I am trying to place two figures from .pgf file input side-by-side. I want them to have independent captions (so no subfigures). I have tried using the minipage way as follows:  \documentclass{article} \usepackage{pgf}  \begin{document}  Some words.. \begin{figure}     \begin{minipage}[t]{0.5\linewidth}         \centering         \input{figure1.pgf}         \label{Figure1}         \caption{This is caption for Figure 1.}     \end{minipage} \end{figure} \begin{figure}     \begin{minipage}[t]{0.5\linewidth}         \centering         \input{figure2.pgf}         \label{Figure2}         \caption{This is caption for Figure 2.}     \end{minipage} \end{figure}  \end{document}   But instead of getting them side by side, I get them one below the other, like the attached picture. Tried using \scalebox{0.6} before \input the pgf but still the same behavior.. I have tried many different combinations and I can't find a way to make this work...  EDIT: This is not a . I am importing .pgf files. My latex code is identical to the above answer but it doesn't work. pgf files are  if someone needs to test.

How can I put two figures side-by-side? Not two sub-figures, but two actual figures with separate "Fig.: bla bla" captions.  A figure is supposed to spread over the entire text width, but I have two figures which are narrow and long, and I need to save the space in order to withstand the pages limit.


I need a little help with the second half of the proof that $ (\mathbb{Z}  \times \mathbb{Z},+) / \langle(2,3)\rangle $ is cyclic.  I know isomorphism preserves cyclic structure.I looked up the answer on my textbook from where I got this exercise and their proof is like this:  "The function $f : \mathbb{Z} \rightarrow \mathbb{Z}  \times \mathbb{Z} /\langle(2,3)\rangle$ with $f(x) = \widehat{(x,x)}$ is an isomorphism of groups because :   $(x,x)$ is not in $\langle(2,3)\rangle$ for every $x \neq 0$. $(a,b) =(b-a)(2,3)+(3a-2b)(1,1)$ for a,b in $\mathbb{Z}$ .   I think in the first part they try to show that the function is injective but I don't understand the second part,can someone explain it to me?  Thanks alot !

In John Fraleigh's book, A First Course In Abstract Algebra Exercises 15.7 and 15.11, one shows that  $$ (\mathbb{Z} \times \mathbb{Z})/ \langle (1,2)\rangle \cong \mathbb{Z} \times \mathbb{Z}_1 \cong \mathbb{Z} \ \ \ \ \  \mbox{ and  } \ \ \ \ \ (\mathbb{Z} \times \mathbb{Z})/ \langle (2,2)\rangle \cong \mathbb{Z} \times \mathbb{Z}_2 $$  One does this with the first isomorphism theorem. With the same idea I proved for example that  $$ (\mathbb{Z} \times \mathbb{Z})/ \langle (2,3)\rangle \cong \mathbb{Z} \times \mathbb{Z}_1 \cong \mathbb{Z} \ \ \ \ \ \mbox{ and }\ \ \ \ \ (\mathbb{Z} \times \mathbb{Z})/ \langle (2,4)\rangle \cong \mathbb{Z} \times \mathbb{Z}_2 $$ So I conjectured that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_{k}$ where $k=\mathrm{gdc}(m,n)$. For the previous four cases, the homomorphism $\phi: \mathbb{Z}\times \mathbb{Z} \to \mathbb{Z} \times\mathbb{Z}_k$ given by $$ \phi(x,y)=\left(\frac{nx-my}{k}, \ x \ \ (\mathrm{mod} \ k) \right) $$ is surjective with kernel =$\langle (m,n)\rangle$. However, this is not the case when $(m,n)=(4,6)$. So, I cannot use what I did for the four cases to prove the general case.     What I want to know is if my conjecture is true. If so, how can I give a general homomorphism? If it is not true, how can I find $k$, such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$?   Thanks in advance for any help/hint/comment!


I have wrote a Java Class which uses selenium webdriver to quickly pass through a website and test various functions. I have also wrote a seperate class which will be used to execute the takeScreenshot() method. Once the test hits the code which executes the screenshot method, the browser closes and the J-Unit test fails and points to the line where I am calling the takeScreenshot() method. It is a null pointer exception but I cant figure out whats going wrong.. I have read through many articles and cant find an answer. I have read all of the posts on here which identify how to take a screenshot using selenium... The code is below:  **** Screenshot Class ****   public class Screenshot {   private WebDriver webDriver; File source;  public void takeScreenshot() {      try {         source = ((TakesScreenshot) webDriver).getScreenshotAs(OutputType.FILE);         FileUtils.copyFile(source, new File ("/Users/joshuadunn/Desktop/claimsScreenShot.png"));         System.out.println("Screenshot Taken!!!!");      } catch (IOException e) {         e.printStackTrace();     }  }  }   I then create a Screenshot Object and execute its takeScreenshot() method as follows:  @Test public void testClaimsTestToCalcNode() throws Exception {     driver.get(baseUrl + "/");     driver.findElement(By.id("becsStartCalculator")).click();     driver.findElement(By.id("MARITAL_STATUS_false")).click();     driver.findElement(By.id("btn_next")).click();     driver.findElement(By.id("HOME_ABROAD_false")).click();      *** This is where the null pointer is ***     *******************************     screenshot.takeScreenshot();     *******************************       driver.findElement(By.id("btn_next")).click();     driver.findElement(By.id("DETAILS_STUDENT_YOU_false")).click();   I hope you understand my problem!  EDIT **** - This is not a duplicate.. I am totally aware of what a null pointer is and how it can be fixed. Obviously something in my code is coming through as null, but I dont know what... The screenshot below is the only error i get (stacktrace)

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 on Ubuntu 14.04 and I reside in Dubai and thus I set up my date and time settings accordingly. However, I do not speak Arabic but Ubuntu insists on displaying the date in Arabic. Other applications such as Skype on my Ubuntu machine display date and time in Arabic. Is there anyway I can change this to English?

I have installed Ubuntu 13.04 and set my local time/date and its working, the only thing that's bugging me is that I cannot change it to English. I would like to do this because it is hard to read and it is not showing it in the proper format in the Terminal, please refer to the screenshot below.    Show in the proper format    Not showing in proper format in terminal  How can I change my date/time to English format and keep the local time?


Say I have a 2D array of 4 rows and 5 cols. I want to assign only the  first row elements with their respective indices to get the below 2D array.  0 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0    I first tried this:   array1 = [[0]*cols]*rows print(array1)  for i in range(cols):     array1[0][i] = i print(array1)   Result:  [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] [[0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4]]   Which is not what I intended to do.  Every row is being updated instead of just the first one.  But the following code gives the result I'm looking for.  array2 = [[0 for x in range(cols)] for y in range(rows)] print(array2) for i in range(cols):     array2[0][i] = i print(array2)   Result :  [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]  [[0, 1, 2, 3, 4], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]   The only difference between both the snippets is the way array1 and array2 have been initialized. I'm curious to know why both of them work differently. Would appreciate any help.   -Thank You

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


$$\lim_{(x,y)\to(0,0)}\frac{xy^4}{x^2+y^6}$$  I know the limit is 0 if it exists. I want to solve using squeeze theorem but I don't know what to use for the upper function.

I have some trouble with this: Show that if $a, b \ge 0$, $c, d > 0$ and $\frac{a}{c} + \frac{b}{d} > 1$ then   $$\lim_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$$  we were not really shown how to evaluate multivariable limits other than trying different paths, which wouldn't work when the limit exists, or by applying the squeeze theorem which is my initial plan. Unfortunately I cannot find a proper bound for the denominator and so I am quite lost right now. Any help would be appreciated.


Let's solve the (real) equation $$x^{x^{x^{\dots}}}=2\qquad (x>0).$$ If we call $E(x):=x^{x^{x^{\dots}}}$, it holds that $x^{E(x)}=E(x)$, but our equation says that $E(x)=2$, so it holds that $x^2=2$, whence $x=\sqrt2$. Noew, lets solve $$x^{x^{x^{\dots}}}=4\qquad (x>0).$$ A similar arguments, leads us to to solve $x^4=4$ whose solutions are $x=\pm\sqrt2,\pm i\sqrt2$, so the only positive solution is, again $x=\sqrt2$. But this yields to the contradiction that $2=4$. So, my question is... what's wrong here?  My intutition says that is has something to do with the complex solutions of $x^4=4$, but I'm not really sure. Als0 it may something to do with the convergence of the next sequence: $$S_1(x)=x>0,\qquad S_{n+1}(x):=x^{S_n(x)}$$ but I'm not able to study its convergence.

Solving $x^{x^{x^{.^{.^.}}}}=2\Rightarrow x^2=2\Rightarrow x=\sqrt 2$.  Solving $x^{x^{x^{.^{.^.}}}}=4\Rightarrow x^4=4\Rightarrow x=\sqrt 2$.  Therefore, $\sqrt 2^{\sqrt 2^{\sqrt 2^{.^{.^.}}}}=2$ and $\sqrt 2^{\sqrt 2^{\sqrt 2^{.^{.^.}}}}=4\Rightarrow\bf{2=4}$.  What's happening!?


I've seen examples such as:  Type arrayname[] = new Type[];   also as written as:  Type[] arrayname = new Type[]   I am quite confused about such expressions!  Where exactly should I put the []?

I have recently been thinking about the difference between the two ways of defining an array:   int[] array int array[]   Is there a difference?


I need to implement a universal C function which will invoke super's implementation and return the value. I will inject this function to a target class at runtime. The number of  arguments of the target selector could be any number, and would be known only at runtime.  I implement a C function as following, but I don't know how to invoke the super's implementation with the variable argument list:  id forwardMessageToSuper (id self, SEL _cmd, ...) {      // Is this `super` definition right?     struct objc_super super = {         self,         [self superclass]     };        // How can I pass the variable argument list (...) to super?      id result = objc_msgSendSuper(&super, _cmd, ...);      return result; }   Another question: how and when to use objc_msgSendSuper_stret to invoke super's implementation?

In C, is it possible to forward the invocation of a variadic function? As in,  int my_printf(char *fmt, ...) {     fprintf(stderr, "Calling printf with fmt %s", fmt);     return SOMEHOW_INVOKE_LIBC_PRINTF; }   Forwarding the invocation in the manner above obviously isn't strictly necessary in this case (since you could log invocations in other ways, or use vfprintf), but the codebase I'm working on requires the wrapper to do some actual work, and doesn't have (and can't have added) a helper function akin to vfprintf.  [Update: there seems to be some confusion based on the answers that have been supplied so far. To phrase the question another way: in general, can you wrap some arbitrary variadic function without modifying that function's definition.]


