How do I prove that $\mathbb{F}_p(X^p,Y^p)\subset\mathbb{F}_p(X,Y)$ is not a primitive extension?  And how can I give infinitely many fields $E$ such that $\mathbb{F}_p(X^p,Y^p)\subset E\subset\mathbb{F}_p(X,Y)$?

Is there any example of a field extension $K/F$ where degree of extension $[K:F]$ is finite  but the number of intermediate field is infinite ?


I'm doing an exercise to trace out the second qubit to find the reduced density operator for the first qubit: $tr_2|11\rangle\langle00| = |1\rangle\langle0|\langle0|1\rangle$ I'm just wondering if I do trace for the first qubit, should I have: $tr_1|11\rangle\langle00| = |1\rangle\langle0|\langle0|1\rangle$ or $tr_1|11\rangle\langle00| = \langle0|1\rangle|1\rangle\langle0|$  ? In the Nielsen-and-Chuang textbook, we have $tr(|b_1\rangle\langle b_2|)=\langle b_2|b_1\rangle$. Can I say the left and right hand side are just two ways to locate an element in a matrix? Thanks!!

In the Quantum Operations section in Nielsen and Chuang, (page 358 in the 2002 edition), they have the following equation: $$\mathcal E(\rho) = \mathrm{Tr}_{env} [U(\rho \otimes \rho_{env})U^\dagger]$$ They show an example with $\rho_{env} = |0\rangle \langle0|$ and $U = \mathrm{CNOT}$, and claim that the final solution is: $$P_0\rho P_0 + P_1\rho P_1,$$ where $P_0=|0\rangle \langle0|$ and $P_1=|1\rangle \langle 1|$. These are my steps so far to get this, but I don't know how to trace out the environment after this: Let $\rho$ be $|\psi \rangle \langle \psi |$, so that $\rho \otimes \rho_{env} = |\psi, 0\rangle \langle \psi, 0|$. Applying the unitary $U$, we have $$ |00 \rangle \langle 00| \psi, 0 \rangle \langle \psi, 0 | 00 \rangle \langle 00 |  + |00 \rangle \langle 00| \psi 0 \rangle \langle \psi 0 | 10 \rangle \langle 11 | \\  + |11 \rangle \langle 10| \psi 0 \rangle \langle \psi 0 | 00 \rangle \langle 00 |  +  |11 \rangle \langle 10| \psi 0 \rangle \langle \psi 0 | 10 \rangle \langle 11 |. $$ I don't know how to trace out the environment in the above state. Also, I realize that I have considered only a pure state, if anyone can show it for a general state that would be great.


I'm trying to set up a spreadsheet the will color the background of a cell based on the text within another cell. This would have to be set up in a row so that if (for example) B2: contained "done", then A2 would be colored green. Likewise for B3 and A3, B4 and A4, etc. I understand how conditional formatting works, I just don't know what formula to use to accomplish this.

In my example I would like to conditionally format column B cells. Those marked with x should be formatted according to value in column A (in the example the value is 1):  A | B 1 | x 2 |  3 |  1 | x 1 | x 4 |  8 |  // x can be any value and is here merely to mark the cell that should be formatted   IMPORTANT 2014 NOTE: Conditional formatting based on formula that may include other cells is now possible in Google Sheets, and works very similarly to how Excel spreadsheets work.  explains its use.


Reading through my textbook I came across the following problem and I am looking for some help solving it.  Prove that,  $$\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$$  In a previous problem I solved the following but I wasn't sure how to use it to prove the question above. Prove,  $$\binom{n}{r}=\binom{n}{n-r}$$  Solution:  left Side,  $$\binom{n}{r}=\frac{n!}{(n-r)!r!}$$  right side,  $$\binom{n}{n-r}=\frac{n!}{(n-(n-r))!(n-r)!} = \frac{n!}{(n-r)!r!}$$  Therefore completing the proof,  but how do I solve my first question? thanks!

So I came across Pascal's identity: Prove that for any fixed $r\geq 1$, and all $n\geq r$, $$ \binom{n+1}{r}=\binom{n}{r}+\binom{n}{r-1}. $$  I know you can use basic algebra or even an inductive proof to prove this identity, but that seems really cumbersome. I was wondering if anyone had a "cleaner" or more elegant way of proving it. For example, I think the following would be a decent combinatorial proof.   Proof: Let $S$ be a set with $n+1$ elements, and consider some fixed $x\in S$. There are $\binom{n+1}{r}\;\; r$-subsets of $S$--count them according to whether or not they contain $x$: there are $\binom{n}{r}$ not containing $x$, (each formed by choosing $r$ of the remaining $n$ elements in $S\setminus\{x\}$), and there are $\binom{n}{r-1}\;\; r$-sets containing $x$, (each formed by selecting an additional $r-1$ elements in $S\setminus\{x\}$).   Is that right? Are there any other efficient ways of doing it?


I want to format my Ubuntu and make it as no one used my computer before. Please do not tell me about Disks then format only a portion. Actually I want to format everything and start over again. Please help

I need to format a drive containing an old install of Ubuntu 10.04, to install Vista (not my idea!) Vista setup apparently refuses to format non-FAT32 or NTFS partitions. However, I can't seem to format it from my live CD (Ubuntu 11.04) at all; I keep getting "device is busy" errors. What is the simplest way to format this drive?


I am using matlab2tikz to generate a plot from experimental data and have a problem with the appearance of the plot. Changing the line thickness makes the data look very jagged. This is hard to describe and so I have attached two plots, one with line width set to 0.1pt and the other with the line width set to 0.8pt.     The thicker line is noticeably more jagged, and more importantly, the line is no longer an accurate representation of the data (the data does not jump as high or low).  In fact, this effect is also present for the thinner line, but is not as noticeable. The actual data is not fully smooth, but with the scale chosen the oscillations should not be visible. The last plot is from Matlab, and the data looks normal there.    How can I get a "good" output from PGFplots?

I am trying to plot some experimental data. When I plot the data using tikzpicture/pgfplots, the data seems "noisy". It becomes less "noisy" when I use the keyword each nth point={n}, where I increased n to 1, 10, 50, 100 (see attached picture). However, when increasing n, I am essentially not being true to my recording.  I was wondering if you could help me remove the "noise" that seems artificial while using my whole data set.   every n={1}   every n={10}   every n={50}   every n={100}   The code I use is as follows:  \documentclass[11pt]{article} \usepackage{tikz} \usetikzlibrary{plotmarks} \usepackage{amsmath} \usepackage{pgfplots} \usetikzlibrary{matrix} \usetikzlibrary{decorations.pathmorphing,patterns} \usepgfplotslibrary{external} \tikzsetexternalprefix{figurescache/} \pgfplotsset{compat=newest} \tikzset{external/system call={lualatex \tikzexternalcheckshellescape -shell-escape -synctex=1 -halt-on-error -jobname "\image" "\texsource"}} \tikzexternalize[mode=list and make] \begin{document}  \begin{tikzpicture}[scale=0.6] \begin{axis}[hide x axis, ymax={90}, ymin={-90}, xmin={0}, xmax={400}] \addplot[very thick, color=black, each nth point={1}]table[x=t,y=rec]  {./data/fig1data.dat}; \end{axis}  \end{tikzpicture} \end{document}   Edit: @Darthbith suggested I add the option /tikz/line join=bevel to my axis. It does a phenomenal job in removing the noise. There is a tiny bit of jaggedness when you zoom in to the plot, but it is already great.  is the link to data I have used in the plots I have attached to this post.


I submitted a paper to an Elsevier journal, but it was not assigned to a reference number. They sent me a mail stating that the paper with the managing editor for initial evaluation . After tow weeks later, I got mail stating that the paper is with the Editor. And it was assigned to a reference number. What does this mean? Thanks in advance.

What steps does a manuscript typically go through from submission to publication (or rejection) in a typical journal? How are these steps referred to, in particular by editorial systems, and how long do they each typically take?  Note that this question is about the typical situation and hence not about:   Journals with an atypical workflow, e.g. those that allow for an instantaneous reviewer–author interaction. Exceptional steps or rare occurrences such as withdrawal or .   This is a canonical question on this topic as per . Due to its nature, it is rather broad and not exemplary for a regular question on this site. Please feel free to improve this question.


I just rejected  from a user that seemed to be a sock puppet... although both accounts have 1 rep and were created 4 days apart, it just felt awkward to see the two user names involved.  That said, I would have rejected it anyway, just thought I'd slip a word about that user here; so far it doesn't seem to be doing anything bad, but the pieces are in place:    The suggested edit might have been "accidental", but if it had been approved, that would have been an illicit +2 already... but I don't know if there's another puppet at play (these two haven't actually done anything except posting 1 answer each; the suggested edit seems to be the first "cross-puppet" interaction), so I'd think the best thing to do is just to report it here?

User  joined 2 days ago and asked  about placing a div over an iframe "from Photosynth.net". A few hours later  (who joined 7 days ago) asked  about putting a div over an iframe, showing the source of the iframe as being from photosynth.net 1 hour later user  (who joined 3 days ago) posted  to that question; summarized: "thanks all for reply and sorry for miss understanding [...] wiating the answer and thanks".   Similar questions, English usage, rep, joining time frame, and ethnic usernames is not much to go on. As a non-moderator can I see IP addresses? Is there anything that should be done about these possible duplicate accounts?


I have a command from ImageMagick magick '*.jpg' -resize 120x120 thumbnail%03d.jpg  that resizes all jpeg files in a path.  I want to right click on an image and resize it. how do I edit the ImageMagick code so that it accepts this input.  sorry for the obscure question. is it something like '@' or '$1'? I think bash would be something like magick $1 -resize 120x120 $1

I need to pass an ID and a password to a batch file at the time of running rather than hardcoding them into the file.  Here's what the command line looks like:  test.cmd admin P@55w0rd > test-log.txt


I'm trying to prove the group isomorphism $(\Bbb Z[x]/(x^{n+1}))^\times\cong\Bbb Z/2\Bbb Z \times \prod _{i=1}^n \Bbb Z$.  Obviously I tried to establish a ring isomorphism from $\Bbb Z[x]/(x^{n+1})$ to some ring $R$, a direct product of easier rings, and prove that $R^\times$ equals the RHS of the original isomorphism. In the solutions of similar problems I've seen, one defines a surjective ring homomorphism $\phi : R^\prime[x]\rightarrow R$ of substituting $x$ with an element of $R$ such that the kernel of $\phi$ equals the dividing ideal, and uses the fundamental homomorphism theorem and CRT to show the ring isomorphism.  However this doesn't work for this particular problem; since $x^{n+1}$ has a (unique) multiple root, the kernel of homomorphism of plugging in does not equal to the dividing ideal.  Moreover, since $\Bbb Z[x]$ is not an Euclidean domain, I have no idea what the units of $\Bbb Z[x]$ modulo some ideal are like.  I would appreciate your help.

Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$.   Anyway how and what method is used to prove this. I still have no idea now. really thanks for your help


Any electron (in the shell) at any orbit of around of an atom can be stimulated by photon (of course as depending on the energy level of photon). So that, it can change its orbit and come back previous by emitting photon.  But in the Space, although there is lots of different photons in cosmic waves with all different energy levels and frequencies, the free electrons can not be excited by these photons.  Why? And what is the difference for this free electron and the electron of an atom (which may be interacting with a photon)?  I asked this question, because of photoelectric effect. I try to understand, the situation of an electron after it is separated from atom by a (hitting) photon and this electron can carry energy which we define it as electricity.

As simple as in the title.. I would like to know also some mathematics about it!


The times when a bounty is placed and when it is awarded are apparently .  However, for questions like  which have not been edited, the information is not visible from the question page (although you can access it by ). Can we get a link to the "revision history" even when there are no edits, or some other way to see the bounty info without manually typing in the /posts/[id]/revisions URL? It's strange to show the timing of bounty events only when the edit history is non-empty.

In the latest  I saw this:     2013-02-18: The revision history of a question that was closed as a duplicate is now showing the chosen originals as part of the "Closed as duplicate" notice.   That sounds cool, so I went to go see what it looks like and realized that questions with , but no edits, don't have an "edited <date>" link to click.  This applies to questions which had a bounty posted, or have been closed, reopened, locked, deleted, etc.  Examples:   , revisions:  , revisions:          I realize I can manually type the URL:  https://meta.stackoverflow.com/posts/168761/revisions   But it would be nice to simply click. It could say "revised" instead of "edited" if there were no edits:


Are you aware of any rules, statistics, or guidelines that address the "of" in company names?  For instance, which is more accepted: Institute of Research or Research Institute? Canada Bank or Bank of Canada? What guides the choice?  Thank you in advance.  Justin

In some scientific papers, we see that some professors write "University of Bla" on their papers, while others write "Bla University". What is the difference between "University of Bla" and "Bla University"? Are there any differences at all?


Which of these film introductions demonstrate the correct use of English Grammar? I have used example (1), but have been taken to task for so doing.   Eagle Films present  Eagle Films presents

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


I downloaded the Popcorn-Time from official link. When I try to execute "Popcorn-Time" file, using ./Popcorn-Time, it outputs the following error:  error while loading shared libraries: libudev.so.0: cannot open shared object file: No such file or directory   I've tried installing libudev0 by using:  apt-get install libudev0:i386   But that outputs the following error:   E: Package 'libudev0:i386' has no installation candidate   The image below contains all extracted files from .tar:   Anyone knows how I can execute Popcorn?

I got popcorn time installed using this link:    But I have no clue how to use or run Popcorn time.  Do I open my torrent client and download a movie and then it gets going? or do I have to open it? If I have to open it, how do I do that, I opened the dash and tried clicking on it but nothing happened. Please help me!! :D


We have very limited space in our home for a washer & dryer. We are thinking about putting them outside. We have an outdoor patio where 3 sides are part of the structure (the house). There is also a roof which is part of the house. The fourth side is open. The cement is a step up, elevated from the rest of the patio. We live in Southern California, in the high desert near Mojave. The winters get as low as 20 degrees and the summers up to 115 degrees. We have a lot of wind and some rainfall but not a lot. When it rains, it rains hard. Also the yard is mostly dirt so the dirt blows around a lot. Would this work? Would we still need the air vent? Should we wrap the gas line, wires, etc. What about putting them on a platform, off the ground?

I will be short on usable indoor space for a while, but want to be able to wash clothes on site.   Are there any issues with putting a washer (and perhaps, a dryer) outdoors?  Perhaps it needs to be protected from the rain. Would an EZ-UP style canopy be sufficient?


I am aware that this question is quite similar to another posed on this site, but I specifically need to understand whether you declare you are using the Sneak Attack on a given attack or whether it just happens on its own.  As a related matter, let's say my rogue is dual-wielding and chooses Sneak Attack on the first attack (main hand). If the main hand misses, has he "wasted" his one Sneak Attack attempt or does that then roll over to the off-hand attack?  If the latter, is the implication that the Sneak Attack damage just "happens" whenever you get your first successful hit (which would then have implications for rounds with multiple main attacks)?  Thanks all!

So, if a character multiclasses to a point where they have multiple attacks in a round, I assume you can decide once the hit has been confirmed by the DM, but before you roll damage, whether you make the hit a sneak attack?  I ask because you may know an enemy is weak, and don't want to waste the damage to finish it. I also want to confirm that you cannot declare sneak attack damage after you have already rolled your base damage, to finish off a still standing opponent for example. The "Is it dead? No? Oh! Then sneak attack!" seems dumb and nonsensical to me. I expect it to be like smite, decided on hit, but before damage is rolled.


me, my mother & my cousin applied for a Schengen visa together but my cousin's visa got accepted at once while mine & my mother's got rejected twice. The reason they gave was intended stay is not reliable (the vague answer). We applied thorugh an agent and submitted all the correct documents.I am working and submitted my NOC, my mother is a housewife, submitted her bank statement along with my fathers id and ITR and bank statement.  Please suggest here.....very disappointed. :(

Schengen refusal formulae can be difficult to understand sometimes.  Sometimes an applicant receives a refusal with:       Justification for the purpose and conditions of the intended stay was not reliable.     often accompanied by:       Your intention to leave the territory of the Member States before the expiry of the visa applied for could not be ascertained.   What is meant by this refusal reason?  What are they trying to say?


given a population of discrete values (not a sample), is there any way to check whether the distribution is a power-law, and with what parameters? Of course I can just plot the distribution and see its shape, but that does not allow me extract the power-law parameters.  Any help on how to do that is highly appreciated.

I need to fit data points on a power law and each one of these carries an uncertainty.  I've been using Python, more precisely scipy.optimize.curve_fit to get the job done but I don't know how to handle the uncertainties with it.  I thought about using a linear fit in log-log scale but it seems less precise compared to fitting directly on a power-law (not taking care of the uncertainties, just testing both on generated data and added noise).  I found  but it's not really helping me.  I wouldn't mind using R to do the job if needed.


I know in c++ variables have block scope, for example, the following code works in C++  void foo(){     int a = 0;     for(int i = 0; i < 10; ++i){         int a = 1; //re-define a here.     }   }  but this snippet doesnt work in java, it reports "duplicate local variable a", does it mean java variables dont have BLOCK scope?

The following method does not work because the inner block declares a variable of the same name as one in the outer block. Apparently variables belong to the method or class in which they are declared, not to the block in which they are declared, so I therefore can't write a short little temporary block for debugging that happens to push a variable in the outer scope off into shadow just for a moment:  void methodName() {   int i = 7;   for (int j = 0; j < 10; j++) {     int i = j * 2;   } }   Almost every block-scoped language I've ever used supported this, including trivial little languages that I wrote interpreters and compilers for in school.  Perl can do this, as can Scheme, and even C.  Even PL/SQL supports this!  What's the rationale for this design decision for Java?  Edit: as somebody pointed out, Java does have block-scoping.  What's the name for the concept I'm asking about?  I wish I could remember more from those language-design classes. :)


In $ZF$ without the Axiom of Foundation , can the axiom of choice(AC) be derived from the statement that the power set of every well ordered set can be well ordered(P)? With Foundation, we can prove this from the fact that the universe is $\bigcup\{V_{\alpha}: \alpha\in\mathbf{Ord}\}$, where $\mathbf{Ord}$ denotes the class of all ordinals and for all $\alpha$, $V_{\alpha}=\bigcup_{\beta\lt\alpha} P(V_{\beta})$; so by induction on $\alpha$, $V_{\alpha}$ can be well-ordered under the assumption of P. But I don't know whether AC can be proved from P without the axiom of foundation. Is the axiom of foundation necessary?

Without appealing to the axiom of choice, it can be shown that (Proposition:) if $X$ is well-orderable, then $2^X$ is totally-orderable.  Question: can we show the stronger result that if $X$ is well-orderable, then so too is $2^X$?  Proof of Proposition. Pick any well-ordering of $X$. Then the lexicographic order totally orders $2^X$.  More explicitly: for any two $f,g \in 2^X$, define $f < g$ iff   there exists $x \in X$ such that $f(x) \neq g(x)$, and if $x \in X$ is minimal such that $f(x) \neq g(x)$, then $f(x)=0$ and $g(x)=1$.   It can be shown that $<$ totally-orders $2^X$.


¿Which is the fastest way to check if a host is up or down using python?.   I need to perform ~ 120K pings so it doesn't matter if there is a few of  false negatives.  I have 2 different approaches:   ICMP requests with scapy  Execute os.system("ping -c 1 " . ip)

How do I ping a website or IP address with Python?


In a draft of a letter, later recorded as #246, Tolkien makes a strange statement.  I am interested in the first few sentences of the letter, but I will include the remainder for the sake of context.  In the 'Mirror of Galadriel', 1381, it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. If so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power. But this the Great had well considered and had rejected, as is seen in Elrond's words at the Council. Galadriel's rejection of the temptation was founded upon previous thought and resolve. In any case Elrond or Galadriel would have proceeded in the policy now adopted by Sauron: they would have built up an empire with great and absolutely subservient generals and armies and engines of war, until they could challenge Sauron and destroy him by force. Confrontation of Sauron alone, unaided, self to self was not contemplated. One can imagine the scene in which Gandalf, say, was placed in such a position. It would be a delicate balance. On one side the true allegiance of the Ring to Sauron; on the other superior strength because Sauron was not actually in possession, and perhaps also because he was weakened by long corruption and expenditure of will in dominating inferiors. If Gandalf proved the victor, the result would have been for Sauron the same as the destruction of the Ring; for him it would have been destroyed, taken from him for ever. But the Ring and all its works would have endured. It would have been the master in the end. Gandalf as Ring-Lord would have been far worse than Sauron. He would have remained 'righteous', but self-righteous. He would have continued to rule and order things for 'good', and the benefit of his subjects according to his wisdom (which was and would have remained great). [The draft ends here. In the margin Tolkien wrote: 'Thus while Sauron multiplied [illegible word] evil, he left "good" clearly distinguishable from it. Gandalf would have made good detestable and seem wicked']. -Tolkien, Letter #246  What was Tolkien trying to say with the following line?  If so, so also were the other guardians of the Three, especially Elrond.  If what is so, and Elrond was especially what?  Is Elrond especially likely to master the Ring?  Is he especially likely to imagine that he could master the Ring?  Note:  This is not a duplicate of "", since I am not interested in who is more powerful.  I am only interested in Tolkien's intended meaning when he wrote the letter.  The other question is in-universe, mine is concerned with the letter itself, not the story or the characters within it.

