Row-wise maximum in T-SQL
SQL MAX of multiple columns?
Direct observations of a black hole? Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$ Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$.  Writing out several terms, I think the answer is $1/(n+1)$, but I'm struggling to prove this. I would greatly appreciate it if someone could show how to prove this. While researching my theory that , I noticed that there are surprisingly few posts with zero comments.  Here's what the  looks like:  That graph was generated using the following SQL: select CommentCount, count(*)  from Posts  where CommentCount &lt; 30 group by CommentCount order by CommentCount  The huge distribution disconnect makes me think comments are not being counted correctly. Let $ f $ be a continuous function defined on $ [0,\pi] $. Suppose that      $$ \int_{0}^{\pi}f(x)\sin {x} dx=0,   \int_{0}^{\pi}f(x)\cos {x} dx=0 $$   Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $ Add a way for moderators to cast a normal, non binding close/open vote I think moderators should have the ability to cast a normal, non binding close and open vote like they were a normal user (while of course retaining their ability to cast a binding vote where necessary). This can be used in &quot;grey areas&quot; where a moderator can choose to give his or her opinion, but not make a decision alone; a good example of this is . This also helps in areas not so grey (questions that everyone would agree should be closed) since the OP has the time to see close (1) and possibly edit his or her question. The moderator can then optionally come back after a few minutes and close it for real if it's not improved (or maybe during that time other 4 people voted to close it). This would also fit perfectly in :  Since we’re about to add community moderators on both Stack Overflow and Server Fault, I need to document what it is, exactly, we expect moderators to do. The short answer is, as little as possible! How could I retrieve the exact duplicate value from conditionally formatted list that highlight duplicates? I have imported a webpage table in to Google Sheets. It frequently being updated. A series of calculations has been conducted on the sheet named Shawn Of the link spreadsheet.  I have filtered the my desired results into the Calculation sheet of that linked document... which is in columns A5:A. I then applied =ARRAYFORMULA(if(A5:A200=&quot;&quot;,,A5:A200*{12,13,37,101,111})) in columns B5. The Results of the formula extends from B5:F. This results from a5:F was subsequently conditionally formatted to highlighted duplicates in the aforementioned, i.e. a5:f using the lists of values in K5:K and I5:5. In Columns A5:F, is it possible to generate/place values in the range A5:f with matching name of states and aligned values in J5:K and H5:I? Is there a (Unix) shell script to format JSON in human-readable form?  Basically, I want it to transform the following:  { "foo": "lorem", "bar": "ipsum" }   ... into something like this:  {     "foo": "lorem",     "bar": "ipsum" } Let $R \simeq S$ be isomorphic commutative rings with unity. Prove the following:  a). If $R$ is an integral domain then $S$ is an integral domain.  For this, I said that If I let $f: R \to S$ be an isomorphism and $(R, + , \circ), (S, \oplus, \ast)$, then let $x, y\in R$,  such that $x \circ y = 0_R$, because $f$ is an isomorphism, $f(x \circ y) = f(x) \ast f(y) = f(0_R)$. If I let $R$ be an integral domain then, as per the definition $R$ is commutative, has unity, and no zero divisors.   So $f(x \circ y) = f(x) \ast f(y) = f(0_R)$ where we have either $f(x \circ y) = f(0_R) \ast f(y) = f(0_R)$ or $f(x \circ y) = f(x) \ast f(0_R) = f(0_R)$.   Since $f$ is an isomomorphism, let $s = f(x), t = f(y)| s,t \in S$. Then $s \ast t = f(0_R)$. By definition, $S$ also has unity so $0_S$ exists. If we map $0_R \to 0_S$. Then either $s = 0_S$ or $t = 0_S$.   So then, since $S$ has unity, is commutative, and has a no zero divisors as we showed above, it is also an Integral domain.  I'm not sure I have this correctly.  b). If $R$ is a field then $S$ is a field. I don't really understand how to do this one. Since $S$ is an integral domain, it has a $0_S$. So I need to show that $S$ distributes $\ast$ over $\oplus$.  Any help with these is appreciated Test for convergence  $$\sum_{n=1}^{\infty} \frac{1}{n^n}$$  I'm at a loss on what to do, is this a geometric series $\frac{1^n}{n^n}$? Difference between staticmethod and classmethod What is the difference between a function decorated with  and one decorated with ? What is a valid use case for an "execute only" file permission? I was reading up on chmod and its .  I saw that 1 is execute only.  What is a valid use case for an execute only permission?  To execute a file, one typically would want read and execute permission.  $ echo 'echo foo' &gt; say_foo $ chmod 100 ./say_foo $ ./say_foo bash: ./say_foo: Permission denied $ chmod 500 ./say_foo $ ./say_foo foo Is 'that is' optional? When I write something like this:     I am a man that is doing these things.   Is it correct to shorten it like this?     I am a man doing these things.   