Any hints about where to go from there? Thank you!

I just need a check for my reasoning:  If I have a ring $R=\mathbb{F}_p[X]$ and elements $x,y\in R$ it is true $$(x+y)^p=x^p+y^p?$$ It is true since every other element of expansion has a multiple of $p$ as coefficient.  What about field $R=\mathbb{F}_p[X]/(f)$ where $f$ is polynomial of degree $n$. I think rule still holds for the same reason.   Also what can be said about $x^p$? Is there any general rule about that element? It seems to me that $x^p=x$ since $(\mathbb{F}_p,\cdot)$ has order $p-1$. Am I missing something?


I hope this is not too complex a question and is simple as in: is there a statistical point, like damage taken vs given, when someone can take Roshan?  I understand this gets complicated by other factors like evasion, but assuming things like that aren't factoring in, when can one Rosh alone?

Aside from Ursa, is there any hero that can solo Roshan at an early level, like level 6 or at least below level 10?


I got trapped in a position when I had an observer tping people to a position and it's stuck on repeat.  Anybody who joins my LAN gets tpd. How do I remove the observer from almost 100 blocks away? I've tried /fill and don't know the coords and I don't want to abandon the world. It's really important. anybody know anything?

I set a command block to /tp. It was supposed to activate only if you had 0 time left, and to activate the command block with a hopper clock to keep giving it power.   But it is not checking if you have 0 time left, so it keeps teleporting me. I can't get close enough to the command block to break it, so I'm stuck in a neverending teleport loop.  Any ideas?


Is there a rule of thumb on how to deal with apostrophies in the following cases?  Group name vs. Group's name Car brand vs. Car's brand  And pretty much anything similar.

I would like to know what the rule is to explain why we do not use the genitive construction hotel's room. Instead, we say "a hotel room".  Other examples:      a hospital bed   a bike stand   Would it suffice to ask "What kind of..."?


when wanting to inform someone of some future event, in which way would you say it, and what are the differences, if any?   (you will) be notified (...) (you will) get notified (...)

In spoken English (at least in America), passives are often formed with "to get" rather than "to be;" I would wager the majority of the time:   he got hit by a car I get driven to work I've gotten called for jury duty eight times   Are there specific verbs that prefer "be" to "get," or vice-versa, or semantic differences between these forms? I cannot think of any.


One covid vaccine must be stored at -70 degrees Celsius. What type of substance or mechanism ensures that the structure of the virus mRNA elements is not distorted at this temperature? And why does this vaccine have to be stored at such a temperature? Does the vaccine contain a cryoprotectant?  If not why? Sorry for My English.

These are the ingredients of :  Medicinal:  mRNA  Non-medicinal:  ALC-0315 = ((4-hydroxybutyl)azanediyl)bis(hexane-6,1-diyl)bis(2-hexyldecanoate) ALC-0159 = 2-[(polyethylene glycol)-2000]-N,N-ditetradecylacetamide 1,2-Distearoyl-sn-glycero-3-phosphocholine cholesterol dibasic sodium phosphate dihydrate monobasic potassium phosphate potassium chloride sodium chloride sucrose water for injection   Sucrose is broken up into glucose and fructose by digestion, and so it normally never enters the blood system. Yet here, it is being directly injected into the body. What happens to this sucrose when it enters the blood system, and why choose sucrose rather than the more standard glucose (dextrose)?


I recently hit the max daily rep (200) for providing an  on the English Stack Exchange site.  Even though I am a person of great modesty and humbleness, cough-cough, I feel that it would be nice to know when my answer receives an upvote.  Is this possible?  Is this already occurring and I am missing something obvious?

When you cap, you don't see any upvotes you get on your profile, therefore, you don't have any update on how your questions / answers are doing unless you look at them manually.   Capping the 200 daily rep is not a reason to stop posting here so could I get notified somehow that my posts are being voted on ? Maybe put a little +X in a different color letting me know that I got these votes but I won't get the reputation for it.   I can go and see in my reputation feed inside my profile and see it :    So I don't see why it wouldn't show up in the feed above.  Maybe putting the feed button green without any +X just like when you aquire a badge.