Is there a way that I can get a resulted output to multiple locations at the same time. ls -RsgorCh  >> /Users/User1/Text1.txt will print the output as a text file in the given location. I want to know whether I can get the output to be printed into multiple different locations at the same time. Possible multiple locations can be    Terminal + Folder + Folder etc.. Folder + Folder + Folder etc..   Also the commands can be   grep ls tree etc

How can I write the same content to many text files by using cat or echo in only one command?  For example I want to write "hello" to file1 and file2. I tried:   echo "hello" >> file1 file2   but it didn't work. How can I do it?


In writing, there are many things one can do to make the text better. Some basic rules of thumb include avoiding repetitions, avoiding passive voice, breaking down long and complicated sentences, or letting the reader think for themselves.  Do such rules also apply to scientific texts, and if not, why?  I can think of a few reasons why they may not. For example, avoiding repetition may create confusion — it might not be immediately clear if the alternative term is just a synonym, or if it is different and in what way. Moreover, using more advanced devices (or,  for that matter, sophisticated vocabulary) could be problematic even for native speakers.  Surely we need to make the text as accessible and clear as possible, but it would be great if it were also enjoyable to read. Where lies the right balance?

I was reading  titled "Optimal Symmetric Rendezvous Search on Three Locations." While talking about the history of search problems, the author mentions the following anecdote in passing.     In 2007 a letter writer to the Guardian newspaper queried, “I lost my wife in the crowd at Glastonbury (a music festival). What is the best strategy for finding her?” A reader replied, “Start talking to an attractive woman. Your wife   will reappear almost immediately.”   While I found it quite amusing to read this, I do not often come across papers with such witticisms. Is there an unwritten rule about the tone of sobriety that is considered appropriate in academic papers? Are jokes or anecdotes fine as long as they do not appear forced?


Let $G$ be a set and $*:G\times G \rightarrow G$ an operation with:  (i) $(G,*)$ is associative  (ii) There is a $f \in G$ with $f*a=a$ for all $a \in G$  (iii) For every $a \in G$ exists a $b \in G$ with $b*a=f$  First show that from $b*a=f$ concludes $a*b=f$  Then show that $(G,*)$ is a group.

Let $(G, *)$ be a semi-group. Suppose   $ \exists e \in G$ such that $\forall a \in G,\  ae = a$;  $\forall a \in G, \exists a^{-1} \in G$ such that $aa^{-1} = e$.    How can we prove that $(G,*)$ is a group?


Let's assume we have these three Tables:      Sailors (sid, name, rating), Reserve (sid, bid, day) and Boat(bid,name,color)  I want to JOIN the Table Sailors with the Table Reserve. Are the following statements equivalent? Is someone more effective?  SELECT S.sid, S.name, R.bid   FROM Sailors as S,      Reserves as R    WHERE S.sid = R.sid   SELECT S.sid, S.name, R.bid    FROM Sailors as S INNER JOIN Reserves  as R  ON S.sid = R.sid   Thanks in advance!

Is there any efficiency difference in an explicit vs implicit inner join? For example:  SELECT * FROM table a INNER JOIN table b ON a.id = b.id;   vs.  SELECT a.*, b.* FROM table a, table b WHERE a.id = b.id;


there are some scripts that you have to run them from command line like   python run.py -u alex__a -p 123 -v -f  I want to work with them inside my code I don't know whats the name of them so I wasn't able to google about my question . sorry if it't so simple

How do you call an external command (as if I'd typed it at the Unix shell or Windows command prompt) from within a Python script?


How to set a space above the \mylisting   and is the fontsize set fine? Thank you  \documentclass[12pt,a4paper]{report}  \usepackage[most]{tcolorbox} \newtcbinputlisting[auto counter,list inside=lol,list type={lstlisting}]{\mylisting}[3][]{%   listing file={#3},   title=Listing,   colback=white,   colframe=gray!75!black,   fonttitle=\bfseries,   listing only,   breakable,   title={Soubor \thetcbcounter: #2},   #1 } \newcommand{\listingsfont}{\ttfamily}      \begin{document} \begin{footnotesize} \mylisting[label=h]{h}{h.txt} \end{footnotesize} \end{document}

How to set a font size in listing when I have these settings in the preamble?   \documentclass[12pt,a4paper]{report} \usepackage[most]{tcolorbox} \newtcbinputlisting[auto counter,list inside=lol,list type={lstlisting}]{\mylisting}[3][]{%   listing file={#3},   title=Listing,   colback=white,   colframe=gray!75!black,   fonttitle=\bfseries,   listing only,   breakable,   title={Soubor \thetcbcounter: #2},   #1 } \newcommand{\listingsfont}{basicstyle=\ttfamily\tiny}   \begin{document} \mylisting[label=s]{s}{s.txt}  \end{document}   File s.txt:  x = 5;
 y = 6;
 z = x + y;   I tried   \newtcbinputlisting[auto counter,list inside=lol,list type={lstlisting}]{\mylisting}[3][]{%   listing file={#3},   title=Listing,   colback=white,   colframe=gray!75!black,   fonttitle=\bfseries,   fontsize=\footnotesize,   listing only,   breakable,   title={Soubor \thetcbcounter: #2},   #1 }   There is an error and  \newcommand{\listingsfont}{basicstyle=\ttfamily\tiny}    that does not do anything - the font size remains the same.


I have a few hundred images, few named like   1.jpg 2.jpg  ......  11.jpg  ....  101.jpg    And few others like   deer - 1 -spotted.jpg  deer - 2 - musk.jpg  .....  deer - 11 - river.jpg  .....    I would like to rename 1.jpg to 001.jpg and deer - 1.jpg to deer - 001.jpg.   I tried renaming them with while loop bash script but   mv deer - 1* deer - 01 - spotted.jpg selects deer - 1 , deer - 11, deer - 111   I am looking for cli way and bash script if possible to rename files like above  Thank you

I used Sound Juicer to rip a CD of audio for a language learning book so that I could listen to them on my Android. However, Sound Juicer seems to only have the option of numbering files without leading zeros. Like this:  track_1.mp3 track_10.mp3 track_11.mp3   This leads to some confused ordering on my music player. So, I want to add some zeros to the name, so that they're ordered properly, like this:  track_01.mp3 track_02.mp3 track_03.mp3   How do I accomplish this? I tried using GPRename, but while it has the ability to add numbers, it doesn't seem to have any options for adding leading zeros.  Is there a better program or something I can do at the command line?


Is there any "slowest" velocity that sets a cap on how fast a reference frame passes through time, or can you pass through time infinitely fast given a "slow" enough velocity?

My understanding of Special and General Relativity comes from books which attempt to explain them to non-experts in these fields.   Let A and B be observers, which at some time t(0), are together at some location P fixed to the earth's surface. A and B are provided with "clocks", which at time t(0), are identical lumps of the same radioactive element-that has a very long half-life. A and A's "clock" remain fixed to the earth's surface. B and B's "clock" leave A and stay together, but eventually return to A after some interval of time T (as measured by A's "clock"). If, during this time T, B's velocity relative to A is sufficiently close to the velocity of light or B remains close to a sufficiently massive body, it seems that time can "pass more slowly" for B than for A. So that when B rejoins A, B's "clock" will contain more of the radioactive element than A's "clock"   My question is: Are there any scenarios that B together with B"s "clock" can undergo (during the time T) which will cause time to "pass more quickly" for B than for A? So that when B rejoins A, B's "clock" will contain less of the radioactive element than A's "clock". If there are no such scenarios, is there any fact or law in Relativity theory which rules them out?


I am going offline. Or rather, I will have intermittent or bad Internet access for a year, hopping on random Wi-Fi access points, crappy 3G or dialup connections. How can I keep participating here? I know about:  : Not practical; those are huge and always out of date, by definition, with no easy way to sync incrementally (let alone write) : So that's great; it runs on around 3-4 KB per page, which means one second or more load times. It may help when I do have Internet access, but not when I want to jot down notes of , , ,  and  or comment on issues while offline.  The ideal solution would be a  repository holding all the responses, answers and comments, basically. :) Another option would be to have a way to collaborate more dynamically through email, say be able to receive all the questions with a certain tag and respond by email. From  you can subscribe to receive the latest questions on a given tag, but . Operating the API by email commands would also be great... Those features would enable Stack Exchange sites to be accessed by more people with less privilege, basically. Since Stack Overflow, in particular, is great enabler of learning for programming, it would seem imperative to allow such access to be done more dynamically. Clarification: this is not only about ! If there was an offline application to do the above, that would be fine as well, for example.

Is it possible to receive and post replies to questions via e-mail; in a similar fashion to Google Groups and Facebook wall comments?


I know how it sounds and I feel like a total fool for falling for it. I wish I had done my research before I followed thru with it, but now I don't know what to do from here. I've been talking to someone thru a website for a couple months now and they had offered to send me money before but I was always unsure so I never accepted. I finally decided to trust them and needed a little help with bills and taking my car to the shop for repairs.   When they told me they needed my bank login information I was super hesitant but ultimately gave in because I only had $50 in my account and figured what was the worst that would happen, I'd be out $50 or I'd be up $200. Well the check they deposited ended up being for $5100. Which was insane and blew my mind. I didn't even expect it to go thru, figured it was a mistake. He explained that there had been a mix up with his financial adviser and the money that I was sent was supposed to go to a charity and that he would need me to send that out once the check cleared.   It sounded suspicious and I wish I had trusted my gut but I stupidly waited a couple days, saw the money was in my account and let him know. He wanted me to send it thru CashApp but I told him I didn't have access to that and asked what other ways I could send it for him. We agreed on a money order mailed to an address in the same state he was supposedly from, so I went down to the bank, pulled out the $5100 and went out and got a money order from a local place by me for $4900. Sent it that afternoon, and told him it was in the mail. I hadn't heard back from him after this for a couple days and assumed it was something to do with his mom (whom he told me was in the hospital) so I didn't immediately suspect anything.   I went to message him last night and saw he had blocked me/deleted his account and all the messages were gone. Now my bank is $5100 in the negative, and I've not spoken with my bank yet. I'm honestly scared I'm going to get in trouble and I'm not wanting my family to find out about this at all. I don't want to file a police report or anything like that either if I don't have to. I didn't screenshot anything and I can't remember the address he asked me to send the money too, I don't even have the receipt for the money order to prove that I don't have the cash still. I am absolutely unsure what to do. Going to be contacting my bank tomorrow morning but would love some advice for what to say to them, how to proceed with all of this. Thanks you!!

I live in New Jersey and my son wanted to order some toys from this guy who said he makes them in his house and he could give him the best deal, but before he could send these toys he needed my 16 year old son to put $200 into his bank account. The guy then gave my son his wells Fargo bank account info and told him as soon he deposits the money he will ship his toys. Well, that never happened.  My son called the guy up and he told my son, “I’m only the middle guy, and my boss is in Nigeria and you need to put another $200 in my account because now I have to ship the toys from elsewhere.” So my son deposited another 200 dollars into this guys bank account.  My son has sent these jerks a total of $650. Is there anything I can do to these individuals? At this point even if I don’t get the money back it’s okay but I don’t want this happening to other kids and I want to teach these guys a lesson that you’re not above the law. The guy is still calling my son up saying that he is pissed off that he didn’t get more money.  What can I do now?


