What does ~ in front of the class name signify in C#?
What does the tilde before a function name mean in C#?
Array of zero length Are +1/+1 counters different from +1/+1 effects? Is a +1/+1 counter I get from, say Unleash or Undying different than +1/+1 from something like  or ? How can I create an executable JAR with dependencies using Maven? What's the difference between terms 'link function' and 'canonical link function'? Also, are there any (theoretical) advantages of using one over the other?  For example, a binary response variable can be modeled using many link functions such as logit, probit, etc. But, logit here is considered the "canonical" link function. Does creating an object using reflection rather than calling the class constructor result in any significant performance differences? Pairwise independence of Random variables does not imply indendence Show by a counterexample that for a family $(X_i)_{i\in I}$ of random variables the independence of all pairs $(X_i,X_j)$ with $i,j\in I, i\neq j$ does not imply the independence of the family (It is enough to consider $\mbox{card}(I)=3$.).      Hello, I am searching for a simple example. The professor gave the hint that one might consider random variables which only can take two different values, but I do not know exactly what is meant.  By the way:  We call the family $(X_i)_{i\in I}$ of random variables independent, if $(\sigma(X_i))_{i\in I}$ is independent, whereat we call a family $(\mathcal{E}_i)_{i\in I}$ with $\mathcal{E}_i\subset\mathcal{A}$ independent, if for any finite subset $I_0\subset I$ and any choice $E_i\in\mathcal{E}_i, i\in I_0$, it is $$ \mathbb{P}(\bigcap_{i\in I_0}E_i)=\prod_{i\in I_0}\mathbb{P}(E_i). $$ I want to create a math problem-solution sheet. The coefficients a, b, c must be assigned on the fly at random so the generated pdf will show a numeric quadratic equation rather than a symbolic quadratic equation. Note a must not be zero.  \documentclass{article} \begin{document} \section{Problem} Let \(x_1\) and \(x_2\) be the roots of \(a x^2 +bx +c=0\). Find  \(x_1x_2\).  \section{Solution} \[ x_1x_2=\frac{c}{a} \] \end{document}   Please kindly make the solution get automatically simplified. For example: \frac{c}{a}=3 when a=2 and c=6.    Actually the real case is more complex than this one. Not only the equations must be generated at random, but also the associated graphic plots that I write in PSTricks.     I chose Paulo's answer because using Maxima as the computation engine is very very great idea. Other answers are also good and creative, especially Altermundus'. Make grub keep its default boot under kernel updates I dual-boot my machine and I want it to default to boot into windows so that whenever I restart the machine remotely from my home it will be able to get back into Windows (instead of Ubuntu).  The problem is that every time Ubuntu upgrades the kernel, I have to reset the default boot item of grub back to windows. This is because the grub menu loader uses positions i.e. 6 for default OS to boot. And when Ubuntu installs a new kernel it changes that order.  I am looking for a way to configure grub to remember its default boot item under kernel updates. Why can't the indefinite integral $\int\frac{\sin(x)}{x}\mathrm dx$ be found? I came across a list of functions in my calculus textbook whose indefinite integral cannot be found. It was written that the integral $$\int \frac{\sin(x)}{x} dx$$ cannot be evaluated without any explanation as to why.  I did some research over the internet and found out that the definite integral $$\int_{0}^{\infty} \frac{\sin(x)}{x} dx$$ can be evaluated using Laplace transformation and is equal to $\pi /2$. But I still couldn't find answer to my original question. I read somewhere that the integral cannot be expressed using 'elementary functions'. A little help is appreciated, I'm in Calc 1 going advanced than my course but I am sorry if my post shows lack of research. Thank you! An equivalent condition with $\{0\}$ being the only nilpotent ideal Find all continuous functions $f$ satisfying   $$\int_0^xf=(f(x))^2+C$$ for some constant $C \neq 0$, assuming that $f$ has at most one $0$.  I have a question about the solution to this problem. It says that   Clearly $f^2$ is differentiable everywhere, its derivative at $x$ is $f(x)$ (I'm assuming that this is because the left hand side is differentiable, the right hand side must be differentiable as well). So $f$ is differentiable at $x$ whenever $f(x) \neq 0$, and  $$f(x)=2f(x)f'(x),$$ so $f'(x) = \frac{1}{2}$ at such points. Thus, $f= \frac{1}{2}x+b$ for some $b$ on any interval where it is non-zero; if $f$ has a zero, this gives two possible solutions, with two possible values of $b$, but since $f$ is assumed continuous, they must be the same. So we need $$\int_0^x(\frac{1}{2}t+b)dt=(\frac{1}{2}x+b)^2+C$$  so we must have $b=\sqrt{-C}$ or $-\sqrt{-C}$, leading to two solutions for $C \lt 0$.  