Windows 7 - programs won't run, weird chinese signs
How can I remove malicious spyware, malware, adware, viruses, trojans or rootkits from my PC?
Martingale that is not a Markov process Consider $X = (a+b)^n-a^n-b^n$  where  $a$ and $b$ and $a+b$ are not divisible by $n$, $n&gt;=3$ is positive and prime, $a \ne b$ and both are greater than 1.  By the binomial expansion we know $X$ is divisible by $n$, but how can we study whether $X$ is divisible by $n^2$ or other powers of $n$? Specifically I am interested to prove $X$ is NOT divisible by $n^2$, but I am not sure how to prove or disprove it. chemformula: No auto-completion in TeXstudio? I have trouble getting auto-completion to work with chemformula in TeXstudio. I have other packages working just fine.   The .cwl-file is showing up in "Options > Configure TeXstudio > Completion", and I have it ticked. However, it doesn't work when typing.  I have contacted Clemens Niederberger (who maintains the package), however he recommended I ask here instead.  It is mainly the \ch command I would like to have auto-complete, but all commands would be ideal.  N.B. I'm running TeXStudio 2.9.4 TeXLive 2015 (both newest, at the time of writing) How to run 32-bit app in Ubuntu 64-bit? I installed Ubuntu 14.04 and the current Android development SDK, which contains 32-bit executables. I found that I cannot run those 32-bit binaries. Trying to start them from bash gives me an error: $ ./adb bash: ./adb: No such file or directory  It is there though: $ ls -al ./adb -rwxrwxrwx 1 thomas thomas 1231255 Jan 17 13:31 ./adb $ file ./adb ./adb: ELF 32-bit LSB  executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.8, not stripped.   Same symptom for all the other 32-bit tools in the Android SDK. In olden days one could just install 32-bit libraries on 64-bit Ubuntu to get 32-bit support, but that does not seem to work anymore. How do I run 32-bit apps on a 64-bit Ubuntu distribution? I'm consistently receiving significant delays on Stack Overflow when opening the flag dialog on questions. Delays do not occur on any other StackExchange site I have checked. This started a couple days ago (as far as I can tell).  Delays occur not only when loading the initial screen, but also when loading the submenus. This is slightly confusing for a couple seconds (until you're used to it) since it appears as if the flag dialog has simply vanished.   What's going on here? I demand to know, otherwise somebody will be very upset.  Not me. I'm not going to get that upset over something like this.  But someone will.    Specs (though I know of several others who have this issue):  Windows 7 64-bit Chrome Version 30.0.1599.69m     Ping: 31ms Download: 6.88mbps   Upload: 1.07mbps JavaScript hard refresh of current page I have the following recurrence that I've been pounding on:  $$ a(0)=1\\ a(1)=1\\ a(2)=2\\ a(2n)=a(n)+a(n+1)+n\ \ \ (\forall n&gt;1)\\ a(2n+1)=a(n)+a(n-1)+1\ \ \ (\forall n\ge 1) $$  I don't have much background in solving these things, so I've been googling around looking for different techniques. Unfortunately, I haven't been able to correctly apply them yet. So far I've tried:   Characteristic equations Generating functions Plugging it into Wolfram Alpha Telescoping Observation   I'm sure that one or more of these is the way to go, but my biggest problem right now is figuring out how to deal with the idea that there are different equations for odd and even values of $n$. I'm not necessarily looking for a solution (though it would be gratefully accepted), but any nudges in the right direction would be much appreciated.    To follow up, it turned out that the speed problem described in my comment, below was related to the Decimal implementation in Python 2.7. Switching to Python 3.3 (and Java) made everything many orders of magnitude better. Copying data over with rsync causes size discrepancies Indefinite integral of secant cubed I need to calculate the following indefinite integral:  $$I=\int \frac{1}{\cos^3(x)}dx$$  I know what the result is (from Mathematica):  $$I=\tanh^{-1}(\tan(x/2))+(1/2)\sec(x)\tan(x)$$  but I don't know how to integrate it myself. I have been trying some substitutions to no avail.   Equivalently, I need to know how to compute:  $$I=\int \sqrt{1+z^2}dz$$  which follows after making the change of variables $z=\tan x$. Is 512 bits a more secure hashing than 256 bits? Prove that $T^2$ is the zero transformation if and only if $\mathrm{range}(T) \subseteq \ker(T)$. $\newcommand{\range}{\mathrm{range}}$The full question: $T^2$ means the composition, i.e. $T(T(x))$ Let $V$ be a vector space and let $T: V \rightarrow V$ be linear.  Prove that $T^2$ is the zero transformation if and only if $\range(T) \subseteq \ker(T)$. So far I know that for ($\implies$).  Assume $T^2$ is the zero transformation.  Then $\ker(T^2)=\{0 \in V: T^2(v)=0\}$.  Note that this is $\forall v \in V$. We also know that the $\range(T)=\{0\in V: \exists v \in V: T^2(v)=0\}$. Not sure where to go from here.  Also for the other way, I don't know where to go. Shape of the universe? Can anyone offer any help with this..? I read it at school around 1976 but cannot remember the title nor the author. Thank you in advance!  A lone astronaut called - I think- Steve is stranded on a distant planet when his ship runs low on fuel.   His only companion is - again I think - a parrot. The fuel his ship uses is a filament or wire which is kept on a spool.   On exploring the locale he has landed in he discovers a huge building half-buried in a mountainside. He enters the building and discovers it is a museum filled with thousands of glass cases containing preserved specimens of various life forms as well as machines.   There is a robot curator that does repairs and, as the astronaut finds out, prepares cases for new exhibits.   