I am currently exploring the training of Neural Networks. I have some toy data and I've trained a NN with 2 hidden layers on it and I get 99 % accuracy on the test set. But the problem is that if I add an additional layer, my training set accuracy drops drastically to around 56 %. Thus I wanted to ask If anybody might know why that might be? Is it likely that I've coded something wrong (however I had no problem going from 1 -> 2 hidden layers), or it could be that if I try to train the a simple set on a very complex model (at least for the set), it could give me such erroneous results.  Thank you very much.

I'm training a neural network but the training loss doesn't decrease. How can I fix this?  I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my network's performance doesn't improve on the training set.    This question is intentionally general so that other questions about how to train a neural network can be closed as a duplicate of this one, with the attitude that "if you give a man a fish you feed him for a day, but if you teach a man to fish, you can feed him for the rest of his life." See this Meta thread for a discussion:   If your neural network does not generalize well, see:


I am searching for a way to get a statistics on a very large (multiple times larger than the available RAM) the outputs what byte values in the files are present and how often:  A0 01 00 FF 77 01 77 01 A0   I need to know how many A0 bytes there are in this file, how many 01, and so on. The result could be:  A0: 2 01: 3 00: 1 FF: 1 77: 2   Therefore this question is very close to the question  but non of the existing answers works for larger files. From my understanding all answers require a minimum RAM equal to the size of the file to be tested (up to multiple times).   Hence the answers don't work on systems with small RAM, e.g. a Raspberry for processing a multi-GB file.  Is there a simple solution that works on any file size even if we have for example only 512MB RAM available?

Example: I have the file "mybinaryfile", and the contents in hex are:  A0 01 00 FF 77 01 77 01 A0   I need to know how many A0 bytes there are in this file, how many 01, and so on. The result could be:  A0: 2 01: 3 00: 1 FF: 1 77: 2   Is there some way to make this count directly in shell or do I need to write a program in whatever language to do this specific task?


I do not understand the difference between . I am going to run it on Vmware Fusion on a mac, does it will make a difference ?

At that location there is an ISO image which is described as "This image is adjusted to work properly on Mac systems."  What specific problems on the Mac does this image address that the standard images don't? I ask because I need to know which ISO to recommend to Apple Mac users.


I installed i3 desktop environment and then removed it via software manager since I didn't like it very much.   Now I started to use unity (default) back again. However, now I have a white over blue notifications on the upper left of my screen. I usually see them when wifi is connected or I received an email.  This notification also appears on the login screen and does not let me to write my password during the check of preferred wirelesses.  I need to remove this notification thing.

Problem  I recently upgraded from 13.04 to 13.10, and suddenly notification bubbles don't appear themed as usual in the upper right corner, but they appear as white text on blue background in the upper-left corner. It looks like this:     Unsuccesful attempts to fix it   I tried reinstalling unity, notify-osd, ubuntu-desktop removed notification-daemon which was installed, none of that fixes it. In fact running ps aux | grep notify-osd shows that notify-osd isn't even running. But when I try to start it manually by running /usr/lib/x86_64-linux-gnu/notify-osd I get:  ** (notify-osd:4618): WARNING **: Another instance has already registered org.freedesktop.Notifications  ** (notify-osd:4618): WARNING **: Could not register instance  If I understand well, the instance is registered by the /usr/share/dbus-1/services/org.freedesktop.Notifications.service file, which right now contains:  [D-BUS Service] Name=org.freedesktop.Notifications Exec=/usr/lib/x86_64-linux-gnu/notify-osd   Renaming or deleting that file (and rebooting) has no effect whatsoever (and it is not recreated automatically). This is not a duplicate of  (and by the way I purged gnome-flashback-session along with notification-daemon)   Question(s)  How can I debug this? How can I get notifications to come back to normal?  If additional debug information is needed, I'll be happy to add it (just that I can't find any more).


I was following this video to try and an build a circular wall, however, the Simple Deform modifier isn't working correctly. Instead it just stretches my mesh. Has the modefier changed in the newest version or something? Blend:

I have some problem using the simple deform modifier, for some reason it doesn't rotate on the z axis making a circle but it does the stuff in the image


Asbestos tape-covered ductwork that is coming from the furnace leading to each vent in the entire house. Is it a bad idea to leave it as is without disturbing, or would replacing all hvac system coming from the furnace be a better solution?

I've got an old house with some asbestos tape on the heating vents, and some old floor tiles which are asbestos suspects as well; duct cleaning firms won't do cleaning on the vents with the tape present. Do I really need to call in the space suit guys to get rid of it? If I just cover it with new foil tape, will that encapsulate it safely?  Should I just rip it off myself?


Given the fact: for every $n\in\mathbb{N}$ $$e\left (\frac{n}{e}\right)^n\leq n!\leq en\left (\frac{n}{e}\right)^n $$ Prove directly: $$\binom{n}{k}\leq \left (\frac{en}{k}\right )^k $$  Yes, this inequality is as obvious as obvious gets ($\binom{n}{k}\leq \frac{n^k}{k^k}$), but how do we utilize fact to come to desired result? Have attempted to manipulate the upper/lower bounds of $n!$ so that we get: $$\frac{1}{k!}\geq \frac{1}{e}\left (\frac{e}{k}\right )^k\qquad \frac{1}{(n-k)!}\geq\frac{1}{e}\left (\frac{e}{n-k}\right)^{n-k} $$ combined, results in $$en\left (\frac{n}{e}\right)^n\cdot \frac{1}{e}\left (\frac{e}{k}\right )^k\cdot \frac{1}{e}\left (\frac{e}{n-k}\right)^{n-k}\geq \binom{n}{k}$$ If we extract the part of interest from the above product, we may ask: $$\left (\frac{en}{k}\right )^k\overset{?}\geq \frac{1}{n^k}\left (\frac{n}{e}\right )^{n+1}\left (\frac{e}{n-k}\right )^{n-k}\cdot \left (\frac{en}{k}\right )^k\geq \binom{n}{k} $$ Hence, we ask whether: $$n^{n-k+1}\leq e^{k+1}(n-k)^{n-k} $$ i.e remains to show for $1\leq k\leq n$ $$n\left (\frac{n}{n-k}\right )^{n-k}\leq e^{k+1} $$  Unnecessary work. Begin by evaluating one piece at a time.

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


I made a model of Harry Potter. but when  I render the model it's just a black screen.Duplication is on none. Seams to be nothing wrong with the node setup and render icon is checked on all the objects except the hair which I don't need to render. Thank you for taking the time to read this. Please help.

A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [


By $A'$ I mean the set of limit points of $A$, so $A''$ is the set of limit points of $A'$.  There is no T1 space with such a subset. Proof:  Suppose $X$ is a T1 space and let $A \subset X$. Let $x \in A''$ and $U$ be an open neighborhood of $x$. By definition, there exists $y \in U \cap (A' \setminus \{x\})$. The set $U \setminus \{x\}$ is an open neighborhood of $y$ because $X$ is T1, hence there is a point in $U \setminus \{x\} \cap A - \{y\}$. This is also a point in $U \cap A - \{x\}$, so $x \in A'$.  There is a non-T0 space with such a subset: let $X = \{a,b\}$ have the indiscrete topology, and pick $A = \{b\}$. Then $A' = \{a\}$ and $A'' = \{b\}$.  My question is if there is a T0 (but not T1) space with a subset with this property. It does not seem to be possible with the standard T0 spaces I have checked (particular/excluded point spaces, and other simple spaces).

Claim: If $(X,\tau)$ is not $T_1$ then $A'$ is not necessarily closed for any $A$.  Proof: Here is an example. Take $X=\mathbb{N}$ and let $\tau=\lbrace u\subset\mathbb{N}\mid 1\in u\iff 2\in u\rbrace$. Let $A=\lbrace 2,3 \rbrace$. Since any open set containing $1$ also contains $2$ it follows that $1\in A'$. Hence $\overline{A}=\lbrace1,2,3\rbrace$, as it is the smallest closed set containing $A$. But  $X\setminus A'=\mathbb{N}\setminus\lbrace 1\rbrace$ is not open because it contains $2$ and not $1$. The set of accumulation points $A'$ is not closed.  So, in general, trying to prove that $A'$ is closed in a topological space is an effort in futility?


Pretty common problem here but the posts I've seen are a little different. New Wi-Fi tstat, no C terminal at furnace but plenty of available wiring at both ends. Unlike others problems posted of unwiring and rewiring, couldn't I just take an available wire and combine it to my G connection at the terminal and then connect wire at tstat? If G controls the fan and I know there is power because I can turn on fan manually, is this the easiest fix?  Thanks

So, the spiffy new wi-fi thermostats want power on the C wire from thermostat, but the old thermostat doesn't have a C wire at it.  What's the easiest way to add the C wire/24 volt to the thermostat location?


I noticed some interesting behaviour in my loss history while training my model.    Please note the sudden change in test loss at around epoch 106. A similar drop will appear around epoch ~1000.  It seems to me that the optimizer is able to escape a local minima, is this correct?  Can anyone explain this behaviour to me?  This is with keras version 2.2.4 and the loss function is mean absolute error

I've seen plots of test/training error suddenly dropping at certain epoch(s) a few times during the neural network training, and I wonder what causes these performance jumps:    This image is taken from Kaiming He's Github, but similar plots show up in many papers.


Let $C_o= \{(x_n):x_n \in R, x_n \rightarrow 0 \}$ and $ M=\{(x_n):x_n \in C_0,~~ x_1+ x_2+...+x_{10}=0\}$ then dimension of $(\frac{C_0}{M})$ is equal to

Let $C_{0}=\{(x_{n}):x_{n}\in\mathbb{R},x_{n}\rightarrow 0\}$ and $M=\{(x_{n})\in C_{0}:x_{1}+x_{2}+\cdot\cdot\cdot+x_{10}=0\}.$ I have to find dimension of the space $\frac{C_{0}}{M}.$ According to me its dimension is infinite. But i am not correct. Please tell me what is the exact dimension of the quotient space and how to find it? Thanks in advance.


