G is a graph with 100 vertices and $G \cong \overline{G}$. Is it possible that there is ONLY 1 vertex of valency 50 in G?
Can a self-complementary graph on 100 vertices have precisely one vertex of degree 50?
SQL Server: Cannot insert an explicit value into a timestamp column Can a sql server table have two identity columns? I need to have one column as the primary key and another to auto increment an order number field. Is this possible?  EDIT: I think I'll just use a composite number as the order number. Thanks anyways. If I buy a game from PSN on ps3 Is it permanently mine? OpenGL Line Width I've recently read a  from a local paper that included the following:     The pair was drinking prior to the shooting.   To me, this appears wrong and I would say that the proper way to make the statement would be:     The pair were drinking prior to the shooting.   Is the original article correct? Bravo for allowing comment editing, but what's the explanation for enforcing a five-minute window?  I think this might be over-engineering. If I have a spelling mistake or an inaccuracy I'd like to fix, I don't think the fact that five minutes has elapsed should prevent me from fixing it.  Further, if you are worried people will edit their comments in a way that makes the comment thread nonsensical, they can already do this by deleting their comment. So, limiting the ability to edit isn't really helping much in that regard.  Update  If people don't like this idea, I'm definitely open to hearing your reasons. For now, it seems like an unnecessary limitation of a quite awesome feature.  Update 2  Regarding John's scenario...     Me: Obama is cool!   You: You are right, man!      My edit: Obama is an idiot!   You: You are right, man!   ...this problem can still occur with deletions...     user1: Obama is cool!   user2: No, McCain is cool!   you: You are right, man!        user1: Obama is cool!   ---- deleted -----   you: You are right, man!     So, yes, editing could be abused as you suggest, but discontinuities can occur already because of deletions (and as someone else mentioned, because upvoted comments get prioritized upward).  As for Jeff's argument about rate limiting, I agree that is important, but I don't understand why you can't just use a CAPTCHA to prevent too many edits in a short period of time. What's the quickest Schengen consulate to issue a visa in London? What's the quickest Schengen consulate to issue a Visa in London? Basically I want to travel as fast as possible to France, and since any Schengen visa will work, I want to go to the consulate with the shortest processing time. How do I change / spoof my MAC address and easily switch between multiple ones? My router can do port-forwarding based on MAC addresses. That is, a specific MAC will get a specific IP, for which I can configure a set of ports to be forwarded. In order to easily change that set of ports, I'd like to have different connections in the Network manager.  How do I change the MAC address for a network connection? $$f(x,y) = \left\{\begin{array}{cc} \frac{xy}{x^2+y^2} &amp; (x,y)\neq(0,0) \\ f(x,y) = 0 &amp; (x,y)=(0,0) \end{array}\right.$$  In order to verify if this function is differentiable, I tried to prove it by the theorem that says that if $\frac{∂f}{∂x}$ and $\frac{∂f}{∂y}$ exist and are continuous at the point $(x_0,y_0)$, then the function is differentiable at this point. So I did:  $$\frac{\partial f}{\partial x}(0,0) = \lim_{h\to 0}\frac{f(0+h,0)-f(0,0)}{h} = 0$$ $$\frac{\partial f}{\partial y}(0,0) = \lim_{h\to 0}\frac{f(0,0+h)-f(0,0)}{h} = 0$$  so we have that the partial derivatives at point $(0,0)$ is $0$. Now, if we take the derivative at $(x,y)\neq (0,0)$ and then take the limit of it as $(x,y)\to(0,0)$, we can see if the derivatives are continuous or not. So here it is:  $$\frac{\partial f}{\partial x}(x,y) = \frac{y(y^2-x^2)}{(x^2+y^2)}$$  but   $$\lim_{(x,y)\to(0,0)} \frac{y(y^2-x^2)}{(x^2+y^2)} $$ does not exist (by wolfram alpha... but can anybody tell me an easy way to prove this limit does not exist? easier than taking the limit in different directions?), therefore the derivative is not continuous at $(0,0)$, so we can't say $f$ is differentiable at $(0,0)$, but for $(x,y)\neq (0,0)$ the function is continuous, as it is a quotient of continuous functions. So $f$ is at least differentiable at $(x,y)\neq (0,0)$.   