To prove $\sum_{n=0}^\infty \binom{r}{x}\binom{N-r}{n-x}=\binom{N}{n}.$
Prove equality between binomial coefficients.
How to query MongoDB with "like"? Limit FTP access only to the /var/www with vsftpd I am running vsftpd as ftp server on my linux (rasbian), I log in to the machine as a root user.  I would like to be still locked to using only /var/www, how can I configure vsftpd conf to accomplish it? More examples of Simpson's Paradox, barring the ones on Wikipedia, Titanic, and delayed flights. In Harry Potter, Do Spells Travel in a Straight Line? In the Harry Potter world, when a magical person casts a spell, sometimes they target a specific object, like when Harry has a wand only and needs his broom, he casts "Accio Firebolt" and his broom comes to him.  But a lot of the time people point their wands just in the direction of someone to cast a spell.  One example would be in a duel.  When they do this, are they casting a spell on a particular person or at that person?  It seems, from what I remember of the movies, that some spells travel in a straight line while others specifically target a person or object.  Do any spells travel in one direction, like a laser beam?  What kind of spells are directional (instead of focusing on a particular person or object)?  And can directional spells be deflected or blocked by something like a mirror or another physical object?  (By "directional," I could have said linear, but didn't want to start sounding mathematical or scientific.  In other words, do they travel in one direction, like a laser beam would, or will they change direction to hit the intended target?) While talking about ships and countries, is it a good practice to use the feminine form?  For example:  "Her economy" - while referring to a country's economy "Her flag (or deck etc)" - while referring to a ship  Is this practice common? Is it used today? Can I travel domestically within the United States with my USA expired passport? I need to fly domestically within the United States. The only ID I have is an expired USA passport.  Can I use that to pass T.S.A.?  Can I use it as ID? Possible Beamer bug: Frame number has different color than date in infolines footer I use TeX Live on Mac and I get my weekly updates through the TeX Live Utility. I am working on some slides for an upcoming talk. I am using the same Beamer templates and settings that I always use, so I was surprised to see that the page numbers that I always include at the bottom of my slides suddenly appeared in a different color. Here's an MWE:  \documentclass{beamer} \useoutertheme{infolines} \usecolortheme{beaver} \title{Title} \date{\today} %\setbeamercolor{page number in head/foot}{fg=darkred!60!black} \begin{document} \begin{frame} \end{frame} \end{document}     As you can see in the bottom right corner of the slide the page number appears but its color looks off. Until recently it would look exactly the same color as the date appearing next to it.  By Googling around a bit I managed to figure out how to get this to look normal again using the line commented out in the code above:  \setbeamercolor{page number in head/foot}{fg=darkred!60!black}   By uncommenting this line I got back the desired behavior:    So my question is not so much about how to fix this problem, but about why this is happening in the first place. Is this a bug that was introduced in a recent update, and if so will it be fixed? Is this a deliberate choice on the part of the developers (if so I can't imagine why)? Or am I doing something wrong or is something broken in my TeX setup?  I'd appreciate any insight on this. Thanks in advance! Where can I find my .emacs file for Emacs running on Windows? I tried looking for the .emacs file for my Windows installation for Emacs, but I could not find it. Does it have the same filename under Windows as in Unix?  Do I have to create it myself? If so, under what specific directory does it go? Differentiable functions satisfying $f'(f(x))=f(f'(x))$ I'm looking for a way to access raster layers in an Esri File-GeoDatabase without using ArcObjects or ArcPy, specifically I would like to access the raster layers with GDAL. I understand that the GDAL FileGDB and OpenFileGDB give access to vector datasets within File-GeoDatabases, and that ESRI's own FileGDB C++ API does not support raster access.   Is anyone out there aware of any open source solutions? I'm trying to make a basic Windows application that builds a string out of user input and then adds it to the clipboard. How do I copy a string to the clipboard using Python? Continuous Images of $GL_n(\mathbb{R})$ Which of the following is a continuous image of $GL_n(\mathbb{R})$?  The real line $\mathbb{R}$  The subspace $\{(x,\frac1x):x\in \mathbb{R},x \ne 0\}$ of $\mathbb{R}^2$  $\mathbb{R}^2 \setminus \{(x,\frac1x):x\in \mathbb{R},x \ne 0\}$  $\{(x_1,x_2,...,x_n):x_1^2+x_2^2+...+x_n^2 \le 1\}$ of $\mathbb{R}^n$   How do I proceed? $GL_n(\mathbb{R})$ is not compact, not connected, so I cannot rule out some options using topological properties. Remove specific duplicates (all but latest) When removing duplicate rows, using the below query from  tutorial, how would I go about forcing which of the found duplicates to remove?  