how to upgrade libc6 on debian 7.1?
mod_pagespeed : install earlier version compatible with libc6 2.13 (Debian Wheezy)
Given a 4-vector $p^\mu$ the Lorentz group acts on it in the vector representation: $$ \tag{1} p^\mu \longrightarrow (J_V[\Lambda])^\mu_{\,\,\nu} p^\nu\equiv \Lambda^\mu_{\,\,\nu} p^\nu. $$ However, I can always represent a 4-vector $p^\mu$ using left and right handed spinor indices, writing $$ \tag{2} p_{\alpha \dot{\alpha}} \equiv \sigma^\mu_{\alpha \dot{\alpha}} p_\mu.$$ So the question is: in what representation does the Lorentz group act on $p_{\alpha \dot{\alpha}}$?    There are a lot of questions about this and related topics around physics.se, with a lot of excellent answers, so let me clear up more specifically what I am asking for.  I already know that the answer to this question is that the transformation law is  $$ \tag{3} p_{\alpha \dot{\alpha}} \rightarrow (A p A^\dagger)_{\alpha\dot{\alpha}}$$ with $A \in SL(2,\mathbb{C})$ (how is mentioned for example in ). I also understand that $$ \tag{4} \mathfrak{so}(1,3) \cong \mathfrak{sl}(2,\mathbb{C}),$$ (which is explained for example  by Edward Hughes,  by joshphysics,  by Qmechanic).  So what is missing? Not much really. Two things:   How do I obtain (3) and what is the specific form of $A$, i.e. its relation with the vector representation $\Lambda^\mu_{\,\,\nu}$? Defining the following $$ (\tilde p) \equiv p^\mu, \qquad \Lambda \equiv \Lambda^\mu_{\,\,\nu},$$ $$ \sigma \equiv  \sigma_{\alpha \dot \alpha}, \qquad \hat p \equiv p_{\alpha \dot \alpha},$$ we can rewrite (1) and (2) in matrix form as $$ \tag{5} \hat p \equiv \sigma \tilde p \rightarrow \sigma \Lambda \tilde p  = ( \sigma \Lambda \sigma^{-1}) \hat p,$$ however, this disagrees with (3) which I know to be right, so what is wrong with my reasoning? Why does the transformation law (3) has a form $$\tag{6} A \rightarrow U^{-1} A U,$$ while the usual vector transformation (1) has a form $V \rightarrow \Lambda V$? I suspect this comes from a similar reason to that explained  by Prahar, but I would appreciate a confirmation about this. Significance of $\sqrt[n]{a^n} $?! There is a formula given in my module:  $$ \sqrt[n]{a^n} = \begin{cases}  \, a  &amp;\text{ if $n$ is odd } \\  |a| &amp;\text{ if $n$ is even } \end{cases} $$  I don't really understand the differences between them, kindly explain with an example. How is being able to break into any Linux machine through grub2 secure? There are Recurrent Neural Networks and Recursive Neural Networks. Both are usually denoted by the same acronym: RNN. According to , Recurrent NN are in fact Recursive NN, but I don't really understand the explanation.  Moreover, I don't seem to find which is better (with examples or so) for Natural Language Processing. The fact is that, although Socher uses Recursive NN for NLP in his , I can't find a good implementation of recursive neural networks, and when I search in Google, most of the answers are about Recurrent NN.  Besides that, is there another DNN which applies better for NLP, or it depends on the NLP task? Deep Belief Nets or Stacked Autoencoders? (I don't seem to find any particular util for ConvNets in NLP, and most of the implementations are with machine vision in mind).  Finally, I would really prefer DNN implementations for C++ (better yet if it has GPU support) or Scala (better if it has Spark support) rather than Python or Matlab/Octave.  I've tried Deeplearning4j, but it's under constant development and the documentation is a little outdated and I can't seem to make it work. Too bad because it has the "black box" like way of doing things, very much like scikit-learn or Weka, which is what I really want. Is it possible to run Microsoft Office 2010? Using Regex to generate Strings rather than match them induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$ I encountered the following induction proof on a practice exam for calculus:  $$\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$$  I have to prove this statement with induction.  