On analysing the wire in one of the machines he discovers that is suitable as fuel for his ship so he winds a length of it onto his ships spool and leaves the planet just ahead of the robot collecting him and his parrot as museum exhibits... So, say you are a wizard 15/warlock 2. You have the Lance of Lethargy invocation, which pushes an enemy you target with eldritch blast and hit back 10 feet. Say you put a demiplane entrance ~5 feet behind the enemy you target with it. When you hit, you throw the enemy in. Before all this, you had put a Glyph of Warding in there on one of the surfaces. What would be the limit to the trigger for this? Would it be forced to be touch or proximity, or could you base it off something like hostility towards the caster?      ... When you cast this spell, you inscribe a glyph that later unleashes a magical effect ... You decide what triggers the glyph when you cast the spell. For glyphs inscribed on a surface, the most typical triggers include touching or standing on the glyph, ... (PHB 245)   The key word here is "typical". Based on Google's definition, the informal definition of "typical" is     showing the characteristics expected of or popularly associated with a particular person, situation, or thing.   This means, if my assumption is true, that the triggers in the PHB are only the most common ones. Other than the one about being forcibly at maximum 10 feet in diameter in the PHB, I cannot see a limit. Though I probably should assume this would all be DM discretion, (and I know that I sound like a broken record here) but could the trigger be hostility toward the caster, or something else, like being a specific race, gender, from a specific place, etc., or would it be forced to being something from the PHB? GOTO still considered harmful? Everyone is aware of Dijkstra's  (also  .html transcript and  .pdf) and there has been a formidable push since that time to eschew the goto statement whenever possible. While it's possible to use goto to produce unmaintainable, sprawling code, it nevertheless remains in . Even the advanced  control structure in Scheme can be described as a sophisticated goto.  What circumstances warrant the use of goto? When is it best to avoid?  As a followup question: C provides a pair of functions, setjmp and longjmp, that provide the ability to goto not just within the current stack frame but within any of the calling frames. Should these be considered as dangerous as goto? More dangerous?    Dijkstra himself regretted that title, for which he was not responsible. At the end of  (also  .pdf) he wrote:     Finally a short story for the record.   In 1968, the Communications of the ACM   published a text of mine under the   title "The goto statement considered   harmful", which in later years would   be most frequently referenced,   regrettably, however, often by authors   who had seen no more of it than its   title, which became a cornerstone of   my fame by becoming a template: we   would see all sorts of articles under   the title "X considered harmful" for   almost any X, including one titled   "Dijkstra considered harmful". But   what had happened? I had submitted a   paper under the title "A case against   the goto statement", which, in order   to speed up its publication, the   editor had changed into a "letter to   the Editor", and in the process he had   given it a new title of his own   invention! The editor was Niklaus   Wirth.   A well thought out classic paper about this topic, to be matched to that of Dijkstra, is , by Donald E. Knuth. Reading both helps to reestablish context and a non-dogmatic understanding of the subject. In this paper, Dijkstra's opinion on this case is reported and is even more strong:     Donald E. Knuth: I believe that by presenting such a   view I am not in fact disagreeing   sharply with Dijkstra's ideas, since   he recently wrote the following:   "Please don't fall into the trap of   believing that I am terribly   dogmatical about [the go to   statement]. I have the uncomfortable   feeling that others are making a   religion out of it, as if the   conceptual problems of programming   could be solved by a single trick, by   a simple form of coding discipline!" Change Proxy Settings In Ubuntu I want to use the Ubuntu Software Center to install software, but I cannot download them.  How can I give my proxy settings in Ubuntu terminal (just like we use cmd in Windows to choose IE proxy settings)? Which are the word orders that can be found in English? Besides , which are the  that can be found in English? Are there any that are peculiar to dialects such as Singlish or Indian English? Please provide an example sentence for each order along with pertinent information such as tense, mood, voice, etc. I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra dimensions, and all these dimensions need to fit together in a way such that the extra dimensions are compactified (with a Calabi-Yau or $G_2$ structure).   My question, however is not about the possible $10$, $11$ or $26$ dimensional manifolds that may be possible, but about whether string theorists consider space-time as somehow quantized (or discrete), or rather as a continuous manifold, or are both options possible? In other words, can strings move continuously through space, or are there a discrete set of locations where strings can be, and does string theory rule out one of the options?  How about the same question in loop quantum gravity (LQG)? Should I think of the spin networks in LQG as describing a discrete space-time?  Thanks for your insight, or any references you may be able to provide! If parsing the output of ls is dangerous because it can break on some funky characters (spaces, \n, ... ), what's the best way to know the number of files in a directory?  I usualy rely on find to avoid this parsing, but similarly, find mydir | wc -l will break for the same reasons.  I'm working on Solaris right now, but I'm looking for a answer as portable across different unices and different shells as possible. Will reformatting my hard drive fix bad sectors on it?