Consider the equivalence relation $\sim$ on $\mathbb{Z} \times (\mathbb{Z} \setminus \{0\})$ defined by $(a,b) \sim (c,d)$ if $a \cdot d = b \cdot c$. Describe the equivalence classes in terms of familiar mathematical objects?  The above is a homework problem. I can see some patterns in the equivalence classes, however I'm not sure how to answer or approach the question given. Thanks!

Let $Q$ be the following set of $\mathbb{Z}\times \mathbb{Z}$   \begin{align*} Q=\{(a,b)\in \mathbb{Z}\times \mathbb{Z} | b\neq 0\} \end{align*}   Define the relation $\sim$ on $Q$ as   \begin{align*} (a,b)\sim (c,d)\Leftrightarrow ad=bc \end{align*}   Prove that $\sim$ is a relation of equivalence, and give the class of equivalence of $[(2,3)]$. Furthermore the general order of equivalence of $[(a,b)]$. Try to give a description $Q/\sim$.   I've asked the same question (I deleted it one hour later) but it didn't look well when I didn't try to add what I tried. Here we go. I have proven that $\sim$ is a relation of equivalence by showin it's i) reflexive, ii) symmetric and iii) transitive.   i) $\forall (a,b)\in Q:(a,b) \sim (a,b)$.   $\forall (a,b)\in Q:(a, b) \sim (a, b) \Leftrightarrow ab \stackrel{\surd}= ab$  ii) $(a, b) \sim (c, d) \Rightarrow (c, d) \sim (a,b)$  $(a, b) \sim (c, d) \Leftrightarrow ad = bc$ and $(c, d) \sim (a, b) \Leftrightarrow  cb = da$   then $ad = bc \stackrel{\surd}\Rightarrow cb = da$.  iii) $[(a, b) \sim (c,d) \wedge (c, d) \sim (e, f)]  \Rightarrow (a, b) \sim (e, f)$  $(a, b)\sim (c, d) \Leftrightarrow ad = bc$, $(c, d) \sim (e, f) \Leftrightarrow cf = de$ and $(a, b) \sim (e, f) \Leftrightarrow af = be$  then $((ad = bc) \wedge (cf = de))\stackrel{\surd}\Rightarrow af = be$.  The class of eq. $[(2,3)]$ is the class, that contains the element $(2,3)$, so for every element $(a,b)$ in this class satisfies $(a,b) \sim (2,3) \Leftrightarrow 3a=2b$, that is \begin{equation} [(2,3)] = \lbrace (a,b) \in \mathbb{Z}\times\mathbb{Z} | b \neq 0 \wedge 3a = 2b \rbrace \end{equation}  So now I've shown what I tried to show. Is there something I'm missing or something I should have mentioned? I need some help to answer the rest. Thanks.


I am using the newest version of Ubuntu 14.04 and I like the global menu bar feature but I want the menus to always be visible not only when I hover my mouse over it. Is there a way to do that? Because the menus (like File, Edit, View etc.) disappear as soon as you move your mouse away from the menu bar at the top... :( Please help!  Thanks!

Will there be a way to disable auto-hide behavior of global application menu in Unity. While I would prefer to have this behavior disabled by default (as it is bad UX), it looks like it's here to stay, so I'm wondering if, as a user, I will be able to turn it off.


I am trying to catch the legendary lake guardians, and have already caught Axelf and Mesprit.  I enter Nameless Cavern at exactly 20:00, but nothing happens. I look over the portal, but all it says is "A mysterious ring is floating in the air...".  How do I catch Uxie?

Every time since a few days ago after I caught Mespirit, when I go to the portal in the Nameless Cavern and I press A to interact. All that happens is a short dialog sequence and nothing else. I know the requirements are along the lines of having 3 max happiness Pokemon with you in your party which I do. I have also downloaded the recent update/patch from the eShop if that helps at all. How can I make Uxie and Azelf appear in the cavern?


I am writing my PhD thesis right now. I do not have any published paper by now, but a manuscript which will be published probably after or at the same time of my defense. Can I just Copy/ Paste some parts (discussion for example) from my manuscript in thesis? Would be any problem afterwards for publishing this manuscript? In other words, I am afraid if the reviewers of paper say that “you cannot Copy and Paste the discussion of your thesis, without rephrasing it”.

I recently finished my PhD thesis which will be published as a book soon. Now I'm wondering if it's possible or allowed to submit parts to a journal?  Normally the process would be the other way round I think: Submitting papers and "gluing" them together for the thesis. I've read the guidelines of some journals which state "that the work described has not been published before" or that "Papers must present scientific results that are essentially new".


As I understand, in JavaScript every object has a prototype and it exposes some default properties. I have the following code where I'm trying to set the Year property of two objects through prototype. But both the calls are failing.  How can I override toLocalString() for any object if I don't have access to the prototype? Please note that the following code is to test on the prototype property, but my intention is to override the toLocalString() method.  var car = {     Make: 'Nissan',     Model: 'Altima' };  car.Year = 2014; alert(car.Year);  alert(car.prototype); // returns undefined  car.prototype.Year = 2014; // Javascript error  // --------------  function Car() {     this.Make = 'NISSAN';     this.Model = 'Atlanta'; }  var v = new Car(); v.prototype.Year = 2014; // JavaScript error alert(v.prototype);

I'm not that into dynamic programming languages but I've written my fair share of JavaScript code. I never really got my head around this prototype-based programming, does any one know how this works? var obj = new Object(); obj.prototype.test = function() { alert('Hello?'); }; var obj2 = new obj(); obj2.test();  I remember a lot discussion I had with people a while back (I'm not exactly sure what I'm doing) but as I understand it, there's no concept of a class. It's just an object, and instances of those objects are clones of the original, right? But what is the exact purpose of this ".prototype" property in JavaScript? How does it relate to instantiating objects? Update: correct way var obj = new Object(); // not a functional object obj.prototype.test = function() { alert('Hello?'); }; // this is wrong!  function MyObject() {} // a first class functional object MyObject.prototype.test = function() { alert('OK'); } // OK  Also these  really helped a lot.


Is it possible to use \includegraphics within the caption of a figure?  When I try, I get an error.  Here is a complete (sans graphics) minimal example that also demonstrates why I want to do this:  \documentclass{article} \usepackage{graphicx}  \newcommand{\Triangle}{\raisebox{-0.3em}{\includegraphics[height=1.25em]{triangle}}}  \begin{document}  % this use of \Triangle below works fine: \Triangle  \begin{figure}[ht] %  \includegraphics{...}    \caption{example caption \Triangle . } \end{figure}  \end{document}     I do this because I need to include small symbols into the text, which I have as PDF graphics (it's not just a basic triangle---I know I could get that as a character).  If I remove the \newcommand part and just do a plain \includegraphics, I get the same error.  This is the error I get:  ./Untitled.tex:12: Argument of \@caption has an extra }. <inserted text>                  \par  l.12    \caption{example caption \Triangle . }

Similar to , I would like to insert an external icon inside figure captions, something like:  \begin{figure} \caption{text with \includegraphics{icon} somewhere inside} \includegraphics{image} \end{figure}   How might this be done?


This is a PC with no prior OS, I slapped Ubuntu on temporarily. I do prefer Ubuntu but it's (unfortunately) just not well optimised for games ;_; Anyway I'm pretty computer illiterate when it comes to partitioning, OSes and BIOSes so if anyone can tell me how to remove Ubuntu easily and leave my PC like it was when it was put together with no OS. Thanks!

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


Let $(W_t)$ be a Brownian motion. Under what minimal condition on the function $\sigma$ can we say that the solution of $$dM_t = \sigma(M_t,t) dW_t$$ is a martingale with regard to its own filtration? Same question if $(W_t)$ was a generic martingale, not necessarily a Brownian motion.

Could you kindly list here all the criteria you know which guarantee that a continuous local martingale is in fact a true martingale? Which of these are valid for a general local martingale (non necessarily continuous)? Possible references to the listed results would be appreciated.


I know the films aren't canon, but it's stated quite often (in Hogwarts A History) that one cannot apparate in and out of Hogwarts.  So how can Dumbledore do it in the film?

In the film The Deathly Hallows Pt. 2, right before The Battle of Hogwarts starts, Draco Apparates to the dungeons to get Goyle and Blaise Zabini.  Since it's impossible to apparate or disapparate within the walls of Hogwarts (aside from Dumbledore, of course) how was Draco able to do so?


I am a new learner of Java language and for the past two years I have been working with C++. I am gonna need something equivalent to cin.ignore() in Java.

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


I tried to dual boot Ubuntu with Windows 7 and it turned out that I booted only Ubuntu. All my data in windows 7 OS are gone. Is there any chance I can retrive those data? And I want to dual boot windows 7 now. How do I do it? If I do it will it be enough for me to get the datas back?

I am on Ubuntu 12.04 64-bits  I accidentally deleted a NTFS 255 GB partition using Gparted, and yes it contains LOTS of important data.  Upon realizing the deletion I haven't yet created any file-system on it. So it still shows Unallocated.    I tried Testdisk , but it shows entire partitions created from the beginning.  This sdb is my secondary drive with Xubuntu and Kubuntu on it. And that 255 GB NTFS  partition was cross platform storage drive.  I am currently in sda with Ubuntu and Win7 in dual boot, which enables me to use it as Safe recovery option rather then Live USB drive.   First ,  should i allocate it to ? file-System for better recovery .  Second , i really need to recover data from this drive so please give me possible  suggestions and proven methods of data recovery.  Third ,does Testdisk requires deleted partition to be allocated for its recovery .  I am currently trying the answer seen here  with Testdisk scanning for partition second time, hoping to recover it.   It looks a duplicate but i can't confirm if the OP got it right. Since my first doubt is to allocate it or not.  If any clarification required please do comment ,i will add it.  Edit: TestDisk deeper search results.      The following partitions can't be recovered:          Partition               Start        End    Size in sectors     >  HPFS - NTFS          22241 107 11 55592   3 27  535777280        FAT32 LBA            274460 158 19 460576 228 16 2989957948  NTFS, 274 GB / 255 GiB & for FAT32 LBA 1530 GB / 1425 GiB


When I do a sudo apt-get update, I encounter the following:  Fetched 189 B in 10s (18 B/s)                                                   W: There is no public key available for the following key IDs: 1397BC53640DB551 W: GPG error: http://download.opensuse.org ./ Release: The following signatures were invalid: KEYEXPIRED 1436387333 W: Failed to fetch http://dl.google.com/linux/chrome/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)  E: Some index files failed to download. They have been ignored, or old ones used instead.   What would be a good/recommended way to fix this?