DELETE FROM dbo.ATTENDANCE      WHERE AUTOID NOT IN (SELECT MIN(AUTOID) _ FROM dbo.ATTENDANCE      GROUP BY EMPLOYEE_ID,ATTENDANCE_DATE)    And this works great. The reason why I am using this one is because the only unique id available is one in the IDENTITY column. And to determine if there are duplicate rows I have to look at a combination of multiple columns.    But if I have a set of duplicate rows how do I / how does SQL Server decide which to remove? And how would I force it to remove all but the one with the highest IDENTITY value?  EMPLOYEE_ID     ATTENDANCE_DATE     AUTOID A001            2011-01-01          1 A001            2011-01-01          2   If I would run the query now it happens to remove the second one, with AUTOID 2. But I am trying to remove all but this one (because this is the one latest added). Question for any programmer—and cat lover—working from his home office. So many times my keyboard is taken over violently by my two cats who think it’s the right place for a nap. And almost every time when they do this I’m was in this precious 100% concentration phases before I get interrupted.  I tried it with a burning an anti-mosquito coil under the desk but they got used to the smell pretty fast.  EDIT: And no I don’t want to keep the cats away completey from my room. How does one attack a two-time pad (i.e. one time pad with key reuse)? My question might appear the same as the question , but actually I did read all the answers and none of them helped me with the details I need.  I am new to cryptography and my problem is with two time pad attacks on OTP. The problem I had in my course was that I have 10 ciphertexts encrypted with the same key $K$. I am then given another ciphertext that I should decrypt.  I know that XOR-ing two ciphers gives me the XOR of their original messages.  My question is what is the correct thing to do after that?  I tried to take 3 ciphertexts $C_1, C_2$ and $C_3$.  Then get $S_1 = C_1 \oplus C_2  \oplus $' ', also get $S_2 = C_1 \oplus C_3 \oplus$ ' '.  After that I compared all corresponding characters in $S_1$ and $S_2$,  and if $S_1[i] = S_2[i]$ then I calculate $S_1[i] \oplus C_2[i]$ to get $K[i]$.  I tried this on paper before coding and it worked, but I might be missing something.  Is this the right approach? Why does it work? I have installed Ubuntu on, but now I am trying to install NVIDIA CUDA Toolkit for the GPU. When I install it, it says that there is no driver found, so I have tried to install the driver, but I don't know why after installation, the system not coming up. Maybe it is because of the wrong version of the driver.   When I tried to detect the driver version using sudo lshw -C display , it showed this information:    But here it doesn't say that what is the product name of the driver, and also when I go Software &amp; Updates -> Additional Drivers, then it says NVIDIA Corporation: Unknown.    What should I do? Bind variable with dotted name not working in dynamic SOQL As mentioned in , it's possible to use bind variables in dynamic SOQL queries.  This seems like a great way to avoid SOQL-injection, and to build a query string once but use it multiple times with different values in the variables.  I'm working on a method that returns a list of objects.  It accepts a class with multiple properties as its only parameter.  The properties of this class are used to filter the results to just the required records.  It will eventually be driven by a Visualforce component, which will be configured by querystring parameters in the URL.  I just ran into an issue where the query fails when I use dotted bind variables.  If I copy the constructed dynamic SOQL into a static query, it works fine.  This may be a bug, because in doing tests I found that :foo.bar would actually try to use local variable bar.  Here's one of my queries, which uses related custom objects.  I've stripped it down to just the part that's failing (wrapped for legibility):  result = Database.query('SELECT Name, Another_Object__r.Name,      Another_Object__r.Custom_Field__c      FROM Custom_Object__c       WHERE Another_Object__r.Custom_Field__c = :filter.deviceType');   The error reported is System.QueryException: Variable does not exist: filter.deviceType.  As mentioned above, the query works fine as static SOQL, just not dynamic:  result = [SELECT Name, Another_Object__r.Name, Another_Object__r.Custom_Field__c FROM Custom_Object__c WHERE Another_Object__r.Custom_Field__c = :filter.deviceType];   It also works in this case:  String deviceType = filter.deviceType; Database.query('SELECT Name, Another_Object__r.Name, Another_Object__r.Custom_Field__c FROM Custom_Object__c WHERE Another_Object__r.Custom_Field__c = :deviceType');   I haven't read about this being a known limitation.  I don't know if I should be using some other syntax/notation in the query -- the dotted notation appears correct.  Time to report a bug?  Thoughts on workarounds other than creating local variables to stand in for each member of the class? Which of the following is most correct?      The distance of the shortest path must not be higher than 10km.   The distance of the shortest path must not be greater than 10km.   The distance of the shortest path must not be bigger than 10km.   Or is there an even better word? Why do fonts look messed up in Adobe Acrobat? What is an "Emergency Call," and can I  set number for it?