Can anyone please help me with this proof? What is the typical orbital life of an artificial satellite? The orbit of satellites around Earth eventually decays, or so I read. This is typically caused either by atmospheric drag, or by tides. I would assume most satellites have a limited service life in orbit. Hence the question - What is the typical orbital life of a satellite? How long before it's successor must be launched into orbit ?  EDIT: For instance, a weather satellite How to remove snap completely without losing the Chromium browser? I am wondering whether or not there is a way to completely remove snap from Ubuntu 19.10 without losing the ability to install important applications like Chromium.   When I just recently updated to the newest Ubuntu release I realized that the installer programmatically reinstalled snap, although I had manually removed it before. Additionally the installer removed Chromium, which was installed via the repositories, and reinstalled it via snap.   As I don't want snap to be installed on my machines for various reasons my question is if anybody knows a safe way to remove it, and to get the Chromium DEB back to the sources?  Is there a PPA? Could I use a source of an Ubuntu flavor additionally, which didn't remove the Chromium Deb from its sources? I'm a happy Minecraft player. I place my blocks, mine my coal, and generally nobody gets hurt. Lately though, those mean creepers have been sneaking up on me from behind, and killing me. Why? Because my framerate is so darn low.  Adjusting the graphics option (Fancy to Fast) and the render distance help, but they are not enough. I have seen mention of outside optimizations and programs that people have made/used.  What hacks, tricks, and mean mods can I use to improve my Minecraft FPS? I'm trying to compute this integral, $$\int_{0}^{\infty}\frac{\ln x}{x^{a}(x+1)}dx \hbox{ where } 0&lt;a&lt;1$$ I drew a typical Pacman contour with branch cut at positive real axis. Then, we have $$\int_{\Gamma}\frac{\ln z}{z^{a}(z+1)}dz=\left(\int_{L_{1}}+\int_{L_{2}}+\int_{C_{R}}+\int_{C_{\epsilon}}\right)\frac{\ln z}{z^{a}(z+1)}dz$$ The function has a pole at $z=-1$. Then, by residue theorem, the whole integral becomes  \begin{align*} \int_{\Gamma}\frac{\ln z}{z^{a}(z+1)}dz&amp;=2\pi i\text{res}(\frac{\ln z}{z^{a}(z+1)};-1)\\&amp;=2\pi i\lim_{z\rightarrow-1}(z+1)\frac{\ln z}{z^{a}(z+1)}\\&amp;=2\pi i\lim_{z\rightarrow-1}\frac{\ln z}{z^{a}}\\&amp;=2\pi i\frac{\ln e^{i\pi}}{e^{i\pi a}}\\&amp;=2\pi i\frac{\ln1+i\pi}{e^{i\pi a}}\\&amp;=-\frac{2\pi^{2}}{(e^{i\pi})^{a}} \end{align*} On $L_1$, $z=xe^{i\epsilon}$ where $\epsilon\leq x\leq R$  On $L_{2}$, $z=xe^{i(2\pi-\epsilon)}$ where $\epsilon\leq x\leq R$  On $C_{R}$, $z=Re^{i\theta}$ where $\epsilon\leq\theta\leq2\pi-\epsilon$  Lastly on On $C_{\epsilon}$, $z=\epsilon e^{i\theta}$ where $\epsilon\leq\theta\leq2\pi-\epsilon$  So I tried to compute them separately and I anticipate the curves will both go to $0$ by ML inequality, and two linear integrals will consist of the term $\int_{0}^{\infty}\frac{\ln x}{x^{a}(x+1)}dx$ and hence simply solve for it. But I'm having trouble physically solving it out. I think the log is throwing me off. Can anybody please help me? I want to subtract a constant number from my data to get new data file. For example, I want to subtract  10 from my data.   data.txt  Id  a   b   c   d   e 1   1   2   3   4   5 2   2   3   4   5   6 3   3   4   5   6   7 4   4   5   6   7   8 5   5   6   7   8   9 6   6   