Bound on $(x-x_0)(x-x_1) \dots (x-x_n)$ for equidistant points
Error term in equally spaced nodes
Two Answers, One Question Sometimes, when I answer a question on Stack Overflow, I have two different answers that are equally valid. This happens most when answering architectural questions where there are many valid ways to solve a problem.  Is it better to put each alternative into a single answer, or put each alternative in its own answer?  Posted each alternative separately will allow the voting system to float the best answer to the top, but I don't want to be accused of rep whoring by "flooding" a question with answers.  What's your opinion? One or two answers? A specific file on our production servers is being modified at apparently random times which do not appear to correlate with any log activity.  We can't figure out what program is doing it, and there are many suspects.  How can I find the culprit?  It is always the same file, at the same path, but on different servers and at different times.  The boxes are managed by , but the puppet logs show no activity at the time the file is modified.  What kernel hook, tool, or technique could help us find what process is modifying this file?    lsof is unsuitible for this, because the file is being opened, modified and closed very quickly.  Any solution that relies upon polling (such as running lsof often) is no good.      OS: Debian testing Kernels: Linux, 2.6.32 through 3.9, both 32 and 64-bit. Integral of Sinc Function Squared Over The Real Line Integral $\int\frac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$ Integrate  $\displaystyle\int\dfrac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$   I tried dividing by $\cos^2(x)$ and then substituting $\tan(x)=t$. What is the difference between the Bash operators [[ vs [ vs ( vs ((? I am a little bit confused on what do these operators do differently when used in bash (brackets, double brackets, parenthesis and double parenthesis).  [[ , [ , ( , ((   I have seen people use them on if statements like this :  if [[condition]]  if [condition]  if ((condition))  if (condition) Set Text Color for textView Android Linear vs nonlinear differential equation How to distinguish linear differential equations from nonlinear ones? I know, that e.g.: $$ y''-2y = \ln(x) $$ is linear, but $$ 3+ yy'= x - y $$ is nonlinear. Why? In how many ways can a number be expressed as a sum of consecutive numbers? Given the following class  public class Foo {     public int FooId { get; set; }     public string FooName { get; set; }      public override bool Equals(object obj)     {         Foo fooItem = obj as Foo;          if (fooItem == null)          {            return false;         }          return fooItem.FooId == this.FooId;     }      public override int GetHashCode()     {         // Which is preferred?          return base.GetHashCode();          //return this.FooId.GetHashCode();     } }   I have overridden the Equals method because Foo represent a row for the Foos table.  Which is the preferred method for overriding the GetHashCode?  Why is it important to override GetHashCode? Can a Half-Elf have Drow Ancestry? What are "Community Wiki" posts? Some questions and answers are marked Community Wiki and are owned by a community wiki user:  (In fact, this very question is one of them)  Why have Community Wiki posts? How do Community Wiki posts work? How does a post become a Community Wiki post? How can the Community Wiki status be removed from a post? How can I find Community Wiki posts? Axis with trigonometric labels in PGFPlots How do I make the axis labels use multiples of \pi in PGFPlots? How can I view and examine the Android log? Mask and convert color in photo/video I am very new to blender still.  I want to simply change the color of an object in the video.  I want to know if there is good way to do this.  