texworks with texlive setup for the bibiliography
Question mark or bold citation key instead of citation number
Are planets actually moving in elliptical orbits around the Sun or do they move in circular orbits around their center of mass? In every derivation of Kepler's Laws that I have seen, we assume that the sun is stationary. However, in other places I have read that celestial bodies move about their barycentre (center of mass). So are planets actually moving in elliptical orbits around the Sun or do they move in circular orbits around their center of mass? color code in SharePoint calendar Let $f:R\rightarrow R$ be a function such that all its successive derivatives exist in all $R$ and also $f(x)f''(x)\leq 0$ everywhere.  If $\alpha$ and $\beta$ be two successive roots of $f(x)=0$.   Then prove that $f'''(x)=0$ for atleast one $\gamma \in(\alpha,\beta)$.  My Attempt:  I began by taking an example $f(x)=(x-1)(2-x)$ and let $x=1$ and $x=2$ be its two successive roots.The statement is trivially true.  Then I took the function $f(x)=e^{-x}(x-1)(2-x)$.The statement is true here also so on and so forth.  But what would be the exact proof I wonder. It appears to be a question of Rolle's Theorem. What's the difference between faking, mocking, and stubbing? I know how I use these terms, but I'm wondering if there are accepted definitions for faking, mocking, and stubbing for unit tests?  How do you define these for your tests?  Describe situations where you might use each.  Here is how I use them:  Fake: a class that implements an interface but contains fixed data and no logic.  Simply returns "good" or "bad" data depending on the implementation.  Mock: a class that implements an interface and allows the ability to dynamically set the values to return/exceptions to throw from particular methods and provides the ability to check if particular methods have been called/not called.  Stub: Like a mock class, except that it doesn't provide the ability to verify that methods have been called/not called.  Mocks and stubs can be hand generated or generated by a mocking framework.  Fake classes are generated by hand.  I use mocks primarily to verify interactions between my class and dependent classes.  I use stubs once I have verified the interactions and am testing alternate paths through my code.  I use fake classes primarily to abstract out data dependencies or when mocks/stubs are too tedious to set up each time. The LaTeX Wikibook :     Please understand: you do not have to use floating tables. It only   looks more professional. If you want to place your tables where they   lie in your source code, do not use table at all! This is a very   common misunderstanding among newcomers.   LaTeX works with an intricate , but I often prefer immediate placement with the H placement specifier (enabled by the float package).  My understanding is that captions and table/figure numbering require the table/figure environments. Is this really so, or are there ways around that? What other reasons are there for using table/figure if we know that we don't want a particular object to float? Why was Gotham City changed from a mostly fictional city to New York City in the Nolan trilogy? In Batman Begins, Gotham City has a futuristic/fictional and run down look: think of Oldtown, the trains built by the Wayne Corporation etc.   In The Dark Knight Rises, Gotham City looks like plain old real world New York City — we don't see the trains anymore. Oldtown is just a standard poor neighborhood. Lots of the locations used in the movie are easily identified as real world NYC locations: the stock exchange or East River bridges for example.   My question is: Why did Nolan change Gotham city from a shady fictional more cartoon-like town to plain old NYC?   Edit: The examples from Batman Begins and The Dark Knight Rises were just for illustration; I didn't intend to limit the question to those two movies.  Edit 2: I specifically want to know why Gotham City was changed from a cartoon-like city in Begins to an almost real-world NYC in The Dark Knight Rises (via not so cartoon-like but not yet real-world like Chicago in The Dark Knight Rises). Why it's NYC or Chicago is not so important for me. But why, e.g., were the trains which featured prominently in Begins gone in The Dark Knight Rises? There was only a very short in-universe time-span between the events of the two movies, yet Gotham changed drastically. How to integrate $\int x^2 \sin^2(x)dx$ I don't know how to integrate $\int x^2\sin^2(x)\,\mathrm dx$. I know that I should do it by parts, where I have  $$ u=x^2\quad  v'=\sin^2x \\  u'=2x \quad v={-\sin x\cos x+x\over 2}$$  and now I have  $$ \int x^2\sin^2(x)\,\mathrm dx = {-\sin x\cos x+x\over 2} x^2 - \int 2x{-\sin x\cos x+x\over 2}\,\mathrm dx\\ ={-\sin x\cos x+x\over 2} x^2 - \int x(-\sin x\cos x+x)\,\mathrm dx\\  $$  so I have to calculate $$ \int x(-\sin x\cos x+x)\,\mathrm dx=-\int x\sin x\cos x\,\mathrm dx+\int x^2\,\mathrm dx$$  I know that $\int x^2\,\mathrm dx = {1 \over 3}x^3+C$ but I don't know what should I do with $$\int x\sin x\cos x \,\mathrm dx$$ Should i use parts again or what? Please help. Format numbers in django templates Accessing a property of derived class from the base class in C# In C#, what is the best way to access a property of the derived class when the generic list contains just the base class.  