This is a follow-up to the question asked regarding SVD and dimensionality reduction ().  In that question I asked how to use SVD for dimensionality reduction. Although not stated, the ultimate goal here is to use the reduced feature set and input them into a classification or regression algorithm.  I have learned that SVD is a technique used by prcomp in R, as the "v" matrix from a run of svd on a centered and scaled matrix is the same as the loadings (eigen vectors) from a PCA using the traditional eigen decomposition on a correlation matrix:  data(iris)  #these two match eigen(cor(iris[,-5])) #eigen vectors svd(scale(iris[,-5]))$v   This has helped with my understanding of the connection between SVD and PCA. However, I have two additional questions:  1) Why do the following differ in signs for the first PC? Is this OK?  svd(cor(iris[,-5]))$u svd(scale(iris[,-5]))$v   2) To match the output of prcomp, one can multiply the scaled/centered original data by the 'v' matrix from SVD:  PCSCORE1<-scale(iris[,-5]) %*% SVD2$v[,1:2]  #PC scores from SVD PCSCORE1[1:10,]  #PC scores from first 2 PC  #matches this PCA<-prcomp(iris[,-5], center = TRUE, scale =TRUE)  PCA$x[1:10,1:2]   but I have seen in multiple locations (e.g. ) and the rapidminer package (a machine learning tool written in JAVA) that just the 'u' matrix that results from running svd on the center/scaled input matrix X is used as the PC scores.   What is the connection of u to Xv and if u can be used, why does prcomp compute Xv? Mechanically u is Xvdiag(1/d) so the eigen vectors related to the largest eigen values are scaled down - why is this used?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SVD and PCA?  Or in other words, how to use SVD of the data matrix to perform dimensionality reduction?


Hello I recently have been having trouble learning to model in blender.  I know how to use the program and understand its interface but have trouble putting those skills together to create the desired effect.  Do you guys have any suggestions on the best way to learn this.  Thank you.

Since asking for tutorials, videos, resources, links to other content or downloads is considered off topic here, this is a specifically created Community Wiki which gathers resources for Blender and it has been approved by the .  Just write in the appropriate answer/section. If you have concerns, questions, post a  question, so we don't clutter the comments, but you can link your meta question from the comments.  Questions regarding such resources are not allowed anymore, except for very specific and on topic requests (ask on  if you're unsure about your question). Follow the instructions made in the question about how to post, what can be posted, etc.  Learning             Assets    (also see: )   Reference Images/Blueprints (also see: )    Tools    (also see: )      Other   Special Interest ()     Also see the .


I have a website where we created a unique and informational content and now we want to target same content City wise. So I don't have much to change as just changed the city name for other pages. So will google count it a duplicate content? As it's mine content so should not be the case. And also it's highly relevant on the page so won't impact the page experience and information is highly relevant on the page? Will google count this as a good practice? Do I need to make any SEO changes here?

I'm not sure exactly what these "filler pages" are called, so I couldn't do a proper search.  If I have a business, say a plumbing/heating company in NYC, and I created these HTML pages:  New-York-City-plumbing-company.html Manhattan-plumbing-company.html Brooklyn-plumbing-company.html  New-York-City-heating-service.html Manhattan-heating-service.html Brooklyn-heating-service.html   and the content for each page type was the same, except the name of the city/neighborhood changed, i.e.
[Neighborhood] Plumbing Company

description of plumbing service

[Neighborhood] Heating Service

description of heating service
   Would this be helpful, harmful, or neutral in terms of SEO? I'm a little afraid Google might see that 95% of the content is the same, minus the name of the neighborhood, and punish my site for it.


I am a bit confused. When multiple data (plural) transfer takes place, which would be the correct expression: a. "data are transferred" b. "data is transferred"  Or both expressions are correct?  Thanks and best regards

Which sentence is correct:     In this section you can make a payment: verify carefully that all the data submitted is correct and confirm by clicking the Proceed button.   or     In this section you can make a payment: verify carefully that all the data submitted are correct and confirm by clicking the Proceed button.


Is it correct to say that, in the Bias-Variance trade-off:  the bias error represents the ability of the model to possibly map the trend of the training set ?   and the variance represents how much the model is prone to variations if the dataset changes ?

I've been trying to find an answer to this question for a long time.  What are the relationships/differences between Bias, Variance and Residuals?  I think I do understand Bias, Variance and Residuals as separate concepts. Correct me if I'm wrong -  Bias is the difference between the average expected results from different runs of the model and the true values from data.  Variance is the variability in the expected results (predictions) of a given data point between different runs of the model.  Residual is the difference between the expected results from a model and the true values from data. y - y^ Residual seems somewhat similar to Bias. But is that my misunderstanding? Please explain to me in plain words and also simple equations the relationships or differences between these three.


I'll keep it brief as the issue is simple. While I don't have a lot of rep on SO, I cannot find any where a reason as to why I am no longer able to ask questions.  I have 32 rep, and have no had any excessive amount of bad standing questions. I do not believe I have actually had any bad standing questions. The part I am confused about is that I have asked questions this week on the 2 IP's I use mainly, and none of the questions got downvotes. I am now unable to ask question at my work or my house.  I have read through other posts about the question block issues and things to fix them, but I am confused as to why I am unable to ask questions on my 2 IP's. Is there a measurable amount of rep that I can keep track of to fix this/how much I need? Could there be an issue that I am just overlooking? I am just concerned because I use SO often and have a question I would like to ask about something I cannot find anything on.  I am a CS major so I am willing to do whatever I need to figure out this issue, as the site says making another account does not work. Thank you for your help ahead of time.

If you are reading this, you may have been affected by one of our post quality bans. If so, it is important that you  to understand what has happened and how to regain the permissions that you lost. While trying to ask a question, one could see:  We are no longer accepting questions from this account. See  to learn more.  Likewise, for answers:  We are no longer accepting answers from this account. See  to learn more.   Why am I getting this message? Are deleted posts taken into account too? Is a question/answer ban the same as a suspension? How do I avoid getting a question ban? How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account? Can I simply create a new account? I'll just ask somewhere else on the SE network, and they'll migrate my question to the correct site! Will a ban on one Stack Exchange site affect my standing on other sites in the network? Does this apply to meta sites too? My account is in good standing. Why am I still blocked?


Please consider the following command:  find . -type f -name '*.*' -exec mv '{}' '{}_foo' \;   How does find prevent endless loops in this case?  On one hand, I believe to know that find does not work like shell globs do, i.e. it does not fetch a list of all *.jpg files, stores that list internally and then processes the list entries. Instead, it gets the files to process "incrementally" from the underlying O/S and processes each of them as soon as it knows about it (let's ignore a certain amount of buffering which might take place since this is irrelevant to the question). After all, as far as I have understood, this is the main advantage of find over globs in directories which have a lot of files in them.  If this is true, I would like to understand how find prevents endless loops. In the example above, 1.jpg would be renamed to 1.jpg_foo. From discussions on StackOverflow and elsewhere, I know that renaming might result in the file (name) occupying a different slot in the directory file list, so chances are that find encounters that file a second time, renames it again (to 1.jpg_foo_foo), and so on.  Obviously, this does not happen.

While answering  it struck me that it seems find, in the following example, potentially would process files multiple times:  find dir -type f -name '*.txt' \     -exec sh -c 'mv "$1" "${1%.txt}_hello.txt"' sh {} ';'   or the more efficient  find dir -type f -name '*.txt' \     -exec sh -c 'for n; do mv "$n" "${n%.txt}_hello.txt"; done' sh {} +   The command finds .txt files and changes their filename suffix from .txt to _hello.txt.  While doing so, the directories will start accumulating new files whose names matches the *.txt pattern, namely these _hello.txt files.  Question: Why are they not actually processed by find? Because in my experience they aren't, and we don't want them to be either as it would introduce a sort of infinite loop. This is also the case with mv replaced by cp, by the way.  The  (my emphasis)     If a file is removed from or added to the directory hierarchy being searched it is unspecified whether or not find includes that file in its search.   Since it's unspecified whether new files will be included, maybe a safer approach would be  find dir -type d -exec sh -c '     for n in "$1"/*.txt; do         test -f "$n" && mv "$n" "${n%.txt}_hello.txt"     done' sh {} ';'   Here, we don't look for files but for directories, and the for loop of the internal sh script evaluates its range once before the first iteration, so we don't have the same potential issue.  The GNU find manual does not explicitly say anything about this and neither does the OpenBSD find manual.


Are these all noun clauses? And what part of speech is whatever in each of them? Are they pronouns, determiners, or something else?         I'll take whatever you can give.       (direct object)   Using whatever tools were available, they accomplished much.   (direct object of the participle)   I am against prejudice in whatever form it takes.  (object of the preposition)      Thanks!  Note: The post “whatever” as pure determiner?” did not answer my question, but instead created some of my confusion. Additionally, that post focused on adding the relative pronoun that to the noun clause. It did not focus on what the proper term for a noun clause is, along with the determiners and pronouns that are associated with them. See my own answer to my question in the answer section below.

My dictionaries and references define, and I've always thought of, one of the functions of the word whatever as a "relative determiner."  In a sentence like, "I will help you in whatever way is possible,"  inserting the relative pronoun "that" between "way" and  "is", or replacing "whatever" with "the" - a pure, non-relative determiner - (I reckon) renders it ungrammatical:     *I will help you in whatever way that is possible.   *I will help you in the way is possible.   However, I do often encounter utterances like the first one above, such as:     My hope and intent is to contribute in whatever way that I can.   I wish to be of service to the local communities in whatever way that is possible.   where "that" is used, and thus "whatever" can be replaced by "the" without  making the sentences ungrammatical (if they are grammatical to begin with):     My hope and intent is to contribute in the way that I can.   I wish to be of service to the local communities in the way that is possible.   Is this usage of "that" with "whatever" wrong, though colloquial?


Under Linux, when a process crashes, a core dump will be created.  However, I want to create a core dump when the process doesn't crash, but looks buggy. A remote expert need the core dump to analyze.  Under Windows, we can create a dump file of a process through task manager, and after that, the process is still running.  Is it possible under Linux?

Is it possible to get gdb or use some other tools to create a core dump of a running process and it's symbol table?  It would be great if there's a way to do this without terminating the process.    If this is possible, what commands would you use?  (I'm trying to do this on a Linux box)


I have an integer number, and the number can be expressed in 32 bits. And I want to count the number of true values. For example: An integer 5566 can be expressed by 00000000 00000000 00010101 10111110, the number of true values is 9. The calculation should consider the performance because it's used for a large data set. In java, it seems that I need to convert the integer into byte[] first, and then convert into a boolean[] and then start counting, and I think there is a better way with better performance and less conversion.

8 bits representing the number 7 look like this:  00000111   Three bits are set.     What are algorithms to determine the number of set bits in a 32-bit integer?


Generally when somebody creates a console program he writes   #include <iostream> #include <stdlib.h>  int main(){     std::cout<<"hello world"<<std::endl;     system("pause"); }   The std must be included to call cout and endl statements.  When I create a library using the headers and the code in the .h and .cpp, and then I include that library, I must use the name of functions/clases/structs/etc directly. How can I make it so I have to use a pre-word like the std for cout and endl?

