How to accumulate values of each two rows across a line in linux?
How to sum up values of each two rows across their line in linux
Is there an analog to the Runge-Lenz vector for a 3D spherically symmetric harmonic potential? Passing multidimensional arrays as function arguments in C In C can I pass a multidimensional array to a function as a single argument when I don't know what the dimensions of the array are going to be?  Besides, my multidimensional array may contain types other than strings. I'm starting a Windows Forms application from the command promt and I need to get the exit codes that the windows forms application generates. The command promt starts the application and returns immediatly. But the application executes in the background. Is there a way to get the Exit codes?  Kind Regards  Christian. Highlight a word with jQuery Change hanging indent in description list I'm trying to get a description's list hanging indent to lie flush with the first line of text.  I have a description list such as the following:  \begin{description}  \item[Label the first] Lorem ipsum dolor sit amet, consectetur adipisicing                         elit, sed do eiusmod tempor incididunt ut labore et                         dolore magna aliqua.  \item[The longest label] Ut enim ad minim veniam, quis nostrud exercitation                           ullamco laboris nisi ut aliquip ex ea commodo                           consequat.  \item[Shrtlbl] Duis aute irure dolor in reprehenderit in voluptate velit esse                 cillum dolore eu fugiat nulla pariatur. \end{description}   This produces the following output:    I would like to have each paragraph indented so that the following lines are flush with the first letter of the list item's text, the way it's laid out in my TeX.  For instance, the "s" of "sectetur" should be right under the "L" of "Lorem".  I've tried looking through the documentation of , but I can't seem to find a good option.  I tried specifying [leftmargin=3cm, style=sameline], but this results in the following:    This isn't quite right: I'm trying to get each item lined up differently, so that the "L" of "Lorem" is not necessarily flush with the "U" of "Ut" or the "D" of "Duis".  Does anybody know a good way to do this? What is the most accurate way to retrieve a user's correct IP address in PHP? How do I change the extension of multiple files? Proving $\sum\limits_{k=0}^{n}\cos(kx)=\frac{1}{2}+\frac{\sin(\frac{2n+1}{2}x)}{2\sin(x/2)}$ I am being asked to prove that $$\sum\limits_{k=0}^{n}\cos(kx)=\frac{1}{2}+\frac{\sin(\frac{2n+1}{2}x)}{2\sin(x/2)}$$ I have some progress made, but I am stuck and could use some help. What I did: It holds that $$\sum\limits_{k=0}^{n}\cos(kx)=\sum\limits_{k=0}^{n}Re(\cos(kx))=\sum\limits_{k=0}^{n}Re(\cos(x)^{k})=Re(\sum\limits_{k=0}^{n}\cos(x)^{k})=Re\left(\cos(0)\cdot\frac{\cos(x)^{n}-1}{\cos(x)-1}\right)=Re\left(\frac{\cos(x)^{n}-1}{\cos(x)-1}\right) $$ For any $z_{1},z_{2}\in\mathbb{C}$ we have it that if $z_{1}=a+bi,z_{2}=c+di$ then $$\frac{z_{1}}{z_{2}}=\frac{z_{1}\overline{z2}}{|z_{2}|^{2}}=\frac{(a+bi)(c-di)}{|z_{2}|^{2}}=\frac{ac-bd+i(bc-ad)}{|z_{2}|^{2}}$$ hence $$Re\left(\frac{z_{1}}{z_{2}}\right)=\frac{Re(z_{1})Re(z_{2})-Im(z_{1})Im(z_{2})}{|z_{2}|^{2}}$$ Thus, $$Re\left(\frac{\cos(x)^{n}-1}{\cos(x)-1}\right)=\frac{(\cos(nx)-1)(\cos(x)-1)-\sin(nx)\sin(x)}{(\cos(x)-1)^{2}+\sin^{2}(x)}=\frac{\cos(nx)\cos(x)-\cos(nx)-\cos(x)+1-\sin(nx)\sin(x)}{\cos^{2}(x)-2\cos(x)+1+\sin^{2}(x)}=\frac{\cos(nx)\cos(x)-\cos(nx)-\cos(x)+1-\sin(nx)\sin(x)}{-2\cos(x)+2}=\frac{\cos(nx)\cos(x)-\cos(nx)-\cos(x)+1-\sin(nx)\sin(x)}{-2(\cos(x)-1)}= \frac{=\cos(nx)\cos(x)-\cos(nx)-\cos(x)+1-\sin(nx)\sin(x)}{-2(-2\cdot\sin^{2}(x/2))}=\frac{\cos(nx)\cos(x)-\cos(nx)-\cos(x)+1-\sin(nx)\sin(x)}{4\sin^{2}(x/2)}=\frac{\cos(nx)\cos(x)-\cos(nx)-\cos(x)+1-\sin(nx)\sin(x)}{4\sin^{2}(x/2)}=\frac{\cos(x(n+1))-\cos(nx)-\cos(x)+1}{4\sin^{2}(x/2)} $$ This is the part where I am stuck, I would appriciate any help or hint on how to continue. Edit: Given the corrections by André I get: $$(\cos(nx+x)-1)(\cos(x)-1)+\sin(nx+x)\sin(x)=\cos(nx+x)\cos(x)-\cos(nx)-\cos(x)+1+\sin(nx+x)\sin(x)$$ so $$\cos(nx+x)\cos(x)+\sin(nx+x)\sin(x)=\cos(xn+x-x)-\cos(nx)=0$$ Edit 2: I found anoter mistake in the above, I will try to correct Edit 3: When multiplying correctly the above it works out :-) Ways of getting three of a kind in a 52 card deck This question has probably been asked before, but just to be clear here, I am NOT asking for the answer, I know the answer.  What i want to know is why my solution is not equivalent to the actual solution.  Three of a kind in a deck means you draw 3 cards of the same rank, and 2 other cards each of different ranks.  So. The solution in my book is the following: (13 C 1)(4 C 3) * (12 C 2)(4 C 1)(4 C 1)  The logic is the following:  1) Choose 1 out of the 13 ranks, then for the 4 cards in the chosen rank, pick 3.  2) Choose a combination of 2 ranks from the remaining 12, then for the 4 cards in each rank, choose 1.  Total combinations: 54912  My solution is the following:  ((13 C 1)(4 C 3)) * ((12 C 1)(4 C 1)) * ((11 C 1)(4 C 1))  1) My logic for the 3 of a kind is the same as the solution.   