7   8   9   10 7   7   8   9   10  11 8   8   9   10  11  12 9   9   10  11  12  13 10  10  11  12  13  14 11  11  12  13  14  15 12  12  13  14  15  16 13  13  14  15  16  17 14  14  15  16  17  18   Required output:  out.txt   Id  a   b   c   d   e 1   -9  -8  -7  -6  -5 2   -8  -7  -6  -5  -4 3   -7  -6  -5  -4  -3 4   -6  -5  -4  -3  -2 5   -5  -4  -3  -2  -1 6   -4  -3  -2  -1  0 7   -3  -2  -1  0   1 8   -2  -1  0   1   2 9   -1  0   1   2   3 10  0   1   2   3   4 11  1   2   3   4   5 12  2   3   4   5   6 13  3   4   5   6   7 14  4   5   6   7   8 What is the difference between == and === in php. I am unsure when to use both.  Updated note: So that it shows up in StackOverflow search, the difference between == and === is the same as the difference between != and !==. Continuing my work through Dummit &amp; Foote's "Abstract Algebra", 3.1.36 asks the following (which is exactly the same as exercise 5 in ):     Prove that if $G/Z(G)$ is cyclic, then $G$ is abelian. [If $G/Z(G)$ is cyclic with generator $xZ(G)$, show that every element of $G$ can be written in the form $x^az$ for some $a \in \mathbb{Z}$ and some element $z \in Z(G)$]      The hint is actually the hardest part for me, as the quotient groups are somewhat abstract. But once I have the hint, I can write:  $g, h \in G$ implies that $g = x^{a_1}z_1$ and $h = x^{a_2}z_2$, so \begin{align*}gh &amp;= (x^{a_1}z_1)(x^{a_2}z_2)\\\  &amp;= x^{a_1}x^{a_2}z_1z_2\\\ &amp; = x^{a_1 + a_2}z_2z_1\\\ &amp;= \ldots = (x^{a_2}z_2)(x^{a_1}z_1) = hg. \end{align*} Therefore, $G$ is abelian.  1) Is this right so far?  2) How can I prove the "hint"? Do I have to do any configuration to start brace expansion? When I run mkdir {1..10}, it just creates a dir naming {1..10}. Base64 Encode String in VBScript I have a web service load driver that's a Windows Script File (WSF), that includes some VBScript and JavaScript files. My web service requires that the incoming message is base64 encoded. I currently have a VBScript function that does this, but it's very inefficient (memory intensive, mostly due to VBScripts awful string concatenation)  [Aside; Yes, I've seen . The concatenation is happening in a loop across messages that are 1,000's to 10,000's bytes in size.]  I've tried using some custom string concatenation routines; one using an array and one using ADODB.Stream. These help, a little, but I think it would help more if I had some other way of encoding the message rather than via my own VBS function.  Is there some other way of encoding my message, preferebly using native Windows methods? Other users have been leaving me angry and hostile comments accusing me of plagiarism and saying that I'm a liar and I should stop stealing answers. But I have only been copying content from other sites, not taking answers from other users.   I don't understand what is wrong here. Shouldn't we be focused on building all the content and knowledge in a single place, much like Wikipedia does?  What does it matter that I copy and paste content I've found elsewhere so long as the question gets an answer? Can you deliver it [when,after] it [is | will be] assembled? Right now we are assembling a device. I am asking another person if he is can deliver it [after/when] we finish. What question construction is the most correct?  Can you deliver it after it is assembled?  Can you deliver it after it will be assembled?  Can you deliver it when it will be assembled?  Can you deliver it when it is assembled? Recent feature changes to Stack Exchange I'm trying to deactivate/remove/uninstall a default Client Side Web-Part (the Yammer one) in modern pages and I don't find a way to do it:    I would like the Yammer option to be not visible in the menu. Any ideas?  Thank you very much in advance!