Is there a field $K \subset \mathbb{R}$ such that $1 < [\mathbb{R} : K] < \infty$? i.e a proper subfield of $\mathbb{R}$ such that the field extension $\mathbb{R}/K$ is finite.

Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite? Here $[\mathbb R:K]$ means the dimension of $\mathbb R$ as a $K$-vector space.  What I have tried:   If we can find a finite subgroup $G\subset Gal (\mathbb C/\mathbb Q)$ such that $G$ contains the complex conjugation, it will be done by letting $K$ be the fixed field of $G$. But I don't know whether such a group exists. Maybe we can start with finding a suitable subgroup of $Gal(\bar{\mathbb Q}/\mathbb Q)$ and then lift it to $Gal(\mathbb C/\mathbb Q)$, where $\bar{\mathbb Q}$ denotes the algebraic closure of $\mathbb Q$. By isomorphism extension theorem, we can find many automorphisms of $\mathbb C$, none of them carries $\mathbb R$ to itself except for the identity. This is because $Gal(\mathbb R/\mathbb Q)$ is the trivial group. For example, now suppose $\{x_\alpha\}\subset \mathbb R$ is a transcendence basis over $\mathbb Q$. Let $\sigma$ be a permutation of $\{x_\alpha\}$, then by the isomorphism extension theorem, $\sigma$ extends to an automorphism of $\mathbb C$, which we still denote by $\sigma$. Then $L=\sigma(\mathbb R)$ is a copy of $\mathbb R$ and $\mathbb R$ is algebraic over $K=\mathbb R\cap L$. How large can $K$ be? Is it possible that $[\mathbb R:K]$ is finite?   Does anyone has some ideas?  Thanks!


I'm trying to read a file containing several variable length lists. Each list is on one line and I read it into a vector. But the last element on each line is getting stored into the vector twice.   I've coded it along the following lines:  ifstream file; file.open("myfile.txt", ifstream::in); string line; while(!file.eof()) {         getline(file, line);         stringstream buffer(line);         vector<int> temp;         while (!buffer.eof())         {                 buffer >> num;                 temp.push_back(num);         }         for(vector<int>::iterator i = temp.begin(); i != temp.end(); ++i)                 cout << *i << ' '; }   Lines of input consist of tab separated integers. There is also a tab after the last element of each line. For a line like  1    3    4    2       The expected output is  1 3 4 2   The output I'm getting is  1 3 4 2 2

The following C++ code uses a ifstream object to read integers from a text file (which has one number per line) until it hits EOF. Why does it read the integer on the last line twice? How to fix this?  Code:  #include <iostream> #include <fstream> using namespace std;  int main() {     ifstream iFile("input.txt");    // input.txt has integers, one per line      while (!iFile.eof())     {         int x;         iFile >> x;         cerr << x << endl;     }      return 0; }   input.txt:  10   20   30   Output:  10   20   30   30   Note: I've skipped all error checking code to keep the code snippet small. The above behaviour is seen on Windows (Visual C++), cygwin (gcc) and Linux (gcc).


I run a startup and we send quite a lot of emails. I've started to BCC these emails that my software sends to myself as an alias. For example:  layke@example.com might be my main email and I'm now sending them to  layke+blind@example.com as a bcc to field, (in addition to the clients email as the main "to" field).  The problem is that I can't seem to create a filter for these emails in my Inbox. I want to archive them immediately, but it doesn't appear as though there is a way to do this.   If I search for emails, I can't see them. I guess this is because Gmail doesn't store the BCC field (even if it's sent to you).     Headers of email:    I think my only option is to create a fully fledged inbox JUST for these BCC's as I can't find any way to identify and label them.

