I am trying to take the inverse Fourier transform of $\frac{1}{k^2+a^2}$. I know what the answer is (something like $e^{-|x|}$), but I'm having trouble actually doing the integral in the inverse Fourier transform.  First I noted that $\frac{1}{k^2+a^2}$ is even in $k$, so it's inverse Fourier transform is $$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty \frac{1}{k^2+a^2} \cos(kx) dk$$  Where do I go from here? I tried integration by parts, but that didn't lead anywhere. And looking at the Fourier transform of  $e^{-|x|}$ didn't really help.  Ideas?
I need help to calculate the  Fourier transform of this funcion  $$b(x) =\frac{1}{x^2 +a^2}\,,\qquad a &gt; 0$$ Thanks.
Text won't appear in interface? There is one problem, it seems that text won't appear on my program. The three images show the errors and also my laptop specs (I believe I just have very small amount of laptop power that makes Blender glitch).  Everything else works fine (zooming, panning, rotating, etc.) and the buttons are still there and do what they're supposed to do, but the text just won't appear.  Might anybody know how to fix this?        The drive update didn't help either. I know a way around it though, does anybody know a page which shows screenshots of more or less the buttons on blender This is about the seemingly controversial shield to ground connection. The system is basically a body-worn intel-based computer, powered by a battery. Two USB 3.0 (or 3.1 Gen1) cables come out to a PCB that contains two USB 3.0 hub chips (). Two external cameras plug in to this usb hub PCB (one camera for each hub). So the usb hub PCB has 4 usb connectors (2 upstream and 2 downstream).  The question is, what to do with each of the usb connector shields? The main directive is USB connection robustness.  I have seen many recommendations. For example:  Recommendation 1  TI's TUSB8020B hub reference design  ties all shells directly to ground.    Intel's  also recommends to tie to ground (although this was written for USB 2.0).    Recommendation 2  TI's TUSB8020B EVM (and datasheet) connect shields together, and to ground using RC filter:    Microchip's  also ties shields together and uses an RC filter, but a 3 orders of magnitude smaller R:    Recommendation 3  Cypess  ties each shield independently to ground using either LC or L filter (chokes really):    The cameras themselves (off the shelf) use Cypress recommendation (LC to ground). The embedded computer seems to tie to ground from visual inspection and checking continuity to ground, but I'm not 100% sure (schematics are not available).  Now we face the shield dilemma with the hub PCB (which by the way currently does not have a metallic enclosure, it is a 3d printed plastic enclosure).   What is your say? Help finding this set Lets define the following:  Let A be a set. A is innumerable if and only if there exists a bijective function from A to $\mathbb{N}$  Proof that there exists an innumerable set $B \subseteq \mathcal P \left({\mathbb{N}}\right)$ such that it has the following properties:  1) $X\cap Y =\emptyset$ for all $X,Y \in B$ such that $X \neq Y$  2) $\mathbb{N}= \bigcup B$  3) All elements of B are innumerable.  Any help is appreciated. I don´t know how to find this set ... How would I shift my whole set of equations/calculations at the left, to be aligned with "Example"?        \documentclass[11pt,a4paper]{report} \usepackage{amsmath,amsfonts,amssymb,amsthm,epsfig,epstopdf,titling,url,array} \usepackage{parskip}   \theoremstyle{plain} \newtheorem{thm}{Theorem}[chapter] % reset theorem numbering for each chapter \newtheorem{lem}[thm]{Lemma} \newtheorem{prop}[thm]{Proposition} \newtheorem*{cor}{Corollary}  \theoremstyle{definition} \newtheorem{defn}[thm]{Definition} % definition numbers are dependent on theorem numbers \newtheorem{exmp}[thm]{Example} % same for example numbers \newtheorem{conj}[thm]{Conjecture}  \theoremstyle{remark} \newtheorem*{rem}{Remark} \newtheorem*{note}{Note}   \title{My Thesis Title} \author{My Name} \date{\today} \renewcommand\labelenumi{(\theenumi)} \renewcommand\theenumi{\roman{enumi}} \setlength{\parindent}{1em}  \begin{document}  \chapter{Addition}  \begin{exmp}  Here is an example. \begin{align} \nonumber (a+b)^3 &amp;= (a+b)^2(a+b)\\ \nonumber &amp;=(a^2+2ab+b^2)(a+b)\\ \nonumber &amp;=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\ \nonumber &amp;=a^3+3a^2b+3ab^2+b^3 \nonumber \end{align} \end{exmp} \end{document} I have a dedicated server with 2 TB storage.   My problem is that the whole storage is allotted to the root partition.   Whenever I try to resize it using lvresize, the root partition gets corrupted and then I have to reprovision the server.   