Formula for the general case of $\sum_{n=1}^\infty \frac{H_n}{n^2} = 2\zeta(3)$
Generalized Euler sum $\sum_{n=1}^\infty \frac{H_n}{n^q}$
How and when is old-releases.ubuntu.com updated? A message may be accompanied with a digital signature, a MAC or a message hash, as a proof of some kind.  Which assurances does each primitive provide to the recipient?  What kind of keys are needed? What does it mean for two objects to "touch"? What would be the the mathematical equivalent of this excel formula? =PMT() I need to create a JavaScript form that does the same calculation as this =PMT() function.   mortgage = 220000 rate= 4.75% term = 30   The example formula I have is =PMT(4.75%/12,30*12,220000*-1)  What would be the equation for this function? I tried to look up this function but it doesn't explain it very well. How do I set a variable to the output of a command in Bash? Why are newer generations of processors faster at the same clock speed? Why, for example, would a 2.66 GHz dual-core Core i5 be faster than a 2.66 GHz Core 2 Duo, which is also dual-core?  Is this because of newer instructions that can process information in fewer clock cycles? What other architectural changes are involved?     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this question. Feel free to edit the answers to add additional details. W.K.T, any user(with more than 2k rep) can review 20 suggested edits per day.  Today I saw the newly appointed moderator  reviewed more than 20.    Is it possible for moderators to review more than the daily limited count?  If yes, can any moderators can do it at any time?  I didn't see this before. states:  Imports are always put at the top of the file, just after any module comments and docstrings, and before module globals and constants.  However if the class/method/function that I am importing is only used in rare cases, surely it is more efficient to do the import when it is needed? Isn't this: class SomeClass(object):      def not_often_called(self)         from datetime import datetime         self.datetime = datetime.now()  more efficient than this? from datetime import datetime  class SomeClass(object):      def not_often_called(self)         self.datetime = datetime.now() Sequences or 'chains' of adjoint functors Suppose we have (some categories and some functors such that) $F_1$ is left adjoint to $G_1$, $G_1$ left adjoint to $F_2$, $F_2$ left adjoint to $G_2$. Will $F_1$ then be equal to $F_2$ (and $G_1$ to $G_2$)?  Or can there exist arbitrarily long 'chains' of adjoint functors that do not trivialize? Is the converse of Cayley-Hamilton Theorem true? The question is motivated from the following problem:     Let $I\neq A\neq -I$, where $I$ is the identity matrix and $A$ is a real $2\times 2$ matrix. If $A=A^{-1}$, then the trace of $A$ is   $$ (A) 2 \quad(B)1 \quad(C)0 \quad (D)-1 \quad (E)-2$$   Since $A=A^{-1}$, $A^2=I$. If the converse of  is true, then $\lambda^2=1$ and thus $\lambda=\pm1$. And then $\rm{trace}(A)=1+(-1)=0$.   Here are my questions:   Is  $C$ the answer to the quoted problem?  Is the converse of Cayley-Hamilton Theorem, i.e.,"for the square real matrix $A$, if $p(A)=0$, then $p(\lambda)$ is the characteristic polynomial of the matrix $A$" true? If it is not, then what's the right method to solve the problem above? Caption above subtables with subcaption package breaks numbering of following table I need to display math in my report, but is it possible to remove the vertical space around align*?  A little example is the following (where I just want the align* to have the same vertical space as a \\  \documentclass[10pt,danish,a4paper,oneside,fleqn]{report}  \usepackage[english]{babel} \usepackage{amsmath}  \begin{document}  ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss \begin{align*}   A{\cap}B\ &amp; =\ {\left\{{b,d,e}\right\}}{\;}{\cap}{\;}{\left\{{a,b,f,g}\right\}}   \\   \nonumber\ &amp; =\ {\left\{{b}\right\}} \end{align*} ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss \\ ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss  \end{document} Does Windows use the fastest drive for the page file? Suppose I have a 6 GB page file on an SSD and another 6 GB page file on a traditional mechanical 5400rpm SATA drive.  Does Windows take into account the difference in the performance characteristics between the two drives when deciding which page file to use?  If it matters, I'm asking about Windows 7 and higher.  I reviewed this  but it doesn't appear to factor in the case of dissimilar storage speeds. Highlighted source code inline with Latex/Minted? Hi I can compute a Basic Loan Amortization Schedule, But now I'm trying to Calculate a Seasonal Loan Amortization Schedule . So for example A loan starts at January And Will go on for 3 years, with Monthly Payments. Interest is at 3% Annually and is compounded Annually. During the months of September, October, November, December It'll only accumulate Interest But no payments and principal. Principal is 100000. How Do I calculate Payments and interest. Can two PS4s log in to the same PSN account? Both myself and my boyfriend have PS4s.  Can I just get a single PSN account and sign both consoles into the same account, or do I need to get two separate accounts? I have two Xbox 360's, one WiFi and the other wired through the same Linksys E3000 router with DD-WRT (v24-sp2 (04/13/11) std-usb-nas firmware).   Mine (the wired one, though hers has been wired in the past and it didn't appear to help) always seems to be open (green), and hers is either moderate or closed (oj/red)  Even with the original router firmware I've never been able to get both consoles into "open nat" mode, and it makes playing certain games together almost impossible for me and my wife  because we can't seem to get into the same game.   I have uPnP enabled and the DMZ disabled, and some minor port forwarding to allow for a Minecraft server (Ports 25565 and 25566 for a testing copy of the server), but other than that the settings are mainly at their default, on the xbox's and the router.   Are there any settings I can configure to allow this to work properly? Drupal out of the box comes with a page (which is the default homepage) that is assigned to the node path.  How do I avoid users reach it, and redirect them to the actual homepage of the site? How do I edit PDF files produced by LaTeX in Illustrator? Fonts are not found When I try to use Adobe Illustrator (CS4) to edit a PDF file produced by LaTeX with several equations in it, Illustrator complains that it can't find the fonts:  The font CMBX10 is missing.  Affected text will be displayed using a substitute font. The font CMMI10 is missing.  Affected text will be displayed using a substitute font. The font CMMI6 is missing.  Affected text will be displayed using a substitute font. The font CMMI7 is missing.  Affected text will be displayed using a substitute font. The font CMMI8 is missing.  Affected text will be displayed using a substitute font. The font CMMIB10 is missing.  Affected text will be displayed using a substitute font. The font CMR10 is missing.  Affected text will be displayed using a substitute font. The font CMR7 is missing.  Affected text will be displayed using a substitute font. The font CMSY10 is missing.  Affected text will be displayed using a substitute font. The font CMSY6 is missing.  Affected text will be displayed using a substitute font. The font CMSY7 is missing.  Affected text will be displayed using a substitute font. The font MSBM10 is missing.  Affected text will be displayed using a substitute font. To preserve appearance, some text has been outlined.   How do I find &amp; install the necessary fonts? Dual boot Ubuntu (14.04) with Windows 10