Embedding .bin files in C++ executable
Embed data in a C++ program
showing that a group of order 45 is abelian I'm trying to understand the following proof from Dummit &amp; Foote (pg. 137) which shows why a group of order 45 is abelian. I understand everything but the last two sentences. Why is it that $|G/C_G(P)|=1$? Also, is it always true that $G/Z(G)$ is abelian? Thank you! What are the pros and cons of the leading Java HTML parsers? Each site got a &quot;hot&quot; tab, where its contents are calculated based on . However take a look on the screenshots below and see for yourself that &quot;hot&quot; got nothing to do with many of the questions listed there. :    :    As you can see, there are questions with negative score, no answers, and even closed. I won't be surprised to see spam in there as well. This can't be any worse. What I suggest, instead of fixing the formula or patching it, simply have the hot tab show the same questions as the Hot Network Questions sidebar. (from the specific site only, of course.) Since the hot questions &quot;pool&quot; (as seen ) is limited to 100 for the whole network, either expand it or have the per-site list show questions with less hotness points - it would still be better than what we have now. I'm very new to presentations in LaTeX (I've been using PowerPoint for years but have finally converted). I am wondering how to get a GIF into a section. If need be, I can convert a GIF into lots of pictures and have them overlay to give the impression of movement. calculating mean of a random variable raised to a power What are the differences between "lay" and "lie"? I am trying to use a  as input and then creating a query with it - so I need a .    I was surprised to find that it couldn't do the conversion implicitly or explicitly - but I don't even know how I would do this, as the Java API is still fairly new to me. Area 51 layout breaks when zoomed to 90% Display lost/negative reputation in topbar achievements When you get reputation, you get a +X green spot on your reputation feed telling you that you gained reputation and if you drop down the menu, you get more detail.  How about we make it that when you lose more than you got since the last time you checked, you see it red with a little -X.  For example, let's say you've just looked at the reputation bar so any old rep notification is gone and you ask a new question. 3 users downvote your question and 1 upvotes it. You will see it green because you gained 5 rep but you should see it red because you are at -1 rep.   This would help people improve their questions / answer by seeing, as soon as they get on the site, that they got negative feedback and that something needs to be checked / changed.    It shows here so it could very well be applied to the notification count: double r = 11.631; double theta = 21.4;   In the debugger, these are shown as 11.631000000000000 and 21.399999618530273.  How can I avoid this? Can someone provide a proof that every quadratic residue, when working in $\mathbb Z_p$, where $p$ is a prime, has exactly two roots? Indeed, there cannot be only one root as for any $a^2$, we know $a$ and $-a$ are both roots. So then we need only show that there cannot be more than two- does this follow from some argument for the number of roots a quadratic can have modulo a prime? I'm not well-acquainted with the theorems pertaining to prime moduli. Linear regression not fitting well I do a linear regression using R lm function:  x = log(errors) plot(x,y) lm.result = lm(formula = y ~ x) abline(lm.result, col="blue") # showing the "fit" in blue     but it does not fit well. Unfortunately I can't make sense of the manual.  Can someone point me in the right direction to fit this better?  By fitting I mean I want to minimize the Root Mean Squared Error (RMSE).    Edit: I have posted a related question (it's the same problem) here:   and the raw data here:    except that on that  x is what is called errors on the present page here, and there are less samples (1000 vs 3000 in the present page plot). I wanted to make things simpler in the other question. What are the differences between vector graphics and raster graphics? Why do heavier objects fall faster in air? Location of /etc/fstab in El Capitan I want to activate the . But I can't find the /etc/fstab on my mac. osx 10.11.5 El Capitan Is there a way to use the covariance matrix to find coefficients for multiple regression? For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by  $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, and $e$ is the explanatory variable's index.  If one only has the covariance matrix, is it possible to calculate the coefficients for a model with multiple explanatory variables?   ETA: For two explanatory variables, it appears that $$\beta_1 = \frac{Cov(y,x_1)var(x_2) - Cov(y,x_2)Cov(x_1,x_2)}{var(x_1)var(x_2) - Cov(x_1,x_2)^2} $$ and analogously for $\beta_2$. I'm not immediately seeing how to extend this to three or more variables. How to edit 'etc/hosts' file in non-rooted phone? I'm using LineageOS 14.1 and don't want nor need to root it. How can I remount /system rw and edit /system/etc/hosts?  All answers in "" expect a rooted phone. In addition to showing reputation scores, SO should rank users. In the users section, users are ordered by the reputations they have.  Each user should also have a unique rank, since many users can have the same reputation score.  Rank must follow the order laid out by reputation, but for those having similar reputation, an additional formula should be defined which can rank users based on tags, time since registration, frequency of activity and/or helpfulness of their answers.  What are your thoughts on this? How do I manually install Adobe Flash player for Chromium? Ramanujan log-trigonometric integrals I discovered the following conjectured identity numerically while studying a family of related integrals.  Let's set $$ R^{+}:=  \frac{2}{\pi}\int_{0}^{\pi/2}\sqrt[\normalsize{8}]{x^2 + \ln^2\!\cos x} \sqrt{ \frac{1}{2}+\frac{1}{2}\sqrt{ \frac{1}{2}+ \frac{1}{2}  \sqrt{ \frac{\ln^{2}\!\cos x}{ x^2 + \ln^2\! \cos x}}}}\,\mathrm{d}x, \tag1 $$ $$ R^{-}:=  \frac{2}{\pi}\int_{0}^{\pi/2}\frac{1}{\sqrt[\normalsize{8}]{x^2 + \ln^2\!\cos x}} \sqrt{ \frac{1}{2}+\frac{1}{2}\sqrt{ \frac{1}{2}+ \frac{1}{2} \sqrt{ \frac{\ln^{2}\!\cos x}{ x^2 + \ln^2\! \cos x}}}}\,\mathrm{d}x. \tag2 $$ We may numerically observe with at least 500 digits of precision that $$  \begin{align} &amp; R^{+}R^{-} \stackrel{?}{=}1 \tag 3 \\\\ &amp; R^{+} \stackrel{?}{=} \sqrt[\normalsize{4}]{\ln 2} \tag4 \\\\ &amp; R^{-} \stackrel{?}{=}\frac{1}{\sqrt[\normalsize{4}]{\ln 2}}. \tag5 \end{align} $$  How can we prove it?  A version of this has been sent to Eric Weisstein, these integrals are on Mathworld as .