I am interesting in teaching myself General Relativity, since I only learned Special Relativity during my bachelor in Physics. Now, I have turned into math, but nevertheless I remember enjoying theoretical physics and in particular relativity, I know that G.R. is a beautiful mathematical construction. I know the basis of Differential Geometry (Riemannian, Pseudo-Riemannian, Banach manifolds and Lie groups). I ordered General Relativity by Robert M. Wand. But honestly, I found the notation to be very cumbersome.  I know physicists find it more useful to deal with tensors in general in terms of a coordinate system, but I myself feel more comfortable with the abstract definition knowing a priori how such tensor should transform (from chart to chart). Also, Einstein summation convention does not do too much for me, I often forget whether or not I was summing. So, is there a good book you could recommend me to learn the general theory of relativity? I am more interested in the foundations and fundamental principles than in the applied stuff (Black holes, gravitational lenses, etc.).
What are some good books for learning general relativity?
opengl storing multiple indices into indices buffer After parsing collada files I found out that we have to load two(or more) indices each pointing to say a vertex or normal etc. like this (&lt;p>3 0 2 0 0 0&lt;/p>)  Is there a way to load (and use)these indices to indices buffer(ELEMENT_ARRAY_BUFFER) like this (vnvnvn...) ; where v is vertex pointer, n is normal pointer from the above. with vertices loaded to VBO1 like (vvvv...) and in VBO2 like (nnnn...). So that we dont have to repeat the normals in VBO2.  VBO like (vnvnvn...) is also ok. (and not something like this ), I'm not trying to use multiple indices buffer. I'm trying to put all the given indices into one index buffer and use them alternately.  (If I wasnt clear i will try for more clarification.) Can I use multiple regression when I have mixed categorical and continuous predictors? It looks like you can use coding for one categorical variable, but I have two categorical and one continuous predictor variable. Can i use multiple regression for this in SPSS and if so how? thanks! I have recently bought a Logitech M510 as my main mouse switching over from a magic mouse. I didn't realize missing horizontal scrolling would be such an issue, but apparently it is.   Now a mac does support horizontal scrolling by holding shift + scrolling, this is however amazingly slow.   I have the Logitech Control Center installed, which offers a few extra options, but nothing regarding the horizontal scroll speed. The scrolling speed options offered there only affect vertical scrolling.    Can the vertical speed be one setting and the horizontal speed another? How do you transpose tensors? We transpose a matrix $A$ by replacing $A_{ij}$ with $A_{ji}$, for all $i$ and $j$.  However, in case $A$ has more than two dimensions (that is, it is a tensor), I don't know how to apply the transpose operation.   If A has dimensions $3\times 3 \times 8$, then what will replace $A_{ijk}$?  If $A$ has shape $3\times 3\times 8\times 8$, then what will replace $A_{ijkl}$? Implications and Ordinary language unsigned int vs. size_t S1300I scanner issues under Ubuntu 16.04 using Sane In theory this scanner does work under Linux and Ubuntu.  I've found this document that I tried to follow.    I install sane, copy firmware, confirm the location in the config etc.  Everything looks good.  Potential problem areas  sudo sane-find-scanner   output:  # sane-find-scanner will now attempt to detect your scanner. If the # result is different from what you expected, first make sure your # scanner is powered up and properly connected to your computer.  found SCSI processor "Marvell 91xx Config 1.01" at /dev/sg5 # Your SCSI scanner was detected. It may or may not be supported by SANE. Try # scanimage -L and read the backend's manpage.  could not fetch string descriptor: Pipe error could not fetch string descriptor: Pipe error found USB scanner (vendor=0x04c5 [FUJITSU], product=0x128d [ScanSnap S1300i]) at    libusb:005:007 could not fetch string descriptor: Pipe error # Your USB scanner was (probably) detected. It may or may not be supported by # SANE. Try scanimage -L and read the backend's manpage.  # Not checking for parallel port scanners.  # Most Scanners connected to the parallel port or other proprietary ports # can't be detected by this program.   Okay.  So the scanner is detected and listed, it prints a bunch of extra noise that   # scanimage -L  No scanners were identified. If you were expecting something different, check that the scanner is plugged in, turned on and detected by the sane-find-scanner tool (if appropriate). Please read the documentation which came with this software (README, FAQ, manpages).   Okay, let's verify the firmware files:  ls -lh  /usr/share/sane/epjitsu  total 136K -rw-r----- 1 root root 65K Jan  1 17:49 1300_0C26.nal -rw-r----- 1 root root 65K Jan  1 17:49 300_0C00.nal   Looking at the configuration file: (snippets)  # Fujitsu S300 firmware /usr/share/sane/epjitsu/300_0C00.nal usb 0x04c5 0x1156  # Fujitsu S1300 firmware /usr/share/sane/epjitsu/1300_0C26.nal usb 0x04c5 0x11ed   Last thing I tried was to pull the line from sane-find-scanner and update the config  sane-find-scanner returns a different product ID.   I updated the config file above, restarted the sane service, I ran scanimage -L still, scanner not detected.  For reference I had this working on this same computer under a virtualbox VM.  If I can get it to work under windows that would be ideal.  Any suggestion would be much appreciated.    Update: I revisited the behavior after adding the 1300i firmware and it's still not working but.  Once in a while when I do run this is the output.  If I run it again it'll fail.  scanimage -L device `epjitsu:libusb:005:008' is a FUJITSU ScanSnap S1300i scanner   also sudo gscan2pdf and sudo simple-scan both fail to detect a scanner.  It fails with and without sudo permissions. What Happened to TK-421? Why do investors pay trillions for minority stakes in companies, when their only potential payback is modest uncertain dividends? I'm struggling to understand the core reason to invest in stocks as a minority shareholder. Majority shareholding makes more sense as you effectively control the company, so you can pay yourself dividends or even sell the entire company at will. You can guarantee your own payback.  