I come from a Java background, where packages are used, not namespaces. I'm used to putting classes that work together to form a complete object into packages, and then reusing them later from that package. But now I'm working in C++.  How do you use namespaces in C++? Do you create a single namespace for the entire application, or do you create namespaces for the major components? If so, how do you create objects from classes in other namespaces?


In some cases, I have edited the title and tags of some questions and then answered.  A while ago, I revisited some of those questions and it felt awkward to see that I posted an answer and also edited the question (because a user can theoretically re-write a question completely), so I stopped editing questions that I'd answer.  Recently, I have found unanswered questions that I can answer, and sometimes those questions have incorrect tags, tags in titles and other details that I could fix as well.  Instead of struggling with myself to choose if I should or shouldn't do this I ask here.  Is it OK to edit a question you're posting an answer to? If it is, is there anything I should bear in mind to prevent any possible misunderstanding?

I have a question about editing practices:  Does it look good to edit a question you have just answered?  For example: say I had just answered a question, then saw that the question had some minor formatting issues. Should I edit it? Does it turn up voters off when they see that I am answering a question I changed, possibly to better suit my answer?


Say I have a list of files a.txt, b.txt, c.txt, is it possible to pass it to zip command as arguments and make it zip it in one file say a.zip?

I wish to store a few folders in a zip file and then convert that zip file into a jar.  I have the following folders : META-INF and org.  I tried the following command:  zip META-INF/ org/ wordcount.zip   But wordcount.zip was not created.


At the moment I'm developing a corporate identity for the beamer class of my institute. In fact a power point solution is available and I'm trying to rebuild a tex-friendly version.  However, at the moment I'm trying to build a custom TOC, which is repeated with each new section (this I already accomplished), with special format: I want the sections to be in rounded beamercolorboxes, but the whole TOC should be displayed (in the manner of \tableofcontents[currentsection]).     My current code is in the MWE.   \documentclass{beamer} \setbeamercolor{test}{fg = white, bg = red}     \AtBeginSection[]{         \begin{frame}         \begin{beamercolorbox}[rounded = true]{test}         \thesection.\ \insertsection \\         \end{beamercolorbox}         \end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document}  \section{This is the first section} \begin{block}{This is the first block}     Blocktext \end{block}  \section{This is the second section, but I also want the the first one displayed with its box!} \begin{frame}{frame}     Frametext  \end{frame} \end{document}   Afaik there is no way to get the round boxes around the sections in the normal TOC or am I missing something? That's why I'm trying to make my own TOC.  Hopefully I could explain myself well enough...  Best regards  Patrick

How can I create a fancy-looking table of contents for a Beamer presentation?    \documentclass{beamer} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}  \begin{document}  \frame{ \tableofcontents }  \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{}  \end{document}


Basically, I need to make a testifier commands that checks for players to hold Blue or Red wool in the hand. To do this I've tried the following:  /testfor @a[team=Blue] {SelectedItem:{id:minecraft:wool}}   (it says that the UUID is in invalid format, but the team specification is not necessary so I removed it)  /testfor @a {SelectedItem:{id:minecraft:wool}  (It seems it only works with white wool)  /testfor @a {SelectedItem:{id:minecraft:wool 14}   Still not working and  /testfor @a {SelectedItem:{id:minecraft:wool,Data:14}}   But still not recognizing it as red wool... I just can't understand how and where I put the block variation Data...

Let's say I want to track a group of players to see which one of them (if any) have a specific block type in their inventory that's of a specific datavalue; for instance Red Wool (minecraft:wool with a data value of 14).  I already know how to detect if a player has any wool in their inventory: /testfor @a {Inventory:[{id:"minecraft:wool"}]}. However, this doesn't discriminate between the various colours.  It'll find anyone with any colour wool, whereas I want to find only players with red wool.  I've tried modifying the data tag to also include a data value, such as /testfor @a {Inventory:[{id:"minecraft:wool",data:14}]} but this results in unmatched NBT tags and the  error message <Player> did not match the required data structure.  Obviously it's because data (or Data, damage, dataID, etc.) isn't the name of the NBT tag, or that the structure is wrong.  I realize I can accomplish this using the /clear command, but that's a bit clunky when running on a 20Hz /fill clock.  How can I filter out specific data values when using the /testfor or /scoreboard players commands?


I'm having trouble fitting my list of notations/nomenclature in one page for my thesis.  I tried looking for a solution to allow printing nomenclature across multiple pages and didn't find one.   My next thought is to use the groups to print one group at a time with \printnomenclature  Is it possible to print a single group with \printnomenclature?  Edit: Adding a minimum example (sorry for the length needed to push to multiple pages with columns)  The multicols use is what's causing the paging to fail (MWE pointed that out).  Is there a way to page with columns?  \documentclass[titlepage]{article} \usepackage{multicol}   % List of notations generation \usepackage[intoc]{nomencl} \renewcommand{\nomname}{List of Notations} %\nomlabelwidth=15mm \makenomenclature \makeindex  \begin{document}      \begin{multicols}{2}          \printnomenclature[2cm]     \end{multicols}        \nomenclature{$a$}{Blah blah blah blah blah}     \nomenclature{$b$}{Blah blah blah blah blah}     \nomenclature{$c$}{Blah blah blah blah blah}     \nomenclature{$d$}{Blah blah blah blah blah}     \nomenclature{$e$}{Blah blah blah blah blah}     \nomenclature{$f$}{Blah blah blah blah blah}     \nomenclature{$a1$}{Blah blah blah blah blah}     \nomenclature{$b1$}{Blah blah blah blah blah}     \nomenclature{$c1$}{Blah blah blah blah blah}     \nomenclature{$d1$}{Blah blah blah blah blah}     \nomenclature{$e1$}{Blah blah blah blah blah}     \nomenclature{$f1$}{Blah blah blah blah blah}     \nomenclature{$a2$}{Blah blah blah blah blah}     \nomenclature{$b2$}{Blah blah blah blah blah}     \nomenclature{$c2$}{Blah blah blah blah blah}     \nomenclature{$d2$}{Blah blah blah blah blah}     \nomenclature{$e2$}{Blah blah blah blah blah}     \nomenclature{$f2$}{Blah blah blah blah blah}     \nomenclature{$a3$}{Blah blah blah blah blah}     \nomenclature{$b3$}{Blah blah blah blah blah}     \nomenclature{$c3$}{Blah blah blah blah blah}     \nomenclature{$d3$}{Blah blah blah blah blah}     \nomenclature{$e3$}{Blah blah blah blah blah}     \nomenclature{$f3$}{Blah blah blah blah blah}     \nomenclature{$a4$}{Blah blah blah blah blah}     \nomenclature{$b4$}{Blah blah blah blah blah}     \nomenclature{$c4$}{Blah blah blah blah blah}     \nomenclature{$d4$}{Blah blah blah blah blah}     \nomenclature{$e4$}{Blah blah blah blah blah}     \nomenclature{$f4$}{Blah blah blah blah blah}     \nomenclature{$1a$}{Blah blah blah blah blah}     \nomenclature{$1b$}{Blah blah blah blah blah}     \nomenclature{$1c$}{Blah blah blah blah blah}     \nomenclature{$1d$}{Blah blah blah blah blah}     \nomenclature{$1e$}{Blah blah blah blah blah}     \nomenclature{$1f$}{Blah blah blah blah blah}     \nomenclature{$1a1$}{Blah blah blah blah blah}     \nomenclature{$1b1$}{Blah blah blah blah blah}     \nomenclature{$1c1$}{Blah blah blah blah blah}     \nomenclature{$1d1$}{Blah blah blah blah blah}     \nomenclature{$1e1$}{Blah blah blah blah blah}     \nomenclature{$1f1$}{Blah blah blah blah blah}     \nomenclature{$1a2$}{Blah blah blah blah blah}     \nomenclature{$1b2$}{Blah blah blah blah blah}     \nomenclature{$1c2$}{Blah blah blah blah blah}     \nomenclature{$1d2$}{Blah blah blah blah blah}     \nomenclature{$1e2$}{Blah blah blah blah blah}     \nomenclature{$1f2$}{Blah blah blah blah blah}     \nomenclature{$1a3$}{Blah blah blah blah blah}     \nomenclature{$1b3$}{Blah blah blah blah blah}     \nomenclature{$1c3$}{Blah blah blah blah blah}     \nomenclature{$1d3$}{Blah blah blah blah blah}     \nomenclature{$1e3$}{Blah blah blah blah blah}     \nomenclature{$1f3$}{Blah blah blah blah blah}     \nomenclature{$1a4$}{Blah blah blah blah blah}     \nomenclature{$1b4$}{Blah blah blah blah blah}     \nomenclature{$1c4$}{Blah blah blah blah blah}     \nomenclature{$1d4$}{Blah blah blah blah blah}     \nomenclature{$1e4$}{Blah blah blah blah blah}     \nomenclature{$f4$}{Blah blah blah blah blah}      asdf  \end{document}

The title is pretty much I want to ask. More detail, the nomenclature entries should be sorted in groups like:   Nomenclature     Acronyms     Symbol  Description     % no Dimensions and Units      ...     Greek Symbols     Symbol  Description             Dimensions     Units     ...     Roman Symbols     Symbol  Description             Dimensions     Units     S       Surface area vector     L^2            m^2     ...    Superscripts     Symbol  Description     % no Dimensions and Units      ...    Dimensionless Numbers     Symbol  Description     Definition     ...   e.g. expected entries like this:       My current nomenclature settings for grouping [book class]:  %---------------------------------------------------------- %                        Nomenclature %---------------------------------------------------------- %\renewcommand{\nomname}{List of Symbols and Abbrev.} \renewcommand\nomgroup[1]{%   \ifthenelse{\equal{#1}{A}}{%    \item[\textbf{Acronyms}] }{%                  A - Acronyms     \ifthenelse{\equal{#1}{R}}{%      \item[\textbf{Roman Symbols}]}{%            R - Roman       \ifthenelse{\equal{#1}{G}}{%         \item[\textbf{•} Symbols }]}{%          G - Greek           \ifthenelse{\equal{#1}{S}}{%            \item[\textbf{Superscripts  }]}{{%          S - Superscripts         \ifthenelse{\equal{#1}{U}}{%          \item[\textbf{Subscripts }]}{{%                 U - Subscripts         \ifthenelse{\equal{#1}{X}}{%          \item[\textbf{Other Symbols }]}%            X - Other Symbols                     {{}}}}}}}}}} %\ifpdf \renewcommand{\nomlabel}[1]{\hspace{1 em}#1}%{\hspace{1.5 em}#1} \renewcommand*{\nompreamble}{\markboth{\nomname}{\nomname}}   But how to extend it with Dimensions and Units?


