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Distance from the surface as an input node for use with volumetric materials As the title says, I'm wondering if there is a continuous function such that $f$ is nonzero on $[0, 1]$, and for which $\int_0^1 f(x)x^n dx = 0$ for all $n \geq 1$. I am trying to solve a problem proving that if (on $C([0, 1])$) $\int_0^1 f(x)x^n dx = 0$ for all $n \geq 0$, then $f$ must be identically zero. I presume then we do require the $n=0$ case to hold too, otherwise it wouldn't be part of the statement. Is there ay function which is not identically zero which satisfies $\int_0^1 f(x)x^n dx = 0$ for all $n \geq 1$?  The statement I am attempting to prove is homework, but this is just idle curiosity (though I will tag it as homework anyway since it is related). Thank you! Some questions might be asked on three different sites, each site needing three different answers. For example, a question about a text editor.  So perhaps there should be a way to link the questions on the three different sites. Adding a link manually in the questions is certainly possible, but perhaps a feature officially supporting this will be beneficial. Cryptoclass Throws Error. Invalid private key. Must be 16 bytes. Sending 16 characters long key key__c :- abcdefghijklmnop  public static String decrypt(String data) {     EncryptionSettings__c settings = EncryptionSettings__c.getOrgDefaults();     if (settings.key__c == null) {         throw new FacebookException('Cannot decrypt without a key!');     }     Blob key = EncodingUtil.base64Decode(settings.key__c);     return Crypto.decryptWithManagedIV('AES128', key, EncodingUtil.base64Decode(data)).toString(); }  public static String encrypt(String data) {         EncryptionSettings__c settings = EncryptionSettings__c.getOrgDefaults();     Blob key = null;     if (settings.key__c == null) {         checkUserCanCustomizeApplication();         key = Crypto.generateAesKey(128);         settings.key__c = EncodingUtil.base64Encode(key);         insert settings;     } else {         key = EncodingUtil.base64Decode(settings.key__c);     }     return EncodingUtil.base64Encode(Crypto.encryptWithManagedIV('AES128', key, Blob.valueOf(data))); } I have the need to synchronize the data in certain Salesforce tables (user, account, opportunity, lead, task, contact, etc.) to a local database. For reasons that I won't go into here, I can't use the streaming API. I want to kick off a local process every X minutes that will:   Go through each of the tables on my list Insert any new records Update any existing records that were updated Delete any records locally that were deleted on the server (either deleted directly or indirectly (e.g. through a foreign key relationship, like when an account is deleted its associated tasks are deleted as well).   Can you please offer advice on what API's might be good to use here, and whether one stands out more than the others? Are there any specific design recommendations that might be useful for achieving this goal? Or is there really no practical difference between what REST vs SOAP can do?  It comes down to what is the easiest to maintain/implement? Is there some other route that might be beneficial to use (example: bulk data load to start out followed by outbound messaging tied to all of the objects in question to get updates/inserts/deletes)?   I am using C#/.net. Meaning of hash symbol in pin name I'm reading the datasheet of a PSRAM (available ). In the top-right hand corner all the pins are listed. Some of the pin names end with a hash, e.g. LB#, OE#.  What does the # notation mean for pins? What exactly are the Python scoping rules?  If I have some code:  code1 class Foo:    code2    def spam.....       code3       for code4..:        code5        x()   Where is x found?  Some possible choices include the list below:   In the enclosing source file In the class namespace In the function definition In the for loop index variable Inside the for loop   Also there is the context during execution, when the function spam is passed somewhere else. And maybe  pass a bit differently?  There must be a simple reference or algorithm somewhere.  It's a confusing world for intermediate Python programmers. Why can't I just think the spin as rotating? I'm going mad about the problem.  I really don't understand why do electron have 1/2 spin number, why they are not actually spinning.  I can accept that the electrons have their own magnetic field, which is certain, but why do they have $\hbar\sqrt3/2$ of angular momentum, and I don't know what the heck is spin number.  I've read the definition of  and  more than a hundred times but there is no betterment. I've smashed my head in my desk more than a hundred times either.  My question is the title. Why can't I just think the spin as rotating?  What I've saw recently,     electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out? I am lost.   