I always thought it was the other way around, but then I read this (Letter 246):     "Of the others only Gandalf might be expected to master him – being an emissary of the Powers and a creature of the same order, an immortal spirit taking a visible physical form. In the 'Mirror of Galadriel', 1381, it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. If so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power."   This "especially Elrond" confuses me. I don´t think that Elrond is inherently more powerful than Galadriel, who is described as the greatest of the Noldor, except for Fëanor (and possibly even his equal).  A quote from Unfinished Tales says:     "...In this he (Tolkien) emphasized the commanding stature of   Galadriel already in Valinor, the equal if unlike endowments of   Fëanor; and it is said here that so far from joining in Fëanor's   revolt she was in every way opposed to him."   Furthermore,      "A queen she was of the woodland Elves, the wife of Celeborn of   Doriath, yet she herself was of the Noldor and remember the Day before   days in Valinor, and she was the mightiest and fairest (so even   fairer than Arwen I would guess) of all the Elves that remained in   Middle-earth."   (The Silmarillion, of the Rings of Power)  And again...     "Galadriel was the greatest of the Noldor, except Fëanor maybe, though   she was wiser than he, and her wisdom increased with the long years."   (the Shibboleth of Fëanor)  Restating it:     "These two kinsfolk (Fëanor and Galadriel), the greatest of the   Eldar in Valinor, were unfriends for ever." "Who together with the   greatest of all the Eldar, Luthien Tinuviel, daughter of Elu Thingol,   are the chief matter of the legends and histories of the Elves."   (Unfinished Tales)  The latter means that Luthien, Fëanor and Galadriel are the chief matter of the history and legends. It seems to me that Tolkien thought of those three as the creme de la creme of the elven crop.  Reading all that I have serious problems believing that Elrond could be superior to her. As great as Elrond is, descending from Melian, he is no equal of Fëanor, who is said to be the mightiest of all elves, and if Galadriel is his equal, then there is no way that Elrond would be mightier than her.  Maybe I just read this "especially Elrond" wrong; it could as well mean that especially Elrond was deceived into thinking that he could master the ring, because that was the deceit of the ring. And Tolkien said explicitly that only Gandalf could possibly master it.  So, what do you think?


Let's say I have the following sentence: "I didn't like the cake (the cookies were better), but I absolutely hated the egg rolls."  Would it be grammatically correct (and colloquially okay, to someone who would be reading it) to change it to this:  "I didn't like the cake—the cookies were better—but I absolutely hated the egg rolls."  because I think it's okay to use em dashes instead of parentheses (according to other questions I've read), but I'm taking out the comma before "but" too. Is that okay?

When do you use commas and when do you use parentheses to provide more detail about something?  For example:   The suspect, Tom Wilson, is now being charged with murder. The suspect (Tom Wilson) is now being charged with murder. John Smith, a member of the jury, agreed with the verdict. John Smith (a member of the jury) agreed with the verdict. The first example, the one about the fox, is the more valid one. The first example (the one about the fox) is the more valid one.   I realize that the first example, the one that uses parentheses, is probably more valid in this case (if anyone has a better example, please include it), but when, if ever, would you favor parentheses?  Update: I realize that dashes are sometimes used for similar situations, so I'd appreciate information on these as well.  For example:   The children—who are wearing shoes—will go on the trip The children, who are wearing shoes, will go on the trip The children (who are wearing shoes) will go on the trip


People say that negative sign has something to do with Lenz's law. I understood that negative sign is used to get correct sign of emf according to definition of emf. But how we can relate negative sign with Lenz's law definition? If there is any relation Lenz law then how do you come to know that with only a negative sign?

If we write out Maxwell's equations with magnetic charges, we get $$ \begin{align} \nabla \cdot \mathbf{E} &= 4 \pi \rho_e \tag{1}\\ \nabla \cdot \mathbf{B} &= 4 \pi \rho_m \tag{2}\\ -\nabla \times \mathbf{E} &= \frac{\partial \mathbf{B}}{\partial t} + 4 \pi \mathbf{J}_m \tag{3}\label{Eq:Faraday}\\ \nabla \times \mathbf{B} &= \frac{\partial \mathbf{E}}{\partial t} + 4 \pi \mathbf{J}_e \tag{4}\label{Eq:Ampere} \end{align} $$ In particular, Faraday's law \eqref{Eq:Faraday} contains a minus sign that Ampere's law \eqref{Eq:Ampere} does not. This always struck me as odd because it's often said the fields are dual to each other (i.e. you can replace E with B and "get the same result"), but that requires a bit of mental recalibration to accommodate that minus. So I'm curious what the origin of that negative is and what it means. Are there any intuitive explanations for how to think about it?


Lecture book just stated that:  $(n-1)^2/\sigma^2$ is a chi squared distribution with $(n-1)$ degrees of freedom where $n$ sample size, $S^2$ sample variance and $\sigma$ population standard deviation,but how do I prove such thing. Thanks, any tips hints would do.

It's a standard result that given $X_1,\cdots ,X_n $ random sample from $N(\mu,\sigma^2)$, the random variable $$\frac{(n-1)S^2}{\sigma^2}$$ has a chi-square distribution with $(n-1)$ degrees of freedom, where $$S^2=\frac{1}{n-1}\sum^{n}_{i=1}(X_i-\bar{X})^2.$$ I would like help in proving the above result. Thanks.


WHY our time would run slow if we move with the speed close or  equal to the speed of light, and is that time dilation restricted to only just '' time' ' or it affects our biological time also (does it stops or  slows down our ageing process) ??

I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the universal speed limit.    So, if I were to travel in a spacecraft at (practically) the speed of light, would I freeze and stop moving?  Would the universe around me freeze and stop moving?  Who would the time stop for?


python manage.py runserver 0.0.0.0:8000  how to make this command running if terminal close  for now i use screen and it works any other way to do that? i mean for production how to link it to ngix or apahce in ubuntu server?

How do I run a program in the background of a shell, with the ability to close the shell while leaving the program running? Lets say my UI is having problems or for some reason, I need to boot up a program from the terminal window, say, nm-applet:  nm-applet   When it's started, it occupies the foreground of the terminal window.  Is there any simple way to run the program in the background without needing to leave the terminal open or have it occupy the whole terminal?  On that note, I did find a way to run programs from the terminal and have it allow for other inputs, by appending an ampersand (&) to the command as such:  nm-applet &   But this isn't much use as any processes started in the terminal are killed once the terminal is closed.


How to prove that $\sin(x \sin x)$ is not uniformly continuous on $\Bbb{R}^+$?  My attempt: I know that $\sin x$ is uniformly continuous on that interval when $\sin{x^2}$ is not.  Yes It is duplicate of one question. But the answer was not satisfactory. That's why I am posting it again.  Any help will be highly appreciated.

I want to prove or disprove that $f(x)=\sin(x\sin x)$ for all $x\in (0,\infty)$ is uniformly continuous.  We know that $g(x)=x\sin x$ is not uniformly continuous on $(0,\infty)$. But what about $f$? I am not getting any hint. Any help is appreciated.


I have been stuck on this for a while now, if someone could show me some insight it would be much appreciated. The stack trace console points to the frame.add(showname); as well as to new GradeProg(); The console states:  Exception in thread "main" java.lang.NullPointerException at java.awt.Container.addImpl(Container.java:1040) at java.awt.Container.add(Container.java:958) at javax.swing.JFrame.addImpl(JFrame.java:540) at java.awt.Container.add(Container.java:363) at GradeProg.<init>(GradeProg.java:39) at GradeProg.main(GradeProg.java:68)   From what I understand, due in part to this great site, was that the showname variable was not initialized, though I believe I already initialized it. Here is the code:  import java.awt.*; import java.awt.event.*; import javax.swing.*;  @SuppressWarnings("serial") public class GradeProg extends JFrame implements ActionListener {  JLabel label, label2, showname, showgrade; TextField field, field2; JFrame frame; JButton enter; String grade, name; int parse;  public GradeProg() {      frame = new JFrame("Student Grades");     frame.setLayout(new GridBagLayout());     frame.setDefaultCloseOperation(EXIT_ON_CLOSE);     frame.pack();     frame.setVisible(true);     frame.setSize(600, 300);      label = new JLabel("Student Name: ");     field = new TextField("", 12);      label2 = new JLabel("  Score  ");     field2 = new TextField("", 5);      enter = new JButton("Enter");     enter.addActionListener(this);      frame.add(label);     frame.add(field);     frame.add(label2);     frame.add(field2);     frame.add(enter);     frame.add(showname);     frame.add(showgrade);  }  @Override public void actionPerformed(ActionEvent e) {      parse = Integer.parseInt(field2.getText());      if (parse >= 90 && parse <= 100) {         grade = "A";     } else if (parse >= 80 && parse <= 89) {         grade = "B";     } else if (parse >= 70 && parse <= 79) {         grade = "C";     } else if (parse >= 60 && parse <= 69) {         grade = "D";     } else if (parse >= 0 && parse <= 59) {         grade = "F";     }      showgrade = new JLabel("Grade: " + grade);     showname = new JLabel(field.getText()); }  public static void main(String[] args)  {     new GradeProg(); }  }   Again, any help or overall suggestions would be much appreciated. Thakns

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 have been following the developments around the Shawyer EM drive for about 2 years now as NASA and other parties test it out in various environments. To preface, I would very much like to see the EM drive work so sorry in advance if I am afflicted with a case of confirmation bias.  The most recent test in Dresden, Germany (the paper by M. Tajmar et al.) to me seems like another test that proves this idea may have some validity. As you may know if you are thinking about answering this question, the main concern with this idea is that it violates the momentum conservation principle (i.e., there must be something else that is causing the "thrust" force the experimenters are observing).   At this point, I need to say my background in physics is only through quantum mechanics and special relativity. I have dabbled in General Relativity and Quantum Field Theory, but don't yet have the mathematical prowess to fully appreciate them. I am an engineer, not a physicist, so forgive me if my arguments are a bit flawed. That's why I'm asking after all!  From thermodynamics, we know energy must be conserved (energy conservation). Conventional wisdom would say that momentum must also be conserved; however, I have begun to think this is solely a classical dynamics idea. I know in quantum mechanics, the transfer of momentum is also conserved, but when I try to correlate this with General Relativity's view of the world in terms of the stress-energy tensor, I find that momentum flux (and thus in my mind, momentum) is merely a product of an energy density. After all, if mass is just energy in the form of mass-energy, why can't this mass-energy move thus making momentum? It would seem to me that the so-called "conservation of momentum" is just another way of saying "energy is conserved" in a different way.  In the Shawyer drive, energy is conserved: you still have to provide energy to the system, and in return you get thrust. If momentum is truly just another form of energy, why do skeptics think this can't work?  So to be succinct (sorry, that was long-winded), why is the momentum conservation law so important if everything boils down to energy at the end of the day? If everything (and I mean everything) truly is just different forms of energy, shouldn't it be obvious that it must be possible to convert it from one form to another via some pathway or process?  Thanks in advance for helping me with my little thought!