I am using Google Apps for Domains to handle my personal email. I have the following filter configured:  Matches: to:(username@example.com) Do this: Skip Inbox, Mark as read, Delete it   Here is the exported filter XML:  <entry>     <category term='filter'></category>     <title>Mail Filter</title>     <id>tag:mail.google.com,2008:filter:1348992826412</id>     <updated>2012-09-30T08:16:38Z</updated>     <content></content>     <apps:property name='to' value='username@example.com'/>     <apps:property name='shouldMarkAsRead' value='true'/>     <apps:property name='shouldArchive' value='true'/>     <apps:property name='shouldTrash' value='true'/> </entry>   Despite this rule, mail to the username@example.com address is not being matched by the filter. Here is one example headers of a mail that was not caught by the filter:  Delivered-To: username@example.com Received: by 10.49.35.178 with SMTP id i18csp10155qej;         Sun, 30 Sep 2012 02:09:09 -0700 (PDT) Received: by 10.68.225.68 with SMTP id ri4mr32446176pbc.115.1348996149371;         Sun, 30 Sep 2012 02:09:09 -0700 (PDT) Return-Path: <b730@mail.tbb.com.tw> Received: from mail.tbb.com.tw ([210.202.75.124])         by mx.google.com with SMTP id c5si10659paz.41.2012.09.30.02.09.07;         Sun, 30 Sep 2012 02:09:08 -0700 (PDT) Received-SPF: neutral (google.com: 210.202.75.124 is neither permitted nor denied by best guess record for domain of b730@mail.tbb.com.tw) client-ip=210.202.75.124; Authentication-Results: mx.google.com; spf=neutral (google.com: 210.202.75.124 is neither permitted nor denied by best guess record for domain of b730@mail.tbb.com.tw) smtp.mail=b730@mail.tbb.com.tw Received: By OpenMail Mailer;Sun, 30 Sep 2012 16:05:41 +0800 (CST) From: "Loan Financial Private Company" <b730@mail.tbb.com.tw> Reply-To: micheajoh@w.cn Subject: Loan Financial Private Company Message-ID: <1348992338.5369.b730@mail.tbb.com.tw> Date: Sun, 30 Sep 2012 16:05:41 +0800 (CST) MIME-Version: 1.0 Return-Path: b730@mail.tbb.com.tw Content-Type: text/plain; charset=big5 Content-Transfer-Encoding: quoted-printable   Note that I have tens of other similar filters that do properly match mail per address. It is only this one address / filter combination that is failing to match mail.  To proactively address the obvious red herrings and ensure that the discussion remains focused: I am aware of the dangers of posting a live email address publicly. I am aware of Gmail's excellent spam filters. I am aware of the arguments against catch-all email addresses.


I'm looking at  and trying to apply it in my scenario.  My batch file is as follows:  @echo off REM // https://stackoverflow.com/a/39084914/122687 set QT_OPENGL=angle start "D:\ProgramFilesOnD_NoSpaces\Qt\Qt5.7.0\Tools\QtCreator\bin\qtcreator.exe"   And I've created a shortcut (pinned to the Windows 7 start menu) that points to this batch file.  When I click the shortcut, the following happens:   а command prompt window appears for an instant, then it disappears another command prompt windows appears. It doesn't disappear, and it looks like this:      Nothing else happens.   Any idea what's going wrong?

I have a Virtual Machine in Virtual PC 2007.  To start it from the desktop, I have the following command in a batch file:  "c:\program files\Microsoft Virtual PC\Virtual PC.exe" -pc "MY-PC" -launch   But that leaves a dos prompt on the host machine until the virtual machine shuts down, and I exit out of the Virtual PC console.  That's annoying.  So I changed my command to use the START command, instead:  start "c:\program files\Microsoft Virtual PC\Virtual PC.exe" -pc MY-PC -launch   But it chokes on the parameters passed into Virtual PC.  START /? indicates that parameters do indeed go in that location.  Has anyone used START to launch a program with multiple command-line arguments?


I'm facing this error while updating or installing anything in my ubuntu. Here is the full error:   W: An error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: http://repo.mysql.com/apt/ubuntu bionic InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8C718D3B5072E1F5  W: Failed to fetch http://repo.mysql.com/apt/ubuntu/dists/bionic/InRelease  The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8C718D3B5072E1F5  W: Some index files failed to download. They have been ignored, or old ones used instead.   How can I solve all this type of errors?