Now, to verify differentiability at $(0,0)$ I think we must use the limit definition of differentiablity: A function is differentiable at $(0,0)$ iff: $$\lim_{(h,k)\to (0,0)} \frac{f(0+h,0+k)-f(0,0)-\frac{\partial f}{\partial x}(0,0)-\frac{\partial f}{\partial y}(0,0)}{\|(h,k)\|} = 0$$  Let's calculate this limit:  $$\lim_{(h,k)\to (0,0)} \frac{f(0+h,0+k)-f(0,0)-\frac{\partial f}{\partial x}(0,0)-\frac{\partial f}{\partial y}(0,0)}{\|(h,k)\|} = \\ \lim_{(h,k)\to (0,0)} \frac{\frac{hk}{h^2+k^2}}{\sqrt{h^2+k^2}} = \\ \lim_{(h,k)\to (0,0)} \frac{hk}{(h^2+k^2)\sqrt{h^2+k^2}}$$  which I think, it's a limit that does not exist, therefore the function isn't differentiable at $(0,0)$ If asking a question or giving instruction towards a group of objects where the number is unknown (and possibly could be one) what is the correct way to phrase the sentence? Which of the following sentences are more correct:     Has there been any studies regarding this and if so what has been the   conclusion?   OR     Has there been any studies regarding this and if so what have been the   conclusions? I am building a java server that needs to scale. One of the servlets will be serving images stored in Amazon S3.  Recently under load, I ran out of memory in my VM and it was after I added the code to serve the images so I'm pretty sure that streaming larger servlet responses is causing my troubles.  My question is : is there any best practice in how to code a java servlet to stream a large (>200k) response back to a browser when read from a database or other cloud storage?  I've considered writing the file to a local temp drive and then spawning another thread to handle the streaming so that the tomcat servlet thread can be re-used. This seems like it would be io heavy.  Any thoughts would be appreciated. Thanks. Evaluate the integral $\int e^{-x}x^n dx$ Evaluating the integral $\int_{0}^{\infty}  e^{-x}x^n dx$ where n=0,1,2 ...   1st Integration by part: let $a=x^n$, $da= nx^{n-1} dx$, Also $db=e^{-x}$, $b=-e^{-x}$ We have $$ -x^n e^{-x} + n\int x^{n-1}e^{-x} dx$$  2nd: let $a=x^{n-1}, da= (n-1)x^{n-2}, db= e^{-x}, b= -e^{-x}$ We have $$-x^n e^{-x} + n\left[x^{n-1}(-e^{-x}) - \int(n-1)x^{n-2}\cdot -e^{-x}\right]$$  How would you find the general form? What would it be? Sophomore's dream: $\int_0^{1} x^{-x} \; dx = \sum_{n=1}^\infty n^{-n}$ How to turn off Wireless power management permanently How to pass arguments to addEventListener listener function? The situation is somewhat like-  var someVar = some_other_function(); someObj.addEventListener("click", function(){     some_function(someVar); }, false);   The problem is that the value of someVar is not visible inside the listener function of the addEventListener, where it is probably being treated as a new variable. Why is ++i considered an l-value, but i++ is not? Why is ++i is l-value and i++ not? Is it really impossible to calculate in advance the result of throwing dice? Multiple monitors, multiple workspaces? I connected my laptop to my LCD. Using the laptop display hotkey I can switch between different modes - only laptop monitor on, only LCD monitor on, both on and display the same view, both on and the desktop is stretched (divided).  But, I'm looking for something else - I would like to have two workspaces, one visible on the laptop monitor and the other on the LCD.  Is that possible? Why is $2\pi i \neq 0?$ Command to italicize text with slanted numbers I often find myself adding a lot of \textsl{} around inside \emph{} or \textit{} blocks because I find italicized digits to look too "showoffy" and "baroque" and to hinder legibility (I'm using $$ when the number has a mathematical sense, but this situation occurs in less technical texts like CVs, and such.).  Could someone help me write a renewcommand to automate this, or better, a single low level command that makes \emph, \itshape, \textit and friends choose slanted over italic for numbers? I'm not too familiar with the low level latex font selection system nor with a way to detect digits from regular letters.  Edit: MWE of what I need and what I want to avoid  \documentclass{article} \begin{document} He thought: '\emph{Why 1234567890 apples?}' then he realized '\emph{ah yes, he has \textsl{1234567890} childs}' \end{document}   gives:   I find the italicized version (first one) of 2,3,4 and 7 to look especially bad.