In 2006, New Scientist magazine published an article titled 1 [] about the  [] which stirred up a fair degree of controversy and  that New Scientist was engaging in pseudo-science.   Since the original article the inventor claims that a "Technology Transfer contract with a major US aerospace company was successfully completed", and that papers have been published by Professor Yang Juan of The North Western Polytechnical University, Xi'an, China. 2   Furthermore, it was  that the Chinese were going to attempt to build the device.  Assuming that the inventor is operating in good faith and that the device actually works, is there another explanation of the claimed resulting propulsion?  Notes:  1. Direct links to the article may not work as it seems to have been archived. 2. The abstracts provided on the  website claim that they are Chinese language journals which makes them very difficult to chase down and verify.


I'm trying to prove that the trace of a nilpotent matrix is $0$. Here's what I have:  Let $A \in M_n(k)$, where $k$ is a field. If $A$ is nilpotent then, in fact, $A^n=0$, (this result was proven in the previous problem.) By Proposition 20 on page 428 (Dummit & Foote) the characteristic polynomial of $A$ divides some power of the minimal polynomial of $A$, and so is of the form $x^m$ for some $m \ge t$. Thus, the eigenvalues of $A$ are all equal to $0$ and the only solution to the equation $xv-Av=0$ is the trivial solution. Since it is assumed that $v \neq 0$, then it must be that $A=0$.   This is a much stronger conclusion than the conclusion I'm aiming for and so I am suspicious. I probably made an error. Please help.

Does anyone know a proof from the first principles that a nilpotent matrix has zero trace. No eigenvalues, no characteristic polynomials, just definition and basic facts about bases and matrices.


Lost assassins creed save progress by reinstalling Windows system.  Any idea how to recover it ?

I have a harddisk with two partitions: one for windows and one for data. I've reinstalled windows on the first partition and formatted the data partition with full format (without /Q option) making sure that all my data is backed up. After that I've created the same folder structure (without files inside) on data partition as it was before formatting.   I then realized that all my photos were NOT backed up :((((  I've tried several tools to recover my data without any success:   Wordershare Photo Recovery Active File Recovery R-Studio PhotoRec from CGSecurity Recuva   There are max 50Mb of new data on that partition, so data overwriting is minimal.  What is the reason why I'm not able to recover my data with data recovery tools: full format or same folder structure?  And... can I get my photos back or they are lost forever?


I have a website where the database mysql collation was in latin_1 and the php files were set with <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">.  Now, the old website worked with PHP 5.4, I'm working with a 5.6 right now so I had to make lost of translations and changes. I'm still working on them, but I still have problems with speciale characters. I changed the db collation with UTF8mb4_unicode_ci and changed the charset of the files where it was written with <meta content='text/html; charset=UTF-8' http-equiv='Content-Type'>  I still get errors, seeing sometimes Ã for é and � for ' . Is there something I'm missing? Did I do something wrong? Thanks in advance.

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


I'm trying to post some piece of gradle script at it doesn't look like code. Here it works: buildscript {     repositories {         mavenCentral()     }     dependencies {         classpath 'com.android.tools.build:gradle:0.5.+'     } }  But on stackoverflow if look like regular text with indents:  Browser: 31.0.1650.57 System: OSX 10.9

Consider the following piece of Markdown code:  This is some regular text.      >>> def factorial(n):     ...     return 1 if n < 2 else n * factorial(n - 1)     ...   * This is a list item.      >>> def factorial(n):     ...     return 1 if n < 2 else n * factorial(n - 1)     ...    Notice that the second code block is preceded by a list item.   Why is the factorial code not properly formatted under these circumstances? To demonstrate the problem, I'll insert the Markdown code show above:    This is some regular text.  >>> def factorial(n): ...     return 1 if n < 2 else n * factorial(n - 1) ...     This is a list item                 def factorial(n):       ...     return 1 if n < 2 else n * factorial(n - 1)       ...               This applies to numbered as well as unnumbered lists.


Recently, I answered   question. A generalized version of what was proved is the following.  Lemma: For $n\in\mathbb{N}$ and $a_1,a_2,\ldots,a_{2n+1}\in \mathbb{Q}$, if for each $1\le i\le 2n+1$, the numbers $\{a_j:1\le j\le 2n+1\wedge j\neq i\}$ can be divided into two sets of size $n$ with equal sum, then all $a_i$ must be equal.  Proof: At first, we limit ourselves to $\mathbb{Z}$. If for some $a_1,a_2,\ldots,a_{2n+1}\in \mathbb{N}$, for all $1\le i\le 2n+1$, the numbers $\{a_j:1\le j\le 2n+1\wedge j\neq i\}$ can be divided into two sets of size $n$ with equal sum, we call $a_1,a_2,\ldots,a_{2n+1}$ a solution.  For any solution $a_1,a_2,\ldots,a_{2n+1}$ and a positive integer $m$, $a_1-m,a_2-m,\ldots,a_{2n+1}-m$ is also a solution. If all the $a_i$ are even, then $\frac12a_1,\frac12a_2,\ldots,\frac12a_{2n+1}$ is a solution as well.  Now, the sum of every $2n$ elements is even, therefore, each $a_i$ has the same parity as the sum of all $a_i$, therefore, all $a_i$ have the same parity.  WLOG, we can assume one of the $a_i$ to be $0$, so all $a_i$ are odd. This means we can divide them all by $2$ and still have a valid solution. However, since one of them is still $0$, they're all even again, so we can divide them all by $2$ again, but then one of them is still $0$ and so on. So all the $a_i$ are finite and divisible by arbitrarily large powers of $2$, so all $a_i$ are equal to $0$.  For $a_1,a_2,\ldots,a_{2n+1}\in\mathbb{Q}$, simply multiply all of the $a_i$ by the product of the denominators to translate the problem to the integers. Q.E.D.  Question: Is the lemma also true for $a_1,a_2,\ldots,a_{2n+1}\in \mathbb{R}$?

Let $S$ be a finite collection of real numbers (not necessarily distinct). If any element of $S$ is removed then the remaining real numbers can be divided into two collections with same size and same sum ; then is it true that all elements of $S$ are equal ?  (I know the result is true if the "reals" are replaced by "integers".)


Let $G$ be a undirected graph and $A$ be a its adjacency graph. How should I proof that there is at least one triangle in $G$ if there exist $i,j$ such that neither $(A)_{ij}$ nor $(A^2)_{ij}$ is $0$? Sorry but I have no idea to show this. Can someone help me to show this? Thank you in advance.

Show that a graph $G$ contains a triangle (1) if and only if there exist indices $i$ and $j$ such that both the matrices $A_G$ and $A^{2}_{G}$ have the entry $(i, j)$ nonzero, where $A_{G}$ is the adjacency matrix of $G$ (2).  $1 \implies 2$  If the graph contains a triangle, the entries in the matrix which correspond to edges between the vertices that that make up the triangle will be non-zero.  Each such pair $(i,j)$ will also be non-zero in $A^{2}_{G}$, because there is a path of length two between $i$ and $j$ (within the triangle), starting from $i$, using another vertex $k$ and ending in $j$.  $2 \implies 1$  If $(i,j)$ is 1 in $A_{G}$, then the vertices $i$ and $j$ must be connected. Furthermore, if $(i,j)$ is 1 in $A^{2}_{G}$ that means there must be some other vertex $k$ through which we can go to $j$ starting from $i$. Hence the edges $(i, j)$, $(i, k)$, $(k, j)$ makes up the triangle.  I had trouble writing down this proof properly. Is the main idea correct?


It's suggested that he work hard.lt's suggested that he works hard.  Which one is correct?  I think,  It is suggested that he works hard. This is correct one.  But,  how ? I am confused.  Please clear them.

Why is this sentence correct?     She suggested that he go to the cinema.   I would definitely use goes instead of go.


Today, I just received an upvote on 9 of my answers at about the same time. I've read a little on here and saw that "serial" upvoting causes you to lose the rep after. My question is, I also got a badge because of this, will I lose the badge as well?   Also, if they upvote 9 of my answers, will the legitimate one that they upvoted first get it's rep removed as well? Or just the other 8?

I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?


I apologize if my knowledge and Java standardization is poor. I'm new to the language and self-taught. I'm trying to put together an inventory program, and I'm using observable lists to store instances of a part class that has two subclasses. The observable lists are stored in an Inventory class. At any point in the program runtime, if there's an instance of a Part being added to the Parts List, a null pointer exception is thrown. The segments of code below are stored in separate files. public abstract class Part { private int partID; private String partName; private double partPrice; private int partStock; private int partMin; private int partMax;  public Part(){     this(0, null, 0, 0, 0, 0); }  public Part(final int partID, final String partName, final double partPrice, final int partStock, final int partMin, final int partMax){     this.partID = partID;     this.partName = partName;     this.partPrice = partPrice;     this.partStock = partStock;     this.partMin = partMin;     this.partMax = partMax; }  public void setPartID(final int partID) {     this.partID = partID; }  public int getPartID() {     return this.partID; }  public void setPartName(final String partName) {     this.partName = partName; }  public String getPartName() {     return this.partName; }  public void setPartPrice(final double partPrice) {     this.partPrice = partPrice; }  public double getPartPrice() {     return this.partPrice; }  public void setPartStock(final int partStock) {     this.partStock = partStock; }  public int getPartStock() {     return this.partStock; }  public void setPartMin(final int partMin) {     this.partMin = partMin; }  public int getPartMin() {     return this.partMin; }  public void setPartMax(final int partMax) {     this.partMax = partMax; }  public int getPartMax() {     return this.partMax; }  }  public class InHouse extends Part{  private int machineID;  public InHouse() {     this(0, null, 0, 0.0, 0, 0, 0); }  public InHouse(final int partID, final String partName, final int partStock, final double partPrice, final int partMin, final int partMax, final int machineID) {     super(partID, partName, partPrice, partStock, partMin, partMax);     this.machineID = machineID; }   public void setMachineID(final int machineID) {     this.machineID = machineID; }  public int getMachineID() {     return this.machineID; }   public class Outsourced extends Part{     private String companyName;  public Outsourced() {     this(0, null, 0, 0.0, 0, 0, null); }  public Outsourced(final int partID, final String partName, final int partStock, final double partPrice, final int partMax, final int partMin, final String companyName) {     super(partID, partName, partPrice, partStock, partMin, partMax);     this.companyName = companyName; }   public void setCompanyName(final String companyName) {     this.companyName = companyName; }  public String getCompanyName() {     return this.companyName; }   Pardon the "Inventory2." My NetBeans behaves as though "Inventory" is a file that already exists, even though there's nothing of the like in my project files. public class Inventory2 { public static ObservableList<Part> parts;  public Inventory2() {     parts = null;  }  public static void addPart(Part part) {     parts.add(part); }   This is a code snippet that generates a null pointer exception. Inventory2 inventory = new inventory2();     final InHouse partToAdd = new InHouse();             partToAdd.setMachineID(1234);             partToAdd.setPartName("generic");             partToAdd.setPartStock(2);             partToAdd.setPartPrice(10);             partToAdd.setPartMin(1);             partToAdd.setPartMax(15);             partToAdd.setPartID(1);     inventory.addPart(partToAdd);

