Duplicating and arranging a list
List creation/manipulation
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $ I'm having trouble calculating the integral  $$\int_{- \infty}^\infty \frac{\sin x}{x+i}\,dx $$  using residue calculus. I've previously encountered expressions of the form   $$\int_{- \infty}^\infty f(x) \sin x \,dx $$  where you would consider $f(z)e^{iz}$ on an appropriate contour (half circle), do away with the part of the contour that wasn't on the real axis by letting the radius go to infinity, then recover the imaginary part of the answer to get back the sine. However here, I can't replace the sine with $e^{iz}$ in my complex function because $$\operatorname{Im} \frac{e^{ix}}{x+i} \neq \frac{\sin x}{x+i}\cdots$$  How to remedy this? I'm not sure if substituting $\sin x = \frac{1}{2i}(e^{ix}-e^{-ix})$ and solving two integrals is how this problem is meant to be solved, although I'm 99% sure it would work What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for all.  $$\frac{\partial y}{\partial x}, \frac{\delta y}{\delta x}, \frac{\mathrm{d} y}{\mathrm{d} x}$$   For what I know, $\mathrm{d}$ is used as a small infinitisemal change (and I guess the straight-up letter $\mathrm{d}$ is usual notation instead of italic $d$, simply to tell the difference from a variable). Of course we also have the big delta $\Delta$ to describe a finite (non-negligible) difference. And I have some vague idea that $\partial$ is used for partial derivatives in case of e.g. three-dimensional variables. Same goes for $\delta$, which I would have sworn was the same as $\partial$ until reading this answer on Math.SE:    Then to make the confusion total I noticed an equation like $\delta Q=\mathrm{d}U+\delta W$ and read in a physics text book that:     The fact that the amount of heat [added between two states] is dependent on the path is indicated by the symbol $\delta$...   So it seems $\delta$ means something more? The text book continues and says that:     a function [like the change in internal energy] is called a state function and its change is indicated by the symbol $\mathrm{d}$...   Here I am unsure of exactly why a $\mathrm d$ refers to a state function.   So to sum it up: down to the bone of it, what is $\delta$, $\partial$ and $\mathrm{d}$ exactly, when we are talking derivatives in physics.  Addition  Especially when reading a mathematical process on a physical equation like this procedure:  $$\delta Q=\mathrm{d}U+p\mathrm{d}V \Rightarrow\\ Q=\Delta U+\int_1^2 p \mathrm{d}V$$  It appears that $\delta$ and $\mathrm{d}$ are the same thing. An integral operation handles it the same way apparently? Reasons not to use a 741 op-amp? Error: invalid environment block. Press any key to continue...   The error message appears immediately after the boot screen on purple background. Ubuntu 12.04.1 LTS. While drawing a simple 3D (fake 3D in fact) cube, I realized that the corners end up with unwanted extensions of the line. I understand this is related to the width of the lines themselves, but how can I remove them? An alternative solution of drawing the desired figure is also welcomed.  Example:  \documentclass{article} \usepackage{tikz}   \begin{document} \begin{tikzpicture}  \draw[draw=black,fill=gray!20] (0,0) --(4.8,0)-- (4.8,5)--(0, 5)--cycle; \draw[draw=black,fill=gray!20] (4.8,5) -- (4.9,4.8)--(4.9,-0.1)--(4.8,0)--cycle; \draw[draw=black,fill=gray!20] (0,0) -- (0.1,-0.1)--(4.9,-0.1)--(4.8,0)--cycle; \draw[dashed,draw=black] (4.8,5) -- (4.9,4.8)--(0.1,4.8)--(0.,5)--cycle; \draw[dashed,draw=black] (0.1,-0.1)--(0.1,4.8)--(0.,5)--(0,0)--cycle; \end{tikzpicture} \end{document} Why do I get (author?) when I use \citet with natbib? I would like to show the author names using \citet but I get just the reference number. Here is a minimal code:  \documentclass{report} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{natbib}  \begin{document}   The author \citet{toschi09} has shown that ..  \bibliographystyle{plain} \bibliography{foo}  \end{document}   And here is foo.bib  @article{toschi09, author = {Toschi, F. and Bodenschatz, E.}, title = {Lagrangian Properties of Particles in Turbulence}, journal = {Annual Review of Fluid Mechanics}, volume = {41}, number = {1}, pages = {375-404}, year = {2009},  }   What I get is:     The author (author?) [1] has shown that ..   Any help will be more than welcome, thank you! Say I want to book a flight from Fort Lauderdale to Chicago.  Say the airline also flies to St. Louis from Fort Launderdale but has a connecting flight through Chicago.  If I book that flights from FLL->ORD->STL and just get off in Chicago, what possible problems can I run into, assuming I didn't check any bags and only have carry on?  This scenario exist for Southwest, but I wanted this be more of a general question that would apply to all airlines. How to prevent automatic redirection of 404 errors and "incorrect" URLs? Wordpress has a feature whereby it will automatically redirect your URLs if it percieves them to be written wrongly. Here is an example: I have a page called my-page  If I go to:  www.mysite.com/something/my-page/   it will immediately redirect me to   www.mysite.com/my-page/   as nothing exists at the first URL.   How can I turn this feature off, and instead just get a 404 if incorrect URL's are typed in? I'm using ubuntu 14.04 LTS. When I start my pc and click on any bookmark from the file manager it shows this error:   Unable to find the requested file. Please check the spelling and try again. Unhandled error message: Error when getting information for file '/media/angel/DOC/edu': No such file or directory   But when I open DOC drive and again clink on the same bookmark it works properly. Can anybody tell me why is this happening and how to solve this issue?   