Whether Logfile Shrinking is good or bad one for Performance in SQL?
Why Does the Transaction Log Keep Growing or Run Out of Space?
Sometimes it is convenient to refer to a group of equations by a letter and a number.  For example:   2+1   (A1) 2+4   (A2) x^4   (B3) x^e   (B4)   Placing  \tag{A\theequation}\label{eqn:thisone}\stepcounter{equation}} instead of just \label{eqn:thisone} works, but seems hacky (especially manually stepping the counter).   Is there a better way? In X-Men Origins: Wolverine,      Wolverine is shot through the head with what appears to be a vibranium bullet by William Stryker. He remarks that the brain will grow back but the memories won't.   So the projectile penetrated the adamantium skull and damaged the brain. Adamantium is an inorganic substance. It will survive anything that would otherwise destroy the rest of Wolverine's body. But if anything (such as vibranium) manages to damage the adamantium, it is not covered by Wolverine's healing abilities.  Does this mean that Wolverine has an Achilles' heel on his forehead? If so, how did he take a bullet to the exact same spot in X-Men: United (at Ice Man's home)? How can I set desktop defaults for new users? How can I set up desktop defaults, much like most distributions do, for every new user? (ex. default wallpaper, apps, etc) Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$? Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc):   For any given set, the intersection with the empty set results in the empty set. For any real number, multiplication with zero results in zero. Let $G$ be a group of order $56$. (We do NOT assume the Sylow-$7$ subgroup to be normal.) Then either the Sylow-$2$ subgroup is normal or the Sylow-$7$ subgroup is normal. How to prove?  My idea: consider the case $n_2=7,n_7=8$. Then the number of elements in all Sylow $2$ -subgroups and Sylow $7$-subgroups is at most exactly $(7-1)*8+(2-1)*7+1=56$. This cannot give a contradiction. We need to prove that $G$ is simple. Then $|G||(8!/2)$. To prove $G$ simple, we need to prove there does not exist normal subgroups of order $2$ and order $4$. But I do not know how to prove. Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes. My 3 years old doesn't tell me when he needs to use the bathroom My son is 3 years old and doesn't tell me when he needs to use the bathroom. It has been 5 months now that I took his diaper off him. I just do not know what I should do.  Should I put a diaper on him again?  I mean, is this normal? Please help. I get frustrated sometimes.  He doesn't want to potty at all! I did train him before but now that he understands, he doesn't want to go to potty. How to see the error messages when I get the white screen of death? How can I see the error messages when the site I am working on gets a white screen? best way to pick a random subset from a collection? I have a set of objects in a Vector from which I'd like to select a random subset (e.g. 100 items coming back; pick 5 randomly). In my first (very hasty) pass I did an extremely simple and perhaps overly clever solution:  Vector itemsVector = getItems();  Collections.shuffle(itemsVector); itemsVector.setSize(5);   While this has the advantage of being nice and simple, I suspect it's not going to scale very well, i.e. Collections.shuffle() must be O(n) at least. My less clever alternative is  Vector itemsVector = getItems();  Random rand = new Random(System.currentTimeMillis()); // would make this static to the class      List subsetList = new ArrayList(5); for (int i = 0; i &lt; 5; i++) {      // be sure to use Vector.remove() or you may get the same item twice      subsetList.add(itemsVector.remove(rand.nextInt(itemsVector.size()))); }   Any suggestions on better ways to draw out a random subset from a Collection? operators as strings I need to evaluate a mathmatical expression that is presented to me as a string in C#.  Example noddy but gets the point across that the string as the expression.  I need the evaluate to then populate an int.  There is no Eval() in C# like in others langugaes...  String myString = "3*4";   Edit:  I am on VS2008   Tried the Microsoft.JScript. = Its deprecated method (but still complies - warning)  However the Microsoft.JScript dll that I have doens work on      public object InvokeMember(string   name, BindingFlags invokeAttr, Binder   binder, object target, object[] args);   Complains that there is a missing ";"  go figure...  