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


I'm wanting to change the configuration of my home network. A partial schematic of the network is as follows:    when I say "partial" there are other things connected to the ADSL router which for simplicity, I've left out.  Please pay particular attention to the "Wireless Client"s at the bottom. I want to change their configuration such that the network looks like this:    So you can see, I want to make these clients wired clients, which will go into some box (marked ?????), and to have that box talk to the wireless network.  My question is firstly, is it possible? Assuming it is possible, what type of hardware does "?????" need to be? Or, do I need a couple of pieces of hardware?  I will pre-empt the question "why" by giving a little background. Currently, "Wireless Client #1" and "Wireless Client #2" are not computers, but are satellite tv receivers. Neither has wireless functionality, I currently (for each of them) have a wireless bridge dongle going into the RJ45 socket, thereby allowing them to talk out to the wlan and ultimately to the web. I'm looking at getting some more clients of this type, and I don't really want to buy a dongle for each. I'd sooner sit some kind of router/access point/bridge with the receivers under the tv, and have that router/access point/bridge communicate with the wireless network on the clients' behalf. But I'n not exactly sure what that box needs to be.   Lastly, the obvious option of plumbing into the adsl router amd bypassing the wireless network altogether, I'm put off this option purely because of the geography of the house. I'm not really ina position to lay cables right now.

I have a number of servers in my room, and I'd like to have a high-speed wired LAN within the room between my servers and my desktop and laptop. My internet access is provided by a cable modem connected to a wireless router, and I'd like it to stay that way (my Internet connection setup is at the other end of the house). Are there any routers (wireless or wired) out there that could provide a wired LAN in my room, but use a wireless connection as the Internet source? (the router in my room would be connected to my house's hotspot and use that as the Internet connection for the LAN in my room).


Let $X =\{  x_1x_4=x_2x_3\;, (x_2,x_4) \neq (0,0)\} \subset \mathbb{C^4}$, i.e. not both of $x_2,x_4$ are zero. Define a function $\phi$ on $X$ by $\phi(x)=\left\{\begin{matrix} \frac{x_1}{x_2} & ,x_2 \neq 0 \\   \frac{x_3}{x_4}& ,x_4 \neq 0   \end{matrix}\right.$.      Prove that there are no two polynomials $f,g \in \mathbb{C}[x_1,x_2,x_3,x_4]$ such that for all $x \in X$, $\phi(x)=\frac{f(x)}{g(x)}$.   In fancier words, $\phi$ is a regular function on an open subset $V(x_1x_4-x_2x_3) \setminus V(x_2,x_4)$ of an affine variety that can not be defined by a single choice of polynomials.  I don't have a good approach. I tried the following: we know that on the open subset where $x_2\neq0$ and $x_4\neq0$ we have pointwise both $f(x)x_2=g(x)x_1$ and $f(x)x_4=g(x)x_3$, and I think these relations hold on all of $X$, since they are true on a Zariski-dense subset of $X$, and the set where they hold is a closed subset of $X$. This tells us a bit about the nature of such $f,g$ since e.g. $g$ must vanish whenever $x_2=0,x_1 \neq 0$.

Look at the example 2.1.7 at page 19 of these  (which is the same example present in Mumford's red book at page 21). The author shows that a regular function isn't a ratio of two polynomial, and in particular in the above example inside the open set $U$ we have the following regular function: $$\phi(p)=\left\{\begin{array} {lll} \frac{X_1}{X_2} & \textrm{if $p\in X_2\neq 0$}\\\\ \frac{X_3}{X_4} & \textrm{if $p\in X_4\neq 0$} \end{array}\right.$$   I agree with the fact that $\frac{X_1}{X_2}=\frac{X_3}{X_4}$ in $K(X)$ when $X_2\neq0$ and $X_4\neq0$, but the point is that such two functions shoud be the same in the whole $V$ to make sensible the example. Infact in in the intersection $\{X_2\neq0\}\cap\{X_4\neq0\}$ we have the regular function described by $\frac{X_1}{X_2}$ or $\frac{X_3}{X_4}$, but what about the rest of $U$?


My wife and step-daughter, both from the Philippines, wonder if they can go via London Heathrow when going from Oslo, Norway, back to Manila, Philippines.  There are SO many rumours that you'll need a VISA just for transfer, so what is the FACT?  They are Philippine citizens, with a valid visa for Norway/Schengen (BUT the old one is expired, and the new one not in their Passports yet...) if THAT matters - and on their way back to their homeland.  They'll go with a SAS-flight from Oslo to Heathrow, and a Catay Pacific from Heathrow to Manila. Will they need any VISA for the transfer...?

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


Let $G$ be a group and $H$ be its subgroup. Then, is the set $W=\cap_{g\in G} gHg^{-1}$ a normal subgroup?   I think the answer is yes, because the set is equal to the stabilizer of the action of $H$ on $G$ with action as conjugation, which is the normalizer of $H$. Any ideas. Thanks beforehand.

Is there a better (more direct or intuitive) proof for this proposition than I have come up with below? I am not sure whether it could be simiplified:  Let $G$ be a group with $H \leq G$. Then $K = \bigcap_{g \in G} gHg^{-1}$ is normal in $G$.  Let $a \in K$. Then $a \in gHg^{-1}$ for all $g \in G$. Therefore for all $g_1,g \in G$, $g_1ag_1^{-1} \in g_1gHg^{-1}g_1^{-1} = (g_1g)H(g_1g)^{-1}$ and so $g_1ag_1^{-1} \in K$ since $g_1g \in G$. Then $K$ is normal in $G$.


Caroll, while proving the Newtonian limit takes $$g_{ab} = \eta_{ab} + h_{ab}$$ He then just writes down the inverse metric to 1st order as $$g^{ab} = \eta^{ab} - h^{ab}$$ I don't see how this calculation has been done. It looks like some kind of  Binomial theorem has been used but I don't see how. Can anyone help me with the steps in between and what the inverse metric will look like to 2nd or 3rd order in $h$?

From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert<<1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert<<1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$


Otherwise stable Ubuntu machine have an issue since installing that is critical freezing without apparent reasons. There are high probabilities that the issue been caused by NVDIA videocard.       sudo blkid output:  /dev/sda2: UUID="0E5C95E45C95C73D" TYPE="ntfs" PARTUUID="1ef0523b-02" /dev/sda5: UUID="16EA-1372" TYPE="vfat" PARTUUID="1ef0523b-05" /dev/sda6: UUID="fe90c52c-c1b7-4845-971e-e7ed5cb45ac4" TYPE="ext4" PARTUUID="1ef0523b-06"   /etc/fstab:  # /etc/fstab: static file system information. # # Use 'blkid' to print the universally unique identifier for a # device; this may be used with UUID= as a more robust way to name devices # that works even if disks are added and removed. See fstab(5). # # <file system> <mount point>   <type>  <options>       <dump>  <pass> # / was on /dev/sda6 during installation UUID=fe90c52c-c1b7-4845-971e-e7ed5cb45ac4 /               ext4    errors=remount-ro 0       1 /swapfile                                 none            swap    sw              0       0 /dev/mapper/cryptswap1 none swap sw 0 0   /etc/crypttab:  cryptswap1 UUID=f09a516a-22c0-475c-b749-31ffed5c7bda /dev/urandom swap,offset=1024,cipher=aes-xts-plain64   ls -alh /swapfile:  -rw------- 1 root root 2.0G May  3 13:31 /swapfile

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


I tried sudo apt-get install php-pecl, but I get this output:  Reading package lists... Done  Building dependency tree         Reading state information... Done  E: Unable to locate package php-pecl

I've tried it a 100 times I'm really new to Ubuntu and ended with a bunch of error that I don't even understand can any one please help me??  Here is what I did:   I installed PHP  I installed libcurl then php5-dev I tried installing PECL extension and it says PHPIZE not found.


I am trying to call a function with a variable though a imported functions file and i am getting a error:  AttributeError: 'module' object has no attribute 'i'  I have 3 files I am working with, list.txt functions.py and run.py  In my run.py I am opening list.txt and setting whats there to a list and removing the white space. Then i am looping though the list and trying to call a function based off of the list item. But the code is not taking i as a function but as a str i think. How do i turn i in to something that the function will understand and run?  list.txt contains:  foo bar  functions.py  class get_stuff:     def foo(self):         print('I just ran foo')     def bar(self):         print('I just ran bar')   run.py   import functions with open(list.txt) as f:      xx = [xx.rstrip('\n') for xx in f] for i in xx:      print ('working on item: ' + i )     functions.get_stuff.i()   I am new to python and am having a hard time finding out a way to fix my problem. I have goolged this for a few hours and while i am finding answers that fit they don't cover imported functions just functions that are in the same script. I might be looking at it the wrong way, maybe I am missing something super easy or this might be the completely wrong way of pythoning! Any help will be great!

What is the best way to go about calling a function given a string with the function's name in a Python program.  For example, let's say that I have a module foo, and I have a string whose content is "bar". What is the best way to call foo.bar()?  I need to get the return value of the function, which is why I don't just use eval. I figured out how to do it by using eval to define a temp function that returns the result of that function call, but I'm hoping that there is a more elegant way to do this.


Does anyone know how to get Japanese or other double-byte character sets to appear correctly in email?  I'm sending Japanese in email. While I can see the characters, people in Japan have been telling me that they cannot see the characters. That's kind of makes my emails useless @_@  I've tried setting all kinds of character sets in the web.config and in the CDO config, but haven't found out how to get the characters to display properly.