I added some extra repositories with the Software Sources program. But when I reload the package database, I get an error like the following:     W: GPG error:  trusty InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8BAF9A6F   I know I can fix it using apt-key in a terminal, according to the official Ubuntu documentation. But I would have liked to do it graphically. Is there a way to do this without using a terminal?


Show that arbitrarly close to any rational number there is a real (non-rational) number. In other words, show that to each real $\varepsilon>0$ and each rational $r\in\mathbb Q$ there exists $x\in\mathbb R\setminus\mathbb Q$ with $\left|x-r\right|\lt\varepsilon  $   No idea how to prove this one. Perhaps I can define some sort of sequence and show it converges...?

Possible Duplicate:          I am trying to prove that there exists an irrational number between any two real numbers a and b. I already know that a rational number between the two of them exists. My idea was to say represent a and b as $a = \sqrt{2} x, b = \sqrt{2} y$ for some $x, y \in \mathbb{R}.$ We know that there exists $\frac{m}{n}$ s.t. $x < \frac{m}{n} < y,$ so multiplying everything by the root of 2, we have $$\sqrt{2}x = a < \frac{\sqrt{2}m}{n} < \sqrt{2}y = b,$$ and so we have an irrational number in between two reals. Is this 'legit?' Are there 'better/'more elegant ways to go about this? I would really appreciate seeing alternatives proofs of this, as many as possible.


In episode 13 of Charlotte, there is a ZHIEND song playing about halfway in the episode, just before Yu in insane mode starts stealing other people's abilities, such as the bomb ability.

It's towards the end of the episode, something about Sinking Ships but I can't find the song.


Derivatives, both ordinary and partial, appear often in my mathematics courses. However, my teachers have never really given a good example of why the derivative is useful. My questions:   Other than the usual instantaneous rate of change, what are some common uses of the derivative?  What does the partial derivative tell us? And what does the total derivative tell us?    I find that often times, the derivative is simply explained as "the instantaneous rate of change".  I am thinking about switching my major, because the applications of math at such an elementary level seem trivial when professors just push symbols and don't have any real world motivation included in their lectures.    P.S. This question is not a duplicate of  I do not want to know why we differentiate. I want to know why it is important past our undergraduate learning. What are the applications beyond Calculus 3? Beyond academia, what makes the derivative important in complex situations?

I'm currently learning how to differentiate, but as most entirely new things are rather abstract, I cannot really get a hold of the reason why I'm differentiating.   For example, we have a function, $y=x^3$. The derivative of $x^3$ is written as $y'=3x^2$. The differential of $x^3$ could be written as $d(x^3)=3x^2\,dx.$  Okay, I think. What then, I wonder? This is not really telling me anything. Beautiful math, though.  (The answers to  do not give me very much mathematical intuition behind why we differentiate.)


So, the nucleus of an atom can be broken to protons and neutrons, and those can be broken down to quarks.  Electrons however are a different story, they can't be broken down since they are elementary particles but they do have mass.  So the higgs boson itself does not give mass to particles but the interaction between the Higgs field and the Higgs boson does? How does the electron for example interact with the Higgs field?

I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding?


I have been observing my cat and found that when confronted with an unknown item, she will always use her front left paw to touch it.  This has me wondering if animals exhibit handedness like humans do? (and do I have a left handed cat?)  One note of importance is that with an unknown item, her approach is always identical, so possibly using the left paw means allowing a fast possible exit based on how she positions her body.  This question is related to . However, I question the "paw-ness" as a consequence of how the cat is approaching new items (to be ready to flee), whereas the other question remarks about the high number of "right-pawed" dogs and questions the influence of people for this preference.

For example, almost every dog I've met in my life (more than 20 subjects) uses their right paw touching one while asking for attention. Can it be used as a criterion for calling them dextral? If not, what?  However, I realize that even those dogs who live in the street might get influenced by dextral people:     There is no domestic animal which has so radically altered its whole   way of living, indeed its whole sphere of interests, that has become   domestic in so true a sense as the dog (Konrad Lorenz)   Is there any research about it?