The error I am having when trying to update my package list.  W: GPG error: http://download.opensuse.org ./ Release: The following signatures were invalid: KEYEXPIRED 1436387333  W: Failed to fetch http://ppa.launchpad.net/samrog131/ppa/ubuntu/dists/trusty/main/binary-amd64/Packages  404  Not Found  E: Some index files failed to download. They have been ignored, or old ones used instead.


I have a laptop with hybrid Intel/AMD graphics. As far as I know, the configuration is muxless. This causes not-detection of discrete graphic card. And now my problem: I don/t know how to turn the discrete card completely off. I think it is powered all the time, because of critically short battery work time(approx. 3 hours instead of windows 7-8). Tlp and adjusting the brightness do not bring expected effect. I would really appreciate any help.

On Ubuntu 12.04 my Sony Vaio VPCSE with Intel® HD Graphics 3000 and AMD Radeon™ HD 6630M worked fine with the Catalyst Control Center version 12.6. Also the switching between integrated and discrete graphic card was working.  In both cases, I followed this .  But it is not working on Ubuntu 12.10.   I tested the tutorial with the Catalyst Control Center from the Ubuntu Software Center, the version 12.8 and version 12.9. Always the same problem: After installation process I am able to boot in the login-screen. But after entering the password for my username, only the background-image appears. Unity seems not to be starting. I am only able to reach the context-menu by right clicking the mouse button.  I also tried , but is also does not work for me.  Any ideas what to do to fix this problem?   Update: Same problem on Ubuntu 13.04!  Update: Solution for 13.04 ist not working on Ubuntu 13.10!


How can I get the pid of a subshell?  For example:  $ echo $$ 16808   This doesn't work, because the original shell expands $$:  $ ( echo $$ ) 16808   Why does single quoting not work? After the original shell removes the single quote, does the subshell not expand $$ in itself?  $ ( echo '$$' ) $$   Why does eval not work either? Is eval run by the subshell?  Why does it give me the original shell's PID?  $ ( eval echo '$$' ) 16808   Thanks.

I'm reading "BASH pocket guide of Oreilly". It said:      The process ID of the current Bash process.   In some cases, this can differ from $$.   Above explanation , explained $BASHPID variable.  Question: which cases?


I just started to open for myself programming in python. I know how to find factors for example of 30. I will get [1,2,3,5,6,10,15,30]. But I need this output 30 = 2 * 3 * 5. Thank you in advance!

Here's the very dumb way:  def divisorGenerator(n):     for i in xrange(1,n/2+1):         if n%i == 0: yield i     yield n   The result I'd like to get is similar to this one, but I'd like a smarter algorithm (this one it's too much slow and dumb :-)  I can find prime factors and their multiplicity fast enough.  I've an generator that generates factor in this way:  (factor1, multiplicity1) (factor2, multiplicity2) (factor3, multiplicity3) and so on...  i.e. the output of   for i in factorGenerator(100):     print i   is:  (2, 2) (5, 2)   I don't know how much is this useful for what I want to do (I coded it for other problems), anyway I'd like a smarter way to make  for i in divisorGen(100):     print i   output this:  1 2 4 5 10 20 25 50 100     UPDATE: Many thanks to Greg Hewgill and his "smart way" :) Calculating all divisors of 100000000 took 0.01s with his way against the 39s that the dumb way took on my machine, very cool :D  UPDATE 2: Stop saying this is a duplicate of  post. Calculating the number of divisor of a given number doesn't need to calculate all the divisors. It's a different problem, if you think it's not then look for "Divisor function" on wikipedia. Read the questions and the answer before posting, if you do not understand what is the topic just don't add not useful and already given answers.


We know there are differences between the books and the movies (the Battle of Hogwarts, etc.). Which version is considered canon? Also, if the books are canon in cases of contradiction, are things that don't contradict the books, but do include details that are not in the book, such as hermione being white in the movies, canon?

There are many different Harry Potter works including:   books short stories movies card games video games toys amusement parks web content   Which ones are considered to be canon?


Just a curiosity in this book of an high school with the title The powers with exponent rational  the $$\large \color{red}{a^{\frac mn}=\sqrt[n]{a^m}}, \quad a\geq 0$$ is given like a definition. I don't remember if there was a proof. But is there one or should we give it as a definition?

The way that I was taught it in 8th grade algebra, a number raised to a fractional exponent, i.e. $a^\frac x y$ is equivalent to the denominatorth root of the number raised to the numerator, i.e. $\sqrt[y]{a^x}$. So what happens when you raise a number to an irrational number? Obviously it is not so simple to break it down like above. Does an irrational exponent still have a well formed meaning?  The only example that comes to mind is Euler's identity, but that seems likes a pretty exceptional case. What about in general?


Why does the velocity of air flowing over the top surface of aerofoil increase, when there is no contraction in area over the top?

I understand the common explanation of lift, which describes the airflow over the top of the wing as moving faster than the air below the wing.  However, I don't quite understand why the air moves faster.  I've read some explanations citing a circulation effect among others, but haven't found a good, clear explanation for the exact cause.  Can someone help me out?


Hi to everyone and thanks in advance for your time reading this question.  Im kinda new on this SEO stuff and there is something that I can't figure out how it works despite all the readings that I did.  I've developed a new website which allows users to add recommendations for every kind of bussiness, places, professionals, etc, so other people can see if travel to X place is worth it for example.  From what I've read so far (and from what I've understood, which are actually two different things haha) its important to make user and search engines friendly URLs and have proper keywords, title and h1 tags.  (I've read this post  and a few more)  That's not a problem because I can do that on server-side code, but what I actually don't understand is how Google shows pages that collect info from databases on his search results.  Lets put an example just to detail this a little bit more.  If we go to Google and search for "abercruz paginas amarillas" google show us a link that send us to a page from "paginasamarillas.com" which has all the details about that store.  Instead if we go to Google and type, "abercruz yousug" (which is my page) nothing shows up. I know that it could take a few days to Google to index my page but I don't understand HOW could Google "search" into my database (or page, or whatever) to end with the correct URL which shows the details of that Commerce   If someone could explain me that or help me a little bit understanding how to rank content that is generated from a database I will very grateful.  Thanks again!

I have a very stupid question. I developed a website that has only one page at the public html directory(index.php).  all content are dynamically loaded as different pages.   How can i SEO my pages for google?  i mean like the what we type in this site are .............i believe stored in database and search engine find these pages like any static pages...  Just a little tip would be appreciable.......!


I have an array of an object called storing, some of the object's attribute (skuID) is the same with some of the other storing with different (storingID), how do i make my array distinct depending on their (skuID)?  Storing(string storingID, skuID, storageID, price, expiry)   I have tried this but it doesn't work:  List<storing> storingAll = (List<storing>)Session["storingAll"]; List<storing> displayedStoring = storingAll.Distinct().ToArray();

I am playing with LINQ to learn about it, but I can't figure out how to use Distinct when I do not have a simple list (a simple list of integers is pretty easy to do, this is not the question). What I if want to use  on a list of an Object on one or more properties of the object?  Example: If an object is Person, with Property Id. How can I get all Person and use Distinct on them with the property Id of the object?  Person1: Id=1, Name="Test1" Person2: Id=1, Name="Test1" Person3: Id=2, Name="Test2"   How can I get just Person1 and Person3? Is that possible?  If it's not possible with LINQ, what would be the best way to have a list of Person depending on some of its properties in .NET 3.5?


Is there any way to derive Stirlings formula that only requires some undergraduate knowledge of calculus, real analysis and perhaps some identitets involving the gamma function, maybe Wallis product, and things along those lines? If not, and I know this is a rather vague question, what is the simplest but still sufficiently rigorous way of deriving it? I had a look at  but the comments seems quite messy. Wikipedia was not particularly helpful either since I have not learned about Laplace's method, Bernoulli numbers or the trapezoidal rule.

Suppose we want to show that $$ n! \sim \sqrt{2 \pi} n^{n+(1/2)}e^{-n}$$  Instead we could show that $$\lim_{n \to \infty} \frac{n!}{n^{n+(1/2)}e^{-n}} = C$$ where $C$ is a constant. Maybe $C = \sqrt{2 \pi}$.   What is a good way of doing this? Could we use ? Or maybe take the log of both sides (e.g., compute the limit of the log of the quantity)? So for example do the following $$\lim_{n \to \infty} \log \left[\frac{n!}{n^{n+(1/2)}e^{-n}} \right] =  \log C$$


I'm new at Linux and I just download Ubuntu 12.04 LTS.  I found a spot that showed me how join my Windows Active Directory.  It has me add couple lines into the 'hosts' but I'm not able to edit the file because I do not have the permission.  I'm not the owner.  I use chmod with it rwx and still it will not let edit the file.  How do you change the permission?  Thanks

I can't seem to edit and save config files in the root system (eg: /etc/dhcp/dhcpd.config); it just says "permission denied" or the save option is blocked in the text editor.  I'm pretty sure I'm a root user, but how do I make sure? If I am a root user, how do I fix this?


today I was learning about list slicing in python, and I have a question about the rules by which python "operates/slices" these lists. How is it possible that I don't get an error message when clearly the range is wrong? li=[1,2,3,4,5,6]  li[1:12:1]   [2,3,4,5,6]

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


Suppose $q$ is a prime power, $r$ is some positive integer. We can construct the field $\mathbb{F}_q$ where there are $q-1$ non-zero elements. The relation $x\sim y \iff y \text { is a (non-zero) scalar multiple of } x$ in the set of nonzero vectors $\mathbb{F}_q^r-\{0\}$ is an equivalence, and $cx=c'x \iff c=c'$ by cancellation law in $\mathbb{F}_q$. Therefore there are equally sized equivalence classes and there are $\frac{q^r -1}{q-1}$ of them, which is an integer. Now is there a way in elementary arithmetic showing that $\frac{q^r -1}{q-1}$ is an integer?

Prove that for all natural number $x$ and $n$, $x^n - 1$ is divisible by $x-1$.  So here's my thoughts: it is true for $n=1$, then I want to prove that it is also true for $n-1$  then I use long division, I get:  $x^n -1 = x(x^{n-1} -1 ) + (x-1)$  so the left side is divisible by $x-1$ by hypothesis, what about the right side?


I bought my canon 700D a month ago. Now, I want to do some macro photography, but I do not want to purchase any expensive lens for this at least at this stage. I came to know about some accessories like extension tubes, which are not very expensive but claim to provide the required magnification. Are they really useful? Are there any other accessories( not expensive ), that I can use for macro photography?