Is there any option to resize the root partition without unmounting in lvm?  I am trying to reduce the root partition to 100GB.  Vgs  root@s93079:/home/customer# vgs   VG        #PV #LV #SN Attr   VSize VFree   s93079-vg   1   2   0 wz--n- 1.82t    0   Lvs  LV     VG        Attr       LSize  Pool Origin Data%  Meta %  Move Log Cpy%Sync Convert   root   s93079-vg -wi-ao----  1.79t    swap_1 s93079-vg -wi-ao---- 32.00g   Fdisk - l  Device     Boot  Start        End    Sectors  Size Id Type /dev/sda1  *      2048     499711     497664  243M 83 Linux /dev/sda2       501758 3907028991 3906527234  1.8T  5 Extend /dev/sda5       501760 3907028991 3906527232  1.8T 8e Linux  Disk /dev/mapper/s93079--vg-root: 1.8 TiB, 1965782204416 byt es, 3839418368 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk /dev/mapper/s93079--vg-swap_1: 32 GiB, 34355544064 byte s, 67100672 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes   Vgdisplay   --- Volume group ---   VG Name               s93079-vg   System ID   Format                lvm2   Metadata Areas        1   Metadata Sequence No  3   VG Access             read/write   VG Status             resizable   MAX LV                0   Cur LV                2   Open LV               2   Max PV                0   Cur PV                1   Act PV                1   VG Size               1.82 TiB   PE Size               4.00 MiB   Total PE              476870   Alloc PE / Size       476870 / 1.82 TiB   Free  PE / Size       0 / 0   VG UUID               dPrEwA-77pM-pGai-9jZB-ldMZ-iL20-HAe9 Dj   lvdisplay /dev/s93079-vg/root   --- Logical volume ---   LV Path                /dev/s93079-vg/root   LV Name                root   VG Name                s93079-vg   LV UUID                bpGNau-XirV-P7PA-8d6k-OCOy-TAwN-HXl FVI   LV Write Access        read/write   LV Creation host, time s93079, 2016-08-27 09:22:05 -0500   LV Status              available   # open                 1   LV Size                1.79 TiB   Current LE             468679   Segments               1   Allocation             inherit   Read ahead sectors     auto   - currently set to     256   Block device           254:0   Lvdisplay /dev/s93079-vg/swap_1  --- Logical volume ---  LV Path                /dev/s93079-vg/swap_1  LV Name                swap_1  VG Name                s93079-vg  LV UUID                j74PLZ-E9gK-9Bbb-EkKq-xRJv-TuU4-FgH gm  LV Write Access        read/write  LV Creation host, time s93079, 2016-08-27 09:22:05 -0500  LV Status              available  # open                 2  LV Size                32.00 GiB  Current LE             8191  Segments               1  Allocation             inherit  Read ahead sectors     auto  - currently set to     256  Block device           254:1   Df - h  /dev/dm-0       1.8T  923M  1.7T   1% / udev             10M     0   10M   0% /dev tmpfs           3.2G  8.5M  3.2G   1% /run tmpfs           7.9G     0  7.9G   0% /dev/shm tmpfs           5.0M     0  5.0M   0% /run/lock tmpfs           7.9G     0  7.9G   0% /sys/fs/cgroup /dev/sda1       236M   33M  191M  15% /boot Convergent or divergent $\sum_{n=1}^{\infty} \frac{e^nn!}{n^n}$? Any suggestion/hint, not the whole solution, how to determine convergence/divergence of $$ \sum_{n=1}^{\infty}\dfrac{e^n \cdot n!}{n^n} $$ I'm currently stuck. I am indian citizen on H1b visa in US. I am planning to visit France in Oct 2014. Can I apply for Schengen visa now about 3/4 months in advance. Are there any restrictions that on early you can apply for Schengen visa. What is an observer in quantum mechanics? My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.  What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally? How did they dispose old Joe's wife's body in the movie Looper (2012)? The reason given in the movie Looper for sending targets to the past is that it is difficult to dispose bodies.  From ,     Thirty years into the future in 2074, time travel is invented, but is   immediately outlawed. However, because by that point tracking   technology has rendered it nearly impossible to dispose of bodies   secretly, crime bosses turn to time travel to send their targets to   the past to be killed using "loopers": hired guns paid in silver to   kill whoever is sent to them.   When trying to capture old Joe, they kill his wife. So how did they dispose the body of his wife? Or is it difficult to dispose bodies only in US and not in China? And they came for old Joe only because the Rainmaker wanted to close the loops?  