Is this expected or is there anything wrong with my machine?

On every bootup it's the same:  /dev/sda1: clean, 908443/38690816 files, 44176803/154733312 blocks   Is it some kind of option Ubuntu uses to ensure filesystem consistency or is there something wrong with my HDD? fsck takes up to 30s while booting and so about triples the time needed otherwise.  Full output (partly in German):  Begin: Loading essential drivers ... done. Begin: Running /scripts/init-premount ... done. Begin: Mounting root file system ... Begin: Running /scripts/local-top ... done. Begin: Running /scripts/local-premount ... done. Begin: Running /scripts/local-bottom ... done. done. Begin: Running /scripts/init-bottom ... done. fsck von util-linux 2.20.1 /dev/sda1: sauber, 908443/38690816 Dateien, 44176803/154733312 Blöcke udevd[623]: unknown key 'SYSFS{idVendor}' in /lib/udev/rules.d/45-libticables.rules:6  udevd[623]: invalid rule '/lib/udev/rules.d/45-libticables.rules:6'   * Starting mDNS/DNS-SD daemon                                                 [ OK ]  * Starting Reload cups, upon starting avahi-daemon to make sure remote queues are populated                                                                   [ OK ]  * Starting configure network device security                                  [ OK ]  * Starting bluetooth daemon                                                   [ OK ]  ####* Starting all other stuff


Can every abelian group converted into ring(by defining multiplication operation) with identity with same order. We can convert every group G into ring by defining a.b = 0 for all a and b in G. But this ring has no multiplicative identity

Given some Abelian group $(G, +)$, does there always exist a binary operation $*$ such that $(G, +, *)$ is a ring? That is, $*$ is associative and distributive:  \begin{align*} &a * (b * c) = (a*b) * c \\ &a * (b + c) = a * b + a * c \\ &(a + b) * c = a * c + b * c \\ \end{align*}  We also might have multiplicative identity $1 \in G$, with $a * 1 = 1 * a = a$ for any $a \in G$. Multiplication may or may not be commutative.  Depending on the definition, the answer could be no in the case of the group with one element: then $1 = 0$. But the trivial ring is not a very interesting case. For cyclic groups the statement is certainly true, since $(\mathbb{Z}_n, +, \cdot)$ and $(\mathbb{Z}, +, \cdot)$ are both rings. What about in general? Is there some procedure to give arbitrary abelian groups ring structure?


I have two computers running windows 10. I wanted to connect both of them at the same time to an  external hard disk drive. Are there any hard disk drives that can accept two USB ports?

I want to connect 3 Windows computers (2 Windows XP, 1 Windows Server 2003) to an external USB hard drive via USB.  I would like each computer to be able to directly read and write to the HD as if it were directly connected to each computer.    Using special file transfer software isn't a viable solution.  Sharing the HD over the network also won't work for me.  Is this possible?  Thanks for any advice!


Let $K$ be a field and let $R$ be a $K$-algebra with unity which is finite dimensional as a $K$-vector space. Prove that $R$ has only finitely many prime ideals all of which are maximal. (Hint: Chinese remainder theorem)   My attempt: We have $R \simeq K^n$, for some $n$, as vector spaces. I claim that there are finitely many ideals of $K^n$. Let $I$ be an ideal of $K^n$ and $(a_1, a_2,...,a_n) \in I$. For every entry $a_i$, we have two choices, either $a_i=0$ or not.  So we get $2^n$ many cases, and any case give a particular ideal of $K^n$ which are distinct from others.  Is my proof correct or am I missing some point? If it is true, how can we give a proof by using the Chinese remainder theorem? Thanks!

Let $K$ be a field and $A$ an affine $K$-algebra. Show that $A$ has (Krull) dimension zero (is artinian) if and only if it is finite dimensional over $K$.