Aparently, encoding japanese emails is somewhat challenging, which I am slowly discovering myself. In case there are any experts (even those with limited experience will do), can I please have some guidelines as to how to do it, how to test it and how to verify it?  Bear in mind that I've never set foot anywhere near Japan, it is simply that the product I'm developing is used there, among other places.  What (I think) I know so far is following: - Japanese emails should be encoded in ISO-2022-JP, Japanese JIS codepage 50220 or possibly SHIFT_JIS codepage 932 - Email transfer encoding should be set to Base64 for plain text and 7Bit for Html - Email subject should be encoded separately to start with "=?ISO-2022-JP?B?" (don't know what this is supposed to mean). I've tried encoding the subject with    "=?ISO-2022-JP?B?" + Convert.ToBase64String(Encoding.Unicode.GetBytes(subject))   which basically gives the encoded string as expected but it doesn't get presented as any japanese text in an email program - I've tested in Outlook 2003, Outlook Express and GMail    Any help would be greatly appreciated    Ok, so to post a short update, thanks to the two helpful answers, I've managed to get the right format and encoding. Now, Outlook gives something that resembles the correct subject: =?iso-2022-jp?B?6  Japanese test に各々の視点で語ってもらった。  6相当の防水?=  However, the exact same email in Outlook Express gives subject like this: =?iso-2022-jp?B?6  Japanese test 縺ｫ蜷・・・隕也せ縺ｧ隱槭▲縺ｦ繧ゅｉ縺｣縺溘・ 6逶ｸ蠖薙・髦ｲ豌ｴ?=  Furthermore, when viewed in the Inbox view in Outlook Express, the email subject is even more weird, like this: =?iso-2022-jp?B?6  Japanese test ??????????????? 6???????=  Gmail seems to be working in the similar fashion to Outlook, which looks correct.  I just can't get my head around this one.


I want to have a script that takes the current working directory to a variable. The section that needs the directory is like this dir = pwd. It just prints pwd how do I get the current working directory into a variable?

I want to assign the result of an expression (i.e., the output from a command) to a variable and then manipulate it – for example, concatenate it with a string, then echo it.  Here's what I've got: #!/bin/bash cd ~/Desktop; thefile= ls -t -U | grep -m 1 "Screen Shot"; echo "Most recent screenshot is: "$thefile;  But that outputs: Screen Shot 2011-07-03 at 1.55.43 PM.png Most recent screenshot is:   So, it looks like that isn't getting assigned to $thefile, and is being printed as it's executed. What am I missing?


I have no clue on this one so I hope you can help me out on this one.  Let $x,y \ge 0 $ and $0 \lt n \le 1$. Then $$ (x+y)^n \le x^n +y^n$$

If $0 < \alpha < 1$, then       $$ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $$      for $x$, $y$ positive.   Is this inequality true in general?  I tried using Young's Inequality: For $z,t > 0$, and for $n$, $m$ such that $n+m=1$, then   $$ z^n + t^m \leq nz + mt $$  So, using this we have   $$ (x+y)^{\alpha} \cdot 1^{1 - \alpha} \leq \alpha(x+y) + (1-\alpha) = \alpha x + \alpha y + (1-\alpha)$$  which is not as tight as I want.


I have an application in python .How can i create its Android build(apk file). I have no idea how to do this job.Please comment if you have done this. It is a application based on python and opencv related to the image processing.

We are working on an  version and this platform has a nice Python API..  However, there is nothing official about Python on Android, but since  exists, is there a way to let the snake and the robot work together??


I want to reduce video dimension to 720:480 & keep original aspect ration when input video width > 720 else, keep original dimension and aspect ratio.  I am trying to reproduce this script in a Windows batch file and it fails:    set $width=720 set $height=480 ffmpeg -i file8.3gp -vcodec libx264 -preset slow -crf 20 -filter:v "scale=iw*min($width/iw,$height/ih):ih*min($width/iw,$height/ih), pad=$width:$height:($width-iw*min($width/iw,$height/ih))/2:($height-ih*min($width/iw,$height/ih))/2" -threads 0 -acodec libvo_aacenc -b:a 128k out.mp4   The errors I'm getting:  ffmpeg -i file8.3gp -vcodec libx264 -preset slow -crf 20 -filter:v "scale=iw*min($width/iw,$height/ih):ih*min($width/iw,$height/i h), pad=$width:$height:($width-iw*min($width/iw,$height/ih))/2:($height-ih*min($ width/iw,$height/ih))/2" -threads 0 -acodec libvo_aacenc -b:a 128k out.mp4 ffmpeg version N-54691-g7f4a1fd Copyright (c) 2000-2013 the FFmpeg developers   built on Jul 12 2013 16:31:48 with gcc 4.7.3 (GCC)   configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-av isynth --enable-bzlib --enable-fontconfig --enable-frei0r --enable-gnutls --enab le-iconv --enable-libass --enable-libbluray --enable-libcaca --enable-libfreetyp e --enable-libgsm --enable-libilbc --enable-libmodplug --enable-libmp3lame --ena ble-libopencore-amrnb --enable-libopencore-amrwb --enable-libopenjpeg --enable-l ibopus --enable-librtmp --enable-libschroedinger --enable-libsoxr --enable-libsp eex --enable-libtheora --enable-libtwolame --enable-libvo-aacenc --enable-libvo- amrwbenc --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libxavs -- enable-libxvid --enable-zlib   libavutil      52. 39.100 / 52. 39.100   libavcodec     55. 18.102 / 55. 18.102   libavformat    55. 12.102 / 55. 12.102   libavdevice    55.  3.100 / 55.  3.100   libavfilter     3. 80.101 /  3. 80.101   libswscale      2.  3.100 /  2.  3.100   libswresample   0. 17.102 /  0. 17.102   libpostproc    52.  3.100 / 52.  3.100 Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'file8.3gp':   Metadata:     major_brand     : 3gp5     minor_version   : 256     compatible_brands: 3gp53gp4     creation_time   : 2005-10-28 17:36:40   Duration: 00:00:04.93, start: 0.000000, bitrate: 46 kb/s     Stream #0:0(eng): Audio: amr_nb (samr / 0x726D6173), 8000 Hz, mono, flt, 8 k b/s     Metadata:       creation_time   : 2005-10-28 17:36:40       handler_name    : Apple Sound Media Handler     Stream #0:1(eng): Video: mpeg4 (Simple Profile) (mp4v / 0x7634706D), yuv420p , 176x144 [SAR 1:1 DAR 11:9], 35 kb/s, 15 fps, 15 tbr, 600 tbn, 1k tbc     Metadata:       creation_time   : 2005-10-28 17:36:40       handler_name    : Apple Video Media Handler File 'out.mp4' already exists. Overwrite ? [y/N] y [Parsed_scale_0 @ 0000000000318640] Invalid size 'iw*min($width/iw' [AVFilterGraph @ 00000000024c0540] Error initializing filter 'scale' with args ' iw*min($width/iw:flags=0x4' Error opening filters!

I need to fit videos to 640x360 (the maximum my phone's player can handle), while also preserving aspect ratio, but I also want the video to be unchanged if it is smaller than 640x360 (no point in up-scaling it after all).  Is there a way to get this behavior using ffmpeg's command line?


I have a bash script with a loop that uses pdftotext to convert many pdfs to text. Below is the relevant portion of the code: cd /data/user/Data/Reports/pdf/ dirs=(A*/) for directory in "${dirs[@]}" do     cd "/data/user/Data/Reports/pdf/$directory"     files=(*.pdf)     mkdir -p "/data/user/Data/Reports/txt/$directory"     for file in "${files[@]}"     do         filePrefix=${file%.pdf}         saveFilename="/data/user/Data/Reports/txt/$directory/$filePrefix.txt"         pdftotext "$file" "$saveFilename"     done done  Most of the cases are successful, but many of them give me an error like the following and don't create the text file:  I/O Error: Couldn't open text file '/data/user/Data/Reports/txt/AAL-US/AAL-US5_032.txt'  When I submit the following directly in the terminal, the pdf correctly converts to txt without any issues: pdftotxt /data/user/Data/Reports/pdf/AAL-US/AAL-US5_032.pdf /data/user/Data/Reports/txt/AAL-US/AAL-US5_032.txt  The typical issue with this error is that I have misspecified the filepath, but I'm confident that isn't the case here as it works when I submit it directly through the terminal. Why would it work for most file conversions and fail for some? Any guidance would be much appreciated. Thanks. Edit: The error does not seem to happen for the same files every time. This time through, the code had no issues with AAL-US as in the error I first mentioned above. The text file ADSK-US8_032.txt does not exist. I just tried to convert this file to text directly in the terminal and it gave me the same error. And there is still space in the filesystem: inode use is at 54% and storage is at 60%. I have been working on my school's linux cluster and I did just learn that the cluster is having storage issue and giving "No space left on device" error - not sure if this is related. Here is an excerpt from stdout stderr from what I ran last night:  I/O Error: Couldn't open text file '/data/user/Data/Reports/txt/ADSK-US/ADSK-US8_032.txt' dirCounter=12/127; fileCounter=1919/1988; directory=ADSK-US/; filename=ADSK-US8_032.pdf; duration=0; datetime=06/24/20 22:31:31;  In case it is helpful, here is the full code I submitted: cd /data/user/Data/Reports/pdf/ statusFile="/data/user/Projects/Reports/pdfTxtConversion/meta/pdf2textStatus.txt" dirs=([A-C]*/) totalDirs=${#dirs[@]} dirCounter=1  for directory in "${dirs[@]}" do     echo "-------------------------------------------"     echo "Processing directory $directory"     echo "-------------------------------------------"      cd "/data/user/Data/Reports/pdf/$directory"     if [ $? -ne 0 ]; then         echo "failed to cd to $directory from $PWD"         exit 1     fi        files=(*.pdf)     totalFiles=${#files[@]}     fileCounter=1      mkdir -p "/data/user/Data/Reports/txt/$directory"     for file in "${files[@]}"     do         startTime=`date +%s`         filePrefix=${file%.pdf}         saveFilename="/data/user/Data/Reports/txt/$directory$filePrefix.txt"             pdftotext "$file" "$saveFilename"            endTime=`date +%s`         conversionDuration=$((endTime-startTime))         msg="dirCounter=$dirCounter/$totalDirs; fileCounter=$fileCounter/$totalFiles; directory=$directory; filename=$file; duration=$conversionDuration; datetime=$(date +"%D %T");"         echo $msg >> $statusFile         echo $msg         ((fileCounter++))     done      ((dirCounter++))  done

According to  and my own understanding, the tilde expands to the home directory:  $ echo ~ /home/braiam   Now, whenever I want the shell expansion to work, i. e. using variable names such $FOO, and do not break due unexpected characters, such spaces, etc. one should use double quotes ":  $ FOO="some string with spaces" $ BAR="echo $FOO" $ echo $BAR echo some string with spaces   Why doesn't this expansion works with the tilde?  $ echo ~/some/path /home/braiam/some/path $ echo "~/some/path" ~/some/path


What i wan't to say is "we can't fit in X in the modern world" but it doesn't portrays the correct meaning what i mean is that its wrong to mould X according to the parameters of the modern world, is there a better word than "Fit in"

What other word or words can be used to replace "fit in"? E.g. "I believe I will fit in with your organization."