public class ClassA : BaseClass {    public object PropertyA { get; set; } }  public class ClassB: BaseClass {     public object PropertyB { get; set; } }  public class BaseClass { }  public void Main {     List&lt;BaseClass&gt; MyList = new List&lt;BaseClass&gt;();     ClassA a = new ClassA();     ClassB b = new ClassB();      MyList.Add(a);     MyList.Add(b);      for(int i = 0; i &lt; MyList.Count; i++)     {         //I would like to access PropertyA abd PropertyB from the derived classes             } } I've seen documentation whereby an \alph command is put around the \begin{enumerate} somewhere, but I'm not entirely sure how that operates... How do I install/update drivers on Debian 9? I just installed Debian 9 on my laptop, however Wifi isn't working and I'm not sure if my graphic card is either. I'm sure that it's just a lack of drivers, but I've never actually had to update drivers on Linux before. So how do I do that? Film about some dude who fell in love with a star (a literal stellar object) Yes, the plot is pretty weird. There is this "star" (whose incarnation is a woman dressed in white) and some random guy who falls in love with her. There's the arc of "if you cross a specific border you'll die" which applies to our lady "star". Well, I also remember that they have some kind of a tubular case, and when one opens it, lightning files out.  I watched the film somewhere around 2010, it's in English and when I try to remember it, I get the vibe of a mediocre Hollywood fantasy romance. Several badge descriptions contain raw HTML I was reading through some badge descriptions and noticed that Synonymizer's description needs to be updated. As it stands, there is raw HTML (an href) in the description:    EDIT: after reading comments by @ColeJohnson, I have come to the understanding that this post comes off as whiny. I want to make it very clear that I wasn't ever trying to complain. My first reaction was to fix the perceived error myself. When I realized I was unable to do so, I figured the best course of action would be to find someone who would be able to make the necessary edits. Hence the post here. Why can I only change my Stack Overflow name once every 30 days? What's the difference between align and align*? After some brief searching I can't find the difference between align and align*. Google summarily ignoring the * is making it harder I think.  Can you tell me the difference between these two?  Moreover, can you tell me where you generally go for this type of information? As a relatively new user I'm still building up my resources. We  that there's a difference in meaning between try used with the infinitive and  try used with the gerund:     I tried sending her flowers. (Meaning: An experiment: I sent her flowers to see what will happen).   I tried to send her flowers. (Meaning: I tried to go through the procedure necessary to send flowers to her. The procedure might have been difficult.)   (per Michael Swan's PEU, Unit 299.6)   Will the same distinction hold if we use trying:     A man is trying setting up a password on his computer. (Is he experimenting, wanting to see what will happen?)   A man is trying to set up a password on his computer. (Is he trying to go through all the necessary steps, probably difficult, of setting up a password?) In C#, should I use string.Empty or String.Empty or "" to intitialize a string? In C#, I want to initialize a string value with an empty string.  How should I do this?  What is the right way, and why?  string willi = string.Empty;   or  string willi = String.Empty;   or  string willi = "";   or what? Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$ Suppose $(M,d)$ a metric space. I want to show that      If every continuous real-valued function on $M$ attains a maximum, then $(M, d)$ is compact.   I was trying to do this by assuming $M$ non-compact and showing explicitly a function which does not attain a maximum. If $M$ is not bounded it's enough to take the distance from a fixed point as we can always find a sequence which "exits" every compact and pushes the distance at infinity. But what if $M$ is bounded? Notify users of a question they closed being edited or nominated for reopening "Effect" vs. "Affect" I've noticed that some people use effect and affect interchangeably. What are the differences between these two and when are the proper situations to use each of them?