I have a project with the following layout:  project_root     __init__.py     typing         __init__.py         bset.py (contains a class BSet)     environment         __init__.py         environment.py   from within environment.py I'm trying to import bset.BSet  from ..typing import bset  def do_something():     b = bset.BSet()   When I try to run environment.py (either directly, or under my test runner) I get:  Traceback (most recent call last):   File "environment/environment.py", line 3, in <module>     from ..typing import bset ValueError: Attempted relative import in non-package   I'd like the whole thing to function as a module ("project_root"), and I thought I had it working but I appear to have made a change that broke it.  What is the correct way to set up the inter-submodule dependencies?

Imagine this directory structure:  app/    __init__.py    sub1/       __init__.py       mod1.py    sub2/       __init__.py       mod2.py   I'm coding mod1, and I need to import something from mod2. How should I do it?    I tried from ..sub2 import mod2 but I'm getting an "Attempted relative import in non-package".  I googled around but found only "sys.path manipulation" hacks. Isn't there a clean way?      Edit: all my __init__.py's are currently empty    Edit2: I'm trying to do this because sub2 contains classes that are shared across sub packages (sub1, subX, etc.).  Edit3: The behaviour I'm looking for is the same as described in  (thanks John B)


I got help on the previous parts of this question but I'm at a loss about where to go from here. I can prove the linear functional is bounded and that the norm is less than two but this last part I am stuck on and the hint isn't helping me. Any help would be really appreciated.

I'm trying to work through some example questions for my class but there is no mention of "Piecewise affine functions" anywhere and I'm completely stumped on how to do this.  Any help would be appreciated please.


Search seems to be broken,   Search does not return any results for <%#  I looked at :  https://meta.stackoverflow.com/help/searching   But It did not help.   update: With more trial and error I turns out that if I do search like: "<%#" Then I do get results.   page says use quotes only for phrases, but  quotes are needed in this case also.   I would like to suggest to update the search help page. As It is the first location people will look when their search fails.

I tried to find a related question here, but was unsuccessful.  Someone on SO asked ... I tried searching SO and was presented with the search options page. Even Google fails at this search.  So my question is, is there some way to search for an exact word (in quotes) that won't cause it to fail?


Can any one tell me the exact diff between call by pointer and call by reference. Actually what is happening on both case?  Eg:   Call By Reference:  void swap(int &x, int &y) {    int temp;    temp = x; /* save the value at address x */    x = y;    /* put y into x */    y = temp; /* put x into y */     return; }  swap(a, b);   Call By Pointer:  void swap(int *x, int *y) {    int temp;    temp = *x; /* save the value at address x */    *x = *y; /* put y into x */    *y = temp; /* put x into y */     return; }    swap(&a, &b);

I know references are syntactic sugar, so code is easier to read and write. But what is the difference between a pointer variable and a reference variable?


Let us consider the following scenario.  This is the partial code in the main.tex file and which includes code from other tex files like acknowledgements.tex,certificate.tex, abstract.tex etc.,    ....................   \include{certificate}   \include{abstract}   \include{introduction}   \include{Chap1}   \include{Chap2}   ...................   Now let my PDF counting page numbers from certificate, but I want to count the page numbers from chap1.  Is it possible to force counting from a particular page.  Note: There may be counting for certificate,abstract and introduction too, but from chap1 counting has to start from 1. It is good if there is no counting before chap1.

Problem:  Start page numbers from chapter one and also reflect this in the TOC.  Currently the code for TOC is:  \renewcommand{\contentsname}{Table of contents}  \setcounter{secnumdepth}{2} \setcounter{tocdepth}{2} \tableofcontents   I would appreciate if I can be pointed in the right direction. So far I have understood that you can use \chapter* in order not to include a chapter in the TOC.  Questions:  1) How would you force Latex to start numbering from chapter 1 and forward?  2) How can you start page numbering from the first chapter?


Is there any intuitive reason or deeper meaning to why the following equality holds?  $$\left(\sum_{i=0}^n i\right)^2 =  \sum_{i=0}^n i^3$$  I'm not looking for a proof of this, I'm looking for some explanation for this equality if it isn't just a coincidence.