I've looked everywhere and can't find a solid answer. According to the documentation, Java throws a  error under the following circumstance:     Thrown when a stack overflow occurs because an application recurses too deeply.   But this raises two questions:   Aren't there other ways for a stack overflow to occur, not only through recursion? Does the StackOverflowError happen before the JVM actually overflows the stack or after?   To elaborate on the second question:  When Java throws the StackOverflowError, can you safely assume that the stack did not write into the heap? If you shrink the size of the stack or heap in a try/catch on a function that throws a stack overflow, can you continue working? Is this documented anywhere?  Answers I am not looking for:   A StackOverflow happens because of bad recursion. A StackOverflow happens when the heap meets the stack.

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


I'm trying to find out what font this is. It seems to have support for math mode.

Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag.


Hello I have a doubt about the next partition identities  $P(n: even \; number \; of \; odd \; parts)=P(n: distinct\; parts, \; number \; of \; odd\;  parts\;  is\; even)$  Also for the case when both instances of "even"  are changed to odd.  I need to show a bijection of but I can't figure out how. I have been trying with one example (n=6) to see any particular characteristic however I can not have the equality.  I trying to solve the problem by using a bijection between the partitions of each side because I am not allowed to use function now.  So, any  hint would be appreciated!

I'm trying to prove the following Integer Partition claim :   $p$(n│even number of ODD parts) = $p$(n│distinct parts ,number of ODD parts is even) .  So I tried to prove a stronger claim :   $p$(n│number of odd parts) = $p$(n│number of distinct parts) :  Using generating functions :   DISTINCT PARTS =  $$(1+x)\cdot(1+x^2 )\cdot(1+x^3 )\cdot(1+x^4 )\cdot\cdot\cdot\cdot$$  = $$\frac {1-x^2} {1-x} \cdot \frac {1-x^4} {1-x^2} \cdot \frac {1-x^6} {1-x^3} \cdot \frac {1-x^8} {1-x^4}\cdot\cdot\cdot\cdot$$  $$ \frac {1} {1-x} \cdot \frac {1} {1-x^3} \cdot \frac {1} {1-x^5} \cdot \frac {1} {1-x^7} \cdot\cdot\cdot\cdot $$  = ODD PARTS  But I'm not sure regarding the proof , does it really prove that even number of odd parts equals distinct parts ,where number of ODD parts is even ?   Thanks


I read about HMAC and want to be sure if it protects against replay attacks as well.

I am considering a system where a small device accepts messages/commands from another device over a wireless channel.  I am worried about replay attacks.  The messages will be encrypted.  What are well-vetted schemes for protection against these attacks?  I am not too keen on timestamps (as described in ) as I don't really want to have to keep clocks synchronised.  I am currently thinking of using HMAC but want to be sure that I'm doing the right thing.


I have used Ubuntu 14.04 as a server to host my company website and mailsystem. The system was online for 3 weeks before I was not able to send or receive emails.  A few minutes of debugging showed the reason: No more disk space.  Filesystem      Size  Used Avail Use% Mounted on udev            3.9G     0  3.9G   0% /dev tmpfs           799M  8.7M  790M   2% /run /dev/xvda1      7.8G  7.4G     0 100% / tmpfs           3.9G     0  3.9G   0% /dev/shm tmpfs           5.0M     0  5.0M   0% /run/lock tmpfs           3.9G     0  3.9G   0% /sys/fs/cgroup tmpfs           100K     0  100K   0% /run/lxcfs/controllers tmpfs           799M     0  799M   0% /run/user/1000   Question: How can I locate the directory that occupies all the disk space?   I have tried using df -hs /path/to/directory on all root directories without luck. There is 4GB of space that is not accounted for.

I have only one disk in my computer, a 80 GB SSD. It is formatted as a single ext4 partition (no swap), and all the usual folders are installed on it (I keep lots of data on external media, but /home and all the rest is on the SSD).   Today I booted it and I got a message that the drive is full. I opened Disk Usage Analyzer to look at what takes up space. It insists that 67.8 GB of the disk are used, and that / is taking up 36.4 GB. Which leads to the question, where are the missing 30 GB, if not on the file system?!    Just to have a comparison, I added up all the sizes of all readable folders listed in Nautilus as subfolders of / (including the hidden ones). I got 20.9 GB. Trash was unreadable, but I know it has 16.2 GB, so the sum is 36.1 GB, around the same as what Disk Usage Analyzer is reporting. There were some system folders which were unreadable, like proc, but I doubt that they add up to 30 GB - else it wouldn't be possible to install Ubuntu on small disks, and I've seen it run on 2.5 GB. I think they must be the 0.3 GB difference between my calculation and the Disk Usage Analyzer's report.   So I'd like to know, what is eating up these 30 GB and how do I get it to free them?     Edit with answers to CYREX's questions   Booted from Ubuntu 10.10 64-bit live CD (same as my system).  fsck result:   root@ubuntu:~# fsck /dev/sda1 fsck from util-linux-ng 2.17.2 e2fsck 1.41.12 (17-May-2010) /dev/sda1: clean, 265956/4890624 files, 18073343/19537408 blocks  Booted from the SSD. Emptied the trash, and the 16 GB from there are now free. The 30 GB are still missing.    I'm not experienced enough to know what counts as weird in a log. Here are my messages log and my syslog since last boot. Maybe you can find something in them:       Here it got really strange. I plugged in an external 500 GB HDD. Disk Usage Analyzer overreported the available space, then showed space missing (76 GB used, but only 24 in folders).      Booted again from the LiveCD, started the Disk Usage Analyzer from it and got the same results as from the installed Ubuntu, within 1-2 GB.   Edit with answer to CodeMonk:  That would have been a nice solution, but the partition is really 80 GB - I mean 74 GB + marketing "error", anyway the whole disk is formatted. It also shows that over 50 GB are used, so where are the 30 GB if not in files and folders?    GParted also reports the correct size of the external HDD.


I have the following colorbar drawn with pgfplots:  \documentclass{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.15} \begin{document}  \begin{tikzpicture} \begin{axis}[     hide axis,     scale only axis,     height=0pt,     width=0pt,     colorbar horizontal,     point meta min=0,     point meta max=1,     colorbar style={         width=8cm,         xmin=0,         xmax=1,         xtick={0,0.1,...,1}     }]     \addplot [draw=none] coordinates {(0,0)}; \end{axis} \end{tikzpicture}  \end{document}   I expected to have x ticks from 0 to 1 in 0.1 increments, but pgfplots omits the tick at 1:  As a quickfix one can just write 2 instead of 1, then pgfplots draws the tick at 1, but can anyone explain what I did wrong in the first place?


\documentclass[letterpaper,12pt]{article}  \begin{document}  \begin{table} \caption{Test test test test test} \begin{tabular}{c c c c} \hline\noalign{\smallskip} $V_{a}$ & $B$ & $r$ & $e/m$\\ (V) & (T) & (m) & (C/kg)\\ \hline\noalign{\smallskip} 1 $\pm$ 1 & 2.04 $\pm$ 0.04 & 2.36 $\pm$ 0.1 & 1 $\pm$ 1\\ \hline\noalign{\smallskip} \end{tabular} \end{table}  \end{document}   I'd like to keep the formating of the table above how it is. It is the caption that I'd like to change. I don't like how it seems to be hanging off the right side of the table. I think the caption should be aligned with the left side of the table. How would I do this?

I am using this for captions:  \usepackage[font=small,format=plain,labelfont=bf,up,textfont=normal,up]{caption}   But they all come out centred - I want them aligned with the left margin - how can I do this?


When optimizing the cost function below for the BD/NBD model, I saw that the implementation in python (  ) takes the logs of all the terms of the equation in order to avoid underflow (since we are multiplying very small numbers).  We can then separate this expression in A1, A2, A3 and A4, like that:  So the questions are:   1) when optimizing parameters of a model (in this case, maximizing the four attributes r, alpha, a and b), why taking the log does not change the whole thing? I mean, is maximizing f(x) the same as maximizing log(f(x)), generating thus the same values for r, alpha, a and b? What is the mathematical reasoning behind it?  2) In the algorithm, when returning the result, the second part of the expression is replaced by the logsumexp (below),     instead of using the regular math transformations, like this    Why is this valid?

I don't understand how sometimes given an optimization problem, a function could get its optimal solution by minimizing or sometimes just by reformulation it becomes maximizing. Can you please give me an example for this?


$$f(x) = \int \limits_{t=1}^{t=x^2} t\sin^2(t)\operatorname d\!t$$  Do I use U-substitution and have the answer as $$f'(x) = 2x*x^2\sin^2(x^2)$$  Or does this question require integration by parts?   Thanks.

I need help on finding the derivative of this:  $$g(x) = \int_1^{x^2} (x-t)\sin^2(t)dt$$  I thought about taking out x and having it as a constant but how?


I get the following error running apt-get update:  W: The repository 'cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1) xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Some index files failed to download. They have been ignored, or old ones used instead.   How should I proceed?

Every time I try update (using sudo apt-get update) my Ubuntu I get this problem:  W: The repository 'cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1) xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. W: The repository 'ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-amd64/Packages  404  Not Found E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-i386/Packages  404  Not Found E: Some index files failed to download. They have been ignored, or old ones used instead.   How can I fix it? I use Ubuntu 16.04 LTS


This question was asked in a masters exam for which I am preparing.  Let $A$ be an $m\times n$ real matrix. (a) Show that $N(A) \cap \operatorname{Im}(A^{T})=\{0\}$, where $A^{T}$  is the transpose of $A$. (b) If for two suitable matrices $B$ and $C$ we have  $AA^{T}B=AA^{T}C $ then show that  $A^{T}B=A^{T}C$.  Attempt: (a)  Let $v \in N(A) \cap  \operatorname{Im}(A^{T})$. As $v=A^{T}w$, for some $n\times1$ of order  $w$  and multiplying it by $A$ I get $0=Av=A(A^{T}w)$. But I don't know how to proceed now as rank of $A$ is not given. (b) I did a bit of manipulation and got $AA^{T}(B-C)=0$ (it's trivial to see) but I don't know how should I proceed next. I have done a course on linear algebra and studied from Hoffman-Kunze. Kindly provide some hints.

