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Change the passphrase of an ecryptfs directory Derivatives of $ \frac{1}{r} $ and Dirac delta function I am trying to understand the formula \begin{equation} \nabla^2\left(\frac{1}{|{\bf r}-{\bf r}'|}\right) = - 4 \pi \delta(\bf{r}-\bf{r}'), \qquad\qquad {\rm (I)} \end{equation} where ${\bf r}=(x,y,z)$. This is something heavily used in electrostatics and the steps to 'show' this is often the following: The first derivative reads \begin{equation} \nabla \frac{1}{| {\bf r} - {\bf r}' |} = - \frac{ {\bf r} - {\bf r}'}{| {\bf r} - {\bf r}'|^3} \end{equation} And taking the second derivative gives zero, except for the singularity at ${\bf r} = {\bf r'}$. Then from the divergence theorem we have \begin{equation} \int dV \,  \nabla^2 \frac{1}{| {\bf r} - {\bf r'}|} = \int dS  \,\,{\bf n} \cdot ( \nabla\frac{1}{|{\bf r} - {\bf r}'|}) = -4 \pi \end{equation} where the integration is performed over a sphere centered at ${\bf r}'$. Q1: Is there a more direct proof for equation (I)? Then my main question is about the separate second-order differentials. For instance, we can obtain, by direct computation \begin{equation} \partial_x^2 \, \frac{1}{| {\bf r} - {\bf r}'|} = \frac{ 3 (x-x')^2 }{| {\bf r} - {\bf r'} |^5} - \frac{1}{| {\bf r} - {\bf r}'|^3} \end{equation} Q2: Should there be a $\delta$ function on the r.h.s of this equation? If you have a statically allocated array, the Visual Studio debugger can easily display all of the array elements.  However, if you have an array allocated dynamically and pointed to by a pointer, it will only display the first element of the array when you click the + to expand it.  Is there an easy way to tell the debugger, show me this data as an array of type Foo and size X? What does "in spades" mean? C# Structs: Unassigned local variable? css vertical centering how could i vertically center a &lt;div&gt; within a &lt;div&gt; ?  my code so far:  &lt;div style="height:322px;overflow:auto;"&gt;     &lt;div style="border: Solid 1px #999999;padding:5px;"&gt;     &lt;/div&gt; &lt;/div&gt;   i have tried "top:50%;" and "vertical-align:middle;" without success  EDIT: okay so it's been discussed a lot. and i've maybe started another mini flame war. but for argument sake, how would i do it with a table then? i've used css for everything else so far so it's not like i'm not trying to employ "good practices".  EDIT: the inner div does not have a fixed height How to look up a symbol or identify a letter from a math alphabet or other character? OAuth 2.0 access token request failed with error "must use HTTP POST" OAuth 2.0 Auth token request failed with below error   { "error": "invalid_request", "error_description": "must use HTTP POST" }   What does this error mean?  I am using Postman. Have a connected app. I have used Post method, Url has https. Same request works for other Orgs. Did I missed any configuration/Permission check?  https://testOrg.lightning.force.com/services/oauth2/token?grant_type=password&amp;client_id={{CLIENT_ID}}&amp;client_secret={{CLIENT_SECRET}}&amp;username={{USER_ID}}&amp;password={{PASSWORD}} This is a trivial problem, but it annoys me that I can't get to the bottom of it:  I'm running Windows 8, Powershell version 3.0. By right-clicking on the title bar I can go into the Properties and change the font, size, background colour etc without any problems.  After closing and restarting Powershell, all of the changes I've made stick except that if I've set the font to Lucida Console then on reopening I get the Raster font.  (Note that all of the above applies to when I run Powershell as Administrator.)  So:   If I set the font to Lucida, then it switches to Lucida for the remainder of the session. If I set the font to anything other than Lucida, then it stays as that after closing and reopening. If I alter the window sizes or text colours or anything else, the changes persist after reopening. The only thing that goes wrong is that if I set the font to Lucida, it switches to 'Raster fonts' when I reopen. But cmd and powershell ISE don't have this problem - only the powershell console.   Can anyone suggest what might be going wrong?  (One observation I've made is that upon re-opening Powershell after setting the font to Lucida, at first the width of the window is what it would be if the font were Lucida, but then after a second, it widens slightly to accommodate the raster font.) Recovering a accidently deleted file in Ubuntu I'm using ubuntu 9.10 and accidently deleted a specific file within a directory on my system. I checked in the Trash bin and could not locate the file. I deleted it 10mins ago, are there any tools available that I can recovery this file? It's a really important file.  