I recently proved that  $$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k \right)^2$$  using mathematical induction.  I'm interested if there's an intuitive explanation, or even a combinatorial interpretation of this property. I would also like to see any other proofs.


I have ordered a new 27" iMac with macOS Mojave. I use 64-bit version of Adobe CS6.  Will macOS Mojave run it?

I have some Adobe applications that I use for occasional work (Photoshop, Illustrator, Lightroom, Acrobat).  These are the versions prior to the CC version (Creative Cloud) and they work on El Capitan through High Sierra.  I don't do enough graphics work justify the cost of a monthly CC license and these older version have been more than enough for what I want to do.  Now, with the new Metal framework of Mojave, will the Adobe Apps continue to function?  Contacting Adobe results in a support call that (magically) turns into a sales call for CC.  Has anyone tested Adobe CS5 or 6 products on Mojave beta as of yet and if so, what were the results?


I'm tying to dive into multiplayer game programming.  The game is quite simple, it's a 2D scroller mobile game, the player need to touch the screen in order to move 1 step and it could contain up to 4 players at max. 1 of the player could create a room for other players to join.  I was thinking that I would use TCP for this and will only send packets when 1 of the player trigger an event like moving or exiting the game. Is my approach is correct? Since from what I've read, many games are created in UDP instead of TCP.  In case of UDP, what is sent between the clients and the server? The position of each entity in the game at a fix time interval?  I'm really new multiplayer programming. I'd appreciate if someone would share their story.  Thank you.

Back in the day, TCP connections over dialup/ISDN/slow broadband resulted in choppy, laggy games because a single dropped packet resulted in a resync. That meant a lot of game developers had to implement their own reliability layer on top of UDP, or they used UDP for messages that could be dropped or received out of order, and used a parallel TCP connection for information that must be reliable.  Given the average user has faster network connections now, can a real time game such as an FPS give good performance over a TCP connection?


Is there a difference between asking a question with "Would you..." and asking the same question with "Can you..."?  For example,     Would you take the trash out?   Can you take the trash out?   Both can be answered with either "Yes/No" or by actually taking the trash out. Are the questions used in different circumstances? Is one more "correct" than the other?

Most people say I wish I could, I wish you would.    Can we use I wish I can, I wish you will?    I'd like to know what the main differences between the usage of can/will and could/would are when wishing.  Is it related to the subjunctive? Because one says “I wish I were”, not “I wish I am”, so are would and could the subjunctive forms of can and will?  Or is it something else entirely?


In this  when asked why Darth Vader is a favorite character among children George Lucas says;     "... and who is more power than Darth Vader? Some will be attracted to   Luke Skywalker because he is the good guy, but ultimately we know that   Darth Vader is more powerful than he is. As time goes you discover   that he more powerful because he is the ultimate father, who is all   powerful."   Looking at this question  there many answers in the primary canon and Legends canon on who that might be.   Does this quote from Lucas  give us a clear answer that Darth Vader is the most powerful, or is Lucas' quote being given in the narrow field of Darth Vader vs Luke Skywalker? I understand this George Lucas we are talking about... so there might be a contradiction in another interview or something was ret-conned at a later time!  Also, at the time the interview was given I think the answer would be limited to Episodes I-VI. Answers would have to come from G-canon.

I just saw a  where Starkiller vaporized an entire platoon of stormtroopers with a single energy blast or something.  What are the effective limits on the Force and who is its most powerful user within both the accepted canon and Legends?


In a  I encountered:  To an inattentive reader, the expressions,  “I am the man, who commands you”  and  “I am the man, who command you”   [reformatted, EA]  may appear to be precisely equivalent. This, however, is by no means the case —(See “The Etymology and Syntax of the English Language explained,” p. 261, fourth Edition.).  I could not find the 4th edition of the referred book, and unfortunately not sure I understand the difference here.