I was using Linux mint and windows 10 together(in different partitions). Few months I was using freely. Today I got a message in windows 10(new updates available or shutdown and update) then, I clicked on shutdown and update. After finishing the update 50% automatically restarted my laptop. It happens multiple times when we install windows 10. Since than I am unable to start my laptop  I am not sure why this happens as far as I know this happens when there's no grub loader. Here what I tried  I was watching some videos and searching on Google how to fix it. I got an solution I amt not sure it will work or not they took a live USB and they had windows on there USB but, I have Linux mint in my USB will it work?  I am using live USB(Linux mint). I was trying to mount linux disk. sudo mount /dev/sda4 /mnt. Then, I get an error mount: /mnt: wrong fs type, bad option, bad superblock on /dev/sda4, missing codepage or helper program, or other error. Device     Boot     Start       End   Sectors   Size Id Type /dev/sda1  *      1026048 272532369 271506322 129.5G  7 HPFS/NTFS/exFAT /dev/sda2       272533504 273694719   1161216   567M 27 Hidden NTFS WinRE /dev/sda3       273696768 274747391   1050624   513M  b W95 FAT32 /dev/sda4       274749438 625141759 350392322 167.1G  5 Extended /dev/sda5       623144960 625141759   1996800   975M 82 Linux swap / Solaris   /dev/sda4 is linux. I am sure for disk size   When I use Windows 10 above disk are visible without linux mint disk. When I use Linux Mint every disks are visible. Here something happening like this.

I have  dual boot with Linux and Windows on my machine, So apparently after I made a new disk partition, I think I messed up the  Linux partition. Now after I boot my machine I get the grub rescue console. I tried to fix this with these commands  :  Set boot =(hd0, 6)  Set prefix=(hd0,6)/boot /grub   This Commands run fine but when I type :  Insmod normal   I get unknown file system  error   Any ideas?


How can I increase the font of the title? For some reason it doesn't react to \huge or \Large etc. \documentclass[a4paper,12pt]{article} \usepackage{cmap} \usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc}  \usepackage[english,russian]{babel}  \usepackage{caption}  \title{\Huge Latex}  \begin{document}      \maketitle  \end{document}  And also I can't center the title on the page. It turns out only indented  \title{\Huge \\[5cm] Latex}, but I think this is not correct and there should be an easier way.

A publication I am submitting to has the rather annoying requirement of needing the document title to be size 16pt (and the regular text size being 12pt, which I know how to do). I have absolutely no idea how to change the font size of the title (beyond adding \Large, \LARGE etc. but none of these correspond to 16pt).  How would I go about setting the font size of the title to a specific size?


Drupal core search doesn't re-index the site and it always shows this message.  0% of the site has been indexed. There are 453 items left to index.  What settings do I need to change to make Drupal re-index the site properly?

I have a website that has about 100,000 nodes. In the core search page (admin/config/search/settings) it shows that:  There are 80801 items left to index.  It index 100 (or at most 500) nodes per cron run but it's useless. I want to bulk index the whole site (all nodes) for core search. How can I do that? The  and  modules are created for this but there are only a few users use these modules and I couldn't be sure to use them. And also there is a module called  for modifying the cron per job but it's still useless for me because there are thousands of nodes to index. (Note: I want to do this for core search not for other search solutions).


I am a new user of ubuntu 20.04. I installed and put swap partition in my laptop's (Dell inspiron 7520) original 30 Gb SSD. My main SSD is 480 Gb, ubuntu is in a 100 Gb partition. I made the WHOLE partition as root (/), so I can't have a /home and a /swap partition in the SAME SSD. Is it possible to REPARTITION my ubuntu installation so I can have a /home and (if possible) a /swap partition located in the same disk? Thanks in advance.

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


If I have HTML that looks like this:

Fig. 1: Some caption

   Is there a way to use CSS so that the div with class figure has a width that is only large enough to contain the image and caption? I want to put a rectangular border around both, but I don't want to have to guess the div's width in pixels.  example below (div.figure has a width that seems to expand to fill its available width)    div.figure {    border: 1px solid black;  }

Fig. 1: Some caption

I have a layout similar to:  <div>     <table>     </table> </div>   I would like for the div to only expand to as wide as my table becomes.


How could I prove the above statement?  For $G$ nilpotent and $N \lhd G$, how do I show that $N \cap Z(G) \neq 1$?

Having problems with the following statement:     If $N$ is a nontrivial normal subgroup of a nilpotent group $G$ then $N \cap Z(G) \neq \langle e \rangle$   Here $Z(G)$ denotes the center of $G$.   I've solved the finite case, where I reduced the problem to proving that a p-$group$ has this property. The infinite case resists my attempts though.   Since $G$ is nilpotent, the ascending central series ends with $G$ itself: $\langle e\rangle \subseteq Z_1(G) \subseteq \ldots \subseteq Z_n(G) = G$ where $Z_1(G) = Z(G)$. Since $N \subseteq G$, there must be a smallest $i$ such that $N \cap Z_i(G) \neq \langle e \rangle$. I would like to show that $i = 1$ in this case, or perhaps just show that $N \cap Z_i(G)$ commutes with elements of $G$. Could somebody give me a tip in the right direction?


It is possible to add the password to the ssh config in order not to type any more the password every time I am going to login to the remote host?

I have a remote server. I planned to use public keys to connect over ssh without typing the password but the remote system rejects public key authentication.  So what is the best way to do it? What about using sshpass?


I'm trying to demonstrate that $\left( 1+\frac1 n \right)^n$ is bigger than $2$. I have tried to prove that $\left( 1+\frac1 n \right)^n$ is smaller than $\left( 1+\frac1{n+1} \right)^{n+1}$ by expanding  $\left( 1+\frac1n \right)^n = \sum\limits_{i=0}^n \left( \frac{n}{k} \right) \frac{1}{n^k}$ and $\left( 1+\frac1{n+1} \right)^{n+1} = \sum\limits_{i=0}^{n+1} \left( \frac{(n+1)}{k} \right) \frac{1}{(n+1)^k}$ but it doesn't seem to work.  What am I missing? Also, is there a method to demonstrate that without induction?

How to prove that $ 2<(1+\frac{1}{n})^{n}$ for every integer $n>1$. I was thinking by induction, it works for $n=2$ but then I couldn't move forward.


Why is the area of parallelogram not equal to the product of the distances between the two pairs of parallel sides? A parallelogram is just a rectangle that has a triangle cut off from one side and added to the other; so then why is the area not equal to the product of the distances between the two pairs of parallel sides?

Below the parallelogram is obtained from square by stretching the top side while fixing the bottom. Since area of parallelogram is base times height, both square and parallelogram have the same area.    This is true no matter how far I stretch the top side.    In below figure it is easy to see why both areas are same.   But it's not that obvious in first two figures. Any help seeing why the area doesn't change in first figure?


Is it true that if $U \subset V$ are vectors spaces, one can always find a vector space $X \subset V $ so that $V = U \oplus X$?  I know this it true when $V$ is finite dimensional, but is it true also in the infinite dimension case?  Thanks.

I'm reading Axler "Linear agebra done right" and in Chapter 1 he discusses subspaces and direct sum. My question is, are there subspaces of the infinite-dimensional vector spaces, e.g. a functional Banach space with sup norm $V$ that directly sum to the entire space $$V = U_1\oplus U_2$$ (except for trivial $U_1=\{0\}$, $U_2 = V$).


I need to get a list of the orphaned users in each DB, together with the database name in which they are found in. I did the below which gives the orphaned users in each DB, but I cannot figure out how to include another column next to each user found to show in which the DB. I tried using the DB_NAME() but to no avail.  use master; GO  CREATE PROCEDURE orphaned_u AS BEGIN DECLARE @command varchar(1000)  SELECT @command = 'use ?  if DB_ID("?")>4 EXEC sp_change_users_login ''Report'' ' EXEC sp_MSforeachdb @command END  CREATE TABLE tempTable (     user nvarchar(1000),     User_sid sql_variant  )  INSERT INTO tempTable EXEC master..orphaned_u  SELECT * FROM  dbo.tempTable    I have already looked at  but preferable I use the above code and find a way to display the database name in a column with the already built-in stored procedure sp_change_users_login ''Report''

In SQL Server 2005, is there a way to find users that either don't exist at the server level (an account that was deleted at server level but wasn't disassociated from databases before it was deleted) or accounts that aren't linked (an account may have been deleted at the server level but not db level, then readded but the db level was never cleaned up).  I've got a very messy server and it would be awesome if there was a query to run to find these.


sudo apt-get remove --purge virtualbox-6.1  Reading package lists... Done Building dependency tree        Reading state information... Done The following packages were automatically installed and are no longer required:   libdouble-conversion3 libfprint-2-tod1 libllvm10 libllvm10:i386 libpcre2-16-0 libpython2-stdlib libpython2.7-minimal libpython2.7-stdlib   libqt5core5a libqt5dbus5 libqt5gui5 libqt5network5 libqt5opengl5 libqt5printsupport5 libqt5svg5 libqt5widgets5 libqt5x11extras5   libxcb-xinerama0 libxcb-xinput0 linux-headers-5.8.0-38-generic linux-hwe-5.8-headers-5.8.0-38 linux-image-5.8.0-38-generic   linux-modules-5.8.0-38-generic linux-modules-extra-5.8.0-38-generic python-is-python2 python2 python2-minimal python2.7 python2.7-minimal   qt5-gtk-platformtheme qttranslations5-l10n Use 'sudo apt autoremove' to remove them. The following packages will be REMOVED:   virtualbox-6.1* 0 upgraded, 0 newly installed, 1 to remove and 0 not upgraded. After this operation, 216 MB disk space will be freed. Do you want to continue? [Y/n] Y debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable (Reading database ... 275945 files and directories currently installed.) Removing virtualbox-6.1 (6.1.18-142142~Ubuntu~eoan) ... debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable dpkg: error processing package virtualbox-6.1 (--remove):  installed virtualbox-6.1 package pre-removal script subprocess returned error exit status 1 dpkg: too many errors, stopping debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable vboxdrv.sh: failed: modprobe vboxdrv failed. Please use 'dmesg' to find out why.  There were problems setting up VirtualBox.  To re-start the set-up process, run   /sbin/vboxconfig as root.  If your system is using EFI Secure Boot you may need to sign the kernel modules (vboxdrv, vboxnetflt, vboxnetadp, vboxpci) before you can load them. Please see your Linux system's documentation for more information. Errors were encountered while processing:  virtualbox-6.1 Processing was halted because there were too many errors. E: Sub-process /usr/bin/dpkg returned an error code (1)

I'm trying to install the flashybrid but when I enter the apt-get install flashybrid command, I get this error:  root@user-desktop:/home/user# apt-get install flashybrid Reading package lists... Done Building dependency tree Reading state information... Done flashybrid is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 0B of additional disk space will be used. debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable Setting up flashybrid (0.15+nmu2) ... debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable dpkg: error processing flashybrid (--configure): subprocess post-installation script returned error exit status 1 Errors were encountered while processing: flashybrid E: Sub-process /usr/bin/dpkg returned an error code (1)   I also tried this one to find what is already using that file:  root@user-desktop:/home/user# lsof | grep /var/cache/debconf/config.dat lsof: WARNING: can't stat() fuse.gvfs-fuse-daemon file system /home/user/.gvfs Output information may be incomplete. dpkg-prec 4672 root 4rW REG 8,6 39658 1697827 /var/cache/debconf/config.dat   But I don't know how to fix this.