Let $A$ be a $m\times n$ real matrix. If for two suitable matrices $B$ and $C$, $$AA^TB=AA^TC$$ can we conclude that $A^TB=A^TC$?  I know $AA^T$ is a symmetric matrix. Every real symmetric matrix is diagonalizable. But I am not sure how to use this information. Thanks for reading and helping me out with hints.


I have just migrated to Mojave and with no applications open, except whatever runs in the background, I receive the Out of Application Memory panel.  The only app it shows as running is Finder.  I am running on a Mac Mini with 815 Gbytes available on my system drive. I did not have this error before upgrading to Mojave.

macOS is regularly popping up a "Force Quit Applications" dialog:       Your system has run out of application memory.      To avoid problems with your computer, quit any applications you are not using.   How is that possible if there are only a few open apps?


I have a system $A x ~ b$ where vector $b$ is not actually in the span of matrix $A$. I want to use a least squares approach to minimize the distance between the two vectors. $$\begin{aligned} \min_x \Vert \mathbf Ax - b\Vert ^2 &= (\mathbf Ax-b)^T (\mathbf Ax-b) \\ &= x^T \mathbf A^T \mathbf A x - (\mathbf Ax)^Tb - b^T \mathbf Ax + b^Tb \\ &= x^T \mathbf A^T \mathbf A x - 2b^T \mathbf Ax + b^Tb \end{aligned}$$ I'm struggling to understand how to arrive at $$0 = 2 \mathbf A^T \mathbf Ax -2 \mathbf A^T b$$ I understand that some sort of derivative with respect to $x$ has been taken in order to minimize the distance, but what does it mean to take a derivative of a matrix product with respect to a vector? I have never come across such a calculation? Thanks in advance.

It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$?


Sometimes when one is using any app, almost at the moment when one is going to click or push key "enter", a window appears in a "pop-up style" related to another app (example : dialog of updates) and with all the momentum in the fingers, one finishes pushing "accept" over the popup window and not the planned app. Most cases are not critical, but they can consume some of time.  Is there some home-made or professional solution for this?

I'm using Maverick with Compiz enabled.  I've searched AskUbuntu and Google. AskUbuntu doesn't have anything on this topic and everything Google turns up is a couple years old.  I'm doing browser tests and my tests are constantly spawning new Firefox windows. The problem is, when the window is spawned it takes focus. This is incredibly annoying as I'm usually in the middle of typing somewhere else. This doesn't only happen with my tests, but is the most common example I run into. Sometimes my IDE decides it wants focus when something special happens (like when something is done compiling) and then later I'll find fragments of IM messages I've typed in my code. This is driving me crazy. I've looked in both Gnome settings and Compiz settings and can't find a way to prevent that from happening.  Does anyone know of a way to prevent an app from stealing focus when it is opened? I'd rather have the taskbar flash at me or something to get my attention.


Consider the following MWE:  \documentclass{article} \usepackage[showframe]{geometry} \begin{document} \bigskip This is a test. \end{document}   This renders as follows:    As you can see, the \bigskip fails to leave a vertical space. This is a common nuisance, which I normally deal with by preceding the command with either \hbox{}, or ~. For instance:  \documentclass{article} \usepackage[showframe]{geometry} \begin{document} \hbox{}\bigskip This is a test. \end{document}   renders:    What I want to know is (1) why does this happens, (2) why do \hbox{} and ~ work here, and (3) what is the best practice around this issue. (I imagine this has to do with vmode and hmode, but I don't really know what's going on.)

I'd like to, first thing before writing anything on a page, add some vertical space.  Minimal (non)working example:  \documentclass{article} \begin{document}  \vspace{250px} I want to be further down on the page :(  \vspace{250px} Haha! Sucker :D \end{document}     How can I get the first \vspace to work, just like the second one?


From the drop-down menu, top right corner, I have access only to the volume, brightness control, and power on or off buttons.   None of the other icons launch, including Account Settings, Wifi control, wired connection, and the control center.   Output of apt policy gnome-control-center:  Installed: (none) Candidate: 1:3.28.2-0ubuntu0.18.04.2 Version table:    1:3.28.2-0ubuntu0.18.04.2 500       500 ca.archive.ubuntu.com/ubuntu bionic-updates/main amd64 Packages    1:3.28.1-0ubuntu1 500       500 ca.archive.ubuntu.com/ubuntu bionic/main amd64 Packages

I have no way of accessing any of my settings on my fresh install of Ubuntu 17.10.  I installed 15 minutes ago, added a few core packages, one of which was wine where dpkg failed and I had to restart it.  And it keeps telling me randomly that an install failed of : libsane1 (experimental).  After I installed those packages, no settings available.  The menus are gone, their icons are gone, they won't load even if they have an icon.    As soon as I got the first error message from dpkg, I did a   sudo apt-get remove libsane1   which went perfectly well and appeared to clear up the error.  Then back and did a   sudo apt-get install libsane1   which also went perfectly fine and no problems seemed to exist.  Only during the installation of wine-hq-staging on my fresh and clean ubuntu does the error appear.  Well it also appears on winehq-stable too but I did not use that this occasion.


I noticed a tag wiki that needed some content this afternoon and got to editing that one and several others that were being used on questions but had no content. I was going to keep filling in empty tag wikis but stopped because there appeared to be no way to filter the tag list so I could see the blank ones. Is there a way to do that?

Is there a way I can search the Tags for tags with no tag wiki created yet?


I find there are two methods to calculate the amplitude in QFT.  First method:  Use LSZ reduction formula  $$\langle p_1\cdots p_m;out|k_1\cdots k_n;in\rangle=\big(\frac{i}{\sqrt{Z}}\big)^{n+m}\int d^4x_1\cdots d^4y_m e^{-ik_1\cdot x_1}\cdots e^{ip_m\cdot y_m}(\Box_{x_1}+m^2)\cdots (\Box_{y_m}+m^2)\langle0|T(\phi(x_1)\cdots\phi(y_m))|0\rangle$$  Then we only need to solve $n+m$-point correlation function. In general, $n$-point function is  $$G(x_1,\cdots x_n)=\frac{\langle 0|T(\phi_I(x_1)\cdots\phi_I(x_n)\exp(-i\int H_I(t^\prime)dt^\prime))|0\rangle}{\langle 0|T(\exp(-i\int H_I(t^\prime)dt^\prime))|0\rangle}$$  And we can solve the correlation function perturbatively.  Second method:  Using adiabatic switch and interacting picture, one can derive  $$\langle p_1\cdots p_m|S|k_1\cdots k_n\rangle=\langle0|a_{p_1}\cdots a_{p_m}\exp(-i\int H_I(t^\prime)dt^\prime)a^\dagger_{k_1}\cdots a^\dagger_{k_n}|0\rangle$$  And we also solve it perturbatively with Wick theorem.  Then my question is:  (1)Are these two methods equivalent up to any order? How to prove.  (2)What's the difference between $|k_1\cdots k_n;in\rangle$ in the first method and $|k_1\cdots k_n\rangle$ in the second method?   (3)If these two methods are equivalent, obviously the second method is easier. What's the motivation to create the first method. Or are there some examples in which the 2nd method fails and we can only use 1st method?   This question may be similar to following question:     However, these questions have not been solved and I explain this question in detail.

Most modern texts spend some time deriving the  that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you are calculating. Yet some earlier texts and even some modern texts (e.g.  by R. Klauber) seem to skip right past this, working everything out in the "interaction" picture. It seems there must be something going wrong with this latter procedure, but I am not quite able to put it together.


If $n$ is an even natural number ($n \neq 0$) then is $2^{n-1}$ divisible by $2^{\varphi (n)}$? Since $n$ is an even number then $n-1$ is an odd number. Hence, $(2,n)=1$. By Euler's theorem, $2^{\varphi (n-1)} - 1$ is divisible for $n-1$. But I don't know what I should do. Any help would be greatly appreciated.

That is:  If $\phi(n) = n$ then $n = 1$  Could someone give me a clue?


For example: I'm an Irish citizen and I want to know if I need a visa for Kyrgyzstan... or I'm American and I want to know what countries I can enter visa free in South America... etc.  I've often found it difficult to quickly find this sort of information online. At best a Google search finds an embassy webpage which you then have to trawl through it to get the actual answer to your question. Are there better approaches out there?

When thinking about travelling, I often have to think about a place to visit, and then look up visa rules for that particular country. This can be a fairly painful process because official government sites can often be hard to find, and advice on (say) guidebooks or Wikitravel tends to be generic.  Is there any resource where I can enter my nationality/residency, and then look up a list of visa rules for various countries?


Microsoft introduced a feature called "" with Windows 8 Enterprise allowing to install Windows on a USB mass storage device similar to Linux Live distributions. The documentation supplied by Microsoft indicates that a  and that  to create the USB image.  On the web and , users report that something equivalent can be achieved without an Enterprise volume license.  However this assumes that the user has install media or an iso-File, containing a file called install.wim. Preinstall OEM versions do not ship with media and neither the Windows partition nor the created recovery medium comes with a file install.wim.  How can you achieve "Windows To Go" with OEM versions?

is one of the most exciting Windows 8 features to me - the ability to pack up your desktop environment and take it with you anywhere is extremely appealing. Unfortunately, it's , which you can't buy for individual use.  Is there an equivalent that works for Windows 8 Professional? I would be satisfied by either a third-party program that does the same thing, or some workaround to enable Windows To Go for non-Enterprise versions.   I'm aware of various WinPE-based live environments, and that's not what I'm looking for. I want the ability to run a full Windows 8 environment off of a flash drive that I can take anywhere.


I would like to understand how the borrow algorithm for simple subtraction ( base 10, the one we learn when we are kids ) works, does anyone have any material on this? Thank you.

I am reviewing take aways. I am having trouble  How do I do $342 - 58$?  For the ones column I made the $2$ into a $12$ so I can do $12 - 8 = 4$ but I must take away one tens. So I get $3 - 5$ in tens column but I cant do $3 - 5$. What do I do now do I borrow something else?


In Ubuntu 16.04 I enter control + ALT + F1 into the command line mode(console mode) and after I type my server name, I can't input anything in "Password:" where it goes immediately to the next line. By the way, I have tried to reboot the computer, change the keyboard and switch to the F1 to F6. However, they didn't work. As shown in the picture, as soon as I type the name of my server in the line of "xxx login:" and press the key "Enter", the cursor jumps to the next line of "Password:".

I upgraded from 16.04 to 18.04. When I press Ctrl+Alt+F3 I get the terminal which prompts for the username. When I type my username and press Enter, it doesn't wait for my password (its as if I pressed Enter without entering anything). Even if I enter something, the text shown in plaintext and then it keeps on saying my password is wrong. After few times, the screen is cleared and it prompts for my username again and the same loop goes on.