I am a math student and I'm willing to read a book about the geometry of the universe and space-time with mathematical description. so please introduce some good textbooks.
What are some good books for learning general relativity?
MacBook Pro - FaceTime HD Camera - Hardware "Failure'? System Report>Camera>No video capture devices were found     USB>Device Tree> No FaceTime HD Camera (inbuilt)listed    What can be the cause for "camera hardware failure"? Could faulty iSight cam wifi antenna cable linkage between logic board and camera board (in display)result in Camera hardware not "found"? Display Top X results for each unique value I am trying to figure out how I can output any machine that has had the latest 3 backups be larger than 10GB. My SQL Table looks similar to the below table:  ComputerID | BackupImageName | WindowsVolumeGUID | FileSize | TimeCreated 1234       | PCBackup.spi    | kjsdfai-dadad-ddd | 10400    | 05-22-20 1234       | PCBackup1.spi   | kjsdfai-dadad-ddd | 10500    | 05-23-20 1234       | PCBackup2.spi   | kjsdfai-dadad-ddd | 10300    | 05-24-20 1234       | PCBackup3.spi   | kjsdfai-dadad-ddd | 10900    | 05-25-20 1225       | PCBackup4.spi   | kjsdfa5-dadad-ddd | 10600    | 05-22-20 1225       | PCBackup5.spi   | kjsdfa5-dadad-ddd | 5000     | 05-23-20 1225       | PCBackup6.spi   | kjsdfa5-dadad-ddd | 10000    | 05-24-20 1225       | PCBackup7.spi   | kjsdfa5-dadad-ddd | 4588     | 05-25-20   I need to output all machines (computerID's) or Volumes (WindowsVolumeGUID) that have their latest 3 files in the list greater than 10000 file size. So from the above table it would output the computerID of 1234 because its latest 3 are greater than 10000 file size and even though the computerID 1225 has 2 files greater than 10000 it would not output the result because there is a break in-between the two large files. The search will need to take into account the WindowsVolumeGUID since some machines have more than one volume and I need to take into account the individual volume backups and count the latest entries based on that.  Alternatively, I can also accomplish the same thing if there is a way to output the top 3 results for each unique WindowsVolumeGUID and not just across the board.   Any help would be greatly appreciated! From the top of my head, Danish "De" (practically never used), German "Sie", Chinese "您", French "vous", Spanish "usted" are a formal way of addressing someone, especially if one isn't familiar with the addressee. Did English ever have this? It sounds as though Proto-Indo-European might have had this (based on my 4 examples), but perhaps someone can enlighten me? I installed jockey-gtk but how do I run it? zuber@zuber-pc:~$ sudo apt-get install jockey-gtk   Reading package lists... Done Building dependency tree        Reading state information... Done The following packages were automatically installed and are no longer required:   nvidia-common python-xkit Use 'apt-get autoremove' to remove them. The following NEW packages will be installed:   jockey-gtk 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. Need to get 0 B/3,158 B of archives. After this operation, 53.2 kB of additional disk space will be used. Selecting previously unselected package jockey-gtk. (Reading database ... 156414 files and directories currently installed.) Unpacking jockey-gtk (from .../jockey-gtk_0.9.7-0ubuntu11_all.deb) ... Setting up jockey-gtk (0.9.7-0ubuntu11) ... zuber@zuber-pc:~$ jockey-gtk The program 'jockey-gtk' is currently not installed. You can install it by typing: sudo apt-get install jockey-gtk   And this not only occur with jockey-gtk. I have same problem with synergy(I did not tried with other software). Is it known problem or am I only one? How do I fix it? Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$. What is the scope of variables in JavaScript? Multiplicative nature of the separability degree In what follows, let $E / F$ be an algebraic extension, $h(x),f(x)\in F[x]$ polynomials, $h(x)$ irreducible.   Definitions.   We say $h(x)$ is separable if it has not repeated factors. We say $f(x)$ is separable if all its irreducible factors are separable. We say $\alpha\in E$ is separable over $F$, if its minimal polynomial over $F$ is. The extension $E/F$ is separable if all the elements of $E$ are separable over $F$. We define the field $$\newcommand\sclo{\operatorname{Scl}}\sclo_F E= \{\alpha\in E : \text{ $\alpha$ is separable over $F$ }\}$$ as the separable closure of $F$ in $E$. The separability degree of the extension $E/F$ is defined as $$[E:F]_s = [\sclo_F E:F].$$   Now, suppose the extension $E/F$ is finite.  My question is: how can one proof that with these definitions, if $B$ is an intermediate field of the extension $E / F$, then $$[E:F]_s = [E:B]_s[B:F]_s?$$  I know that the purpose of the separability degree is to count in how many ways we can extend certain injective homomorphism to an automorphism. If one starts defining separability degree this way, as done in the book by Lang, the result follows without much difficulty.  