My Dell Optiplex 780 is blanccoed, how do I know whether I need a 32 or 64 bit ubuntu?
What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit?
In the Landau theory of phase transitions, is the order parameter a thermodynamic variable of state? In the Landau theory of phase transitions, one typically considers a "free energy" $F$ as a function of the temperature $T$ and the "order parameter" $\psi$: $F(T, \psi)$.  For the sake of clarity, let's consider the liquid-gas transition, in which the order parameter is usually taken to be the difference of densities between the ordered phase and the disordered phase.  In this case, it looks that the order parameter $\psi$ is closely related to the the volume $V$, a global variable of state.  What is the correct interpretation of $\psi$ as a thermodynamic variable?   I consider several logical possibilities, but all interpretations look troublesome to me:    $\psi$ is a variable of state replacing the volume. In this case I have a few related concerns:   Is the "free energy" $F$ the Helmholtz or the Gibbs free energy?    If $F$ is the Gibbs free energy, $F$ should depend on the temperature $T$ and the pressure $p$ (the conjugate variable of the volume), so it shouldn't depend on $\psi$.  If it is the Helmholtz free energy, it's ok that it depends on $\psi$, but the experiments are usually carried out at constant pressure, not constant volume.  Usually, state variables are something one can select at will [for instance, think of the phase diagram $(p, T)$]. However, the order parameter $\psi$ is not selected at will, but it is selected by the system as a result of the minimization process according to the Landau theory.  $\psi$ is yet another variable of state in addition to volume and temperature.    Why the pressure is not usually taken into account as a variable of state, and only the temperature is considered? What is the conjugate variable to $\psi$? Can really $\psi$ and $V$ be taken as independent?  $\psi$ is not a variable of state, is something else.   What else can $\psi$ be from the thermodynamic point of view? Same question as above, why is pressure not usually taken into account in Landau theory? How to find the reduced density matrix of a four-qubit system? I have the state vector $|p\rangle$ made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to find the reduced density matrix of system A.   I know I could separately extract qubits 1,2 and 3,4 into their own state vectors then find their density matrices and compute the reduced density matrix for system A.  I want to figure out how to do this without having to extract and separate the systems. First I would find the density matrix of $|p\rangle$ and then do a partial trace with respect to system B. I am not sure how to do the partial trace of system B since the system contains 2 qubits.  Can anyone help me figure this out? I am using Python and NumPy for reference. Mismatch Reputation in the thumbnail and the actual Reputation /testfor for item enchantment What I have now is:  /testfor @a {SelectedItemSlot:0,Inventory:[{Slot:0b,id:"diamond_pickaxe"}]}   How can I use the /testfor command to test a specific slot for a specific item that is enchanted? Should I install graphics card drivers from Windows Update? Exploiting JavaScript's eval() method Debugging using Nvidia Nsight 2.2 in Visual Studio 2010 Global keyboard capture in C# application I want to capture a keyboard shortcut in my application and trigger a dialog to appear if the user presses a keyboard combo even outside of the app. Similar to Google Desktop Search's Ctrl, Ctrl to bring up the search dialog.  I have tried using some keyboard hook modules out there that basically use Win32 interop to get this effect but each implementation I've tried ties down the keyboard to some extent to where you start getting weird behaviors when the application is doing something intensive. Such as loading a large amount of data, this would cause the keyboard and mouse to lockup.  I'm looking for a lightweight solution that would allow this to be done without tying down the keyboard and mouse. Does "make offline" option in Google Maps works with applications that utilize Google Maps? In newer Google Maps I can make area available offline.  Do other applications that rely on Google Maps (utilize Google Maps Android API) use offline maps? Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction I was looking at: $$\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$$  It's pretty easy proving the above using induction, but I was wondering what is the actual way of getting this equation? For random variable $X$ that follows some distribution, $f(x)$ is the probability density function of that distribution if and only if $$\mathbb{E}[\phi(X)] = \int_{-\infty}^\infty \phi(x) f(x)dx$$ for all functions $\phi$.  Context: My professor used this in lecture to demonstrate a way to find the distribution of $cX$ given random variable $X$ that follows a specific distribution.   What is the name of this theorem? Have I missed any qualifications/caveats? I am in particular curious about whether "for all functions" is correct. My professor mentioned "positive, bounded, deterministic functions," but I am not sure what he meant by that. Where can I find a proof of this theorem? Python setup, install one module as a sub module of another module? MySQL Seems to be crashing quite often, I'd say every hour or so.   