And does it require commas? How is every subset of the set of reals with the finite complement topology compact? While we know that every finite set is compact, how to prove that every infinite subset of $\mathbf{R}$, the set of all real numbers, is also compact in the finite-complement topology (also called the co-finite topology)?   What is the situation in the case of an arbitrary infinite set $X$ with the finite-complement topology? In a particular textbook, the work function of a metal (in the context of the photoelectric effect) is defined as:     the minimum amount of energy necessary to remove a free electron from the surface of the metal   This sounds similar to ionisation energy, which is:     the amount of energy required to remove an electron from an atom or molecule in the gaseous state   These two energies are generally different. For instance, Copper has a work function of about 4.7eV but has a higher ionisation energy of about 746kJ mol-1 or 7.7eV.  I've sort of figured it's because the work function deals with free electrons whilst ionisation is done with a valence electron still bound within the atom. Is the difference due to the energy required to overcome the attraction of the positive nucleus? Search with Auto-Complete (like Gmail / Intellisense) I read about how to enable and disable services in Ubuntu and it seems that there are different possibilities to manage them.  The first method I found is update-rc.d to add new services to startup, which aims on the /etc/init.d folder and its contents.  The other one I found is to edit .conf files in the /etc/init folder.  What's the recommended way to enable / disable / add services and why?  Could you please give a short bulletproof step by step example on how to add a service in Ubuntu and enable and disable it? I am writing a client-side Swing application (graphical font designer) on Java 5. Recently, I am running into java.lang.OutOfMemoryError: Java heap space error because I am not being conservative on memory usage. The user can open unlimited number of files, and the program keeps the opened objects in the memory. After a quick research I found  and others saying on Windows machine the JVM defaults max heap size as 64MB.  Given this situation, how should I deal with this constraint?  I could increase the max heap size using command line option to java, but that would require figuring out available RAM and writing some launching program or script. Besides, increasing to some finite max does not ultimately get rid of the issue.  I could rewrite some of my code to persist objects to file system frequently (using database is the same thing) to free up the memory. It could work, but it's probably a lot work too.  If you could point me to details of above ideas or some alternatives like automatic virtual memory, extending heap size dynamically, that will be great. Is the gravitational constant $G$ a fundamental universal constant? In Windows I used command-line clipboard copy-and-paste utilities...      pclip.exe and gclip.exe     These were UnixUtils ports for Windows (but they only handled plain text). There were a couple of other native Windows utilities which could write/extract any format.    I've looked for something similar in Synaptic Package Manager, but I can't find anything.    Is there something there, that I've missed? ... or maybe this is available in Bash scripting?    The type of utility I'd like will be able to read/write via std-in/std-out or file-in/file-out, and handle Unicode, Rich Text Format, picture, etc. clipboard formats...    NB: I'm not after a clipboard manager. Switch statement fall-through...should it be allowed? For as long as I can remember I have avoided using switch statement fall-through. Actually, I can't remember it ever entering my consciousness as a possible way to do things as it was drilled into my head early on that it was nothing more than a bug in the switch statement. However, today I ran across some code that uses it by design, which got me immediately wondering what everyone in the community thinks about switch statement fall-through. Is it something that a programming language should explicitly not allow (like C# does, though it supplies a workaround) or is it a feature of any language that is powerful enough to leave in the programmer's hands? Edit: I wasn't specific enough to what I meant by fall-through. I use this type a lot:     switch(m_loadAnimSubCt){         case 0:         case 1:             // Do something             break;         case 2:         case 3:         case 4:             // Do something             break;    }  However, I'm concerned about something like this.    switch(m_loadAnimSubCt){         case 0:         case 1:             // Do something, but fall through to the other cases             // after doing it.          case 2:         case 3:         case 4:             // Do something else.             break;    }  This way whenever the case is 0, 1 it will do everything in the switch statement. I've seen this by design and I just don't know if I agree that switch statements should be used this way. I think the first code example is very useful and safe. The second seems kind of dangerous.