Any help would be highly appreciated  My partition is ext4 How to Connect & Share your Internet Connection (Wired & Wireless) I have Ubuntu 12.04 on a HP 430 notebook and this has a single wired internet connection and I would like to share this with a LG Optimus One with Android 2.3.3. I followed  instructions and created a hotspot as shown below, but UbuntuHost is not visible on the LG Optimus One when I enable the Wifi on it.  To summarize, I want my Laptop with an internet connection to act as a WiFi router and access the internet from other devices (LG Optimus One with Android in this case).  What additional steps have to be done? How do Minecraft biomes work? I've never seen any information about the distribution of biomes in a generated world.   First, are all types of biomes, guaranteed to exist in a world? Will I always find snow somewhere, and desert somewhere? I've got one world that doesn't seem to have cactus (so I guess the sand is beaches, no actual desert).  Second, is there any kind of pattern or relation to biomes? Is snow to the North, and desert South, for example?  Third, how about density of biomes? If all types do exist, would I find them all within distance X of my spawnpoint, or have to travel for weeks to find a given type? Age of universe? Well relativity teaches us that time interval between two events is a frame dependent quantity, then how can we say that our universe is 13.8 billion years old? Should it not depend on who is asking this question? First off I'll let you know I'm a total noob at blender I've used 3ds Max up until this point, but the company I'm working for at the moment needs me to use blender so I'm trying to make the transition over.  Literally all I'm making at the moment is a simple book and cannot understand how the bevel tool isn't working similar to how the chamfer tool would in 3ds Max.  I want a nice curved edge for the spine of the book however when I press control + B and try to bevel it bevels the edge unevenly with the new bevel pushing forward.    Is there a way I can get it to bevel evenly like it does in Max? How to tell if a travel location is "affordable"? Disclaimer: The locations are just examples to set up the question and all prices are made up for the sake of the example and question.  Background: Let's say I want to visit London or Busan, and my currency is USD. While comparing the two locations I notice their exchange rates. 1 USD is 0.60 GBP, while 1 USD is 1,200 KRW.   Question: Are there traveler's tips and/or tools when it comes to currency exchanges where I know how much I can get for my "dollar" in a certain travel location? To use the exchange rate above as an example, consider the following. A bottle of water in London costs 0.40 GBP while a bottle of water in Busan costs 2,000 KRW. How would I know the relative value of goods I can get for my "dollar"?  I found  that provides that information but I'm wondering if there are other travel tips or anything to answer my question.   Edit: I replaced Korea with Busan to give it a more precise location and to keep it on the same level as London. Is there more to an interface than having the correct methods So lets say I have this interface:  public interface IBox {    public void setSize(int size);    public int getSize();    public int getArea();   //...and so on }   And I have a class that implements it:  public class Rectangle implements IBox {    private int size;    //Methods here }   If I wanted to use the interface IBox, i can't actually create an instance of it, in the way:  public static void main(String args[]) {     Ibox myBox=new Ibox(); }   right? So I'd actually have to do this:  public static void main(String args[]) {     Rectangle myBox=new Rectangle(); }   If that's true, then the only purpose of interfaces is to make sure that the class which implements an interface has got the correct methods in it as described by an interface? Or is there any other use of interfaces? My objects are semi-transparent, and not one behind the other in the compositor How to access the Keyboard Layout Options in 13.10+ How to address a professor in letter? I'll like to add this functionality to the autocomplete widget in Entityreference field to show node ID next to the titles in the dropdown list. The reason behind the idea is to differentiate between multiple nodes with same title.  Example:    This is a title (3) This is a title (2) This is a title (1)   I know the node ID is shown once a selection is made but I like to show it in the dropdown list in order to pick the right node quickly based on the node ID.