Edit: Output of lsblk is following: (ubuntu is installed in sda5)  NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part  ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom     After opening the disk drive the output of lsblk is bellow:   NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part /media/angel/DOC ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom   The output of sudo blkid gives the following information about sdb6:  /dev/sdb6: LABEL="DOC" UUID="04280A22280A12FA" TYPE="ntfs" Suppose $A$ is a 4x4 matrix such that $\det(A)=\frac{1}{64}$ Can spells or spell-like abilities do non-lethal damage? I'm working on a Paladin/Warlock combination, based off of , and as part of this, I noticed Miniman's remark that Repelling Blast won't be that useful, because as a Paladin, you want people up close and personal when you're in a combat situation, not further away.  However, as a Paladin, your creed sometimes leads you to not want to engage in full-blown combat with a potential adversary -- you may want to drive them off or incapacitate/capture them instead.  With this, I wonder: can Repelling Blast, or other spells and spell-likes (such as invocations), be made to do non-lethal damage?  If so, I'm thinking that it'd be useful in exactly that sort of situation -- halting someone/pushing them away without having to wade into a melee with them or blow them to smithereens. Is there a BNF grammar of the TeX language? I'm looking for a BNF grammar of the TeX language, does it exist?  EDIT  For those of us who are not computer scientists, a BNF grammar is one kind of formal description of a CFG: .  For those who don't know their Chomsky, a CFG is a , which means (very roughly) that substitutions can be made independently of their use context. I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra dimensions, and all these dimensions need to fit together in a way such that the extra dimensions are compactified (with a Calabi-Yau or $G_2$ structure).   My question, however is not about the possible $10$, $11$ or $26$ dimensional manifolds that may be possible, but about whether string theorists consider space-time as somehow quantized (or discrete), or rather as a continuous manifold, or are both options possible? In other words, can strings move continuously through space, or are there a discrete set of locations where strings can be, and does string theory rule out one of the options?  How about the same question in loop quantum gravity (LQG)? Should I think of the spin networks in LQG as describing a discrete space-time?  Thanks for your insight, or any references you may be able to provide! $C \otimes A \cong C \otimes B$ does not imply $A \cong B$ Let $R$ be a commutative unital ring and let $M$ be an $R$-module and let $S$ be a multiplicative subset of $R$.  Today I proved both of the following: $$ S^{-1} R\otimes_R S^{-1}M \cong S^{-1} M$$ and $$ S^{-1} R \otimes M \cong S^{-1} M$$  Now I'm slightly confused.      Either my proofs are wrong or $C \otimes A \cong C \otimes B$ does not imply $A \cong B$. But I can't come up with an example. Can someone give me an example? (Or tell me that my proofs are wrong.) How to decide whether to replace or repair? An idempotent operator is compact if and only if it is of finite rank Would you help me to solve this problem. Show that an idempotent operator on hilbert space is compact if and only if it has finite rank. “Unable to Connect to World” Minecraft PE 1.16.201 So my brother and I have been playing Minecraft together on our iPads for years now, but in September I got a new iPad Pro 3rd Generation and I’ve been having issues with Minecraft ever since. Every time we have tried to join each other’s worlds we get the message “Unable to connect to world”. Recently after the update on December 16th, it worked for about a week without having any issues, but now it has gone back to not letting us connect to the worlds. Both of us are able to connect to other people’s worlds, but not each other’s, we’ve tried many things to fix this but so far nothing has worked. If you have any ideas for what we should do please let me know, thank you so much! What are all the correct answers to the Squirrel's questions, and what is the reward when I get them all correct? I encountered The Squirrel at "A tree."              |   |                                                                         |   |                     "   Hello, I'm The                        |             |                        Squirrel. I can                        |             |                      provide you candies,                     |             |                      and lots of things.                                    |                      I know how much you                                    |        _.-'''-,      love candies. But I                                    |      .'        `\     feel alone in this                                    |     /           /          forest.       "                         |        |    /      .--^_^                                                   |        |    |     /  C ,,\                                                           |    |    |   \  _.)                           ___                            |     \   |   /  \                   ____.----'.-'                            |      '-, \./ \)\)               .-' --  __.-'                   |            \        `-/   );/           ___/  - _.-'                        |             \_________''--'-'________.-' --    /                            |              -   --        -  -     -     __.-'                                              -    --    -     --   --  /                                                 _________________________.-'                                 He asks you some questions. What are the correct answers, and what is the reward for getting them correct? Does "Going Infinite" necessarily end the game? Create an item in sharepoint calender when infopath form is submitted in sharepoint 2010 through workflow