Xorg.conf to only use part of screen
Set Xorg to use only part of the screen
How can I avoid SQL injection attacks in my ASP.NET application? I need to avoid being vulnerable to SQL injection in my ASP.NET application. How might I accomplish this? I'm writing a simple bash script, but I need it to check whether it's being run as root or not. I know there's probably a very simple way to do that, but I have no idea how.  Just to be clear: What's a simple way to write a script foo.sh, so that the command ./foo.sh outputs 0, and the command sudo ./foo.sh outputs 1? Question:     Let $f$ be differentiable on $[0,+\infty)$, such as$$\lim_{x\to+\infty}\left([f'(x)]^2+f^3(x)\right)=0$$show that $$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$$   I think this problem is similar to  and (the  background)  For my problem I guess that if  $$\lim_{x\to+\infty}\left([f'(x)]^{2m}+f^{2n+1}(x)\right)=0,m,n\in N^{+},n,m&gt;1$$ then we have $\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$. Not sure how to make tables, but:  For a binary operation $*$, and set $\{e,a,b,c\}$, in the Cayley table, $a*a$ can be filled with either the identity or an element different from both $e$ and $a$. If in the table the place for $a*a$ is filled with $e$, then the rest of the table can be filled out in two different ways.  What are the two different ways?  Thanks Prove that $2^{1/2}$ is irrational I'm trying to understand each part of this completed proof that my professor did, here is my interpretation in parentheses, please advise as necessary.  Proof: Assume that $2^{1/2}$ is rational, then $2^{1/2}$ = $p/q$ for some integer $p$ and $q$ with $q \neq 0$ and $\gcd(p,q) = 1$  $$(p/q)^2 = 2 = p^2 / q^2 $$ $$\text{ (What was the purpose of squaring √2 and p/q?)}$$  $$p^2 = 2q^2$$ $$ \text{ (Is this basically just canceling out the q^2 on left side, and multiplying the right side?)}$$  2 | p^2 => (2 divides p^2 since it is a factor)  2 | p => (thus 2 divides p)  p = 2k for some integer k => (definition of even)  (2k)^2 = 4k^2 = 2q^2 => (Why are we squaring 2k, and how does 4k^2 = 2q^2?)   q^2 = 2k^2 => (Canceled out 2 on one side, and dividing on other)  2 | q^2 => (2 divides q^2)  2 | q => (thus 2 divides q)  2 | gcd(p,q) => (2 divides gcd of p and q)  2 | 1 Which is a Contradiction (no clue how I got here) Number of sigma algebras for set with 4 elements Edits that shadow a suggested edit inconsistently reject but include the suggestion I have the edit privilege. If I edit a post which has a pending suggested edit, then:  My edit starts from the version resulting from the suggested edit. I'm not notified of that, or even of the existence of the suggested edit. (There's actually a clue, but it's easy to overlook — the edit summary field is pre-filled with the summary from the suggested edit.) The suggested edit is marked as rejected by Community with the message “This edit conflicted with a subsequent edit.” The suggester is not credited in the edit history, my revision combines the suggested edit with my modifications.  This can happen if an edit is suggested while I have the page open: I click on “edit”, and think I'm editing the version that I was just reading, but in fact I'm editing somebody's suggested edits. It also happens if I deliberately visit /posts/12345/edit, which . Examples: a  that I approved and then wanted to ; a  where I . There are two bugs here, but I'm making a single report because they're very closely linked.  I'm not told about the suggestion, so my edit includes content that I'm not aware of, yet is attributed to me. The suggestion is marked as rejected and the suggester is not credited in the edit history, yet the suggested changes are made. I accidentally removed my /etc/apt/sources.list file. Is it hosted by Canonical somewhere so I can re-add it to the system? It's a bit of an emergency, so I hope someone can provide a quick answer. Are locks unnecessary in multi-threaded Python code because of the GIL? If you are relying on an implementation of Python that has a Global Interpreter Lock (i.e. CPython) and writing multithreaded code, do you really need locks at all?  