I am including what I have to test. Cleaning wax and pesticide from apple skin Split Excel table over multiple PowerPoint slides I have a table in Excel which is too long for one PowerPoint slide. So I would like to split it over 2 or 3 slides, but have the header on each of the slides. What is the easiest way to accomplish that? I am using Excel and PowerPoint 2007. Lightning aura:iteration over two objects with dynamic key I want to do simple thing - I want to iterate over list of two objects and use displayColumns as dynamic keys to get values from selectList object:  &lt;aura:attribute name="displayColumns" type="String[]"/&gt; &lt;aura:attribute name="selectList" type="Object[]"/&gt;   &lt;table&gt;     &lt;aura:iteration items="{!v.selectList}" var="elem"&gt;     &lt;tr&gt;         &lt;aura:iteration items="{!v.displayColumns}" var="col"&gt;             &lt;td&gt;{!elem[col]}&lt;/td&gt;         &lt;/aura:iteration&gt;     &lt;/tr&gt;     &lt;/aura:iteration&gt; &lt;/table&gt;   In pure JS I would do: elem[col.value], but in lightning compiler returns:      expecting a positive integer, found 'col' at column 6 of expression:   elem[col.value]: Source   Is there any workaround without creating proper object structure in controller? proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$ I am currently working through Velleman's book How To Prove It and was asked to prove the following  $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$  This is my work thus far  $(P \to Q) \wedge (Q \to P)$  $(\neg P \vee Q) \wedge (\neg Q \vee P)$ (since $(P \to Q) \equiv (\neg P \vee Q)$)  $\neg[\neg(\neg P \vee Q) \vee \neg (\neg Q \vee P)]$ (Demorgan's Law)  $\neg [(P \wedge \neg Q) \vee (Q \wedge \neg P)]$ (Demorgan's Law)  At this point I am little unsure how to proceed.   Here are a few things I've tried or considered thus far:  I thought that I could perhaps switch some of the terms in step 3 using the law of associativity however the $\neg$ on the outside of the two terms prevents me from doing so (constructing a truth table for $\neg (\neg P \vee Q) \vee (\neg Q \vee P)$ and $\neg (\neg P \vee \neg Q) \vee \neg (P \vee Q)$ for sanity purposes)  I can't seem to apply the law of distribution since the corresponding terms are negated.  Applying demorgans law to one of the terms individually on step 2 or 3 doesnt seem to get me very far either.  Did I perhaps skip something? Am I even on the right track? Any help is appreciated This is more of a panic question after reading reviews on Istanbul Atatürk Airport. They said it's messy and hard to navigate, therefore I'm asking questions here in name of my girlfriend who will need to transit through this airport.  My girlfriend (Canadian national) traveling from Toronto (YYZ) to Istanbul (IST) for a couple hours (~4 hrs, so transiting) in order to come to Pristina (PRN). I would like a quick guideline on how to pass through this airport seamlessly without facing any trouble or delay.  Her tickets are both with Turkish Airlines. She purchased it via a third party (Flighthub.ca). It's only one booking and it includes both flights in it.   Once my girlfriend departs, she's obviously required to follow the signs and go to the transit area. Once she's there, will she be required to present a ticket? Where does she get that ticket? Does she get it in YYZ or does she need to visit a counter in IST and get it? After she's got the proper ticket, what does she need to do exactly? Wait in line to have her passport checked? Will they also control her carryon?  After this step, does she simply go to the PRN flight gate and that's it?   We're simply worried about Istanbul Atatürk Airport because of the recent things that happened in Turkey (coup attempt and ISIS attack) and she doesn't wanna somehow end up locked up there. I've read that the airport is a mess lately and a lot of people will be there waiting in line. So, another question: Are 4 hours enough?  I would appreciate a step by step guideline on how she needs to navigate and what she needs to do in that airport to have a smooth experience without facing any delays. Also some misc information on Istanbul Atatürk Airport would be appreciated. I  have had no luck getting the buffer tool to accept anything but degrees as units of measure.  I have found lots of stuff saying the layer needs to be reprojected and saved but it hasn't worked at all for me.   Is there a way I could create a buffer without using ftools or at least force the units to meters somehow?  As a workaround I converted meters to degrees (lat) and used that but the final product needs to be as close to reality as possible.  Things I've tried:   setting every unit option I could find to meters (where possible). setting everything to NAD83/Maryland (data is for Washington, DC) and saving it as such (as layers in ESRI shape files). reimporting the reprojected layers setting relevant layers to Google Mercator   The was tried followed by creating a buffer. Many were tried in combination. QGIS 1.7.3 Slackware64 current (qgis from SBo-13.37 repo, tried on multilib and plain 64it with same results)