The only thing running on this server that is using MySQL is a Drupal installation that I'm working on, there's only one person that's using it and it literally has around three pages - from what I can gather this seems to be a memory issue with innoDB? I'm not great at this stuff so I'm unsure.  Any guidance? Here's the relevant parts from my error.log  140216 14:20:01 [Note] Plugin 'FEDERATED' is disabled. 140216 14:20:01 InnoDB: The InnoDB memory heap is disabled 140216 14:20:01 InnoDB: Mutexes and rw_locks use GCC atomic builtins 140216 14:20:01 InnoDB: Compressed tables use zlib 1.2.3.4 140216 14:20:01 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(135987200 bytes) failed; errno 12 140216 14:20:01 InnoDB: Completed initialization of buffer pool 140216 14:20:01 InnoDB: Fatal error: cannot allocate memory for the buffer pool 140216 14:20:01 [ERROR] Plugin 'InnoDB' init function returned error. 140216 14:20:01 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 140216 14:20:01 [ERROR] Unknown/unsupported storage engine: InnoDB 140216 14:20:01 [ERROR] Aborting  140216 14:20:01 [Note] /usr/sbin/mysqld: Shutdown complete  140216 14:20:02 [Note] Plugin 'FEDERATED' is disabled. 140216 14:20:02 InnoDB: The InnoDB memory heap is disabled 140216 14:20:02 InnoDB: Mutexes and rw_locks use GCC atomic builtins 140216 14:20:02 InnoDB: Compressed tables use zlib 1.2.3.4 140216 14:20:02 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(135987200 bytes) failed; errno 12 140216 14:20:02 InnoDB: Completed initialization of buffer pool 140216 14:20:02 InnoDB: Fatal error: cannot allocate memory for the buffer pool 140216 14:20:02 [ERROR] Plugin 'InnoDB' init function returned error. 140216 14:20:02 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 140216 14:20:02 [ERROR] Unknown/unsupported storage engine: InnoDB 140216 14:20:02 [ERROR] Aborting  140216 14:20:02 [Note] /usr/sbin/mysqld: Shutdown complete   EDIT The server is the lowest-spec DigitalOcean Droplet with 512MB RAM. This particular Droplet is running NodeJS, MySQL and Apache. There's a low-traffic static site, a Ghost blog and this Drupal site I'm developing.   Should I just upgrade the RAM, or is there something I can do to fix this? crossfade between 2 videos using ffmpeg Evaluation of $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7} = $$   $\bf{My\; Try::}$ I have solved Using Direct formula::  $$\sin \frac{\pi}{n}\cdot \sin \frac{2\pi}{n}\cdot......\sin \frac{(n-1)\pi}{n} = \frac{n}{2^{n-1}}$$  Now Put $n=7\;,$ We get   $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7}\cdot \sin \frac{4\pi}{7}\cdot \sin \frac{5\pi}{7}\cdot \sin \frac{6\pi}{7}=\frac{7}{2^{7-1}}$$  So $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7} =\frac{\sqrt{7}}{8}$$  Now my question is how can we solve it without using Direct Formula, Help me  Thanks Why is everybody so concerned about etc/passwd? Here is the content of my vagrant machine of this particular file:  root:x:0:0:root:/root:/bin/bash daemon:x:1:1:daemon:/usr/sbin:/usr/sbin/nologin bin:x:2:2:bin:/bin:/usr/sbin/nologin sys:x:3:3:sys:/dev:/usr/sbin/nologin sync:x:4:65534:sync:/bin:/bin/sync games:x:5:60:games:/usr/games:/usr/sbin/nologin man:x:6:12:man:/var/cache/man:/usr/sbin/nologin lp:x:7:7:lp:/var/spool/lpd:/usr/sbin/nologin mail:x:8:8:mail:/var/mail:/usr/sbin/nologin news:x:9:9:news:/var/spool/news:/usr/sbin/nologin uucp:x:10:10:uucp:/var/spool/uucp:/usr/sbin/nologin proxy:x:13:13:proxy:/bin:/usr/sbin/nologin www-data:x:33:33:www-data:/var/www:/usr/sbin/nologin backup:x:34:34:backup:/var/backups:/usr/sbin/nologin list:x:38:38:Mailing List Manager:/var/list:/usr/sbin/nologin irc:x:39:39:ircd:/var/run/ircd:/usr/sbin/nologin gnats:x:41:41:Gnats Bug-Reporting System (admin):/var/lib/gnats:/us$ nobody:x:65534:65534:nobody:/nonexistent:/usr/sbin/nologin syslog:x:100:103::/home/syslog:/bin/false   Could anybody explain me why it is bad if some evil guy could get this file of my production server? Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero. Let $f$ be an entire function. Suppose $f(z)$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero. How to prove? Totally I have no idea... Please give the solution in detail since I do not understand. Sometimes, a question is perfectly solved by suggestion or actual resolution given in "comments" under it. In such case, how to mark that answer (comment) as "Accepted Answer"? Due to this, the question remains unanswered even if solution is provided in comment. Wrong text instead of reference numbers with the spbasic bibiography style I am writing a paper to a Springer journal and I am trying to use   \bibliographystyle{spbasic} However, instead of the number of the reference in the list of references I get something as:     [Hundsdorfer et al(1995)Hundsdorfer, Koren, van Loon, and Verwer]   followed by the citation  What should I do to get the number in the square brackets?  \documentclass[smallextended]{svjour3} \begin{document} \cite{Hundsdorfer:adv}  \bibliographystyle{spbasic}  \bibliography{moje.bib}   % name your BibTeX data base  \end{document}   I may have to do the bibliography manually, as no Springer provided bibtex style produces the output that can be seen in the journal articles. degree of freedom of a rigid body 5 or 6? I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only three constraints, i.e. three equations that reduce 9 coordinates by 3, 9 - 3 = 6, which gives 6 degrees of freedom?? Did I miss something above?