If the GIL doesn't allow multiple instructions to be executed in parallel, wouldn't shared data be unnecessary to protect?  sorry if this is a dumb question, but it is something I have always wondered about Python on multi-processor/core machines.    same thing would apply to any other language implementation that has a GIL. To put it simple, there's a simple java swing app that consists of JFrame with some components in it. One of the components is a JPanel that is meant to be replaced by another JPanel on user action.  So, what's the correct way of doing such a thing? I've tried  panel = new CustomJPanelWithComponentsOnIt(); parentFrameJPanelBelongsTo.pack();   but this won't work. What would you suggest? Why do hard links exist? Showing that if the center of a group is trivial, then the center of its automorphism group is trivial I entered the USA on a three month visa waiver program from Australia. I am about to return to  Australia and would like to come back again to the USA. How long do I have to wait until I can re-enter the USA for another 3 months? How to fix soft 404 errors in GWT? In GWT I have been receiving soft 404 errors for some URLs of my online shopping website. Ichecked all those URLs and those pages are looking good and there is nothing wrong in that page. Then why I'm receiving that errors?  This is the notification that I received in my GWT:     Dear owner or webmaster,      While crawling your site, we have noticed an increase in the number of   transient soft 404 errors around 2013-06-30 16:00 UTC (London, Dublin,   Edinburgh). Your site may have experienced outages. These issues may   have been resolved. How should an educational institute woo good faculty? What steps must an educational institution wanting to recruit good faculty take? There is a cycle in the academia:    Good doctorates from top universities invariably join other top universities as faculty members.  Good students aspire to study in top universities under excellent faculty members.   Suppose a new educational institution or department springs up and desires to set up a top-quality group, how does it break into this cycle? I suppose this could take some years, but is money-power the only thing that could be wielded by the institute to achieve its end? If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$ I am working on some past prelim problems and one of them is the following: If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$   Update: Following Jackie Chong's advice, I am attempting this problem with the dominated convergence theorem. Since $f\in L^1(\mathbb{R})$, $f$ can be approximated from below by a sequence of continuous functions $f_n$. Then, I believe I can say that, for all $n$ sufficiently large, $|f_n(x+\frac{1}{n})-f_n(x)|\le 2|f(x)|$. (I'm not sure of this part thought). Then $2|f(x)|$ is integrable and hence a dominating function for $|f_n(x+\frac{1}{n})-f_n(x)|$. So by the dominated convergence theorem we can take the limit inside $\lim_{n\rightarrow \infty}\int|f_n(x+\frac{1}{n})-f(x)|dx=\int \lim_{n\rightarrow \infty}|f_n(x+\frac{1}{n})-f(x)|dx=0$ Is this on the right track?  Another approach that I thought may work, but which I'm less certain of is the following: If $f$ can be approximated by $C^1$ functions (I have no real justification for this, so please correct me if its wrong), then for each $n$ and each $x$ there is some $y(x,n)\in B_{1/n}(x)$ such that $|f(x+\frac{1}{n}-f(x)|=\frac{1}{n}|f'(y(x,n)|$ but from here I don't see how to proceed, because just because $|f|$ is integrable, I can't justify $|f'|$ being integrable, but if there is some way to fix this approach, hints would be appreciated.   