I am a photography newbie and have only a 18 - 135mm canon kit lens at my disposal. I wanted to take macro shots but can't really afford a macro lens right now. One very optimistic goal of mine is to capture a single snow flake this winter.   Is there any cheap(er) way to take macro shots? Also, any specific advice from anyone one how to go about photographing a single snow flake.


I have downloaded the ISO from the website and have burned a DVD disc. I now want to load UBUNTU onto my PC and do not know how to proceed, please help.

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


I'm trying to convert a hex string into a byte array to test a SHA2-224 using the test vector from NIST. See: h**ps://csrc.nist.gov/CSRC/media/Projects/Cryptographic-Standards-and-Guidelines/documents/examples/SHA2_Additional.pdf  The code appears to be correct when testing a string using (Encoding.UTF8.GetBytes) and even correct when testing a hex byte using (StringToByteArrayFastest) to convert. However, when I use the C style hex (0xe5e09924) the results are not as expected. It's only when I removed the 0x (e5e09924) and convert the hex to a byte array that I receive the expected results.          public static string ComputeSha224Test1(string strHex)     {         // WORKS         // #2) 4 bytes 0xe5e09924         // fd19e746 90d29146 7ce59f07 7df31163 8f1c3a46 e510d0e4 9a67062d         //         Sha224Digest hash224Test = new Sha224Digest();         // Convert to hex byte to test NIST vector         byte[] byte3 = StringToByteArrayFastest(strHex);         // Encode string for hashing         //byte[] byte3 = Encoding.UTF8.GetBytes(strHex);         hash224Test.BlockUpdate(byte3, 0, byte3.Length);         byte[] result = new byte[hash224Test.GetDigestSize()];         hash224Test.DoFinal(result, 0);         String Hash = BitConverter.ToString(result).Replace("-", "").ToUpper();         return Hash;         //     }   Is there any way to convert a C style hex into a C# style hex?  I got the (StringToByteArrayFastest) code from () and I'm using Visual Studio 2015.  Thank you.

Can we convert a hex string to a byte array using a built-in function in C# or do I have to make a custom method for this?


I'm using biblatex to print my bibliography at the end of my thesis but unfortunately nothing is printed at the end (not even a blank page).   Here's an example of what I'm using:   \documentclass[12pt]{report} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[english]{babel} \usepackage[a4paper, width=150mm, top=25mm, bottom=25mm, bindingoffset=6mm]{geometry}  \usepackage{biblatex} \addbibresource{references.bib}  \begin{document} I'm goint to cite the first reference with \cite{einstein}. \printbibliography \end{document}   Here's what my .bib file looks like:   @article{einstein,     author =       "Albert Einstein",     title =        "{Zur Elektrodynamik bewegter K{\"o}rper}. ({German})     [{On} the electrodynamics of moving bodies]",     journal =      "Annalen der Physik",     volume =       "322",     number =       "10",     pages =        "891--921",     year =         "1905",     DOI =          "http://dx.doi.org/10.1002/andp.19053221004",     keywords =     "physics" }  @book{dirac,     title={The Principles of Quantum Mechanics},     author={Paul Adrien Maurice Dirac},     isbn={9780198520115},     series={International series of monographs on physics},     year={1981},     publisher={Clarendon Press},     keywords = {physics} }   EDIT:   What might be the problem?

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


The filter mechanism (item_filter) below returns fresh html-content (product_data) via an ajax function (load_resorts). In this freshly loaded html content is (also) a class which -when clicked- should trigger a function (via class myresort).  +add   The myresort click function works for the default loaded resorts (on page load), but not for the ones loaded via ajax.  I have used a bind function.    $('.item_filter').on('click', function(event) {   $('.product-data').html('

');   sure = multiple_values('sure');   country = multiple_values('country');   altitude = multiple_values('altitude');   level = multiple_values('level');   size = multiple_values('size');   price = multiple_values('price');   offpiste = multiple_values('offpiste');   family = multiple_values('family');   apresski = multiple_values('apresski');   load_resorts($("#snow1").val(), $("#snow2").val()); });  function load_resorts(ssnow, esnow) {   $.ajax({     url: "ajax.php",     type: 'post',     data:{sure:sure,country:country,altitude:altitude,level:level,offpiste:offpiste,family:family,apresski:apresski,size:size,price:price,ssnow:ssnow,esnow:esnow,filter_order:filter_order},     success: function(result) {       $('.product-data').fadeIn('slow').html(result);     }   }); }  $('span.myresort').on('click', function(event) {   var myres = $(this).attr('data-src');   $.ajax({     type: 'POST',     url: '/v4/ajax/myresorts.php',     data: {       myresort: myres     },     success: function(msg) {       $('#myresorts').fadeOut(800, function() {         if ($('*[data-src="' + myres + '"]').hasClass('loveit')) {           $('*[data-src="' + myres + '"]').removeClass('loveit');           $('*[data-src="' + myres + '"]').html('+add').fadeIn().delay(1000);         } else {           $('*[data-src="' + myres + '"]').addClass('loveit');           $('*[data-src="' + myres + '"]').html('-remove').fadeIn().delay(1000);         }         $('#myresorts').html(msg).fadeIn().delay(1500);        });     }   }); });

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I've a dataset for binary classification. I tried various algorithms using Weka. Then I noticed that if I change the seed of the random number generator I get different classification accuracy results. For example in one run I get 65% and in another run I get 72% accuracy. In all runs I use 10-fold cross validation. Is this variation in accuracy results normal? Or any idea on what might be the cause of the variation? Thanks

I'm training a neural network for a particular problem which can be predicted with 100% accuracy. However, the problem is that results tend to vary between 99% and 100% even if I train 10 different networks and take the average. I was reading around and found that it was due to random weights initialized every time the program ran. Is it okay to set the random seed to 1 and then train 10 different networks and take the average?  This will result in less variation and easy model selection.


— Yeah, just that simple question. It's too easy to consume a lot of RAM in brain-dead mod_XxX (say, mod_php) application, so I'm just wondering what does Apache allow to do as countermeasure.

I'm currently using a Joyent Accelerator to host my webapps, and it's working fine, however I need to reduce costs so I'm downgrading my current plan and that imposes some new memory limits (256M rss, 512M swap). I wasn't too far over them yesterday, but after restarting Apache several times today, I'm now 411M rss, 721M swap (prstat -Z -s cpu).  Searching in Server Fault only gives me lots of ways and specific tools to monitor the server, but no advice on how to reduce/optimize it's memory usage. I've also seen , but I don't think it's good for this particular (or may I say generic?) situation.  The server is running Solaris on a shared CPU, and I'm using a Apache + MySQL + PHP stack.  I'm interested in knowing the steps one can take to troubleshot this and solve the issues. However, I'm also running out of time to lower my memory foot print and downgrade the plan before the current ends, so anything that can make magic and save the day is welcome as well :)


(Hint: Use the Schröder-Bernstein theorem.) I know I need to find two injective functions but I'm yet to find something that makes sense.

Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality  using the SB theorem? Also how does one find a bijection on $f:(0, \infty) \to (0,1)$ such that they have the same cardiniality?


I'd like to prove the following statement:     Given a well-ordered ring $A\neq \emptyset$ with identity $I$ and a   homomorphism $\phi: \mathbb{Z}\to A$ such that $\phi(n) = nI$, then   the set       $$\left\{ a\in A: 0<a<I \right\}$$      is empty.   If $\phi$ was surjective (or bijective), then this would obviously be true. (So, I suspect that that's the case.) But, how could I then prove that?

Though I've seen several cool axiomizations of $\mathbb{R}$, I've never seen any at all for $\mathbb{Z}$.  My initial guess was that $\mathbb{Z}$ would be a ordered ring which is "weakly" well-ordered in the sense that any subset with a lower bound has a minimal element.  However, after seeing  of a discrete ordered ring, I'm less sure. I made that guess under the impression that the fundamental characteristic of $\mathbb{Z}$ is that every nonzero element has exactly one representation of the form $\pm (1+1+\dots+1)$, but that seems to be shared by every DOR.   Presumably, this definition wouldn't exist if every instance of it was isomorphic to $\mathbb{Z}$, so can someone give me an example of another discrete ordered ring? More to the point, what is a sufficient characterization of $\mathbb{Z}$? (and a proof sketch of uniqueness would be nice)  I'm aware that $\mathbb{Z}$ is pretty easily constructible from $\mathbb{N}$, but I want to use this for a seminar and given the audience I am expecting, I would rather not deal with Peano. (And I guess it feels like cheating to say "$\mathbb{N}$ is a well-ordered rig")


I realise this has been asked a few times, but I am wondering how do I find out if I can post / my "rating" before I get the error? I can find my Stack Overflow profile.   Tonight I've got the above message & cannot post a new question to Stack Overflow. (I found / find it hard to find questions I know how to answer :)  Though I've found one good query now I answered. Hopefully the person thinks my answer is good.  EDIT: I know I find many similar queries in meta.stackechange, but I can't find a general answer re reading your profile, etc.

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


I am trying to prove that the automorphisms of the Klein four-group is isomorphic to $S_3$. The first insight is the Klein group is an abelian group of four elements, three of which are order $2$, and must be mapped to other elements of order $2$, and the identity must of course be mapped to itself. So any automorphism "permutes" the non-identity elements. So there are exactly $3! = 6$ of them, matching the number of elements of $S_3$. Then if I call those non-identity maps $f_2, f_2, \ldots, f_6$, I can naturally map them to $S_3$. For example, if the non-identity elements of the Klein group are $a$, $b$, $c$, I can regard these as $1$, $2$, and $3$ (I believe the labelling doesn't matter) and if I swapped $a$ and $b$ and fixed $c$, I can regard this as the transposition $(12)$. By repeating this, I get a natural bijection of sets. I don't know how to "prove" it's a bijection other than to observe the mapping and that it hits everything in $S_3$ exactly once. I don't know, in particular, how to prove that this is a homomorphism, other than by checking every possible pair of isomorphisms, which is a bit laborious. I assume there is a better, cleaner way to do it. UPDATE: After working on this problem more, I have an updated attempt. It's incomplete, but I think it makes some progress.  We realize the Klein 4-group as $V = \{e, a, b, c\}$, where $a,b,c$ are the non-identity elements, each of which has order $2$. Any automorphism $f$ of $V$ must send elements of order $2$ to elements of order $2$, so necessarily it must permute the elements $a,b,c$. I claim that such a permutation is necessarily an automorphism. We observe that the Klein four-group has the property that if we multiply two non-identity elements, we get the third. Since $f$ maps from $V$ to $V$ bijectively, it is also the case that when $f(g)f(g') = f(g'')$, where $g$ and $g'$ are distinct elements and $g''$ is the third. That is, for any $g \neq g' \neq e$, we have \begin{align*} f(gg') = f(g'') = f(g)f(g''). \end{align*} If we take an arbitrary $g \in V$ and then consider multiplying with the identity $e$, we have \begin{align*} f(ge) = f(g) = e f(g) = f(e) f(g), \end{align*} since $f(e) = e$. This proves that $h$ is a homomorphism, and since it is bijective by definition, it is an automorphism. Since every automorphism must send elements of order $2$ to elements of order $2$ and there are exactly $3! = 6$ permutations of $\{a,b,c\}$, there are exactly six elements of Aut(G).   An automorphism is, therefore, uniquely determined on how it permutes the elements ${a,b,c}$, giving a natural bijective map to $S_3$, relabelling these non-identity elements as $1,2,3$. I call $e$ the identity permutation and $f_{abc}$ as the automorphism that maps ${a,b,c} \to {a,b,c}$ (i.e., the identity map) and so forth. The map is: \begin{align*} & f_{a,b,c} \longmapsto e & & \text{both have order $1$} \\ & f_{a,c,b} \longmapsto (23) & & \text{both have order $2$} \\ & f_{b,a,c} \longmapsto (12) & & \text{both have order $2$} \\ & f_{c,b,a} \longmapsto (13) & & \text{both have order $2$} \\ & f_{b,c,a} \longmapsto (123) & & \text{both have order $3$} \\ & f_{c,a,b} \longmapsto (132) & & \text{both have order $3$} \end{align*} This is clearly a bijection of sets: every permutation in $S_3$ was hit exactly once. I still do not know how to show that this is a homomorphism. I constructed the map so that it preserved the order of elements, but is that enough? I could check that $\varphi(xy) = \varphi(x) \varphi(y)$ for each pair, but there must be a way to do it that I'm missing.

