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Do I need a Turkey transit visa for a layover? I have an Indian passport and am planning to visit Germany with a valid visa. To book a flight for Germany (Mumbai – Dusseldorf), I came across some connected flights that stop at Istanbul.  Do I need to have visa for Turkey?  This is the first time I am travelling outside my country, and any information on this will be helpful. Write a well designed async / non-async API What is the $\sqrt{i^4}$?   $i^4$ = $(i^2)^2$ So is $\sqrt{i^4}$ = $\sqrt{(i^2)^2}$ = $i^2$ = $-1$?  Or is $\sqrt{i^4}$ = $\sqrt{1}$ = $1$?  When I plug it into my TI-89 Titanium, I get $1$.  Edit: I now see why $i^4 \neq -1$. $$\sqrt{x^2} = \left|{x}\right| $$ So$$\sqrt{(i^2)^2} = \left|i^2\right| = \left|-1\right| = 1$$ In Python, is there a concise way of comparing whether the contents of two text files are the same? I don't care what the differences are.  I just want to know whether the contents are different. Suppose that we have a vector space $V$ and the subspaces $U=\{(x,x,y,y)\in F^4:x,y\in F\}$ and $W=\{(x,x,x,y)\in F^4:x,y\in F\}$. Then how comes $$U+W=\{(x,x,y,z)\in F^4:x,y,z\in F\}?$$ UBUNTU 14.04 cheese booth not detect webcam Cheese Booth shows an error:     There was an error playing video from the webcam     I test if webcam works fine or not by opening google hangout, its works fine.    Please tell, what is the issue in cheese booth.  Note: Sometimes the cheese booth works fine but most of time not Could someone advise me on how to determine all entire functions $f$ such that $|f'(z)| \leq |f(z)|, \forall z\ ?$  Hints will suffice, thank you. I'm trying to prove the following statements.  Let $G$ be a finite abelian group $G = \{a_{1}, a_{2}, ..., a_{n}\}$.   If there is no element $x \neq e$ in $G$ such that $x = x^{-1}$, then $a_{1}a_{2} \cdot \cdot \cdot a_{n} = e$.   Since the only element in $G$ that is an inverse of itself is the identity element $e$, for every other element $k$, it must have an inverse $a_{k}^{-1} = a_{j}$ where $k \neq j$. Thus $a_{1}a_{1}^{-1}a_{2}a_{2}^{-1} \cdot \cdot \cdot a_{n}a_{n}^{-1} = e$.   If there is exactly one $x \neq e$ in $G$ such that $x = x^{-1}$, then $a_{1}a_{2} \cdot \cdot \cdot a_{n} = x$.   This is stating that $x$ is not the identity element but is its own inverse. Then every other element $p$ must also have an inverse $a_{p}^{-1} = a_{w}$ where $p \neq w$. Similarly to the first question, a rearrangement can be done: $a_{1}a_{1}^{-1}a_{2}a_{2}^{-1} \cdot \cdot \cdot xx^{-1} \cdot \cdot \cdot  a_{n}a_{n}^{-1} = xx^{-1} = e$. And this is where I am stuck since I proved another statement.    Any comments would be appreciated for both problems. I am trying to understand capitalization rules with Mom and Dad. I believe I have it correct below, but please let me know if I do not.     The one thing I learned from my dad was that it was good to earn the trust of one's children. Dad has shown me how good that a dad can be. One day when I went to his house, and Dad wasn't there, I ran outside....   The above passage is just made-up just so that you would see what I mean about capitalization. Let's put numbers by each one, like so:     The one thing I learned from my dad(1) was that it was good to earn the trust of one's children. Dad(2) has shown me how good that a dad(3) can be. One day when I went to his house, and Dad(4) wasn't there, I ran outside....    This is one where I'm not certain. I believe in this sense I'm showing possession here with "my", and it just didn't seem right saying "my Dad". I don't know what the grammar rule is here, or if I even have it right. This one is obvious—it starts the sentence. In this case, I'm using Dad like a name instead of saying "Larry". Therefore, it should be capitalized. Again, just like 3. What should I do to avoid ear pain when flying? Is there a more efficient way to clamp real numbers than using if statements or ternary operators? I want to do this both for doubles and for a 32-bit fixpoint implementation (16.16). I'm not asking for code that can handle both cases; they will be handled in separate functions.  