C# Passing a method as a parameter to another method
Pass Method as Parameter using C#
Why is "cupboard" pronounced with a silent "p"? According to Google at least, the word "cupboard" originated in late Middle English as denoting a board that held cups. Since then, the word has evolved to mean a kind of cabinet.  My question is, given its origin and spelling, why do we pronounce "cupboard" with a silent "p"? Has the pronunciation simply evolved because "cup-board" is too awkward to say, or is there a deeper pronunciation rule that I'm not aware of? Where does the Mac store account pictures? I took a picture to add to my account on Mac.   Now I want to use it on messenger, but I can't find it. On the account config, it's too small. I need to find the original.   Where are the accout pictures stored on a Mac? I want to plot this graph, but I don't know how to code the words in the nodes.     Here is my code:  \documentclass{article} \usepackage{amsmath} \usepackage{titletoc} \usepackage{tikz} \usetikzlibrary{trees,positioning,fit}  \begin{document}{\allowdisplaybreaks[4]}  \tikzstyle{bag} = [text width=2em, text centered] \tikzstyle{end} = []  \begin{center} \begin{tikzpicture}[sloped] \node (a) at ( 0,0) [bag] {$\ln r_0$}; \node (b1) at ( 3,1.5) [bag] {$\ln r_{10} + \sigma_1\sqrt{\Delta t_1}$}; \node (b2) at ( 3,-1.5) [bag] {$\ln r_{10}$}; \node (c1) at ( 6,3) [bag] {$\ln r_{20} + 2\sigma_2\sqrt{\Delta t_2}$}; \node (c2) at ( 6,1.5) [bag] {$\textrm{Mean} = \ln r_{20} + \dfrac{3}{2}\sigma_2\sqrt{\Delta t_2}$\\$\textrm{Mean Change} = \mu_{11}\Delta t_2 = \ln\dfrac{r_{20}}{r_{10}} + \dfrac{3}{2}\sigma_2\sqrt{\Delta t_2} - \sigma_1\sqrt{\Delta t_1}$}; \node (c3) at ( 6,0) [bag] {$\ln r_{20} + \sigma_2\sqrt{\Delta t_2}$}; \node (c4) at ( 6,-1.5) [bag] {$\textrm{Mean} = \ln r_{20} + \dfrac{3}{2}\sigma_2\sqrt{\Delta t_2}$\\$\textrm{Mean Change} = \mu_{11}\Delta t_2 = \ln\dfrac{r_{20}}{r_{10}} + \dfrac{3}{2}\sigma_2\sqrt{\Delta t_2} - \sigma_1\sqrt{\Delta t_1}$}; \node (c5) at ( 6,-3) [bag] {$\ln r_{20}$}; \draw [-&gt;] (a) to node [below] {} (b1); \draw [-&gt;] (a) to node [above] {} (b2); \draw [-&gt;] (b1) to node [below] {} (c1); \draw [-&gt;] (b1) to node [below] {} (c2); \draw [-&gt;] (b1) to node [below] {} (c3); \draw [-&gt;] (b2) to node [below] {} (c3); \draw [-&gt;] (b2) to node [below] {} (c4); \draw [-&gt;] (b2) to node [below] {} (c5); \end{tikzpicture} \end{center}  \end{document}       Update code use  \draw [-&gt;] (a) to node [below] {} (b1.south east); \draw [-&gt;] (a) to node [above] {} (b2.north east); \draw [-&gt;] (b1.south east) to node [below] {} (c1.west); \draw [-&gt;] (b1.south east) to node [below] {} (c2.west); \draw [-&gt;] (b1.south east) to node [below] {} (c3.west); \draw [-&gt;] (b2.north east) to node [below] {} (c3.west); \draw [-&gt;] (b2.north east) to node [below] {} (c4.west); \draw [-&gt;] (b2.north east) to node [below] {} (c5.west); Lost supplementary user groups for GUI login session Ubuntu 16.04.5  Very weird situation - after Xorg crash, now every time when I login into Unity, my user account doesn't have it's system groups like adm, sudo, plugdev, fuse etc. But when I login on virtual console (Alt+F1) or over SSH - all my additional groups are there, as reported by id command.  Neither of /etc/group* or /etc/gshadow* files have changed, my user is still listed there in many system groups.  It looks like some systemd session parameters for GUI logins or lightdm cache files got screwed. But I have no idea where to start looking..  