how to make use of multiple processors with Node.js?
Node.js on multi-core machines
How can I prove  from first principles that $0!$ is equal to $1$? Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$ Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$.  Work so far:  $$x^8 - x = x(x^7 - 1) = x(x - 1)(x^6+x^5+x^4+x^3+x^2+x+1)$$  From here, I think the Zeros of an Irreducible over a splitting field Theorem would be the method. I am unsure how to proceed Let $b_n$ be a sequence which decreases monotonically to zero, prove $\sum b_nz^n$ converges for $|z|\leq 1$ and $z\neq 1$.  So I was able to prove it converges on the open unit disk in the complex plane, but except for a few special points on the boundary, such as $-1$ and $i$, where I was able to use the alternating series test, I can't seem to prove it converges in general on the boundary minus $z=1$.  I feel I have to somehow use the fact that all the numbers on the unit circle except $z=1$ rotate around and around as you raise them to higher and higher powers, thus you get the real and imaginary parts of your series to alternate between sets of positive and negative terms, but in a very irregular way for most initial angles.  I tried to simplify the problem by breaking the series into its real and imaginary parts, and then trying to prove they each converge separately, but I still can't prove either converges:  $$\sum_{n=0}^{\infty}b_ne^{n\theta i} = \sum_{n=0}^{\infty}b_n\cos(n\theta) +i\sum_{n=0}^{\infty}b_n\sin(n\theta).$$ Schengen Visa Application: what are some helpful tips for preparing? Find $\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$ I am trying to find  $$\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$$  My first guess is to look at the reciprocal and isolate factors:  $${2 \over 1}{5 \over 4}{8 \over 7} \dots {3n+2 \over 3n+1}= {\left(1+1\right)}\left(1+{1 \over 4}\right)\left(1+{1 \over 7}\right) \dots \left(1+{1 \over 3n+1}\right)$$ Now we take the natural log: $$\ln{ + \ln\left(1+1\right)} + \ln\left(1+{1 \over 4}\right) +\ln\left(1+{1 \over 7}\right) \dots +\ln\left(1+{1 \over 3n+1}\right)$$ Using $\ln(1+x) \le x$, we get: $$\ln{ + \ln\left(1+1\right)} + \ln\left(1+{1 \over 4}\right) +\ln\left(1+{1 \over 7}\right) \dots +\ln\left(1+{1 \over 3n+1}\right) \le 1 + {1 \over 4} + {1 \over 7} + \dots + {1 \over 3n+1}$$ Now, I'm stuck. I suppose I might use the fact that the RHS is similar to the harmonic series and show that it converges to some log, but I'm not sure how to do that. Do you have any clues? Parallel universe: in every universe, you are presented with a different decision. Does that mean there are an infinite amount of parallel universes? I.e., if in one universe I choose to go left, I am then presented with different choices vs if i choose right, and that creates more universes with more decisions to be made.  Or does it mean that in the end of one's life we end up in the same place, meaning that its just one parallel universe that eventually collides with the other. I'm using using algorithm2e package with the following settings:  \usepackage[ruled,vlined,linesnumbered,noresetcount]{algorithm2e}   But for some subset of algorithms in the same document, I want to use this setting:  \usepackage[boxed]{algorithm2e}   Is there a way to override the default setting just for a subset?  I found a similar question:  Here newenvironment is used to override the default setting of an option. But I want to override the option itself.  I wish there was a way to load a package several times with different options for each instance. How to AutoSize the height of a Label but not the width Is there a general theorem stating why the restricted Lorentz group's exponential map is surjective? The exponential map for the restricted Lorentz group is surjective. An outline of why is shown on the wiki page .  Is there a more general theorem that states that for some class of Lie groups or Riemannian manifolds (which includes the restricted Lorentz group), the exponential map is surjective?  There is a theorem stating that compact, connected Lie groups have surjective exponential maps. But as the restricted Lorentz group is not compact, this isn't applicable. How to make read-only file system writable? At some point, the filesystem on my digital audio player has become read-only. I cannot copy files into it or remove files on it.  Are there some possible reasons for the player's file system to change permissions in this way?  I tried using chmod:  $ sudo chmod a+rw SGTL\ MSCN/  chmod: changing permissions of `SGTL MSCN/': Read-only file system   SGTL MSCN is the mount point of the digital audio player.  What else can I try to make it writeable? I am making a character for a campaign that is starting soon. The character is going to start out as a cleric (War Domain) and will multiclass into artificer (Battle Smith).   I have looked at the multiclassing rules, but I am having trouble making heads or tails of it for a multi-class involving a 2/3 caster (the Artificer) and a full caster (the Cleric).  That leads me to my question: what would a level 15 War Domain cleric/level 5 Battle Smith artificer look like? How many spells per level? How many cantrips? Does the artificer's ability to replace cantrips still apply? PHP regex delimiter, what's the point? Don't replicators make the Ferengi rather pointless? Ferengis are all about acquisition and making a profit. But, in the age of replicators, where everything you want can be produced instantly, what would be the point of their lifestyle? How do I efficiently iterate over each entry in a Java Map? If I have an object implementing the Map interface in Java and I wish to iterate over every pair contained within it,  what is the most efficient way of going through the map?  