Could someone explain? What am I missing? Is there a way to make a fullscreen on VirtualBox? I tried many ways to make a bigger screen in VirtualBox because I do not like the small size of the guest window? Is there is a way to make it big? Show that $S$ is compact. Let $A \in M_n(\bf C)$ and let   $S=\{ A \in M_n(\bf C) : A=A ^*$ and  $\rho (A) \leq 1 \}$, $\rho(A)$ denotes spectral radius of $A$.     Show that $S$ is compact subset of $M_n(\bf C) \cong \bf C^{n^2} $ with usual topology.    $S$ is subset of $\bf O_n(C)$ which is compact so I think its enough to show that $S$ is closed.Please help. What does "all the more" mean and how is it used? Here is a sample context:     As you might expect, the framework also provides some convenience   classes to make the task of writing custom validators all the more agreeable.   (Emphasis added.) mv * folder (avoiding 'cannot move' error) Output two sided, but only on recto page -- occasional images on verso I am preparing a thesis. In order to reduce the number of physical sheets of paper, I need to print certain figures/tables on the verso side. However the university regs state that, while figs/tables may appear on the verso, the body text must appear on the recto side.  I would like to therefore output the vast bulk of the work on the recto page, but with occasional verso pages. Ideally they would be numbered as a "subpage" of the preceeding recto page (e.g. 131, 131a, 132...) or similar.  The approach which I will tentatively adopt is to use a "twoside" flag, then have "empty" and non-numbered verso pages until a page with content is required.   I'm sure I'm not the first person to have had a similar issue, but am unable to imagine other ways of posing the question. Enumerate paragraphs and subparagraphs like sections but with letters I'm using pandoc and in my template.tex exists this code to make the paragraphs and subparagraphs to behave like sections.  % Redefines (sub)paragraphs to behave more like sections \ifx\paragraph\undefined\else \let\oldparagraph\paragraph \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}} \fi \ifx\subparagraph\undefined\else \let\oldsubparagraph\subparagraph \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}} \fi   This code generate number like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.1 paragraph  1.1.1.1.1.1 subparagraph   How to change this code to enumerate with letter like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.a paragraph  1.1.1.1.a.a subparagraph I noticed that if I run ls -F on a directory, some of the entries have a * or a @ after them.   spuder@ubuntu:~$ ls -F /sbin acpi_available*   getpcaps*           lvmconf*                 ntfscp*        start-stop-daemon* agetty*           getty*              lvmdiskscan@             ntfslabel*     status@ alsa*             halt@               lvmdump*                 ntfsresize*    stop@ alsactl*          hdparm*             lvmsadc@      spuder@ubuntu:~$ ls -F ~ daq-0.6.1/  examples.desktop       noname-cache.lib  snort-2.9.1/   Templates/ Desktop/    jpgraph-1.27.1/        noname.sch        snortfiles/    Ubuntu One/ Documents/     According to the ls man pages   spuder@ubuntu:~$ man ls ... -F, --classify   append indicator (one of */=&gt;@|) to entries ...   I'm guessing that @ means symbolic link,     What do these other indicators mean ( */=&gt;@| )  ? Software to draw illustrative figures in papers I would like to have suggestions of good software for drawing illustrations in research papers. I already know about , but this works only on Linux and is at times, clunky when it comes to text. Moreover the resolution is not always perfect making it difficult to manoeuvre the objects. Besides it is tough to learn and master, with all its weird click procedures.   I would love to know about better alternatives. Not talking about graphs here, just block diagrams and explanatory illustrations. java.lang.ClassNotFoundException: org.apache.struts2.dispatcher.ng.filter.StrutsPrepareAndExecuterFilter What's the deal with the phrase "could care less"?  Whilst growing up, I've always known people (parents etc) to use the phrase "couldn't care less", but I've also come across people who use the phrase "could care less" to mean the same thing (that is, "I do not care at all about that").  To me "couldn't care less" seems a lot more logical. If I couldn't care less about something, that implies I do not care about it at all. In contrast to this, to my mind the phrase "could care less" seems to indicate "I do care about this to some degree at least", but that's definitely not the meaning intended.  What's going on here? Is my (logical) analysis correct or in error? How could Argus Filch clean up the whole castle by himself without magic?