This is most likely a lack of understanding of wording on my part. I was considerind the Klein 4-group as the set of four permutations: the identity permutation, and three other permutations of four elements, where each of those is made up of two transposes, (i.e., 1 $\rightarrow$ 2, 2 $\rightarrow$ 1 and 3 $\rightarrow$ 4, 4 $\rightarrow$ 3) taken over the three possible such combinations of four elements.  Here, then, is my question. I am assuming (?) that Aut(G) in this case is the set of permutations of the four elements of the Klein 4-group - or the three non-identity ones for the purpose of showing isomorphic to $S_3$. If this is the case, what does it mean to have a permutation of these three permutations that I mentioned above? As always, thanks for your help.


You can read in my  about my struggle with this part. I made a milestone just now, increasing Indirect clamp will remove the fireflies, however the shadows are now too opaque. Render with Indirect Clamp to 0, lots of fireflies and denoise distort: same settings except I changed Image to Denoiser instead of Noisy image to Denoiser node, still distorted but more detail seem intact:  Render with Indirect clamp set to 2.0, shadow too opaque:  Render with Indirect clamp set to 5.0, this is the best result I got so far but I still feel is nowhere near the ideal result:  This is Andrew's cup in the tutorial, the lighting I am aiming for: Am I focusing too much on Indirect clamp? Are there other settings I should attempt to play around with? I am using Blender 2.92.0 with my GPU Radeon RX 5700 here is my blender file:  If you attempt to render my file please let me know if any settings are local that I need to change, or if they are per blender file.

I feel I am nearing completion of the tutorial but am still having gaps in knowledge on how to render light properly. 2.92.0 blender file:  Overview layout:  Lamp:  128 sample before denoise:  128 sample after denoise:  1024 sample 1080p 100% render before denoise:  1024 sample 1080p 100% render after denoise:  I've been trying different Light paths, but I honestly don't understand the extent of how they interact with each other. I haven't seen any example of what those numbers should be in the tutorial either, if someone knows please let me know.  but it is now again a little bit too opaque, dunno when that happened. :D Not too sure what I am missing out so any suggestions would be lovely! Thank you in advance


Please help. There is a problem I have tried to resolve for some time now. I want to come up with a pattern where i have a table with advertisements on a web platform. These advertisements shall be owned either by individual users (accounts) or by an entity which represents a group of users (accounts) the members of which have permissions on the advertisement. There shall also be a manager of the advertisement. When the advertisement is owned by a group, the accounts dont matter and the info for the group shall be displayed. My problem is that I always come with anti patterns for this schema. Can you suggest me something?  Your help will be highly appreciated.

I'm using PostgreSQL with  as my ORM.  I have one type, User. The second type is Group, which can have any number of users associated with it through a GroupMemberships table. Users can also own any number of Groups.  My third type, Playlist, can belong to either a User OR a group. What would be the best way to design a schema for this type so that it can have either one type of owner or the either?   My first pass I created both associations, but only populated one at a time. This could possibly work, but seems hacky and makes queries difficult.  Additional information  Here are my responses to the clarification requests posted by MDCCL via comments:     (1) If a Playlist is owned by a given Group, one can say that this Playlist is related to one-to-many Users, as long as they are Members of such Group, right?    I believe this is technically true, but this one-to-many association does not exist explicitly.     (2) So, is it possible for a specific Playlist to be owned by one-to-many Groups at the same time?    No, it should not be possible for a Playlist to be owned by one-to-many Groups.     (3) Is it possible for a particular Playlist to be owned by one-to-many Groups and, at the same time, by one-to-many Users who are not Members of such Group?    No, because as in (2) a one-to-many from Playlist to Group should not exist. Additionally, if a Playlist is owned by a Group it is not owned by a User, and vice versa. Only one owner at a time.     (4) What are the properties used to uniquely identify a Group, a User and a Playlist?   They each have a surrogate primary key (id), as well as a natural key (though not primary). These are slug for Group and Playlist, and username for User.     (5) Could a particular Playlist suffer an Owner change?   Although I don't plan on this being a feature (at least initially), I suppose this could hypothetically occur.      (6) What’s the meaning of the Group.Slug and Playlist.Slug attributes? Are their values stable enough to be defined as primary keys or do they change very often? The values of these two properties, along with User.Username must be unique, correct?   These slugs are unique, lowercase, hyphenated versions of their respective entity's title. For example, a group with the title 'Test Group' would have the slug 'test-group'. Duplicates are appended with incremental integers. This would change any time their title changes. I believe that means they wouldn't make great primary keys? Yes, slugs and usernames are unique in their respective tables.


i started learning Java some days ago. I have some experience with C++ and this is why I'm used to pointers, which would make this much easier.  so now my question.   Let's say I have the following Code:  public class Main {      public static void main(String[] args) {          int variable1=2, variable2=2;          input(variable1, variable2);          System.out.println(variable1 + " " + variable2);              // this should output "1 3" on the console       }      private static void input(int variable1, int variable2) {          System.out.println(variable1 + " " + variable2);              // this will output "2 2" on the console          variable1 = 1;         variable2 = 3;     }    }   So the function input() takes the Variables from main and outputs them (correctly). But how can I transfer the changed Variables back to the main function?

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


My question is why the following code prints 1 instead of 500;    When the callback is invoked and it doesnt find the variable count, doesnt it first looked at the context of func1 ?   function func1(cb){   let count = 500   cb() }   let count = 1  function func2() {   console.log(count); }   func1(func2)

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


I was wondering how to create a symbolic link in Ubuntu (12.04 LTS). I've done this before but this time it is a little different.  This command worked before.  user@desktop:/media/backup/folder$ ln -sv file.ods /home/user/file.ods   The last time I I created a file from my backup drive [harddisk].  Now I would like to create a symbolic link to a file present on a fileserver.   This is a virtual machine and probably a network connection to it is required. The fileserver (networkshare) is mounted at /media/fileserver.   I did try to use the same command as mentioned above, however, it create an empty file when opened it askes to be deleted because it is empty and useless.   When I do the command from above, it does not work. So, can someone help me out here?

I am installing p4v in /opt, but /usr/bin is on my path.  Is it possible to create a soft or symbolic link for p4v from /opt to /usr/bin, so I can just type "p4v" since /usr/bin is in my path?


My problem is that I don't know how to include \section*{Some Title} in \rightmark. Currently \rightmark is working fine for all types of pages e.g. list of figures, list of tables, table of content etc. But when there is a page wiith \section*{Some Title}, \rightmark is empty.  Any suggestions how to solve my problem?  MWE:  \documentclass[a4paper,listof=totoc,bibliography=totoc]{scratcl}  \usepackage[headsepline,automark]{scrlayer-scrpage} \clearpairofpagestyles \ihead{Musterhausarbeit\\ \rightmark{} \\ \markboth{#1}{#1}} \ofoot{\thepage}  \renewcommand*{\titlepagestyle}{empty}  \addtokomafont{section}{\clearpage}  \begin{document}     \tableofcontents     \newpage      \listoffigures     \newpage      \listoftables     \newpage      \section*{Some title}     \addcontentsline{toc}{section}{Some title}     \newpage      \section{Some more title} \end{document}

I use  \usepackage{fancyhdr}    then  \pagestyle{headings}    and I want \section*{name of the section} in my headings. How to do it?


The black part of this image is the outline of the State of Georgia, and the orange part is a line that is meant to have the effect of orbiting the state.  I would like to make this illusion, but I don't know how to get the tail end that is meant to look like it is going behind the black outline of the State.   What do I do, because playing around in Illustrator CS6, I can only get the entire orbital behind the state, not just the two tail ends.  Thanks

Let say I have 3 shapes in illustrator: A, B and C. I would like A to overlap B, B to overlap C and C to overlap A. How can I do that?


I would like to understand why the sum and product of algebraic integers are algebraic integers.  For algebraic numbers (not integers) there is the wonderful website  which uses only basic linear algebra. A short version of that is in this MSE-answer:   My Question:  Can this method or something similar be used for algebraic integers?

We know that the set $\mathbb{A}$ of algebraic numbers is a field. But there is a constructive proof of this statement? I.e. : given a sum (or a product) of numbers of the form $\sqrt[n]{q}$ with $ q \in \mathbb{Q}$ we can find a polynomial in $x$, with rational coefficients, that has as solution this sum (or product)? I've find that such a proof can be given using the resultant of the polynomials that have as roots the given numbers, but, as far as I know, the resultant is a number, so how can we find a polynomial?  I would appreciate an example: e.g. how to find the rational polynomial that has root $ \sqrt{2}+\sqrt[3]{3}$.