Obviously, I can do something like:  double clampedA; double a = calculate(); clampedA = a &gt; MY_MAX ? MY_MAX : a; clampedA = a &lt; MY_MIN ? MY_MIN : a;   or  double a = calculate(); double clampedA = a; if(clampedA &gt; MY_MAX)     clampedA = MY_MAX; else if(clampedA &lt; MY_MIN)     clampedA = MY_MIN;   The fixpoint version would use functions/macros for comparisons.  This is done in a performance-critical part of the code, so I'm looking for an as efficient way to do it as possible (which I suspect would involve bit-manipulation)   EDIT: It has to be standard/portable C, platform-specific functionality is not of any interest here. Also, MY_MIN and MY_MAX are the same type as the value I want clamped (doubles in the examples above). Let $f$ be a continuous function on a set $E$.  Is it always true that $f^{-1}(A)$ is always measurable if $A$ is measurable?  I say no.  We know that $\bar{\psi(x)}:=\frac{\phi(x)+x}{2}$ where $\phi$ is the Cantor (or Cantor-Lebesgue) function and $\bar{\psi}:[0,1] \rightarrow [0,1]$.  We know this function maps a measurable subset of $C$ (the Cantor set) into a non-measurable set $W$.  A few observations about $\bar{\psi(x)}$.  It is strictly increasing and continuous, so it has a continuous inverse $\bar{\psi(x)}^{-1}$.  Thus $\bar{\psi(x)}^{-1}(W)=c \subset C$; that is, $\bar{\psi(x)}^{-1}(W)$ is non-measurable, but c is.  Is this correct? Equicontinuity on a compact metric space turns pointwise to uniform convergence I know that   If $\{f_n\}$ is an equicontinuous sequence,  defined on a compact metric space $K$, and for all $x$, $f_n(x)\rightarrow f(x)$, then $f_n\rightarrow f$ uniformly.  I'm having trouble proving this.  I see the same problem  but am having trouble following the proof, particularly with part (3).  Can someone guide me through a proof of this result? Two friends who have unpredictable lunch hours agree to meet for lunch at their favorite restaurant whenever possible. Neither wishes to eat alone and each dislikes waiting for the other, so they agree that each will arrive at a random time between noon and 1 pm, and each will wait for the other for 15 minutes or until 1:00. What is the probability that the friends will meet for lunch on a given day? I'm preparing a new template for our students' projects based on memoir. All this projects are supervised (directed) by one or more professors so I would like to declare a command like \author but called \director.   This way the student can declare \director{My professor} and the template will place and format the name.   I would like to be like \author and not just a simple \newcommand because it can include affiliation, several names, etc.  I don't know where is \author declared, where should I look? Would it be wrong to copy-paste questions from Quora? Derivative of inverse function at a point. Let $f\left(x\right)=x^{13}+3x^{9}+2x^{5}+x^{2}+x+2$ find $\left(f^{-1}\right)'\left(1\right)$. Can somebody show me the method? I am a little confused. How to change background-color on text links on hover but not image links How can I have `date` output the time from a different timezone? I have a server running with the timezone set to UTC. It seemed like that was generally a good practice (please correct me if I'm wrong).  Anyhow, one of the servers I connect to, in order to scp files, is running on EDT and stores files that I need to copy in the format /path/to/filename/data20120913  I looked at trying to rsync files using something like find's -mtime -1 flag for files modified in the last day, but I didn't have any luck.  I don't mind just using scp to copy the current day's file, but as of right now there is a 4-hour window where running date +%Y%m%d will give a different day on each server and that bugs me a little.  Looking through man date I see that I can have the time output as UTC, but I don't see a way to have it output as another timezone like EDT  I suppose I could also use something like the GNU date extension date -d 20100909 +%s to get the date in seconds from the epoch, apply a manual 4 * 60 * 60 second calculation, and see about rendering that as a date - but then when daylight time kicks in it will still be an hour off.  Is there a simpler way to output the date in a YYYYMMDD format for EDT on a server that is set to UTC ? find and echo file names only with pattern found