EDIT 2  Solution - was the codeDom one - it worked for as there are no security issue - only me ever going to be running the code.  Many thanks for the replies ...  And the link to the new Dragon Book  awesome   EDIT 3  Matt dataTable.Compute() also works - even better for the security conscious.  (parameter checking noted) Is the Formula Logically Valid? Can we build capacitors on a PCB board? Rising edge pulse detector from logic gates The circuits I describe are entirely made of 7400 series logic gates (7402, 7404 and 7408 ic). I'm trying to build a rising (positive) edge pulse detector using logic gates.  The following circuit should work in theory:   (see )  I do not expect the short output to be seen through a LED so, to test it, I make it trigger an SR latch to its up state:    However, it doesn't have effect on the latch. So I added an inductor to delay the input to the NOT gates in the pulse detector circuit and it worked:   But now I can see the short flashing output through a LED which I should not because it would mean it is too long to work with a circuit like that:   Which intends to toggle the D Latch output on each clock rising edge (Note that this is a D Latch not a D Flip-flop)  And anyway there is no place for inductors in integrated circuits so there must be a way to do this only with logic gates. Can someone solve this mystery?  BTW It does not show in my schematics but I did put 10K pull-down resistors where there might be floating pins. Union of uncountable cardinals I have to prove the following:  Let $\omega_1$ be the least uncountable cardinal and, for each $n \in \omega$ (here, $\omega$ is the set of natural numbers denoted as an ordinal/cardinal), $n\ge1$, let $\omega_{n+1}$ be the least cardinal that is greater than $\omega_n$. Show that $\bigcup_{n\in\omega}\omega_n$ is a cardinal.  I suppose the proof has something to do with transfinite induction/recursion, but I don't know exactly how I'm supposed to use it. Any thoughts? Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1? I was wondering why do some people use redundant axioms in definitions?  If you just expand $(a+1)(b+1)=(a+1)b+a+1=ab+b+a+1$ $(a+1)(b+1)=a(b+1)+b+1=ab+a+b+1$. Hence, $ab+a+b+1=ab+b+a+1$, then cancel ab and 1. Then, you get it's commutative for free.   Why do we then assume it?   Also, is it even stronger. If we drop the condition that 1 is in R, then can we still deduce a+b=b+a? As clearly the argument just done falls apart if you haven't got 1 in R. Every increasing function from a certain set to itself has at least one fixed point What Does it Really Mean to Have Different Kinds of Infinities? Can someone explain to me how there can be different kinds of infinities?  I was reading "" by  and came across the concept of countable and uncountable infinities, but they're only words to me.  Any help would be appreciated. Find this integral $$\operatorname I=\int\limits_{0}^{1}\dfrac{\arcsin{\sqrt{x}}}{x^4-2x^3+2x^2-x+1}\operatorname d\!x$$  My try: let $$f(x)=x^4-2x^3+2x^2-x+1$$ I found  $$f(1-x)=(1-x)^4-2(1-x)^3+2(1-x)^2-x+1=x^4-2x^3+2x^2-x+1=f(x)$$ so $$I=\int_{0}^{1}\dfrac{\arcsin{\sqrt{(1-x)}}}{x^4-2x^3+2x^2-x+1}dx$$ so $$2I=\int_{0}^{1}\dfrac{\arcsin{\sqrt{x}}+\arcsin{\sqrt{(1-x)}}}{x^4-2x^3+2x^2-x+1}dx$$ then I can't,Thank you very much Is there any way to attract or repel neutrons? I know that neutrons are neutral and have no charge, but is there any other way to interact with them? Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$ I am stuck on how to calculate the following limit: $$\lim_{x\to\infty}x\left(\left(1 + \frac{1}{x}\right)^x - e\right).$$  Definitely, it has to be through l'Hôpital's rule. We know that $\lim_{x\to\infty} (1+(1/x))^x = e$. So, I wrote the above expression as $$\lim_{x\to\infty}\frac{\left(1 + \frac{1}{x}\right)^x - e}{1/x}.$$Both numerator and denominator tend to zero as x tends to infinity. I applied l'Hôpital's rule twice, but I got the limit equal to infinity which is clearly wrong. In the book, it says that the limit should be $-e/2$.  Any help please? Also, in case someone managed to solve it, please tell me which numerator and denominator did you apply your l'Hôpital's rule to in both cases? Thanks a lot  Also, guys can you tell me how to write equations in this forum? Thanks.