I wonder how to achieve it in this way. Show that $f(z)=0$. Suppose that $f:\mathbb{C}\rightarrow\mathbb{C}$ is analytic on the open unit disc and continuous on the closed unit disc. Assume that $f(z)=0$ on an arc of the circle $\{z\in\mathbb{C}:|z|=1\}$. Show that $f(z)=0$. How do I set up new users with skel i have on my server a settings i use for all my users. every time i create a new user i have to copy all the settings over and over.  for example:   .vimrc. .profile .bashrc firefox homepage to our intranet evolution settings (server and username) etc...   i saw skel can do it, is there a easy way to setup a user with my settings when i adduser?  thanks How to Recover truncate table in MySQL? I am getting the "wrong input table name" when use TRUNCATE as following:  TRUNCATE `stats`   The table should bans.  How to recover stats table?  I am using CentOS 6, and MySQL-Server. How to use ssh to transfer files from computer a to local computer I am trying to get some files off of my school Linux account using ssh. I have got the connection to work using:  scp &lt;school_server&gt;: ~/folder I want ~/where I want to go.    But when it goes to transfer folder it gives me the message:  not a regular file    The file contains .java files, and I want the whole folder. Richard Stallman states that Ubuntu "has installed surveillance code". See:   Is this true?   I agree with him that "Any excuse Canonical offers is inadequate....". proof that translation of a function converges to function in $L^1$ Let $f \in L^1(\mathbb{R})$, for $a\in \mathbb{R}$ let $f_a(x)=f(x-a)$, prove that: $$\lim_{a\rightarrow 0}\|f_a -f \|_1=0$$  I know that there exists $g\in C(\mathbb{R})$ s.t $\|f-g\|_1 \leq \epsilon$, this is also true for $f_a$ and $g_a$.  Now I have the next estimation:  \begin{align*} \|f_a-f\|_1 &amp;= \int_{\mathbb{R}} |f(x)-f(x-a)| dx \\ &amp;= \int |f(x)-g(x)+g(x)-g(x-a)+g(x-a)-f(x-a)| \\ &amp;\leq \|f-g\|_1 + \|f_a-g_a\|_1 + \int |g(x)-g(x-a)| \end{align*} my question is: I can argue that $\lim_{a\to0} \int |g(x)-g(x-a)| = \lim_{a\to0} \lim_{T\to\infty} |g(x_0)-g(x_0-a)| 2T$, now I think that I can change the order of the limits here, but I am not sure why?  P.s $x_0$ is some point in $[-T,T]$, and the above is valid from the intermediate integral theorem for continuous functions, right?  Thanks. Foobar2000-like music player? Equality in an integral estimate Let $u,v\in W^{1,p}(\Omega)$ with $1&lt;p&lt;\infty$ and $\Omega$ be a bounded smooth domain in $\mathbb{R}^N$. Suppose, we have $$\int_{\Omega}|\nabla u|^{p-2}\nabla u\nabla v\,dx=\left(\int_{\Omega}|\nabla u|^p\,dx\right)^\frac{p-1}{p}\left(\int_{\Omega}|\nabla v|^p\,dx\right)^\frac{1}{p} $$ Suppose the equality $$ \int_{\Omega}|\nabla u|^p\,dx=\int_{\Omega}|\nabla v|^p\,dx $$ holds. Then can we say that $u=v$ in $\Omega$? I tried in the following way: Since the first given equality, which is the equality in Holder's inequality holds, and by the second given equality holds, we have $|\nabla u|=|\nabla v|$ in $\Omega$. Then I am unable to proceed. Can someone please help to give an argument? pgfplots - draw boxplot without outliers I am creating a boxplot with pgfplots, using the builtin statistics library. I load the input data from a table file.  \usepackage{pgfplots} \usepgfplotslibrary{statistics} ... \begin{tikzpicture} \begin{axis}[boxplot/draw direction=y]    \addplot+[boxplot] table[      col sep=tab,      x expr=\coordindex,      y=aColName] {aFileName}; \end{axis} \end{tikzpicture}   Is it possible to draw the plot without outliers? Or hide them? I don't want to pre-calculate the boxplot values by hand. How to send data to a serial port and see any answer? On Linux, I want to send a command string (i.e. some data) to a serial port (containing control characters), and listen to the response (which also usually might contain control characters).   How can I do this as simplest as possible on Linux? An example is appreciated! For any prime $p > 3$, why is $p^2-1$ always divisible by 24? How to do version numbers? My company is building a product. It's going to be versioned by SVN. It's a webapp so basically there will never be a version out which doesn't have some features in them and thus could always be labeled as beta. But since it's going to be a corporate product I really don't want the "unstable watchout" on there. So how would you go about versioning? Is 1.0 stable? Should the build date be in the version number? Tell me what you guys think! Roman numerals become “too wide” in table of contents Following minimal document:  \documentclass{report}  \begin{document} \renewcommand*\thechapter{\Roman{chapter}} \tableofcontents \setcounter{chapter}{6} % Problem starts at chapter 7 \chapter{Seven} \chapter{Eight} \section{Eight-one} \section{Eight-two} \end{document}   yields this output (cut to size for your convenience):    Clearly, the chapter (and section) headings hang into the chapter (section) numbers. For the previous chapter numbers, this isn’t a problem since all chapter titles are aligned to the same column and the numbers I–VI are sufficiently narrow.  (The same happens regardless of document type, I’m actually using scrreprt with the same result.)  How can I prevent this?