I was going through a c++ code and saw a header file with below declaration:  file a.h class xyz;   But that class was not defined any where in the file. I also wrote a code and it perfectly compiles fine. Just wanted to know what is the use of declaring a class like this as it does't enforces programmer to define.  Thanks in advance!!
I am looking for the definition of when I am allowed to do forward declaration of a class in another class's header file:  Am I allowed to do it for a base class, for a class held as a member, for a class passed to member function by reference, etc. ?
Let $X$ be a non-negative random variable and $F_{X}$ the corresponding CDF. Show,   $$E(X) = \int_0^\infty (1-F_X (t)) \, dt$$   when $X$ has : a) a discrete distribution, b) a continuous distribution.   I assumed that for the case of a continuous distribution, since $F_X (t) = \mathbb{P}(X\leq t)$, then $1-F_X (t) = 1- \mathbb{P}(X\leq t) = \mathbb{P}(X&gt;  t)$. Although how useful integrating that is, I really have no idea. How do I install and manage RPMs? I have a burning desire to install RPMs onto my Ubuntu installation - is this possible? Can I use Yum - or another RPM Package Management tool? How symbol lookup actually works Does Moore's law apply to quantum computing? Plain and simple. Does  apply to quantum computing, or is it similar but with the numbers adjusted (ex. triples every 2 years). Also, if Moore's law doesn't apply, why do qubits change it? Is there something like python's interactive REPL mode, but for Java? Is there something like python's interactive REPL mode, but for Java? So that I can, for example, type InetAddress.getAllByName( localHostName ) in a window, and immediately get results, without all this public static void nightmare() thing? Why isn't there a truly unified package manager for Linux? Why isn't there a unified package manager that acts as an interface between the end-user and the underlying low-level package manager (apt, yast, pacman, etc.)?  Is it hard to do and therefore not practical, or is there a genuine obstacle making it impossible to do? In PHP, is there an easy way to convert a number to a word? For instance, 27 to twenty-seven. I am using Eclipse 3.3 ("Europa"). Periodically, Eclipse takes an inordinately long time (perhaps forever) to start up. The only thing I can see in the Eclipse log is:       !ENTRY org.eclipse.core.resources 2 10035 2008-10-16 09:47:34.801     !MESSAGE The workspace exited with unsaved changes in the previous session; refreshing workspace to recover changes.   Googling reveals  that I remove the folder:  workspace\.metadata\.plugins\org.eclipse.core.resources\.root\.indexes   This does not appear to have helped.  Short of starting with a new workspace (something which I am not keen to do, as it takes me hours to set up all my projects again properly), is there a way to make Eclipse start up properly? Execute shell script or command on idle time I'm searching for the possibility to execute a shell script or command based on idle time in the bash shell.  As an example, if I'm in a SSH session to a server of mine and after X minutes of inactivity in the terminal, I want a command to start a desired program like cmatrix, and when I come back and press a key I will get back where I left. Indefinite integral of $ \int \frac{x^3}{\sqrt{x^2+1}} \,\text{d}x$. Can you please provide any sort of hint or suggestion on how to find the following indefinite integral?  $$\int\frac{x^3}{\sqrt{x^2+1}}\text{d}x$$  I tried substituting everything but it didn't work. I also tried trigonometric substitution but I couldn't find any valid trigonometric identity for $ \sqrt{\cos^2(x)+1} $ or $ \sqrt{\sin^2(x)+1} $. Can I get a certificate from a root CA that I can then use to sign my own web server certificates? I would, if possible, use a signed certificate as an intermediate to sign other certs.  I know that I would have to configure my systems in a certain way with "my" intermediate certificate in order to supply information about the chain of trust to my clients.   Is this possible? Are root CAs willing to sign a certificate like this? Is it expensive?  BACKGROUND  I'm familiar with the basics of SSL as it pertains to securing web traffic over HTTP. I also have a basic understanding of the way the chain of trust works, in that web traffic is secured "by default" if you encrypt with a certificate that has a valid chain all the way back to a root CA, as determined by the browser/OS vendor.  I am also aware that many of the root CAs have begun signing certificates for end users (like me) with intermediate certificates. That may require a bit more setup on my end, but otherwise, those certificates will work fine. I guess this has to do with protecting their all-valuable private key for the CA and the disaster that it would be if i were ever compromised.  EXAMPLES        Now, we are definitely not the size of any of those organizations, but they seem to be doing something like this. It would definitely make the management of these certificates a lot more palatable, especially considering one way we are expanding the reach of our e-commerce platform. How to Install Virtualbox on Windows 10 host? I've always enjoyed solving problems in the complex numbers during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be used/applied and hence am curious.  So what practical applications of complex numbers exist and what are the ways in which complex  transformation helps address the problem that wasn't immediately addressable?  Way back in undergrad when I asked my professor this he mentioned that "the folks in mechanical and aerospace engineering use it a lot" but for what? (Don't other domains use it too?). I'm well aware of its use in Fourier analysis but that's the farthest I got to a 'real world application'. I'm sure that's not it.  PS: I'm not looking for the ability to make one problem easier to solve, but a bigger picture where the result of the complex analysis is used for something meaningful in the real world. A naive analogy is deciding the height of tower based on trigonometry. That's going from paper to the real world. Similarly, what is it that is analyzed in the complex world and the result is used in the real world without imaginaries clouding the problem?  The question:  is nice but covers a more mathematical perspective on interim results that make solving a problem easier. It covers different ground IMHO. How to modify function argument? I'd like to manage my home machines and laptops with Landscape, how can I do this? Why are memory statistics in top and htop different? Whenever I use top and htop commands to see memory stats, they are always different as shown in figures. Which should I trust? What is the difference between a directory name that ends with a slash and one that does not? Is there any difference between a directory name such as  mydirectory   and  mydirectory/   I noticed this happens when I execute ls in some directories - some of the directory names have a slash and some don't. This is problematic because if I want to access a file contained in a directory, I may need to add a slash at the end:  vi $mydirectory"/"$myfile   or simply do   vi $mydirectory$myfile I am trying to write the Euclidean algorithm in the following way:  $A = \lfloor A \div B \rfloor \times B + (\text{remainder of}) \: A \div B $   Now is there any symbol I can use  to say "remainder of A $\div$ B"? I know that in the C programming language there is the operator % for modulus; is that a valid symbol in maths? Can I write A % B? Or is there some other way? Every subspace of a compact space is compact? It seems as if every subspace of a compact topological space (equipped with its relative topology) had ought to be compact as well. Is this true in general?  And in particular, I want to use the fact that every quasi-projective variety is compact with the Zariski topology - I remember having proven it for quasi-affine varieties, but the same proof does not work for quasi-projective varieties. Is every quasi-projective variety compact? JavaScript Regex, where to use escape characters?