I am new Latex. If you see the following snippet, here I have created a table between two paragraph. However, when I compile it with XeLatex, the table goes up keeping both paragraphs down. I expected the table should be between two paragraph(Red Arrow). How to do this. Thank You.    Soundex is a phonetic algorithm designed in 1900’s. Soundex algorithm phonetically encodesgroup similar sounding consonant characters. The process usually excludes vowels except the vowels at the beginning of the word. You can find Kaykobad’s Bangla soundex encoding table in [3,19] and Mumit’s Bangla soundex table in [4]. According to the Mumit’s soundex encoding algorithm returns the following output.  \begin{table} \centering   \caption{Sample result of N. UzZaman and Mumit’s Bangla soundex table}   \begin{minipage}{\textwidth}     \begin{tabular}{lccl}     \hline\hline      Corpus Name & Corpus size & Creation time & Technique of data collection\\     \hline  BDNC01 [6] & 12 Million Words & 6 Years & Manual- Copy and Paste\\ SUMono [7] & 27 Million Words & 4 Years & Manual- Copy and Paste\\ NHMono01 (Our Corpus) & Over 100 Million Words & 2 Months & Automatic – Crawling and scraping with powerful Python’s Scrapy framework.\\     \hline\hline     \end{tabular}     \vspace{-2\baselineskip}   \end{minipage}   \label{table2} \end{table} Soundex is an ancient version of phonetic algorithm and has lots of imperfections. Therefore, we have not used soundex in our spell checker.

Is there any package or a method to force LaTeX to keep floating environments like table and figure closer to where they are declared?


I'm looking to create a function or a macro that takes as an input a number n between 0 and 5 and returns five circles with the n leftmost circles filled, something like this:    I'm still reading documentation, but I've never made a macro or a function like this before, so I cannot show a MWE. Any help will be appreciated.  Thank you very much in advance!

I'm trying to get TikZ to make a sort of experience bar command where I can just call it and enter a number out of say, 6, and it will return that many "filled" dots, and 6 minus that many "unfilled" dots. Problem is, something with the way the "foreach" command counts sizes makes it mess up, either by adding too many dots or not enough or not in the right spot or something (depending on what specifically I do with the index bounds)  For example:   \newcommand{\dotexp}[1]{     \tikz{\foreach \x in {1,...,#1}     \draw[cyan,fill=cyan] (\x/2.5,0) circle (.5ex);     \ifnum#1<6 \foreach \y in {#1,...,6} \draw[lightgray,fill=lightgray] (\y/2.5,0) circle (.5 ex);\fi}     }      gives me    where each line is supposed to be a call for 0, 1, 2,....6 dots, in order.   Any suggestions for a fix? Maybe some way to pre-allocate the dot positioning but just change the color?


What keeps the Electric from shorting to ground?  On my electric panel the Neutral is tied to the ground. The ground is a bare copper wire run back to my water main.  a.  Electricity chooses the path of least resistance.  Is the current happier to go back to the power supply rather then ground which is right there in the house basement?   Why does the AC that comes into the house have 2 wires for the Hot leg and 1 un-shielded wire for the Neutral Leg? If it’s tired to ground I guess it doesn’t need to be shielded. But it will still have the same amount of current flow on it as the Hot leg. The Neutral wire is live wire...  Is neutral supposed to be wired/bonded to ground ?

So to continue my line of electrical questioning (and perhaps narrow down my ), I took a look through the two panels in this house.  There is a 200amp main service in the basement, which then feeds up to a 100amp sub-panel for the main floor.  This 100amp sub feeds a kitchen (fridge, microwave, dishwasher, gas range), a bathroom, 3 bedrooms, and a living room.  The 200amp main feeds the 100amp sub, 2 bedrooms, a living room, a washer/dryer (gas dryer), a utility room (well pump, pressure tank, gas water heater, gas furnace), and an A/C.  My first concern is that the main service panel has the bare ground and neutral wires mixed on the two bus bars.  Reading around, some say this is OK, other's say it is bad.  Any thoughts?  The sub-panel is wired with grounds and neutrals on separate bars.  My second concern- is a 100amp sub sufficient for the main floor?


I have this list:  ['Ben\n', '5 0 0 5 -5 \n', 'Moose\n', '5 5 0 3 0 0 \n', ...]   that carries on like that for a long time.  I need to make this list into a list of tuples like this:  [('Ben', '5 0 0 5 -5'), ('Moose', '5 5 0 3 0 0'), ...] and so on.   I feel like this should be easy. I've already opened the text file and split it into a list by line this way:  e = open("bookratings.txt", "r") elines = e.readlines()   But I don't know where to go from here?

I have a list of arbitrary length, and I need to split it up into equal size chunks and operate on it. There are some obvious ways to do this, like keeping a counter and two lists, and when the second list fills up, add it to the first list and empty the second list for the next round of data, but this is potentially extremely expensive.  I was wondering if anyone had a good solution to this for lists of any length, e.g. using generators.  I was looking for something useful in itertools but I couldn't find anything obviously useful. Might've missed it, though.  Related question:


Let $F = \mathbb{Q}(\sqrt{-3})$ be a quadratic field with associated integer ring $$\mathcal{O} = \mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right] = \left\{a+b\frac{1+\sqrt{-3}}{2} : a,b \in \mathbb{Z} \right\}$$ and field norm $N$ defined by $N(a+b\sqrt{-3}) = a^2 + 3b^2$. Prove that $\mathcal{O}$ is a Euclidean Domain with respect to $N$. Prove that every element of $F$ differs from an element of $\mathcal{O}$ by an element whose norm is at most $1/3$ (this is what I'm stuck on).  Following almost the exact steps to this proof () I write $a = \beta q + r$ and get that $N(r) < \left[\left(\frac{1}{2}\right)^2 + 3 \left(\frac{1}{2}\right)^2\right] *N(\beta) = 1*N(\beta)$, but I'm not sure how I'm supposed to get a bound of $1/3$ instead of $1$.

How does one prove that the class number of $\mathbb{Z}[\zeta_3]$ is $1$?


A number written in base b is a polynomial $\sum {(a_i*b^i)}=a_n...a_3a_2a_1a_0$  The logarithm in base b of the number gives the number of digits (up to with a constant=1 difference), and I want to understand how it does that. Note that as the base gets smaller, the result gets more precise.  I want to understand how the logarithm processes each element of the polynomial to get the result.. The entire process, and not a rough approximation.  I made a program that composes the text of a Taylor series for log(1+x) with a polynomial with 10 terms, but the result is a text file with hundreds of Mb, so it is unreadable.  I understand that the largest term is approximately $n+log_b(a_n)$, but I want a more precise understanding. A rough explanation based on bounds is what I already know. I have no interest on that, unless it is part of the entire explanation.

I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof?


I have a bunch of assignment operations in Visual Studio, and I want to reverse them: i.e  i = j; would become  j = i;  i.e. replacing everything before the equals with what's after the equals, and vice versa  Is there any easy way to do this, say something in the regular expression engine?  Cheers, Ed

After writing code to populate textboxes from an object, such as:  txtFirstName.Text = customer.FirstName; txtLastName.Text = customer.LastName; txtAddress.Text = customer.Address; txtCity.Text = customer.City;   is there way in Visual Studio (or even something like Resharper) to copy and paste this code into a save function and reverse the code around the equal sign, so that it will look like:  customer.FirstName = txtFirstName.Text; customer.LastName = txtLastName.Text; customer.Address = txtAddress.Text; customer.City = txtCity.Text;


Let $A$ be a commutative Noetherian ring and let $I$ and $J$ be ideals of $A.$  Suppose that $I\subseteq J$ and that $A/I \cong A/J$ as rings.  I want to prove that $I=J.$    Observations so far:  1) If we drop the hypothesis $I\subseteq J,$ then the result is false:  $$\mathbb{Q}[X,Y]/(X)\cong \mathbb{Q}[X,Y]/(Y) \text{ but } (X)\neq (Y).$$  2) If $A/I\cong A/J$ as $A$-modules, then $I=J$:  $$I=\mathrm{Ann}_A(A/I)=\mathrm{Ann}_A(A/J)=J.$$  I'm now a bit stuck as to how to proceed. Any hints would be most helpful!  Many thanks :)

Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is it true that $I=(0)$ ?  I know that a surjective ring endomorphism of a Noetherian ring is also injective, and since there is a natural surjection from $R$ onto $R/I$ we get a surjection from $R$ onto $R$, but the problem is I can not determine the map explicitly and I am not sure about the statement. Please help. Thanks in advance.


I'm really stuck in this fairly simple example of conditional probability, I don't understand the book reasoning:     An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards each.   Compute the probability that each pile has exactly 1 ace.       Solution. Define events $E_i, i = 1, 2, 3, 4$, as follows:      $E_1$ = {the ace of spades is in any one of the piles}      $E_2$ = {the ace of spades and the ace of hearts are in different piles}      $E_3$ = {the aces of spades, hearts, and diamonds are all in different piles}      $E_4$ = {all 4 aces are in different piles}      The desired probability is $P(E_1E_2E_3E_4)$, and by the multiplication rule,       $P(E_1E_2E_3E_4) = P(E_1)P(E_2|E_1)P(E_3|E_1E_2)P(E_4|E_1E_2E_3)$      Now, $P(E_1) = 1$ since $E_1$ is the sample space S. Also, $P(E_2|E_1) = \frac{39}{51}$ since the pile containing the ace of spades will receive 12 of the remaining 51 cards (...)   I was lost with $P(E_2|E_1)$, I don't understand why it's $\frac{39}{51}$. I tried to think like this:   by definition, $P(E_2|E_1) = P(E_1E_2)/P(E_1)$ and, since $P(E_1) = 1$, $P(E_2|E_1) = P(E_1E_2)$. But it's obvious that $E_2 \subset E_1 \Rightarrow E_1 \cap E_2 = E_2 \Rightarrow (E_2|E_1) = P(E_2)$.   So I tried to calculate $P(E_2)$ to see if it matched the answer of the book. By definition, $E_2$ is the event where the ace of spades and the ace of hearts are in different piles. So the sample space is $52\choose13,13,13,13$. Now, suppose you take out the ace of hearts and the ace of spades of your deck, now you have 50 cards and there are $50\choose12,12,13,13$ ways of dividing the deck and $4\choose2$ ways of deciding which piles receive 12 cards and which receives 13. After making this division, there are $2!$ ways, for each result, to put back the 2 aces you took off (each one in one of the piles with 12 cards). So  $P(E_2) =$ ${50}\choose{12,12,13,13}$$ {4}\choose{2}$$2!$$/$${52}\choose{13,13,13,13}$$= \frac{39}{51}$  In the end, I found the right answer for $P(E_2)$, but I went through a whole line of reasoning that was not trivial. In the other hand, the book apparently deduces it in a trivial way:     since the pile containing the ace of spades will receive 12 of the remaining 51 cards   What I'm not getting?