I got this problem from my textbook, not school. I tried various methods but was unable to solve the problem.  Let $\alpha$ and $\beta$ be the roots of the polynomial $x^2-3x+1$. I need to find the value of $$ \frac{\alpha^{2014}+\beta^{2014}+\alpha^{2016}+\beta^{2016}}{\alpha^{2015}+\beta^{2015}}$$

We have a polynomial $x^2 + 3x + 1$. There are 2 zeroes of it,  $\alpha$ and $\beta$  Now, what we need to find out is(What I couldn't) is as follows:  $$ \alpha^{2016} + \beta^{2016} + \alpha^{2014} + \beta^{2014} \over \alpha^{2015} + \beta^{2015}$$  Any ideas on how to do it?  Thanks a lot! -bone


I am US citizen traveling to Hong Kong via Beijing. Below are my flights details   Landing in Beijing Friday, 2 October 2015, 08:50:31 Departure to HK Monday, 5 October 2015, 12:00:00  So my total duration is 3 days, 3 hours, 9 minutes and 29 seconds  If I count total number of hours based on the flight times I am over 3 hours 10 minutes. I would like to know if I will run into any issues at the airport? Based on the Wiki posted on the  I should be fine as the 72 hours count begins at the following day. Can anyone please share their experience?

I have a 75 hour trip to Beijing (PEK) coming up in October. I shall enter at PEK on a flight from London, arriving at 0930 and continue onwards by air to Hong Kong three days later at 1230, and I shall be travelling on an ordinary British passport.  I understand that the 72 hour transit visa on arrival actually begins the midnight after my arrival (and not immediately after arrival).   Visa required, except for Holders of British passports endorsed  British Citizen  holding confirmed onward airline tickets to a third country, if arriving in and departing from the same city: - at Beijing (PEK), Chengdu (CTU), Chongqing (CKG), Dalian (DLC), Guangzhou (CAN), Hangzhou (HGH), Shanghai Hongqiao (SHA), Shanghai Pudong (PVG), Tianjin (TSN), Wuhan (WUH), Xi'an (XIY) or Xiamen (XMN) for a max. transit time of 72 hours, starting from 00:01 on the day following the day of entry. - at Guilin (KWL), Harbin (HRB), Kunming (KMG) or Shenyang (SHE) for a max. transit time of 72 hours;   However, although several non-official sources substantiate this distinction, I cannot find any official confirmation of this. Does anyone have any experience in doing this kind of transit?


public class DayAdapter extends BaseAdapter {      private Context mContext;     private Day[] mDays;      public DayAdapter(Context context, Day[] days) {         mContext = context;         mDays = days;     }      @Override     public int getCount() {         return mDays.length;     }      @Override     public Object getItem(int i) {         return mDays[i];     }      @Override     public long getItemId(int i) {         return 0;     }      @Override     public View getView(int i, View view, ViewGroup viewGroup) {          ViewHolder holder;          if(view==null){             view = LayoutInflater.from(mContext).inflate(R.layout.daily_list_item, null);             holder = new ViewHolder();             holder.iconImageView = (ImageView) view.findViewById(R.id.iconImageView);             holder.dayLabel = (TextView) view.findViewById(R.id.dayNameLabel);             holder.temperatureLabel = (TextView) view.findViewById(R.id.temperatureLabel);             view.setTag(holder);         }else{             holder = (ViewHolder) view.getTag();         }         Day day = mDays[i];         holder.dayLabel.setText(day.getDayOfTheWeek());          holder.temperatureLabel.setText(day.getMaxTemperature()+"");         holder.iconImageView.setImageResource(day.getIconId());          return view;     }      private static class ViewHolder{         ImageView iconImageView;         TextView temperatureLabel;         TextView dayLabel;     } }   I get the exception:  FATAL EXCEPTION: main java.lang.NullPointerException at app.com.example.tmrovsky.czywgdynipada.Adapters.DayAdapter.getView(DayAdapter.java:62)   I don't know where there is an error during setting these three: holder.dayLabel.setText(day.getDayOfTheWeek()); and so on. I tried to debug and there is no null value(it's correctly Tueasday). Any ideas, my brothers? :)

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


I am trying to center a graph made with pgfplots with \centering. If I put \centering within a group to limit its scope, the graph does not get centered. If I don't limit the scope of \centering, then everything gets centered.  \documentclass{minimal} \usepackage{pgfplots}  \begin{document} This text should not be centered, but the graph should be.  % \begingroup     \centering     \begin{tikzpicture}         \begin{axis}             \addplot coordinates { (0, 0) (1, 1)};         \end{axis}     \end{tikzpicture} % \endgroup  This text should not be centered. \end{document}

Why does the use of \begingroup, \endgroup negate the effect of centering in the MWE? The MWE below yields a left aligned figure (not desired), with subsequent text on the left (desired):  But if I remove the \begingroup, \endgroup, then things work as desired as far as the \centering goes, but then the subsequent text is also centered?  Question:  I thought the entire purpose of grouping was to localize the effect. So, what is the subtlety of grouping that results in this behavior? How do I keep the grouping, yet also have the centering?  I would like to ensure that any settings that are changed via the inserted figure are kept local to that figure.  Code: \documentclass{article} \usepackage{showframe} \usepackage{pgfplots}  %\usepackage{filecontents}% Commented to prevent overwriting myFig.tex \begin{filecontents*}{myFig.tex}     \def\YLabel{$f(x) = x^2 - x +4$}     \begin{tikzpicture}     \begin{axis}[ xlabel=$x$, ylabel=\YLabel]         \addplot {x^2 - x +4};      \end{axis}     \end{tikzpicture} \end{filecontents*}  \newcommand*{\InsertFigure}[1]{%     \IfFileExists{#1}{%         \begingroup%             \centering%             \input{#1}%         \endgroup%     }{}% }%  \begin{document}     \InsertFigure{myFig.tex}  \textbf{Text on left.} \end{document}


My article has two authors. The first one is the only corresponding author. Hence my LaTeX code for the authors is:  \documentclass[preprint,12pt]{elsarticle} \journal{elsarticle} \begin{document} \begin{frontmatter} \title{Title} \author{AuthorOne\corref{TheOnlyCorrespondingAuthor}} \ead{authorone@gmail.com} \author{AuthorTwo} \ead{authortwo@gmail.com} \cortext[TheOnlyCorrespondingAuthor]{Corresponding author} \end{frontmatter} \end{document}   The output is as follows:    However, as the above clips show, LaTeX automatically adds the asterisk to the last author. Why?  Can anyone solve the problem?  You'd better not to change the based setting in the original elsarticle.cls LaTeX template.

I believe I have followed the template exactly but as this following MWE shows I am getting an asterisk on both authors and not just the corresponding author. Do I have something in the wrong order somewhere?  \documentclass[preprint,12pt]{elsarticle}  \begin{document}  \begin{frontmatter}  \title{Title}  \author{Author One\corref{cor1}\fnref{fn1}} \ead{email@uni.edu} \cortext[cor1]{Corresponding author} \fntext[fn1]{Student}  \author{Author Two\fnref{fn2}} \ead{email2@uni.edu} \fntext[fn2]{Lecturer}  \address{Address Here}  \begin{abstract} Abstract abstract abstract \end{abstract}  \end{frontmatter}  \section{Section1} Start typing...  \end{document}   Thanks


If $x$ is the cosine of the angle between the vectors $a$ and $b$, $y$ is the cosine of the angle between the vectors $a$ and $p$, and $z$ is the cosine of the angle between the vectors $b$ and $p$, can we write $z$ in terms of $x$, $y$ and the magnitudes of $a$, $b$, and $p$?   That is, no dot products should appear in the relation.  All vectors are in $4$-dimensional Euclidean space.

If the cosine of the angle between the vectors $a$ and $b$ is $x$ and the cosine of the angle between the vectors $a$ and $p$ is $y$, then, if we call $z$ the cosine of the angle between the vectors $b$ and $p$, can we write $z$ in terms of $x$ and $y$?  All vectors are in $4$-dimensional Euclidean space.


I am citing a figure from paper. I inserted \cite{..} in the caption of the figure. The figure is referenced as [1], although it is in middle of the document.  \documentclass[12pt,a4paper]{report} \setcounter{tocdepth}{5} \setcounter{secnumdepth}{5} %\renewcommand{\algorithmicforall}{\textbf{for each}} \usepackage{graphicx}  \usepackage{indentfirst} \usepackage{hyperref} \usepackage{color,soul} \usepackage{amsmath} \usepackage{algorithm} %\usepackage{algorithmic} \usepackage{algcompatible} \usepackage{booktabs} \usepackage{caption}  \usepackage{tikz} \usepackage[english]{babel}  \usepackage{natbib} \usepackage[final]{pdfpages} %for embedding another pdf \usepackage{setspace} \captionsetup[table]{skip=10pt} \definecolor{lightblue}{rgb}{.80,.85,1} \sethlcolor{lightblue} \usepackage{verbatim} \usepackage{parskip} \usepackage{enumitem}   \begin{document}  %\renewcommand\bibname{References} %Renames "Bibliography" to "References" on ref page  %include other pages \input{chapters/title.tex} \input{chapters/certificate.tex} %\input{./declaration.tex} %\input{./dedication.tex} %\input{./acknowledgement.tex} %\input{./abstract.tex}   \pagenumbering{roman} %numbering before main content starts \tableofcontents \listoffigures \listoftables  \newpage \pagenumbering{arabic} %reset numbering to normal for the main content  \chapter{Introduction} \input{chapters/Chapter1.tex} \chapter{Literature Review} \input{chapters/Chapter2.tex} \chapter{Techniques Used} \input{chapters/Chapter3.tex} \begin{comment} \input{./chapter_4.tex} \input{./chapter_5.tex} %\input{./appendix.tex} %\input{./references.bib} %\mbox{} %\nocite{*} %\bibliographystyle{ieeetr} %\printbibliography \end{comment}  \newpage %\addbibresource{reference.bib} %\renewcommand{\thepage}{} \bibliography{reference} \bibliographystyle{unsrt} \end{document}

When using the \cite command in figure captions and the ieeetr bibliography style, then  BibTeX numbers the citations as appearing earlier than they do in reality (i.e. the first citation in the document ends up being [42]).  Is there any way to get BibTeX to ignore the \listoffigures section when numbering?


I'm looking to find the instillation date of an app I had on my old phone. I've tried looking on the play store  however it only shows be previous paid purchases.  I've also tried using a android emulator on my pc to view Google Play Games achievements, as it appeared it used to show you the time those achievements are unlocked, however checking it now just shows the achievements and not the times.  EDIT: To clarify the app is no longer installed, hence all answers in the other question are worthless as this is not the same question, as these only answer the question to when the app was installed on the current device, not when they were installed on another phone but are still linked to the account.

Is there a Play Store log file?   Or should I be looking where apps are installed on the phone for time/date stamps?