Will the ordering of elements depend on the specific map implementation that I have for the interface? Plagiarism of Lecture Slides Original Post:  I recently attended a lecture with highly technical content.  One of the middle slides in the deck had a particular phrase that reminded me of something that I had read several years before.  It took me a few minutes, but I found the original source (another slide deck) and am shocked to find that the professor lifted 35 slides verbatim from the original source.  The University holds students accountable for plagiarism and strictly defines plagiarism such that this clearly fits.  The slides were used verbatim and no credit or reference was provided.  Further, logos were added and color schemes were changed to make make them look slightly more like original content.  What should I do?  This professor has a professional full time job and I can imagine this getting swept under the rug, but this is clearly plagiarism and is spelled out very clearly in the student conduct code.  Is this an overreaction or should I pursue this?  This is confounded by the fact that I am very disappointed by the rigor of the course and feel like the professor lacks adequate technical background to teach the course (I guess my suspicions came true).  I'm really busy at work so don't want to deal with a big todo, but believe this really discredits the academic integrity of the course.  Additional content in response to comments:  The University defines plagiarism as "Using another writer's words without proper citation."  There is no proper citation given here, and these are not educational materials.  This is 35 slides from someone else's tutorial presentation.  I do not believe that the professor and the author of the original content have a relationship.  I have emailed the author to enquire about any permissions or relationship.  Still, even with permission, this is still plagiarism as defined be most people and as defined by the University.  All original works in the US are implicitly copyright protected, so there is also a copyright issue, but this is not currently my concern, though it could be of interest to the original author.  I have emailed him, so this is up to him.  This is a US institution and is a top tier highly respected school.  I am also not a lay student, but a Ph.D. with a degree from a top tier university who has served as a faculty member at two top tier universities (including this one).  I have also taught undergraduate courses in the past.  I have never engaged in this type of plagiarism, have never known colleagues to do so, and am shocked that so many people suggest this is par for the course in teaching.  My doctorate is from a school that prides itself on its honor code and takes honor code violations very seriously and I have served on the honor council and deliberated on a case of plagiarism in the past.  I really am shocked by this incident.  Response from Original Author of the Slides:  I have received a response from the author of the slides and he states that the work is his original work, that there are no additional authors of the work, that no one has been given permission to present the work, and that he believes his copyright on the work has been infringed upon.  He has requested additional information to assert his claim on the copyright. I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut wouldn't be able to push in the empty space with his hands or legs to move himself, but with a rocket engine it's possible. How? What might be the explanation for this in General Relativity? How do I extract all the external links of a web page and save them to a file? How do I extract all the external links of a web page and save them to a file?  If you have any command line tools that would be great. what is wrong with this??? please,can anyone help?  \begin{equation} \label{probabilityy} P^{t}({E_{0})=P_{0}+(1-P_{0})P_{1}+ (1-P_{0})(1-P_{1})P_{2}+.......+P_{n}\Pi_{k_{0}}^{n-1}(1-P_{k}) \end{equation} Error in .bib entry, "Too many commas" The code for reference is this  @article{matcontcl,  title= {MATCONT and CL MATCONT},  author = {A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and  B.Sautois},  year = {2006},  journal = {Continuation toolboxes in matlab}, }   This is the error that follows  This is BibTeX, Version 0.99d (TeX Live 2015/W32TeX) The top-level auxiliary file: PropuestaInvestigacion.aux The style file: abbrv.bst Database file #1: biblio.bib Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1049 of file abbrv.bst Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1049 of file abbrv.bst Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1090 of file abbrv.bst Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1090 of file abbrv.bst (There were 4 error messages)   How could I fix it? What's the difference between using black and white mode in-camera, and converting in post? For black and white photography, will there be any quality difference between using the built-in black and white mode, or shooting in color initially and then removing the color later using Photoshop (or similar application)?  I have a high-end compact camera, the .