Java passing values into IN in sql WHERE clause
PreparedStatement IN clause alternatives?
A hard problem on exponential integration Suppose $a : [0 , 1] \to \Bbb R$ is an infinitely smooth function. For $\lambda\ge1$, define $$F(\lambda) := \lambda \int_0^1 e^{\lambda t} a(t) \, dt.$$ If $\sup_{\lambda\ge1}|F(\lambda)|\lt\infty$, then $a$ is the identically zero function. Below are the some results I have derived:   Derivatives of any order of $a$ vanishes at $t = 1.$ For any $\delta\lt1$, $a(t)$ has a zero in the open interval $(\delta , 1).$  The same is true for all the derivatives of $a(t)$. This tells us that the $n^\text{th}$ derivative of $a$ has infinitely many distinct zeros for all natural $n$. If $a$ is analytic, then I can show that $a(t)\equiv 0.$ If $a(t)\ge0$ on $[0 , 1]$, then it is obvious that $a\equiv 0.$   I would appreciate any hint.  Actually $(1)$ and $(3)$ follows from $(2)$. For $(2)$, suppose that $a(1)\gt0$ (the case that $a(1)\lt0$ can be argued in the same way as the following), then there exists $\delta\lt1$ such that $a(t)$ is strictly positive on $I = [1-\delta , 1]$. Then write $F(\lambda) = \lambda\int_0^{1-\delta}e^{\lambda t}a(t)dt + \lambda\int_{1-\delta}^1e^{\lambda t}a(t)dt$. Now there exists $c\gt0$ such that $a(t)&gt;c$ on $I$ since $I$ is compact, so that the second term is bounded below by $c (e^{\lambda}-e^{\lambda(1-\delta)})$. But the first term is only $O(e^{\lambda(1-\delta)})$, so this contradicts the fact that $F(\lambda)$ is bounded. Morever, using the same idea and integration by parts, one can see that $n^{th}$ derivative of $a$ must vanish at $1$. How do I check if an object has a specific property in JavaScript?  Consider:  x = {'key': 1}; if ( x.hasOwnProperty('key') ) {     //Do this }   Is that the best way to do it? Parameter Sniffing (or Spoofing) in SQL Server A while ago I had a query that I ran quite a lot for one of my users. It was still being evolved and tweaked but eventually it stablised and ran quite quickly, so we created a stored procedure from it.   So far, so normal.   The stored procedure, though, was dog slow. No material difference between the query and the proc, but the speed change was massive.   [Background, we're running SQL Server 2005.]  A friendly local DBA (who no longer works here) took one look at the stored procedure and said "parameter spoofing!" (Edit: although it seems that it is possibly also known as 'parameter sniffing', which might explain the paucity of Google hits when I tried to search it out.)   We abstracted some of the stored procedure to a second one, wrapped the call to this new inner proc into the pre-existing outer one, called the outer one and, hey presto, it was as quick as the original query.   So, what gives? Can someone explain parameter spoofing?   Bonus credit for    highlighting how to avoid it  suggesting how to recognise possible cause discuss alternative strategies, e.g. stats, indices, keys, for mitigating the situation Why is my Wi-Fi Process eating >2GB memory For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$ Calculate the limit of two interrelated sequences? I have bought return tickets from London to Lille Europe on Eurostar. The trains on my outward and inbound journeys both stop at Calais Frethun.  Will Eurostar let me get on in Calais on the inbound? What about getting off at Calais on the outbound leg? I suspect leaving the train early is easier than getting on the train 'late'. Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ? Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?  ( I know that there 'is' a   'surjection' , but I don't know whether any surjective homomrophism from $\mathbb R$ to $\mathbb Q$ exist or not . Please help . Thanks in advance ) So, my update to 13.04 didn't go very well. Due to the lack of a decent driver (Yes, i'm unlucky to have a legacy driver which doesn't play nice with the new Xorg.), I had to mess around with stuff to first troubleshoot and afterwards "fix" my system.  I've finally got unity back, but now CtrlAltarrow and CtrlAltShiftarrow don't work anymore. They are bound in "keyboard" > "shortcuts", but nothing happens when I try it. A strange thing is that other keyboard shortcuts, like ctrlaltt to show terminal are still working.  I noticed that CtrlAltarrow doesn't show in the list with "unity shortcuts" (the list that shows when you hold the super key).  Does anyone know how to re-enable this way of workspace switching?  I enabled workspaces in the appearance menu. It doesn't have any effect though. Switching via the workspace-switcher in the unity dash works fine though.  CCSM is installed, but I can't seem to find a way to add keyboard bindings there.     System: ubuntu 13.04 64bit Given that$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$, find $a_7+a_6+a_5+a_4+...