I've more than two XML Document (generated through for loop, based on certain criteria) and want to store them in an array (if possible).  For example: XmlDocument[] xmlDoc = {"xmlDoc1", "xmlDoc2"};  Is it possible to do so? If not, any suggestions?

Probably a really simple one this - I'm starting out with C# and need to add values to an array, for example:  int[] terms;  for(int runs = 0; runs < 400; runs++) {     terms[] = runs; }   For those who have used PHP, here's what I'm trying to do in C#:  $arr = array(); for ($i = 0; $i < 10; $i++) {     $arr[] = $i; }


I am able to derive $$\sin^{-1}x+\sin^{-1}y=\sin^{-1}\left(x \sqrt{1-y^2}+y\sqrt{1-x^2}\right)$$ as follows.  Let $$z=\sin^{-1}{x}+\sin^{-1}y.$$  Now if $z \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$  taking $\sin$ on both sides we get   $$\sin z=x \sqrt{1-y^2}+y\sqrt{1-x^2}.$$   Now taking $\sin^{-1}$ on both sides we get  $$\sin^{-1}(\sin z)=\sin^{-1}\left(x \sqrt{1-y^2}+y\sqrt{1-x^2}\right).$$ But in $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ we have $\sin^{-1}(\sin z)=z.$ Hence  $$z=\sin^{-1}\left(x \sqrt{1-y^2}+y\sqrt{1-x^2}\right)$$ but my book gave this is valid for $x^2+y^2 \le 1$ or $x^2+y^2 \gt 1$ when $xy \gt 0$.  Can I know why?

It is known that the following holds good: $$ \arcsin x + \arcsin y  =\begin{cases} \arcsin( x\sqrt{1-y^2} + y\sqrt{1-x^2}) \;\;;x^2+y^2 \le 1 \;\text{ or }\; x^2+y^2 > 1, xy< 0\\ \pi - \arcsin( x\sqrt{1-y^2} + y\sqrt{1-x^2}) \;\;;x^2+y^2 > 1, 0< x,y \le 1\\ -\pi - \arcsin( x\sqrt{1-y^2} + y\sqrt{1-x^2}) \;\;;x^2+y^2 > 1, -1< x,y \le 0 \end{cases} $$  But I couldn't find a proof for the above. I tried to prove this myself, but failed. I have no clue how to bring in $x\sqrt{1-y^2} + y\sqrt{1-y^2}$ from the conditions like $x^2 + y^2 < 1$. Please understand that I don't have any problem in getting the 'crux' part of the RHS : $ \arcsin( x\sqrt{1-y^2} + y\sqrt{1-x^2}) $. I face trouble only in checking the range of that 'crux' under the given conditions.


EDIT: One note I forgot to add is that I"m using Vmware to run ubuntu. I'm assuming that may be causing the problem?  New to Ubuntu (and Linux) and I'm having trouble installing Cuda 9.0.  During installation via the command sudo sh cuda_9.0.176_384.81_linux.run I'm getting this error:     The driver installation is unable to locate the kernel source. Please make sure that the kernel source packages are installed and set up correctly. If you know that the kernel source packages are installed and set up correctly, you may pass the location of the kernel source with the '--kernel-source-path' flag   First I was getting X server is still running error and by following the steps below, that error is replaced with the above error.  These are the steps I took to get rid of the X server is still running error   Hit CTRL+ALT+F1 and login using your credentials. kill your current X server session by typing sudo service lightdm stop or sudo stop lightdm Enter runlevel 3 (or 5) by typing sudo init 3 (or sudo init 5) and install your .run file.   However, during step 3, when I try to install the file, I get unable to locate kernel source error.  The file that I'm trying to run is cuda_0.0.176_384.81_linux.run which is in my home folder.   During installation:  I hit yes for everything (drivers, CUDA toolkit, CUDA samples) etc.  In the end I get a summary that looks something like this:  Driver: Installation failed XXXX :  Installation skipped XXXX: Installation skipped   How can I fix this installation error?  $ uname -r 4.10.0-37-generic  $ dpkg-query -l linux-headers-\* Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad) ||/ Name           Version      Architecture Description +++-==============-============-============-================================= un  linux-headers- <none>       <none>       (no description available) ii  linux-headers- 4.10.0-28.32 all          Header files related to Linux ker ii  linux-headers- 4.10.0-28.32 amd64        Linux kernel headers for version  ii  linux-headers- 4.10.0-37.41 all          Header files related to Linux ker ii  linux-headers- 4.10.0-37.41 amd64        Linux kernel headers for version  ii  linux-headers- 4.10.0.37.39 amd64        Generic Linux kernel headers   EDIT:  My question is different from the possible duplicate question because the other question doesn't have any references to the error I'm getting:     The driver installation is unable to locate the kernel source. Please make sure that the kernel source packages are installed and set up correctly. If you know that the kernel source packages are installed and set up correctly, you may pass the location of the kernel source with the '--kernel-source-path' flag   I've already tried the marked solution from .

For TensorFlow I would like to install CUDA. How do I do that on Ubuntu 16.04?


public class DataFactory {      class SYNOP implements IDataSources {}     class WRF implements IDataSources {}      public abstract class Factory {         public abstract IDataSources CreateModel();     }      public class SYNOPFactory extends Factory {          @Override         public IDataSources CreateModel() {             return new SYNOP();         }     }      public class WRFFactory extends Factory {          @Override         public IDataSources CreateModel() {                  return new WRF();         }            }      public static void main(String[] args) {          Factory factory = new WRFFactory();      } }   And i got message error like this:     No enclosing instance of type DataFactory is accessible. Must qualify   the allocation with an enclosing instance of type DataFactory (e.g.   x.new A() where x is an instance of DataFactory).   What did i do wrong?  Regards

What is the main difference between an inner class and a static nested class in Java? Does design / implementation play a role in choosing one of these?


Any hint to prove   $$ \sqrt{x+y} \le \sqrt{x} + \sqrt{y}, \qquad \forall x,y \ge 0 $$

How do I prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$? for $x, y$ positive?  This should be easy, but I'm not seeing how.  A hint would be appreciated.


I have spent the past 4 days trying to get Ubuntu and Windows 7 on my computer and every time it boots straight into Ubuntu. I have looked through most of the threads and tried Windows first, Ubuntu first, partitioning the drive, reinstall grub with boot - repair, pretty much every tutorial I can find, I only have one USB drive to boot off of, so this is very time consuming. I have to download the iso file and create a bootable USB everytime I install an OS and it's all for nothing because there is no boot menu. If anyone can help it would be greatly appreciated

After trying (and failing) to install better ATI drivers in 11.10, I've somehow lost my grub menu at boot time.  The screen does change to the familiar purple colour, but instead of a list of boot options it's just blank solid colour, and then disappears quickly and boots into the default entry normally.    How can I get the bootloader back?  I've tried sudo update-grub and also various different combinations of resolutions and colour depths in startupmanager application with no success (640x480, 1024x768, 1600x1200, 16 bits, 8 bits, 10 second delay, 7 second delay, 2 second delay...)   edit:   I have already tried holding down Shift during bootup and it does not seem to change the behaviour.  I get the message "GRUB Loading" in the terminal, but then the place where the grub menu normally appears I get a solid blank magenta screen for a while.  Here are the contents of /etc/default/grub  # If you change this file, run 'update-grub' afterwards to update # /boot/grub/grub.cfg. # For full documentation of the options in this file, see: #   info -f grub -n 'Simple configuration'  GRUB_DEFAULT=0 GRUB_HIDDEN_TIMEOUT=0 GRUB_HIDDEN_TIMEOUT_QUIET=true GRUB_TIMEOUT=10 GRUB_DISTRIBUTOR=`lsb_release -i -s 2> /dev/null || echo Debian` GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX=" vga=798 splash"  # Uncomment to enable BadRAM filtering, modify to suit your needs # This works with Linux (no patch required) and with any kernel that obtains # the memory map information from GRUB (GNU Mach, kernel of FreeBSD ...) #GRUB_BADRAM="0x01234567,0xfefefefe,0x89abcdef,0xefefefef"  # Uncomment to disable graphical terminal (grub-pc only) #GRUB_TERMINAL=console  # The resolution used on graphical terminal # note that you can use only modes which your graphic card supports via VBE # you can see them in real GRUB with the command `vbeinfo' #GRUB_GFXMODE=640x480  # Uncomment if you don't want GRUB to pass "root=UUID=xxx" parameter to Linux #GRUB_DISABLE_LINUX_UUID=true  # Uncomment to disable generation of recovery mode menu entries #GRUB_DISABLE_RECOVERY="true"  # Uncomment to get a beep at grub start #GRUB_INIT_TUNE="480 440 1"


In Linux use use AND Operators and it is represented by (&). In commands we can either use (&&) or (;). So, does a semi Colon (;) is also called an AND Operator?

What is the difference between  echo "Hello " ; echo "world"   and  echo "Hello " && echo "world"   Both seems to run the two commands after each other.


I am studying the textbook Introduction to Probability Models by Sheldon Ross. In Section 3.6 page 151 (10th edition), the author uses the Dirichlet distribution to deduct the coefficient of a "uniform" distribution. The "uniform" distribution is   $$f(p_1,p_2,\cdots,p_m) = \left\{\begin{array}{rl} c, & 0\leq p_i \leq 1, i = 1,\cdots, m, \sum_1^mp_i=1 \\ 0, & \text{otherwise} \end{array} \right.$$  So I check the wikipedia page about Dirichlet distribution. Among all the material I find out that "uniform" distribution (with constraint on the sum of variables) follows a symmetric Dirichlet distribution with $\alpha$'s become identical. $$f(x_1,\dots, x_{K-1}; \alpha) = \frac{\Gamma(\alpha K)}{\Gamma(\alpha)^K} \prod_{i=1}^K x_i^{\alpha - 1}$$ Thus it gives me the result as the author indicate $c=(m-1)!$.   The question is, to me, how to get the coefficient without referring to the Dirichlet distribution or get the coefficient given the kernel of the Dirichlet distribution, of course with the constraint that $\sum x_i = 1$.   I find out a post in the same site, which is to . Part of the solution can answer this question. However, it maybe of some value to help others search on this topic, so I decide not to remove the post.   Since that version is a little bit hard to understand, Can you give a more plain explanation?

Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$, have a joint ditribution as $\text{Dirichlet}(\alpha_1,\alpha_2,\dots,\alpha_k;\alpha_{k+1})$   Joint pdf of $(X_1,\dots,X_{k+1})=\frac{e^{-\sum_{i=1}^{k+1}x_i}x_1^{\alpha_1-1}\dots x_{k+1}^{\alpha_{k+1}-1}}{\Gamma(\alpha_1)\Gamma(\alpha_2)\dots \Gamma(\alpha_{k+1})}$.Then to find joint pdf of $(Y_1,\dots,Y_{k+1})$ I can not find jacobian i.e.$J(\frac{x_1,\dots,x_{k+1}}{y_1,\dots,y_{k+1}})$


I read  but it's still not clear to me if I can offer a bounty to a community wiki answer?