Suppose that a deck of 52 cards containing four aces is shuffled thoroughly and the cards are then distributed among four players so that each player receives 13 cards. Determine the probability that each player will receive one ace.   The answer to this is given as$$\frac{13^4}{\binom {52}4}$$  My doubt is the following:   The book justifies ${\binom {52}{4}}$ as number of possible different combinations of the four positions in the deck occupied by 4 aces. That sounds like a case of arrangements to me, so shouldn't we think about permutations and not combinations if we are concerned about how the aces are to be arranged in the deck ?. Shouldn't the denominator be ${\binom {52}{13}}$ since you are choosing 13 cards for 4 people.


I would like to use the tool . For it I need to paste the execution plan in json format. If I try to get the execution plan in pgAdmin with this query:   EXPLAIN (ANALYZE, COSTS, VERBOSE, BUFFERS, FORMAT JSON) SELECT DISTINCT key FROM test.table   I don't get the whole json:  query plan    Can I get the whole json? Could I export it from the SQL editor?

I've recently installed pgAdmin 1.18.1 and noticed a strange thing:  Long json query results are shortened to 256 symbols and then ' (...)' is added.  Could someone help me disable this shortening?


I have accidentally deleted the content of /etc/bash.bashrc and now I cannot log in as it gives me a loop and I cannot run any interactive programs from the terminal. When I try, I get this error:  XDG_RUNTIME_DIR not set in the environment when trying to run gedit GTK: cannot open display when trying to run google chrome cannot connect to X server when trying to run rstudio   However, I can run non interactive programs (e.g R and python) from the terminal.  What do I need to add in bash.bashrc to get to see X11 or programs that use DISPLAY?

I would like to restore LightDM to its default state, because for some reason /etc/lightdm/unity-greeter.conf is now an empty file.  Deleting /etc/lightdm/unity-greeter.conf and then running sudo apt-get install --reinstall unity-greeter doesn't create a new config file as you might expect.   How can I restore a missing config file?


I am looking for generally accepted standards or "best practices" on how to space logical expressions. I am particularly interested in expressions of the form:    My question arose after I read the following principle somewhere in this site: there should be more space around more important elements. In the equation a + b = c, the relation = is more important than the binary operation +, and therefore, it makes sense to have more space around it. That is why \mathrel{} adds more space than mathbin{}.  However, in the logical expression (a=b \land b=c) \implies a=c, I am not sure that = is the most important element. Here, my intuition tells me that \land should have more space than =, and maybe \land and \implies should have a similar amount of space. Without it, there might be ambiguity between ((a=b)\land(b=c)) and (a = (b\land b) = c). However, the default space is \mathrel{} for =, \mathbin{} for \land, and something that looks bigger for \implies.  I would like to know the answer to the following specific questions   Are there any style manuals that address the best practices on how to space logical expressions? What are some generally accepted principles on how to set space around binary relations, conjunctions, and implications in displayed logical formulas? If using \text{and} inside a displayed logical formula, what is the right amount of space to use around it? Why does LaTeX assign different space to \implies and \iff but not \land and \lor?   I understand that some of these questions could be opinion-based. I hope this question does not go against any community policies.   \documentclass{article} \usepackage{amsmath}  \begin{document} \[     (a=b \land b=c) \implies a=c \] \[     (a=b\ \text{and}\ b=c) \implies a=c \] \end{document}

LaTeX follows typographic standards and does an elegant job of correctly spacing relation symbols like "=" or "∈" and operation symbols like "+" or "∧". For example, in  $a + b  =  x + y$  LaTeX adds more space around "=" than around "+", so that the expression is correctly interpreted as "(a+b)=(x+y)" and not as "a+(b=x)+y" – which is meaningless. See § 3.1 of Downes's .  Consider, though, relations and operations between propositions that involve equalities. For example, we want to say that the equality of a and b implies the equality of x and y. Writing directly   $a  =  b \Rightarrow x  =  y$  or   $a  =  b \mathop{\Rightarrow} x  =  y$  would yield the wrong spacing, suggesting "a=(b⇒x)=y". A way to fix this could be by somehow adding quotation marks around the propositions, to obtain something like  "a = b" ⇒ "x = y"  but this expression looks cluttered. Of course one can also add/remove spacing by hand – but how much?  An even more complex situation appears with probability formulae, for example if we want to say that the equality of a and b is as likely as that of x and y, or consider the sum of the two:  $P(a = b)  =  P(x = y)$  $P(a = b)  +  P(x = y)$  My question is twofold:  – What are the typesetting rules in cases like these?  – How do LaTeX users (who care about correct spacing) approach this problem?  I'd be happy to know about consistent and elegant solutions.  Cheers!


I don't really understand what we are talking about when we say space is homogeneous. What we are measuring? My notion is: it should depend on the entity and with respect to that entity one can decide space is homogeneous or not!  May be I'm asking stupid question, actually the fact is I don't understand the phrase "space is homogeneous" or "space-time is isotropic"

It is sometimes said that the universe is homogeneous and . What is meant by each of these descriptions? Are they mutually exclusive, or does one require the other? And what implications rise because of this?


Some background and my challenge:  Background  I am using Magento 2.x using a virtual machine set-up which runs on Ubuntu 16.04  Challenge  My goal is to be able to test emails sent to me from the Magento application.  In an ideal situation, I would not use an extension or third-party service (although a third-party SMTP server on the linux box could work).    To achieve my goal, I need to be able to register as a customer in the Magento application with any email address (fake or real) and have the email sent to the same external email address, no matter what.  What I've done so far   I've installed postfix I've installed Magento using luma.com as the domain (and set up my hosts file accordingly on my host machine, etc.) I've created a linux user account called "contact" I've configured inet_interfaces in /etc/postfix/main.cf as loopback-only I've set mydestination to $myhostname, localhost.$mydomain, $mydomain I've configured Magento to send its store emails from contact@luma.com I've set up an aliases file as the following:  postmaster:    root root:          contact contact:       me@gmail.com    Then I ran newaliases As far as I recall, email sends fine with this setup.  Hooray!  Next, the catch-all part.  For this, I've tried loads of things, and none seem to work.  From the reading I've done, I've tried the following:  In /etc/postfix/main.cf, I added the following:      virtual_alias_domains = luma.com     virtual_alias_maps = hash:/etc/postfix/virtual   Next, in /etc/postfix/virtual, I encountered my first problem.  As far as I understand from the reading I've done, I'm supposed to use something like:      @example.com   contact   This step apparently ensures that any email sent via postfix (e.g. from the Magento application) which uses an @example.com email address would be routed to the contact linux user I created above.  Then, my thinking was that the system would use the alias I set up to ultimately send out that email from contact@luma.com (via the settings in Magento) through to the external address I set up in the aliases file.  This approach would theoretically allow a user to register for an account with Magento using, say, joe@example.com, and then send the associated Welcome email to my external email address.  The issue with this is that I need the system to do this for any email, not just for emails ending in @example.com  Just for sake of completeness, I'll say that before asking this question, I was most recently researching how to achieve this part of the challenge using pcre tables. I've also tried configuring something using luser_relay, but both of these things are over my head at this point, so I'm lost.  My hope is that someone can offer some guidance as to whether I'm on the right path, where I may have missed something, and ultimately, offer some advice on whether my challenge can be solved and how I might go about solving it.  NOTE: I originally posted this over at stackoverflow but was advised to post it here.  Hopefully this is acceptable. Thanks for reading.

I'm using postfix for my email. I know I can use /etc/aliases and newaliases command to redirect certain email, eg I can redirect root@example.com to user@example.com by putting root: user in my /etc/aliases and then running newaliases. However I'd like to do the equivilant of *: user, so that all email to example.com will get sent to user@example.com.  How do I do this?


I have this form where the user provide us the information, something like this:    the data goes into a table in my database. After that I want to export the data to a pdf file which I already have:    the PDF file is already editable, so is there any way I can put the data into those editable fields?

Does anyone know of a good method for editing PDFs in PHP? Preferably open-source/zero-license cost methods. :)  I am thinking along the lines of opening a PDF file, replacing text in the PDF and then writing out the modified version of the PDF?  I have programmatically created PDF files in the past using FPDF, but found it a little unwieldy at times.


Find all $z$ such that $$(z+1)^6 = z^6.$$  I have moved $z + 1$ to the other side such that $$\left(\frac{z}{z+1}\right)^6 = 1,$$ which then makes it so   $$\frac{z}{z+1} = 1 = \frac{z}{z+1} = e^{ik\pi/3}.$$  I know $k \neq 0$ where $k = 0, 1, 2,\dotsc ,5$, but I don't know where to go from here.

Find all $x$ such that $$x^6=(x+1)^6.$$   So far, I have found the real solution $x= -\frac{1}{2}$, and the complex solution $x = -\sqrt[3]{-1}$.  Are there more, and if so what/how would be the most efficient find all the solutions to this problem? I am struggling to find the rest of the solutions.


imagine if I have hot metal piece I want to cool it as fast as possiple, should I put it in strong circulated water bath or just stick it between 2 thick copper plates ?  the calculated heat diffusivity of copper is :  thermal conductivity x specific heat x density = 385 x 0.385 x 8960 = 1328096 m²/s  while for water it is just : 0.6 x 4.2 x 1000 = 2520 m²/s only !!  so, the copper can transfere heat 527 times faster than water. should I expect that copper will cool the metal piece faster ? or there is something I missed make water have higher cooling power than copper plates ?

It is will known that increasing cooling of a metal casting will lead to finer micro-structure which mean higher mechanical properties. If I have 2 molds one is thick copper die ,& second is just thin-walled copper cup or mold cooled by water. which one of them excepted to cool the molten metal i.e. aluminium faster ?   by calculation it seems that copper die have higher cooling power as it has higher thermal diffusivity , but in real life it seems water have more cooling power. I am so confused.


.......care has provided us with amenities  a)health   b)healthy  I am a bit confused but I think that we should use (healthy) because it is an adjective for (care) and thus a verb can can be brought after them. also, (health care) as whole is used to describe something, so a name must come after it.  What is the correct answer supposed to be?

I would like to know the differences between health food and healthy food. I have looked them up in a dictionary, but, I can find no entry for healthy food, just health food.    So, what is difference between them?