+a_1+a_0$ Given that$$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$$find $$a_7+a_6+a_5+a_4+...+a_1+a_0$$  Is there anyway to do the question without using binomial theorem and expanding the expression on the LHS?? It seems to me that the terms "Teaching Assistant" and "Instructor" refer to a variety of positions. At some places, a teaching assistant is responsible for things like helping the actual lecturer by handing out papers, grading homework, etc., and instructors hold recitation sessions.  At other places, I saw the term "instructor" referring to the lecturer giving the course, while a teaching assistant is the person doing anything else (recitations, grading etc.).  Is there some widely accepted definition of the two positions?  For context: The question arose because I wasn't sure whether I'm using the correct terms in my CV -- I am a math graduate student, and I would like to make a distinction between jobs in which I only graded course assignments/final exams, and courses in which I held recitation classes* (and also participated in grading the final exams). Is it OK to use "Instructor" for the latter? What should the former be referred to as?  *In the course I'm currently teaching, the recitations are planned and written by the ones giving them (without the professors' supervision). Also, the people giving the recitations are not necessarily grad students (some already hold a PhD). I'm elaborating on that because from what I've seen, some of it could be relevant for the definition of the job. Why only light nuclei are able to undergo nuclear fusion not heavy nuclei? Is it because of the binding energy or the binding energy per nuclei .  I am having trouble with this whole binding energy and nuclear fusion concept. Javascript function to convert color names to hex codes Why can't I transform faces, edges, or vertices without transforming the whole object? My problem is that I sometimes lose the ability to independently translate or otherwise transform any parts of a single mesh. If I try, for example, to just translate several faces, edges, or vertices, then the entire mesh will stretch and displace itself in order to follow the translation. Or, alternatively, if I try to translate just one face then the whole mesh will move as if I'm translating in Object Mode.  I'm not really sure I know how to describe this problem properly. I don't even know how to reliably reproduce it. It seems to happen to any given mesh at random, and it doesn't stop happening to that mesh unless I delete and remake it.  I assume that I must be doing something wrong to cause this to happen. Does anyone have any ideas? Thanks. Adding multiple CKEditor instances in jquery Consider the real-valued function  $f(x)=x^r$ where $r$ is a real number.  (1) For what values of $x$ and $r$, is this function differentiable?  (2) How do you prove the power rule, when $f(x)$ is differentiable?  It would be nice if the proof is accessible to a 12th grade student.  EDIT: Perhaps, I have not been very clear about my question.  I am not satisfied with the "textbook proofs" I have seen.  Please established the existence (of the derivative) first before proving the power rule.  That is, please consider first question first.  This is the reason why I call the question a mathematical engineering question.  (If we can we bring high level math down to Grade 12 level, without loosing precision, then I call it good mathematical engineering.) Problem about a process with bins of balls New navigation doesn't appear to alert of question changes when watching a tag I am watching the  tag on Stack Overflow. My filter looks like this:    I do not receive notification of new questions. Previously I'd get notifications like this:    This notification does work when watching the  page of Meta.   Are notifications only active for a certain set of filter options? If so, what are they? If not, can we get them back when watching pages other than the main page? Is it possible to pagebreak aligned equations? The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.  The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the \displaybreak command.  Is there an alternative way to achieve a pagebreak inside an aligned equation?  Here's a sample ofthe equations I'm using  \begin{equation}     \begin{aligned}     ...\\     ...\\  %I need to pagebreak here     ...\\ \end{aligned}\end{equation} The pronunciation of the word "a" Most times we hear that the letter A is pronounced as [ə], but sometimes I hear that it is pronounced as [eɪ] in American English. Such as the following sentence: From VOA Special English:  She says governments must make that goal of a continental free trade area a reality.  The first A is pronounced as [eɪ], the second A  is pronounced as [ə]. Why? Does it have some regularity in it?