2) Choose 1 of the remaining 12 ranks, and 1 card from the 4 cards in the rank.  3) Choose 1 of the remaining 11 ranks, and 1 card from the 4 cards in the rank.  Total combinations: 109824  My solution says that the combinations are exactly double of the book's solution.  I'm just very confused as to why this is. If anyone could explain this to me I would be very appreciative, thank you. Colors and legend in groupplots/barplot In order to compare three items I use the groupplot command. For each item I have n different criteria to compare.    Is it possible to set the color for each criteria itself? Meaning the first bar in every group goes gray, the second pink etc.. The legend than should contain the n compared criteria.  And... how do I manage to let the whole tikz-picture have a width of 0.9\textwith  \documentclass{standalone} \usepackage{pgfplots,pgfplotstable} \usetikzlibrary{pgfplots.groupplots}  \pgfplotstableread{ nr  fii faa foo a   10  15  12 b   12  18  14 c   13  19  15 d   9   13  10 e   7   11  8 f   10  15  12 }\datatable  \begin{document} \begin{tikzpicture} \begin{groupplot}     [group style={columns=3},         ybar,         ymin=0,         ymax=20,         xtick=\empty,         tickpos=both]  \nextgroupplot[xlabel=fii] \addplot [fill=blue] table [x expr=\coordindex, y=fii] {\datatable}; \nextgroupplot[xlabel=faa] \addplot [fill=green] table [x expr=\coordindex, y=faa] {\datatable}; \nextgroupplot[xlabel=foo] \addplot [fill=red] table [x expr=\coordindex, y=foo] {\datatable};  \end{groupplot} \end{tikzpicture} \end{document} When it's OK to omit "where?" Most efficient way to see if an ArrayList contains an object in Java I have an ArrayList of objects in Java.  The objects have four fields, two of which I'd use to consider the object equal to another.  I'm looking for the most efficient way, given those two fields, to see if the array contains that object.  The wrench is that these classes are generated based on XSD objects, so I can't modify the classes themselves to overwrite the .equals.    Is there any better way than just looping through and manually comparing the two fields for each object and then breaking when found?  That just seems so messy, looking for a better way.  Edit: the ArrayList comes from a SOAP response that is unmarshalled into objects. I tried control+shift+power button as well as command+shift+power button. Neither seem to work. Please provide a way to download SEDE data via an API I recently suggested on the Stack Apps site that , and it was suggested I reference the feature request here, for visibility.  My use case is a query that the API does not support, so I thought it would be interesting to get it programmatically from SEDE instead. I wonder if this feature might be of interest to others here?  outlines the current ways that SE data is available via various APIs and UIs.  I wonder if my use case (retrieving revisions filtered by user) might have been supported by OData,  since April of this year.  This question has sort-of , though that was not an explicit feature request, and is now rather out of date. It would be good to find out what the current views are on this topic, and indeed whether there is much demand.  My use-case does not urgently require this, since I can use public SE screen scraping or SEDE CSV downloading. From reading around the SE Meta network, both of these approaches seem to be tolerated, as long as it is done with careful regard to frequency and bandwidth. "You're too clever a man" Using Integration By Parts results in 0 = 1 I've run into a strange situation while trying to apply Integration By Parts, and I can't seem to come up with an explanation.  I start with the following equation:  $$\int \frac{1}{f} \frac{df}{dx} dx$$  I let:  $$u = \frac{1}{f} \text{ and } dv = \frac{df}{dx} dx$$  Then I find:  $$du = -\frac{1}{f^2} \frac{df}{dx} dx \text{ and } v = f$$  I can then substitute into the usual IBP formula:  $$\int udv = uv - \int v du$$  $$\int \frac{1}{f} \frac{df}{dx} dx = \frac{1}{f} f - \int f \left(-\frac{1}{f^2} \frac{df}{dx}\right) dx$$  $$\int \frac{1}{f} \frac{df}{dx} dx = 1 + \int \frac{1}{f} \frac{df}{dx} dx$$  Then subtracting the integral from both sides, I've now shown that:  $$0 = 1$$  Obviously there must be a problem in my derivation here...  What wrong assumption have I made, or what error have I made?  I'm baffled. Unable to preserve ownership in a copy but able with a move? Best practice for typesetting quantifiers? When I work with quantifiers I noted that are very close to the other symbols and the result does not look good, for example  $\exists a\in\mathbb{R}\exists b\in\mathbb{R}\forall c\in\mathbb{R}\forall d\in\mathbb{R}$   Which is the proper form to write quantifiers? I've noticed that if I downvote an answer, the record of the downvote is visible to me in my profile.  But when I view my profile from another browser that's not logged into Stack Overflow, I've noticed that I don't see the record of the downvote.  So I was wondering if the downvote record is visible only to me?  If so, is this done to protect downvoters from retaliation? What's the difference between MathOverflow & Mathematics.SE? If I have a maths question, on which site should I ask:  or ?