However, as a minority shareholder, you don't get to make any of these decisions. You're basically just hoping to eventually, some day get paid, if the majority holders decide so.  Why do so many investors agree to pay now huge sums of money (trillions in total) for something that may eventually pay dividends, and even in the best case, these dividends are only a fraction of the price you paid to acquire these stocks?  The average annual dividend rate for the US stock market is 2%. That means if you bought 100 million worth of shares, you'd have to wait 50 years to recover your investment.  Of course, the most probable way you'd eventually get liquidity for these shares is by selling them to some other starry-eyed investor - which makes the whole thing seem like a giant Ponzi scheme.  Given all that, it's unclear to me why the public is willing to spend so much money to acquire minority shares in companies. Fatal error: Call to undefined function add_action() - an untouched problem The question was asked many times in many ways, but unfortunately is not covered well in most of the answers. I'm having the same issue doing things using include-files.  In my TwentyFourteen child theme's functions.php I used:  require_once get_stylesheet_directory_uri() .'/admin-panel/theme-options.php';   And I'm using . I've used it in many of my projects, the same way mentioned here, without having the error. But recently I'm having the issue in several of my projects. If I take the code to functions.php then everything's fine. But it's occurring only when I'm trying to include/require external file.  I'm having the error:     Fatal error: Call to undefined function add_action() in C:\xampp\htdocs\project\wp-content\themes\my-theme\admin-panel\theme-options.php on line 2   In this case I'm having the error using a child theme (of T14). But even in one of my parent theme I'm facing the issue. But in the same environment my other projects are running well with all the includes and/or requires (where several add_action()s are defined). I'm having issues in ALL the add_action() calls, like CPT assigning, Custom Taxonomy assigning etc. But I'm successfully developing another two projects including external files from inc/ folder where all my CPTs are assigned and their meta boxes too.  I tried reinstalling WordPress, deactivating all my plugins, tried from Child Theme, tried only the same thing by modifying TwentyFifteen (applying default theme), tried require(), require_once(), include(), include, require_once, and require one after another with failure. And I'm using WP 4.1.1 in all the good and problematic installs.  Majority of the previous questions are answered with a simple line:     As the message says, you haven defined the function add_action() and yet you're trying to use it.   But,   how come (isn't it already defined by WordPress)? and why it's differing project to project in the same environment (How come it's out of the scope now only in particular project[s])? $\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$ Broken blog link on pages with lists of moderators The page  has a link like this:  which doesn't seem to exist anymore. This is the same on  And also on Question. Let $M = \left\{ \begin{bmatrix} a &amp; b \\ -b &amp; a \end{bmatrix} \,\middle\vert\,  a, b \in \mathbb R \right\}$.  Show that $(M,+)$ and $(\mathbb C,+)$ are isomorphic.  Show that $(M^{*},*)$ and $(\mathbb C^{*},*)$ are isomorphic.    (Here, $M^{*}$ is defined as excluding the zero-element) I understand that there exists an isomorphism $\phi:M \rightarrow\mathbb C$ defined by $\begin{bmatrix} \alpha &amp; \beta \\ -\beta &amp; \alpha \end{bmatrix}\mapsto \alpha+i\beta$, ie. I can show that $\phi(M_{1}+M_{2}) = \phi(M_{1})+\phi(M_{2})$ and $\phi(M_{1}*M_{2}) = \phi(M_{1})*\phi(M_{2})$. However, I'm unsure how to go about the two subquestions seperately. Can a virtualized machine have the CPU and RAM resources of multiple underlying physical machines? We are studying implementing some virtualized servers here, but we don't know what will be better suitable for us. Some folks are saying better have two huge servers, and others are saying have like a ten middle-end servers.  We have a legacy Visual Foxpro application, which nowadays run on Dual Xeon E5405 @ 2GHz and 16Gb of RAM. The currently server its getting too slow due the number of active users and process running on it. Virtualizing this server will give us the benefit of an faster disaster recovery.  So the question is, having like ten physical servers running at 1.7GHz and 4Gb of RAM, we could virtualize one server into 4 machines, and have one virtualized server running at 6.8GHz and 16Gb of memory? If yes, there is some how if one machine stops, automatically manage this virtual machine to another one, and execute the appropriate maintenance on it, and later back to it again? Output for Print Is there a way to output for Print. I want to save in a higher DPI than the default 72dpi say 300dpi that's a good quality for printed pieces. I tried downloading an add-on but don't know if I am installing it correctly it isn't showing up but the bar in python is green. I'm using the 2.69 version of Blender. If no such feature exists what size have any of you found best for print quality. Thank you Object renders black Is the uncertainty principle a property of elementary particles or a result of our measurement tools? Can Raise Dead revive a character with zero maximum Hit Points? So, a character died from Draining Kiss of a succubus and his Max HP is 0. Can he be restored by Raise Dead, or does he need a higher level spell? Or a Greater Restoration cast on his lifeless body before Raise dead? I'm probably interested in RAW interpretation, since the character is in Adventurerer's league. How to replace subscript symbols Example of a series! Give an example of a convergent series $$\sum_{n=1}^{\infty}a_n$$ such that the series $$\sum_{n=1}^{\infty}a_{3n}$$ is divergent..  I cannot find find any kind of series... I am also be very thankful if you find a divergent series (changing the term convergent)...