Traders (who used to come early to the market) claimed he had probably had some place he sleeps


This appears to be a new question to MSE according to Approach0 (surprisingly).     I'm looking for a detailed description of the difference between $\vdash$ and $\vDash$ in the study of logics, even for nonclassical logics. So: what's the difference?   My own, rather cobbled together understanding is that $\vdash$ concerns the "syntax" of the logic in question, whereas $\vDash$ concerns the "semantics" of (or "meaning behind") the syntax, as determined by some system of interpretation of the syntax.  I am aware that, for a logic $\mathcal{L}$ to be complete, then by definition of completeness, one needs $\Sigma\vDash_{\mathcal{L}} \Delta$ to imply $\Sigma\vdash_{\mathcal{L}} \Delta$.  Similarly, for a logic $\mathcal{L}$ to be sound, one needs $\Sigma\vdash_{\mathcal{L}} \Delta$ to imply $\Sigma\vDash_{\mathcal{L}} \Delta$.  Now, I've dabbled in logic for several years now, so I'm slightly embarrassed that I don't have enough of a grasp of these basic concepts in order to tell the difference a lot of the time.  I'm reading Priest's "An Introduction to Non-classical Logic: From If to Is (Second Edition)." Logics that are both sound & complete are presented there (but such logics typically have gluts, gaps, or some funky "many worlds" interpretation, so as to avoid Gödel's incompleteness theorem(s), I suppose).

I'm confused about the use of symbols $\vdash$ and  $ \models$. Reading the answers to  and  I see that:  the turnstile symbol $ \vdash $ denotes syntactic implication. Then $ S \vdash \psi$ means that $\psi$ can be derived from the formulae in $S$  the double turnstile $ \models $, denotes semantic implication. Then the notation $A \models B$ means simply that B is true in every model in which A is true.  So I understand that, e.g., $(ZFC+ A) \vdash B$ means that $A \Rightarrow B$ is a theorem in ZFC and, in this sense $\vdash$ is a mathematical symbol for a theorem. While $(ZFC+ A) \models B$ means that $ B$ is true in every model of ZFC in which $A$ is true, and, in this sense $\models$ is not a mathematical but a metamathematical symbol.  I understand correctly? And those are the only uses of the two symbols?


I use  Entity Framework together with Linq to fill my gridviews. I would like to get the same data I get from the Linq in an excel. Also a second tab in the same excel sheet should come from another Linq query.  Whats the easiest and best way to do this?

How can I create an Excel spreadsheet with C# without requiring Excel to be installed on the machine that's running the code?


I am getting this message E : Malformed entry 53 in list file /etc/apt/sources.list Line 53 and 54 in the list are : line 53 : deb  main line 54 : # deb-src  main what is the correct entry for this line else how can i fix it? Please Help

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


I have downloaded a json data from an url and deserializing it to a class.   expense = wc.DownloadString(url);  Rec obj = JsonConvert.DeserializeObject<Rec>(expense);   The class is,  public class Rec     {         public string BillNo { get; set; }         public string Date { get; set; }     }   The 'BillNo' is in anchor format. I need loop through each rows to get specific values from the anchor tag. The anchor tag is like mentioned below.  429   From the above anchor tag i need the itemId value '877560220' and the inner text '429'. How to accomplish it in c#.

I'm looking for a library/method to parse an html file with more html specific features than generic xml parsing libraries.


I would like to create a map view with an insert in QGIS to show a zoomed view of my project area and its location on the National map of Zimbabwe in one view. I can not seem to find a tutorial on how to accomplish this. May you kindly assist on how I can create such a map. [![The kind of map view that I would like to produce looks like the view on the attached image.

i want to create 4-5 detailed maps, and then an overview map that has rectangles that markes the locations of the detailed maps. Best case would be if the rectangles were links to the detailed map.   I have managed to make the overview and the rectangles, and think I know how to make the detailed maps one by one. The rectangles are drawn manually on the overview map. All layers that I plan on using are in the same QGIS project.  The final product that I hope to create would be the overview map on the first page, followed by the detailed maps. The overview would have links to the detailed maps, click on the rectangles to open the right detailed map.  Is there a way to link the detailed maps to the overview in QGIS 2.8 print composer?  I'm still not sure if I'm doing something wrong, when I try to create the overview. I want it to show the extents of all of my detailed maps.   Is this possible?