I don't understand the bolded statements. First, how does the differentiability of $f^2$ guarantee that $f$ is differentiable, and why only at $x$ where $f(x) \neq 0$?  Next, why are there two possible solutions if $f$ has a zero, but since $f$ is continuous they must be the same?  Finally, does the last statement mean that if $C \gt 0$, then there is no solution, since we're restricted to real numbers here?  I would appreciate it if anyone answers my questions. Vertical placing of wide accents in superscript The following code  $\widetilde{aaa} \quad L^{\widetilde{aaa}}$  $\tilde{aaa} \quad L^{\tilde{aaa}}$  $\widehat{aaa} \quad L^{\widehat{aaa}}$  $\hat{aaa} \quad L^{\hat{aaa}}$  $\overline{aaa} \quad L^{\overline{aaa}}$  $\bar{aaa} \quad L^{\bar{aaa}}$   produces the following output:    What is the reason for additional vertical spacing for \widetidle and \widehat in superscript and what can one do about it? Dropping z dimension programmatically It seems there is no geoalgorithm to drop z values in the QGIS processing toolbox. Can this be done programmatically using the Python console? At the moment I have to save the layer with unchecked 'Include z-dimension' checkbox (non automatic geometry type): shebang line not working with cr-lf I've been told that when "the" is proceeded by a vowel sound, like "apple" or "hour", it's pronounced as "thee" and not as "thu".  But after listening to a couple of songs, I noticed that sometimes this "rule" is not followed. Take for example the two Katy Perry's songs, "Roar" and "The one that got away". In the first she sings "I got thee eye of thu tiger", but in the second she sings "Thu one that got away".  I don't know if it was sang this way to better suit the song melody (I understand nothing about those techniques), but I got confused. What's the correct pronunciation?  Thanks in advance. Sublime Command not working in SSH server on Ubuntu 14.04? Bonferroni adjustment in SPSS - what does it do? I'm probably being a bit simplistic here, but from what I understand the Bonferroni post hoc test is simply when we adjust the alpha to account for inflated error when several post hoc tests are conducted. You divide the alpha by number of tests. So what exactly does SPSS do when we click the button for Bonferroni?   Shouldn't the dividing of alpha be done by us in interpreting the result, e.g. if we do 10 post hoc tests our alpha criterion should be .005 so if the p value is .012 then it is not significant, but SPSS hasn't done anything there, we have just changed our interpretation. So what exactly is it adjusting? I  here on MSO today, but it was found to have been asked .  I'm not concerned by this (better to be found by more than one user) but, I noticed that the wording in the closure statement is factually incorrect:    No it doesn't have an answer - Not even a sniff of one!  This statement, logically, should be factually accurate and reflect the existence of answers and include singular/plural references to them - or at a minimum use language that covers both scenarios.  Edit: As a result of my question,  and the bug in question has been remedied, but this question still remains valid. Wi-Fi only works after waking MacBookPro7,1 from sleep Been having some issues with the STA drivers from bcrmwl-kernel-source. While the drivers do function, they only seem to function after putting the laptop to sleep, by either closing the lid, or manually putting it to sleep, and waking it up. The laptop here is a MacBookPro7,1 (Mid 2010 13-inch MacBook Pro), running Ubuntu 17.04.  While the issue isn't bad enough to deter me from using the laptop, it is not an elegant solution, and I believe that there can be a solution found somewhere.  For reference, here are the outputs from the Wireless Info script for both before and after: , . Hopefully these are of some use. If you need additional information about the computer, I will be happy to answer. How do I make Endermen spawn more frequently? I'm playing vanilla Minecraft, and am getting ready to head to the end.  I need Eyes of Ender (and hence Ender Pearls), and in my main hunting grounds (a large desert area) as little as one Enderman may spawn per night.  Is there any way to "promote" Enderman spawning so I can get pearls more quickly?