A lightdm log:  $ journalctl -au lightdm  -- Reboot -- systemd[1]: Starting Light Display Manager... systemd[1]: Started Light Display Manager. lightdm[3223]: pam_kwallet5(lightdm-greeter:setcred): (null): pam_sm_setcred lightdm[3223]: pam_unix(lightdm-greeter:session): session opened for user lightdm by (uid=0) lightdm[3345]: pam_succeed_if(lightdm:auth): requirement "user ingroup nopasswdlogin" not met by user "chm" lightdm[4867]: pam_ecryptfs: Passphrase file wrapped lightdm[3345]: pam_kwallet5(lightdm:auth): (null): pam_sm_authenticate lightdm[3345]: pam_kwallet5(lightdm:setcred): pam_kwallet5: pam_sm_setcred lightdm[3345]: pam_unix(lightdm:session): session opened for user chm by (uid=0) lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Failed to write utmpx: Permission denied Is the following conjecture true?     Given an $n&gt;1$ and a $k$ such that $0&lt;k&lt;n$ then $\gcd\left(\binom{n}{k}, n\right)&gt;1$   This was a question asked in my old Number Theory course that I recently remembered. It was posed after we learned that $p\mid\binom{p}{k}$ for $0&lt;k&lt;p$. We never resolved it either way. I expect it to be true and have an elegant answer, but I haven't been able to prove it. My textbook explains the proof, which I don't understand:  "Consider two bases $v_1...v_p$ and $w_1...w_q$ of V. Since the vectors $v$ are linearly independent and the vectors $w$ span V..."  How exactly does $w$ span V?   The book then says the same for vectors $v$, that $v$ spans V and hence $p=q$, but I don't really understand how you can assume that given two sets of vectors that are basis, one set must span V. In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs? Removing OS from Dual Boot computer, and recovering HD space. How far can/should one press philosophical doubt? Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do)? Descartes used 'I think' as this fixed point where the skepticism abates, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy? G is the product of its Sylow subgroups I want to prove the following:     If every Sylow subgroup of $G$ is a normal subgroup, then $G$ is isomorphic to the product of its Sylow subgroups.   So far, I have gotten to realize that for every prime factor $p_i$ of $|G|$, there is exactly one Sylow subgroup and that these form a partition of $G$. However, I am having trouble finding the isomorphism between $G$ and the product which I will call $G_1 \times \ldots \times G_r$. My idea was just to use the mapping $(g_1, \ldots, g_r) \mapsto g_1\ldots g_r$, which is a bijection, but I don't see whether it is a homomorphism. In general, not all elements of $G_i$ commute with elements of $G_j$, so one cannot simply change the order of the elements in the product. Suppose we have two short exact sequences in an abelian category $$0 \to A \mathrel{\overset{f}{\to}} B \mathrel{\overset{g}{\to}} C \to 0 $$ $$0 \to A&#39; \mathrel{\overset{f&#39;}{\to}} B&#39; \mathrel{\overset{g&#39;}{\to}} C&#39; \to 0 $$ and morphisms $a : A \to A&#39;, b : B \to B&#39;, c : C \to C&#39;$ making the obvious diagram commute. The snake lemma states that there is then an exact sequence $$0 \to \ker a \to \ker b \to \ker c \to \operatorname{coker} a \to \operatorname{coker} b \to \operatorname{coker} c \to 0$$ where the morphisms between the kernels are induced by $f$ and $g$ while the maps between the cokernels are induced by $f&#39;$ and $g&#39;$.  