So far...  If $\gcd (a,b) = 1$, by Bezout's Formula  $ax + by = 1$  If $c|(a+b)$, then $cf = a+b$  Then,  $a (x-y) + cfy = 1$   $b(yx) + cfx = 1$  Am I on the right track? Any suggestions? Let $f(z)=\frac{1}{(z-1)(z-2)}$ and $g(z)=\frac{z}{(z-1)(z-2)}$. Let $\gamma$ be the circle of radius 4 centered at the origin and traveled once in the counterclockwise direction. Let $A=\{ z \in \mathbb{C}: |z|&gt;3 \}$  1) I need to show there is no analytic function $G: A \to \mathbb{C}$ such that $G'(z)=g(z)$ for all $z$ in $A$.   2) I also need to show that there is an analytic function $F:A \to \mathbb{C}$ such that $F'(z)=f(z)$ for all $z$ in $A$.  Do I have to integrate to find such function? How to prevent book class from vertically justifying the contents? If we use the book class, the output looks like the following screenshot.    But if we use the article class, the output looks better as follows.    The MWE is given as follows. Note: please enable -shell-escape!  \documentclass[12pt]{article}% please change to article and compare the output.  \usepackage{filecontents} \begin{filecontents*}{"article sample.tex"} \documentclass{article} \usepackage{lipsum} \begin{document} \lipsum[1-20] \end{document} \end{filecontents*}  \usepackage{showexpl}  \lstset {     breaklines=true,     breakindent=0pt,     tabsize=2,     columns=flexible,     language={[LaTeX]TeX},     basicstyle=\small\ttfamily\hbox{}, }  \newcount\x  \newcommand\MyLTXinputExample[2][2mm]{% % #1: length of gap, % #2: filename with .tex,      \lstinputlisting[caption=\url{#2.tex}]{"#2.tex"}     \bgroup         \parskip=#1\relax         \fboxsep=0pt         \pdfximage{#2.pdf}%         \x=0         \loop             \ifnum\x&lt;\pdflastximagepages                 \advance\x by 1                 \noindent\hfill                 \fbox{\includegraphics[width=0.5\dimexpr\linewidth-4\fboxrule-#1\relax,page=\x]{"#2"}}%                                  \ifnum\x&lt;\pdflastximagepages                 \advance\x by 1                 \hfill                 \fbox{\includegraphics[width=0.5\dimexpr\linewidth-4\fboxrule-#1\relax,page=\x]{"#2"}}%             \fi                 \hfill\null\par         \repeat     \egroup }  \PassOptionsToPackage{obeyspaces}{url} \usepackage{hyperref}  \begin{document} \immediate\write18{pdflatex "article sample"} \MyLTXinputExample{article sample} \end{document}   How to prevent book class from vertically justifying the contents? In other words, I want to use the book class but its output (only the justification is under consideration) must look like the output that article class produces. Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis Suppose that we do not know anything about the complex analysis (numbers). In this case, how to calculate the following integral in closed form? $$\int_0^\infty\frac{\cos x}{1+x^2}\,\mathrm{d}x$$ What is the best, easiest, preferably cheapest way to make OS X write to NTFS-formatted drives in Mac OS X? Selling a car with a lien I own a car personally, but it is mortgaged to a bank. I want to sell it to an individual. I haven't the funds to repay the loan until I'm paid for the car. The buyer doesn't want to pay me without a lien release (or guarantee that one is coming). The bank won't release the lien until it gets the funds. What do people do in a case like this? It must be a common case. What should I do? How do injuries work with Polyjuice Potion? We know that if you (using Polyjuice), take the form of someone who had been injured, you assume that injured form (e.g. Barty/Moody). If you are injured, presumably you would be uninjured while under Polyjuice. My question is, is this in real-time? That is, if you take a Polyjuice, and while you're still under its effects, the person being transformed into gets injured (or even dies), will that injury be transferred onto you? And conversely, if you get injured while in someone else's body, will that transfer over to your real body after the Polyjuice wears off, will it disappear, or will it go to the person you turned into? Suppose I have BaseClass with public methods A and B, and I create DerivedClass through inheritance.  e.g.  public DerivedClass : BaseClass {}   Now I want to develop a method C in DerivedClass that uses A and B.  Is there a way I can override methods A and B to be private in DerivedClass so that only method C is exposed to someone who wants to use my DerivedClass? Vertical line for the the right margin in Notepad++ Does anyone know if Notepad++ can display a vertical line on the right margin to indicated that the text will or will not fit on a printed page?  I have looked but I cannot find it.  Word wrap does work, but it wraps by my screen width, not by the width of a printed page. I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference? Stack Overflow is getting a Meta of its own