How to derive this integral identity? There is a particular integral which comes up frequently in physics which a friend and I spent hours trying to figure out with no success. I don't know if this integral has a name so googling has been fruitless. Arfken states the solution in the back flap but I have no idea how to find it  $$\int_{-\infty}^{\infty}{\frac{e^{i\mathbf{k}^{.}\mathbf{r}}}{k^{2}+m^{2}}\frac{dk^{3}}{(2\pi)^{3}}}=\frac{e^{-mr}}{4\pi r}$$  Limits go from -inf to inf for all k. Note that k and r are vectors. Presumably r on the right hand side is $\lvert\mathbf{r}\rvert$ (I could be wrong).  If someone could show how this is derived or provide a link to its derivation it would be greatly appreciated.
Very difficult integral (for me) Could someone point me to an online resource where I can look up  $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty \frac{\cos(\vec k\cdot\vec x)}{\sqrt{|\vec k|^2+m^2}}\,dk_1\,dk_2\,dk_3$$  where $\vec k$ and $\vec x$ are 3-vectors, and $m$ is a constant.  Also, if you know how to do it step by step and want to show off your fancy integration, that would also be very helpful.  Thanks ;)
Vim-latex adds extra brackets when typing empty brackets how to change the distance between tick mark and tick label I'm being asked to determine if $\displaystyle\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ converges. So, using Cauchy's Condensation Test, I reduced the problem to one of determining the convergence of $\displaystyle\sum\limits_{n=3}^\infty\frac 1{n\ln (n\ln 2)}$. Am I on the right path, and how do I proceed from here? Is there a way to avoid "+canned.response" in the email address using Gmail's canned response feature If I set up a filter and send it a canned response, Gmail appends +canned.response to my username in the reply.  For example, given the filter "from:foo@example.com to:me@example.com" set up to send a canned response, when foo@example.com sends me an email the canned response comes from me+canned.response@example.com instead of me@example.com, exposing that I'm using a canned response.  Is there a way to avoid this? VAR/VECM/ARDL optimal lag selection Question 1: Is it necessary to consider AIC and the BIC criteria when selecting the lag for a VAR, VECM or ARDL model OR can I use something else?  Example: Can I pick 12 lags because the model simply produce great results when I do or do I have to use the AIC/SIC criteria?  Question 2: A simple google search tells me that its possible to select lag 4 when quarterly data, 12 when monthly etc. Is that a valid approach ? Understanding MCMC and the Metropolis-Hastings algorithm Over the past few days I have been trying to understand how Markov Chain Monte Carlo (MCMC) works. In particular I have been trying to understand and implement the Metropolis-Hastings algorithm. So far I think I have an overall understanding of the algorithm but there are a couple of things that are not clear to me yet. I want to use MCMC to fit some models to data. Because of this I will describe my understanding of Metropolis-Hastings algorithm for fitting a straight line $f(x)=ax$ to some observed data $D$:  1) Make an initial guess for $a$. Set this $a$ as our current $a$ ($a_0$). Also add $a$ at the end of the Markov Chain ($C$).  2) Repeat the steps bellow a number of times.  3) Evaluate current likelihood (${\cal L_0}$) given $a_0$ and $D$.  4) Propose a new $a$ ($a_1$) by sampling from a normal distribution with $\mu=a_0$ and $\sigma=stepsize$. For now, $stepsize$ is constant.  5) Evaluate new likelihood (${\cal L_1}$) given $a_1$ and $D$.  6) If ${\cal L_1}$ is bigger than ${\cal L_0}$, accept $a_1$ as the new $a_0$, append it at the end of $C$ and go to step 2.  7) If ${\cal L_1}$ is smaller than ${\cal L_0}$ generate a number ($U$) in range [0,1] from a uniform distribution  8) If $U$ is smaller than the difference between the two likelihoods (${\cal L_1}$ - ${\cal L_0}$), accept $a_1$ as the new $a_0$, append it at the end of $C$ and go to step 2.  9) If $U$ is bigger than the difference between the two likelihoods (${\cal L_1}$ - ${\cal L_0}$), append the $a_0$ at the end of $C$, keep using the same $a_0$, go to step 2.  10) End of Repeat.  11) Remove some elements from the start of $C$ (burn-in phase).  12) Now take the average of the values in $C$. This average is the estimated $a$.  Now I have some questions regarding the above steps:   How do I construct the likelihood function for $f(x)=ax$ but also for any arbitrary function? Is this a correct implementation of Metropolis-Hastings algorithm? How the selection of the random number generation method at Step 7 can change the results? How is this algorithm going to change if I have multiple model parameters? For example, if I had the model $f(x)=ax+b$.   