Another thing I was thinking was to first approximate $f$ from below by continuous functions $f_n$ then to define $g_{m,n}=|f_n(x+\frac{1}{m})-f_n(x)| \chi_{[-m,m]}$. Then, for each $n$, the function $g_{m,n}$ is continuous on its support, and since it support is compact, it is uniformly continuous there. Can this be used to justify bringing the limit $\lim_{n\rightarrow \infty}$ inside the integral? Then apply the monotone convergence theorem? I know this idea is probably even more sketchy than my previous one, but if it can be fixed please let me know :)  Thanks! Bad Eyesight and Evolution Why do many humans have bad eyesight, such as near-sightedness, which hampers performance in a wide variety of tasks? Shouldn't there be evolutionary pressure towards better eyesight? Is it possible to import css stylesheets into a html page using Javascript? If so, how can it be done?  P.S the javascript will be hosted on my site, but I want users to be able to put in the &lt;head&gt; tag of their website, and it should be able to import a css file hosted on my server into the current web page. (both the css file and the javascript file will be hosted on my server). Escape velocity from a rotating black hole Under Newton, the escape velocity is  $$v_{esc} = \rm c \ \sqrt{r_s/r}$$  where $\rm r_s=2 \ GM/c^2$. In the nonrotating relativistic case (the Schwarzschild case) the radial escape velocity is the same:  $$v^{\parallel}_{esc} = \rm c \ \sqrt{r_s/r}$$  which is the speed of light, $v={\rm c}$, at the event horizon at $\rm r=r_s$. Since the photon sphere, where an object with $v={\rm c}$ would not escape, but be captured into orbit, is at $r=3 \ {\rm GM/c^2}$, the transverse escape velocity is  $$v^{\perp}_{esc} = \rm c \ \sqrt{r_s/r}\div \sqrt{1-r_s/r}$$  and for the observed (shapiro delayed) velocity ${\rm v}$ the transformation is  $${\rm v}^{\perp}=v^{\perp} \ \sqrt{\rm 1-r_s/r} \ , \ \ {\rm v}^{\parallel}=v^{\parallel} \ (\rm 1-r_s/r)$$  so the observed angular motion is the same as with Newton, yet locally higher, while the observed radial motion is slowed down because of the radial length contraction and time dilation.  But what about the Kerr case where the rotation is significant and the event horizon is at $\rm r=(1+\sqrt{1-a^2}) \ {\rm GM/c^2}$ instead of $\rm r=r_s$?  A testparticle which is locally at rest and therefore corotating with the angular velocity of the frame dragging  $${\Omega = \rm d \phi/ {\rm d t} = {\rm 2 \ a \ r/((a^2+r^2)^2-a^2 (a^2+(r-2) \ r) \sin ^2(\theta ))}}$$  should experience the time dilation factor  $$\rm \dot t = {\rm d t}/ {\rm d}\tau = \sqrt{{\rm ((a^2+(r-2) \ r) (a^2 \cos ^2(\theta )+r^2))/((a^2+r^2)^2-a^2 (a^2+(r-2) \ r) \sin ^2(\theta ))}}$$  relatively to the far away observer, so multiplying $\Omega$ with $\rm \dot t$ should give the local frame dragging angular velocity, which, multiplied with the $\rm \sqrt{x^2+y^2}$ value of the Boyer-Lindquist to cartesian transformation should give the transverse velocity - this is slightly below $\rm c$ for a maximaly rotating black hole (with $\rm a = 1$ - at the edge of the outer equatorial ergosphere where $\rm r=1$ and $\rm R=\sqrt{r^2+a^2}$).  But how do I find the radial and total escape velocity, and what are the rules to convert the shapiro-delayed coordinate velocities $\rm d r/d t \ , \ d \phi/d t \ , d \theta/d t$ to the local 3-velocity components $v^{\parallel}$ and $v^{\perp}$ of a test particle (local meaning relatively to a frame dragged probe with contant $\rm r$)? The radial length contraction seems a bit different than in the Schwarzschild-case, where it is the same as the gravitational time dilation factor... Neural networks output probability estimates? Suppose my training data contains ~100 variables, and each example is tagged as "success" or "failure".  I understand how a neural network can be used to try and predict success vs failure based on the variables.  However I am interested in the neural network outputting the posterior probability rather than success or failure. In fact, I evaluate the efficacy of the NN based on how accurate the probabilities are (eg. AUROC over the entire dataset) rather than % of cases with correct prediction.  Are NN's the right tool for the job here and if so how do you structure the NN to output this?  (NOTE: I'm a ML newbie!)