It's possible to offer and award bounties of reputation on questions.   What is a bounty? How can I find questions that have a bounty attached? How do I start a bounty? When can I start a bounty? Why is the system requiring me to choose a bounty amount that's higher than the minimum? Can I use Markdown formatting in the bounty remarks? Can I edit the remark? How long is the bounty period? How do I award a bounty? Can I award a bounty to my own answer? Can I award a bounty to an old answer? If I offer a bounty on someone else's question, can I award the bounty to their answer? After awarding the bounty, can I remove it or move it to another answer at a later time? What happens if there's no answer after the bounty period? What happens if I feel my question is still unanswered? What is automatic awarding? Are bounty awards exempt from the 200 points/day reputation limit? How does Community Wiki mode affect bounties? How does user deletion or post dissociation affect bounties? Can I award a bounty to an answer from a deleted user or one where the author was dissociated? Can I offer a second bounty after the first one has expired? Can I raise my bounty? What happens if a bounty question is closed or deleted? Why can't I vote to close or migrate a bounty question? What happens if I delete my account while I have an active bounty? Do I keep an awarded bounty when I delete my answer? What happens if a question where I awarded a bounty later gets deleted or migrated? Can I cancel my bounty? Can I affect / divide / share part of my bounty to two (or more) users? How many outstanding bounties can a single user have?      See also:  in the Help Center


came out on December 7th 2015 and as a beginning Python coder I would like to try the very latest version on my Ubuntu installation. At the moment Wily Werewolf 15.10 ships version 3.4 and there are some great improvements in the newest version.  I am currently running Wily Werewolf and I would be keen to hear some methods to update Python to 3.5.1.

How can I install a different version of Python using apt-get?  Obviously I realise I can install using the source tar ball, however I would prefer not to install from source and instead use the package manager, as that's what it's there for. Surely somewhere reputable builds .deb files for the latest Python releases (why python.org don't is beyond me) that I can reference.   What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib


I have a very lengthy string (length is also not fixed) I want to extract a substring lying between 'email' and '@gmail.com'  Suppose it is  xhxjcndjcnkjcnd cjkjcdckjncx email:substring@gmail.comjndhcjkdhcnchjdccb djc   I want to extract the 'substring'  in the String.. Can I do this using regular expression , using sed tool.?

Given a filename in the form someletters_12345_moreleters.ext, I want to extract the 5 digits and put them into a variable.  So to emphasize the point, I have a filename with x number of characters then a five digit sequence surrounded by a single underscore on either side then another set of x number of characters.  I want to take the 5 digit number and put that into a variable.  I am very interested in the number of different ways that this can be accomplished.


I am trying to understand the origin of the plus/cross-sign aberrations commonly seen for point sources in astronomical images, even ones created with professional-grade, high-quality optics. The one in the image below clearly has some chromatic dependence but its pattern tells me it's not purely chromatic aberration. I can't understand what physical cause gives rise to this particular pattern so commonly.  Thanks.

Very often when viewing pictures of the cosmos taken by telescopes, one can observe that larger/brighter stars do not appear precisely as points/circles on the image. Indeed, the brighter the light from star, the more we see this effect of four perpendicular rays "shooting" out from the star.    (Taken from .)   My question is: what are the optics responsible for this effect? I would suppose that both the hazy glow around the stars and the rays shooting outwards are optical effects created by the camera/imaging device, but really can't surmise any more than that. (The fact that the rays are all aligned supports this, for one.) A proper justification, in terms of (geometrical?) optics for both the glow and the rays would be much appreciated.  Here are a few other examples of such images:


I'm customizing switch-to-workspace settings using dconf write /org/gnome/desktop/wm/keybindings/switch-to-workspace-N "['<Alt>5']"  N 11 works but N 14 doesn't. How could I have this shortcut?

I'm trying to make a quicklist on the Workspace Switcher launcher that allows for quick switching to a certain workspace. (My friend sometimes uses my computer and just doesn't enjoy keyboard shortcuts, so I want to help him out.)  So is there a command one could type in a terminal that would force a certain workspace to be focused on?


From home page, choose a favorite tag. the list of questions tagged to it will be displayed-> try editing the favorite tags, script error is thrown. User has to go to the home page to edit the tags again.

Which browsers are officially supported by Stack Exchange?  Also, what else is needed in order to use every feature of the site?


Folks, I have received my phd from a university ranked 60 in usnews and had one year of post doc work after. Right now I am a non tenure track teaching professor at a wellknown university. Eversince I was student I had a dream of being in MIT, Stanford, Caltech or UC berkley. However, since I was neither genius nor rich, I was not able to do this. I even had a phd admission from USC but since it was partially funded I was not able to attend. Anyways, now that I am done with everything, I am still thinking of doing another phd in the above mentioned universities. But, I do not want to leave my current position since I really enjoy teaching and do not want to risk my future for just a dream. A solution I come up is to get a phd while I am working and this is only possible if the above universities are offering online phds. My field is civil engineering and due to my research area I am also interested in applied math. So far I was not able to find any top rank university that offers civil eng. or math completely online. I can get a phd in math from the university that I am teaching with a tuition waver but it is not really what i want. The best university for online math is University of Washington. But university of Washington is not a top rank university and I do not know if it is worth my time and money.   Any suggestions highly appreciated. And please do not call me a loser for trying to get a second phd. :D  Regards,  Jason Ray

I am studying a combined bachelor of engineering (electrical) and bachelor of mathematics; I just started this year and will graduate in 2018. The reason why I am doing double degrees and not a single degree is because I love both electrical engineering and mathematics and I could not ignore any of them. So with this in mind, I am thinking of doing two PhDs when I graduate (one in electrical engineering and one in mathematics). Is this a good path or I should concentrate on only one of them?


The Lorentz transformation is linear in $x,y,z,t$.  Are there are any non linear space transformations that leaves the speed of light constant in all inertial frames? The possibility being that space or matter might not transform in a simple homogeneous way.  Such a transformation which leaves the Maxwell equations invariant I imagine is unlikely.

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity:  Prove that any spacetime transformation $\left(y^0,y^1,y^2,y^3\right)\leftrightarrow \left(x^0,x^1,x^2,x^3\right)$ that preserves intervals, that is, such that  $$\left(dy^0\right)^2-\left(dy^1\right)^2-\left(dy^2\right)^2-\left(dy^3\right)^2=\left(dx^0\right)^2-\left(dx^1\right)^2-\left(dx^2\right)^2-\left(dx^3\right)^2$$  is linear (assuming that the origins of both coordinates coincide). That is, show that $\frac{\partial y^i}{\partial x^j}=L_j^i$ is constant throughout spacetime (that is, show that $\frac{\partial L_j^i}{\partial x^k}=0$).  Thus far all I've been able to prove is that $g_{ij}L_p^iL_q^j=g_{pq}$ (where $g_{ij}$ is the metric tensor of special relativity) and that $\frac{\partial L_j^i}{\partial x^k}=\frac{\partial L_k^i}{\partial x^j}$. Any further ideas?


“London will remain a major financial center,” he said. “At the margin there will some shift to other financial centers in Europe.”  If not, what does it mean?  source:

The results show Singapore’s growing business clout, driven in part by an expanding financial and insurance industry, which makes up about 13 percent of the economy. “London will remain a major financial center,” he said. “At the margin there will some shift to other financial centers in Europe.”   source:


I am just curious to know the direct and precise to prove the identities  (1) $$\cos(A+B)=\cos A \cos B-\sin A \sin B$$ and   (2)  $$\sin(A+B)=\sin A \cos B+ \cos A \sin B$$ I tried to come up with right-angled triangles but I failed to connect them and get some logic out. Thank's in advance.

The "" formulas often come in handy, but it's not immediately obvious that they would be true.  \begin{align} \sin(\alpha \pm \beta) &= \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \\ \cos(\alpha \pm \beta) &= \cos \alpha \cos \beta \mp \sin \alpha \sin \beta \end{align}  So what I want to know is,    How can I prove that these formulas are correct? More importantly, how can I understand these formulas intuitively?   Ideally, I'm looking for answers that make no reference to Calculus, or to , although such answers are still encouraged, for completeness.


In the simple linear regression model, $\hat{b}$ is the sum of independent normally distributed random variables .   Is it false because it talks about $\hat{b}$ and not $b$? because in the simple regression model the equation is $y=a+bx+e$ and not $y=\hat{b}x+a$

In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$?


Let $A, B\subset M$. Prove the following statement:  $A\subset B \iff A^c\cup B = M$  M is universal set and $A^c$ is complement of A.  I can kind a solve this using bunch of reasoning but in no real way using set laws or using arbitrary elements to prove that $A^c\cup B \subset M$ and $M\subset A^c\cup B$. I'm pretty sure its very trivial but I'm just looking for a very formal way to prove.

I need to prove the following letting A and B be subsets of a universal set U. $$A\cup B = U \iff A^c\subset B$$ It just isn't straight forward to me.


Let $G'$ be the commutator subgroup of $G$. Prove that if $H$ is a subgroup of $G$ and $G'\subset H$, then $H$ is normal in $G$.  I do not know how to prove it. I have tried different ways but all of them were unsuccessful. However, I know that $G'$ is normal in $G$ and quotient group $G/G'$ is abelian.  Can anyone demonstrate how to solve that problem.

Question: Let G be a group and let G' be the subgroup of G generated by the set $S=\left \{ x^{-1}y^{-1}xy \mid x,y \in G \right \}$  $\space$  Prove that G' is normal in G. Solved  $\space$  Prove that G/G' is abelian. Solved  $\space$  Prove that if H is a subgroup of G and G' is a subgroup of H, then H is a normal subgroup of G.  I cannot even begin to start on this question. Any hint is appreciated.