Notes/Credits: The main structure of the algorithm described above is based on the code from an MPIA Python Workshop. Partition on sublists beginning with a certain marker elements How do you use unlocked rewards after each mission in Splinter Cell: Double Agent? In the PC version of Splinter Cell: Double Agent, how can you use the rewards that you receive after each mission? For example, the shotgun attachment, or the colored night vision?  My list shows that the rewards are there, but I can not figure out how to use them. 1.In classical mechanics, using Newton's laws, the ellipticity of orbits is derived. It is also said that the center of mass is at one of the foci.   2.Each body will orbit the center of the mass of the system.  My question is : Are the assumptions in 1 and 2 correct?   Follow up question : Assuming the distance from the centre of the mass to each body remains the same, do we have two bodies orbiting the centre of the mass of the system in an elliptical or circular orbit?   Finally : With elliptical orbits, if the heavier mass is supposed to be in one of the foci, if there is any significance to second focus, what is it? Is it a Lagrange point by any chance or does it have some other mathematical property? What is in the space between a nucleus of an atom and its electrons? permission reporting on sudoers I'm looking for a good, consistent and easy way to do a report of sudoers permissions for every user and group on the system. For users, I want the report to include permissions granted via group membership. What's the term for design ala "object.method1().method2().method3()"? What's the term for this design?  object.method1().method2().method3()   ..when all methods return *this?  I found the term for this a while ago, but lost it meanwhile. I have no clue how to search for this on google :) Also if anyone can think of a better title for the question, feel free to change it.  Thanks  Update-Gishu: After reading about it, I feel that your question is misleading w.r.t. code snippet provided.. (Feel free to rollback)  Method Chaining  object.method1().method2().method3()   Fluent Interfaces  private void makeFluent(Customer customer) {         customer.newOrder()                 .with(6, "TAL")                 .with(5, "HPK").skippable()                 .with(3, "LGV")                 .priorityRush();     } What does “{} \;” mean in find (in Linux)? Sometimes I see a command like  find . -name * -exec ls -a {} \;   I was asked to execute this.  What does {} \; mean here? I had an article, but I lost it.  It showed and described a couple of C/C++ tricks that people should be careful. One of them interested me but now that I am trying to replicate it I'm not being able to put it to compile.  The concept was that it is possible to change by accident the value of a const in C/C++  It was something like this:  const int a = 3;          // I promise I won't change a const int *ptr_to_a = &amp;a; // I still promise I won't change a int *ptr; ptr = ptr_to_a;  (*ptr) = 5;               // I'm a liar; a is now 5   I wanted to show this to a friend but now I'm missing a step.  Does anyone know what's missing for it to start compiling and working?  ATM I'm getting invalid conversion from 'const int*' to 'int*' but when I read the article I tried and it worked great. Does anybody know where to download the QGIS toolbar icons? What was the Historical Precursor for .NET Attributes? What languages or platforms influenced the .NET 1.0 Team to build-in the concept of Attributes from the very start? Was this an Aspect-Oriented thing? Serialization? or something else? I was still in VB6-land at this time, and never used any of the pre-1.0 .NET versions. I want to have a script that takes the current working directory to a variable. The section that needs the directory is like this dir = pwd. It just prints pwd how do I get the current working directory into a variable? iOS App stuck in 'Loading...' I tried downloading Tumblr yesterday but it never completed. At the moment I have an App icon stuck at 'Loading...'.  I have tried restarting the iPhone (holding down both home and side buttons at the same time) and I have also tried shutting down the iPhone (holding the side button and swiping).  I have also tried deleting it as usual (holding the icon down and choosing delete but it doesn't go away).  Any ideas on what I can do to get rid of this icon? Printing all instances of a class How to manipulate a CSV file with sed or awk? How can I do the following to a CSV file using sed or awk?   Delete a column Duplicate a column Move a column   I have a big table with over 200 rows, and I'm not that familiar with sed.