It is not hard to show that the morphisms induced by $f, g, f&#39;, g&#39;$ exist, are unique, and that the sequence is exact at $\ker a, \ker b, \operatorname{coker} b, \operatorname{coker} c$. With the use of a somewhat large diagram shown , we can even construct the connecting morphism $d : \ker c \to \operatorname{coker} a$. However, I'm stuck showing exactness at $\ker c$ and $\operatorname{coker} a$. I thought Freyd might have had an element-free proof in his book, but it turns out he proves it by diagram chasing and invoking the Mitchell embedding theorem [pp. 98–99]. Is there a direct proof? Let $f$ be a holomorphic function defined on $\Bbb C$ such that $f^{-1}(\Bbb R)=\Bbb R$. Prove that there exists $a,b \in \Bbb R, \; a \neq 0 \;$ such that $f(z)=az+b \;$ for every $z \in \Bbb C$.  I was given a hint: define the function $g(z)=\frac{f(z)-f(0)}{z}$. such $g$ is also holomorphic in $\Bbb C$ since the only singularity is in $0$, and it is a removable singularity since we can define $g(0)=f'(0)$. Next I thought about proving $g$ is bounded, and thus constant (using Liouville's theorem), but pretty much out of ideas. How can I finish the proof/solve in another way? "Over vs Above" and "Under vs below" Is is possible to say that "Above" means "over" and "Under" means"below", but not the opposite?  According to my grammar:  Over - In a higher position (close or touching) Above - In a higher position  Under - In a lower position (close or touching) Below - In a lower position  Example:     There's a helicopter flying round above / over the school.   I would interpret this sentence as "above" meaning almost touching the school or not. And If I hear "over", the helicopter is almost touching school.  This makes me think about "over" and "on". "On" means that something is touching something, but if "over" can mean also "touch".Well, I would never use "over" to mean "touching something", I would use "on" instead. How to reduce space between image and its caption? Every word is marked as misspelled in TeXstudio Let $(a_n)_{n≥0}$ and $(b_n)_{n≥0}$ be two sequences of a nomed algebra such that $\sum{\| a_n\|}$ and $\sum{\| b_n\|}$ converge, and$ $$$\forall n, \  a_n, b_n \neq 0$$  Show that $(\forall  k \in \mathbb N^*,  \ \sum_{n=0}^{\infty}{a_n}^k = \sum_{n=0}^{\infty}{b_n}^k) \implies \exists\ \sigma \in{\mathfrak S}_{\mathbb N} \ ,\ (a_n) = (b_{\sigma(n)})$  The vector-space should be a finite-dimensional $\mathbb R$-vector-space.   I do not see how to deal with the hypothesis. If you have ideas/hints...  It would be relevant to deal with complex sequences even if it is less general. But I don't think one can generalize using real and complex cases. In what order should you do linear regression diagnostics? In linear regression analysis, we analyze outliers, investigate multicollinearity, test heteroscedasticty.   The question is:  Is there any order to apply these? I mean, do we have to analyze outliers very firstly, and then examine multicollinearity? Or reverse?    Is there any rule of thumb about this? Android app should send edits to edit queue if necessary rather than rejecting them $\int_0^{\pi/2}\ln(\sin(x))$? From this paper:     Shouldn't $du$ be $dt$? And also how do you get from that line to the final result if $du$ is not $dt$? Maximum area of isosceles triangle with perimeter 6 cm Problem. What is the side lengths of an isosceles triangle with $6cm$ perimeter which has the largest area? I solved this problem as below and I would like to learn  that if there is anything wrong: Let us say that the side lengths are $a$ and the bottom length is $6-2a$. By using pythagorean theorem we can conclude that the height $h$ is equal to $\sqrt{6a-9}$. Then, the area of the triangle can be given as $f(a)=(3-a)(\sqrt{6a-9})$. So $f'(a)=-\sqrt{6a-9}+\cfrac{3}{\sqrt{6a-9}}$. Finally, $f'(a)=\cfrac{12-6a}{\sqrt{6a-9}}$ and $f'(a)=0 \iff a =2$.