I know that the net electric field inside a conductor is zero due to field made by induced charges. But , IS IT NECESSARY ? what i mean is that what would happen if the net electric field inside a conductor was not zero . ( what would happen if the electrons are not in equilibrium inside a conductor? )

My textbook says the field inside a conductor must be zero in order for the system to be equilibrium and therefore there must be no excess charge inside.  Their proof:  1) Place a gaussian surface inside the conductor. Since the system is at equilibrium, all points on the surface must have an electric field of zero.  2) Therefore the net flux is zero, implying the charge inside is zero.  3) If there is no charge inside, all excess charge must lie on the surface.  My problem:  "Since the system is at equilibrium, all points on the surface must have an electric field of zero."  Why?  Consider an conductor with no excess charge. To simplify things, say the conductor consists of a 100 free electrons and a 100 ions of charge 1$e^+$. The conductor is neutral and at equilibrium.  Now consider the field on one specific electron. There a total of 99 other electrons and 100  ions. So there would be a net field acting on that specific electron. So even though the system is at equilibrium, the net field on the individual particles is non-zero.  So a system can be at equilibrium, even if the net field inside is non-zero. What am I misunderstanding?  Another example: Consider a system consisting of one electron and one proton. If nothing is holding them back they will attract each other until they touch. After they touch, the force acting on them is still non-zero, yet they wouldn't accelerate.


I am trying to exclude multiple lakes and reservoirs from a Supervised landscape classification but at the moment I have not found a way to do this. So far I have used the following workflows: 1.Draw a polygon -> Clip -> Extract by mask) generates the opposite result. 2.Draw a polygon -> "Raster to Polygon" -> Reclassify -> Set Null, but the reclassification removes RGB symbology Details: I am using an Multiband High resolution Raster image I am working on the latest version of ARCmap for Desktop I would like to retain the RGB Composite symbology

Which tool do I use in ArcGIS 10.1 for Desktop to exclude areas covered by vector polygon layers from a raster layer?   I want to keep portions of the raster layers that exclude the portions covered by the vector layer.


Say we have a battery at a fixed voltage of $V$ charging a capacitor with capacitance $C$.  When the capacitor is fully charged, the energy stored in it will be $\frac{1}{2}QV$, where $V$ is the final voltage of the capacitor (and the voltage of the battery).  However, I'm a little confused as to the work the battery does...  To me, it seems that if the battery pushed $Q$ onto the capacitor, and the voltage of the battery is $V$, it must've done $QV$ of work, which means that the energy stored in the capacitor only accounts for half of it.  Where did the rest of the work the battery did go?

For a simple circuit with a battery supplying a voltage $V$ to a capacitor, let us assume that the charge on the capacitor is $Q$. Now, the work done by the battery or the energy supplied is given by the relation:  $$W=QV$$  But the energy stored in the capacitor is given by:  $$U = \tfrac12 QV$$  The value of $Q$ as well as that of $V$ should be the same in both the equations.  Now my question is, where is the other half of the energy that the battery supplied?


n=0; ((n++));echo "ret=$?;n=$n;" ((n++));echo "ret=$?;n=$n;" ((n++));echo "ret=$?;n=$n;"   from n=1 on, ((n++)) works correctly, only when n=0, ((n++)) return error, and I am using a trap '' ERR that is causing trouble with that  is it some bug?

Try it:  $ a=0 $ let a++ $ echo $? 1 # Did the world just go mad? $ echo $a 1 # Yes, it did. $ let a++ $ echo $? 0 # We have normality. $ echo $a 2   Contrast with this:  $ b=0 $ let b+=1 $ echo $? 0   And this (from ):  $ c=0 $ let ++c $ echo $? 0   What is going on here?  $ bash --version GNU bash, version 4.1.5(1)-release (x86_64-pc-linux-gnu)


I would like to do something like this:  \immediate\write18{git log -1 --pretty=format:"%h-%ad" --date=short > /tmp/temp.dat }   however, xelatex cannot proceed because the % means comment out if I do this:  \immediate\write18{git log -1 --pretty=format:"\%h-\%ad" --date=short > /tmp/temp.dat }   The call is actually:   git log -1 --pretty=format:"\%h-\%ad" --date=short > /tmp/temp.dat   which will have extra \ in it.  How can I let the shell command use % instead of \% ?

How can I write % into an auxiliary file? % will not work, because LaTeX thinks that I start a comment with it (in the main file, not in the auxiliary file!), and \% will write \% into the file. How can it be accomplished?   \documentclass{article} \begin{document} \newwrite\outfile \immediate\openout\outfile=example.dat \immediate\write\outfile{%}% will not work, of course, but neither \% \immediate\closeout\outfile \end{document}


Suppose s="mrunal" I want to print run for that I am doing print(s[1:4]) But in python why print(s[1:3]) is not available. Simply I want to tell that why end in slicing is not that index which we want as last character? s="mrunal"  index 0 = "m" index 1 = "r" index 2 = "u" index 3 = "n" index 4 = "a" index 5 = "l" here index for "n" is 3. Why end index is not same as s[1:3]? Why it is not inclusive? why it uses exclusive?

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


I have a red-hat system with its root and non-root users. I have to create n new root-like users and m new non-root users. Basically I have to clone the 2 kind of users already present on the server.  The purpose is to give to each person able accessing to the server their unique credentials. Someone can act as root, someone else can act as a non-root user.   I considered it different than giving root power to another user, because I have to create new root-like users.

How to Give all the powers Of Root account to another user account? With full command and detail.


So for more context you can look at my last post, but I feel like I went about asking the question all wrong.  What I'm given is one input on one line: month day             eg April 11  What I need to do is, based on the month and day given, determine the season.  So I need to first get the String inputMonth; and get the int inputDay; from the single string providing both.   I am conveniently provided with the months and days of the seasons which resulted in me writing the following:            //I know that the inputDay is wrong           inputMonth = scnr.next();           inputDay = scnr.nextInt();     if( ((inputMonth == "March") || (inputMonth == "march")) && ((inputDay >= 20) && (inputDay <= 31))){      System.out.println("Spring");     }    else if( ((inputMonth == "April") || (inputMonth == "april")) && ((inputDay >= 1) && (inputDay <= 30))){      System.out.println("Spring");     }    else if( ((inputMonth == "May") || (inputMonth == "may")) && ((inputDay >= 1) && (inputDay <= 31))){      System.out.println("Spring");     }    else if( ((inputMonth == "June") || (inputMonth == "june")) && ((inputDay >= 1) && (inputDay <= 20))){      System.out.println("Spring");     }    else if( ((inputMonth == "June") || (inputMonth == "june")) && ((inputDay >= 21) && (inputDay <= 30))){      System.out.println("Summer");     }    else if( ((inputMonth == "July") || (inputMonth == "july")) && ((inputDay >= 1) && (inputDay <= 31))){      System.out.println("Summer");     }    else if( ((inputMonth == "August") || (inputMonth == "august")) && ((inputDay >= 1) && (inputDay <= 31))){      System.out.println("Summer");     }    else if( ((inputMonth == "September") || (inputMonth == "september")) && ((inputDay >= 1) && (inputDay <= 21))){      System.out.println("Summer");     }   else if( ((inputMonth == "September") || (inputMonth == "september")) && ((inputDay >= 22) && (inputDay <= 30))){      System.out.println("Autumn");     }   else if( ((inputMonth == "October") || (inputMonth == "october")) && ((inputDay >= 1) && (inputDay <= 31))){      System.out.println("Autumn");     }   else if( ((inputMonth == "November") || (inputMonth == "november")) && ((inputDay >= 22) && (inputDay <= 30))){      System.out.println("Autumn");     }   else if( ((inputMonth == "December") || (inputMonth == "december")) && ((inputDay >= 1) && (inputDay <= 20))){      System.out.println("Autumn");     }   else if( ((inputMonth == "December") || (inputMonth == "december")) && ((inputDay >= 21) && (inputDay <= 31))){      System.out.println("Winter");     }    else if( ((inputMonth == "January") || (inputMonth == "january")) && ((inputDay >= 1) && (inputDay <= 31))){      System.out.println("Winter");     }   else if( ((inputMonth == "February") || (inputMonth == "february")) && ((inputDay >= 1) && (inputDay <= 29))){      System.out.println("Winter");     }   else if( ((inputMonth == "March") || (inputMonth == "march")) && ((inputDay >= 1) && (inputDay <= 19))){      System.out.println("Winter");     }   else{    System.out.println("Invalid");     }   My issue is that I can't figure out how to determine the month and the day separately from that one input.  Whenever I run this I always end up getting "Invalid". Some people on my last post were showing different ways to go about this but to be honest I'm not familiar with arrays yet (That's next lesson). Thanks in advance guys.

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


I have a specific port number with me and  want to check if it is active or not. I tried:  netstat -an | grep $portnum   Is this correct?

How to check the opened/closed ports on my computer?  I used netstat -a on command line.   Does the port status "LISTENING" indicate that the port is open? Is any port, that is not shown in the output, closed?


This question is more for curiosity than knowledge, but it might still be useful to know.  Is it possible to obtain automatic question bans on meta sites besides Meta Stack Exchange? If so, how much lower is the threshold? I ask because downvotes on Meta have little effect overall and can indicate disagreement, so I would imagine that implementing a question ban system on a meta site would be hard to implement.

Somewhere I heard the automatic question ban on Meta is set lower than on the main site. But looking at the profile of  it looks like there is absolutely no automatic ban on meta.  Is this intended behaviour?


I need to show my website with a "theme" when in header's requests is present a particular key/value.   In Drupal 7 I do this via themekey, but this module does not exist in Drupal 8.   Are there alternatives, or other ways to do this?

I need to switch themes based on URL paths and content types. I would have used ThemeKey, but it's not in a ready state. What are people using in Drupal 8 to do these things?


Can someone tell me what is the name of this one? Then I can check a little more about it.

I used to see these insects frequently in Chennai and Bangalore (South India). I just would like to know if this is a kind of . The lovebug as mentioned in the Wikipedia page is, however, different in appearance, although they too are walking as pairs.  Why are they always walking as attached pairs? It also seems to me that the bigger one drives the motion and decides the direction. Is that true?


I have an old "stereo" movie as a mp4 file.  The sound is only in the left channel, the right channel is silent.  I'd like to use ffmpeg to copy the video stream :  ffmpeg -hide_banner -i video.mp4 -c:v copy ...   and convert the audio to mono by selecting only the left channel :  -map_channel 0.1.0 -map_channel -1   But that didn't change anything :-(  What is the correct ffmpeg command line for that ?  Is it also possible to do that whithout re-encoding ?

How can I use ffmpeg to isolate one channel from an audio file? I have a stereo audio file, and I need the output to be the contents of the right channel in a mono audio file.  While I'm sure it's fairly easy to do, I can't figure it out. Thanks for the help!


I installed QGIS 3 as instructed and the Vector processing tab is missing. I did uninstall all previous versions and Python.

I installed QGIS 3.0.0 on a PC with French as default language. After changing the language of QGIS to English, the 'Vector' menu is empty and there is a French 'Vecteur' menu. Any ideas how to fix this? I cannot change the system language.