I am an Indian citizen, travelling to USA by an American Airlines flight (which is operated by British airways for the first leg). I have a valid tourist/business visa (B1/B2) for USA. My flight will arrive at Terminal 5 at 7 am, and leave from Terminal 3 at 9.30 am at Heathrow, giving me 2.5 hours to make the connection.  I had the following questions -  a) Do I need a direct airside transit visa (DATV) or a visitor-in-transit visa for this connection?  b) Both flights will be on a single ticket. Given this, will I have to pass through UK borders, customs or immigration?  c) Given that I need to move from Terminal 5 to Terminal 3 - are 2.5 hours sufficient to make the connection?
Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.
Access denied when creating keystore for Android app Proving that any permutation in $S_n$ can be written as a product of disjoint cycles I have attempted a proof of this, but upon looking at my notes, I feel it might be incorrect: it is noticeably simpler than the one in my notes.  Proposition: any permutation in $S_n$ can be written as a product of disjoint cycles.  Proof (attempt): $s\in S_n$. Let $\langle s\rangle$ act on $X=\{1,\cdots,n\}$. Define $x\sim x'\iff x'\in\text{Orb}(x)$ for $x,x'\in X:$ this is clearly an equivalent relation, hence the orbits partition $X$. Each orbit corresponds a cycle in $s$, so we are done.  Does this hold, or have I missed something vital? What are some good books for learning general relativity? How to escape  inside  tags I'm trying to write a blog post which includes a code segment inside a &lt;pre&gt; tag. The code segment includes a generic type and uses &lt;&gt; to define that type. This is what the segment looks like:  &lt;pre&gt;     PrimeCalc calc = new PrimeCalc();     Func&lt;int, int&gt; del = calc.GetNextPrime; &lt;/pre&gt;   The resulting HTML removes the &lt;&gt; and ends up like this:  PrimeCalc calc = new PrimeCalc(); Func del = calc.GetNextPrime;   How do I escape the &lt;&gt; so they show up in the HTML? Pretty tricky cmd How much space does Ubuntu take up after it's already installed? I know how much space is required to install Ubuntu.  How much space does a Ubuntu installation take up on the disk? I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere. I just created my new character 2 hours ago and I've reached a town. Sometimes random guards will comment that I look ill, or that I should rest. "You look sick, honey. Do you want to lie down?", isn't uncommon.  Did I unexpectedly get vampirism? I didn't fight any vampires, only a couple of wolves and bandits.  I'm a dark elf, so maybe my race isn't seen much around Skyrim and the remarks are more roleplay than actual illness.  Any ideas? Example of a function $f$ on $X$ to $\mathbb{R}$ which is not $X$-measurable but $|f|$, and $f^2$ are measurable. Question  The following is from Bartle:  Give an example of a function $f$ on $X$ to $\mathbb{R}$  which is not $X-$measurable but is such that $|f|,$ and $f^2$ are measurable.  Relavant Information  A family $\textbf{X}$ of subsets of $X$ is a $\sigma$ algebra in case:   $\phi, \mathbb{R} \in \textbf{X}$ $X \setminus A \in \textbf{X}$ if $A \in \textbf{X}$ If $(A_n) \in \textbf{X}$, then the union $\bigcup_{n=1}^{\infty} A_n \in \textbf{X}$  Any set in $\textbf{X}$ is called $X-$ measurable.   A function is $X-$ measurable if for every real $\alpha$, the set $\{x \in X : f(x)&gt;\alpha\}$ belongs to $\textbf{X}$  Attempt  Consider the following function: $$f=\begin{cases} 1 &amp;\mbox{ if} \ x \not\in\mathbb{Q} \\                   -1 &amp;\mbox{ if} \ x \in \mathbb{Q}  \end{cases}$$ defined from $\mathbb{R}$ to $\mathbb{R}$ with $\textbf{X}$ being the Borel algebra (the $\sigma$ algebra generated by all open intervals $(a,b)$) Then if $\alpha \in [-1,1)$, the set $\{x: f(x)&gt;\alpha\}$ consists of the irrational numbers. If I can show that the irrationals are not in the Borel Algebra, then I would be done since $|f|=f^2$ is a constant and easily shown to be measurable. Unfortunately I do not know how to show that the irrationals are not in the Borel Algebra.  Edit it has been brought to my attention that the irrationals are in the Borel algebra. I think this is because the rationals, being countable, can be shown to be in the Borel algebra by constructing appropriate small neighborhoods around each rational and then taking the intersections. I now seek to construct a set that is not in the Borel algebra  Alternatively I have tried to define a set other than the irrationals that is not in the Borel Algebra and define a similar function but to no avail. I am currently self studying this book so it would be of great help to me if the answer could contain heuristics on how to tell when a set if borel measurable (although I do not require this in the answer). How can I automatically shutdown the system after a specific time? I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?. Layers with different directional drop shadows in Photoshop I am wondering how to have 2 different directional drop shadows in the one file with Photoshop. e.g. 2 different type layers — one has a drop shadow at 90 degrees, the other at -45 degrees.  Currently it seems Photoshop only lets me have 1 universal direction for the whole file, which I find really pointless.   I know how to apply different drop shadows and merge down layers to achieve the same thing, but its tedious and not exactly streamlined for making future changes to that layer.  How is this achieved? How to fix broken taskbar icons in Windows 7 Was Harry Potter a direct descendant of Godric Gryffindor? How to watch videos in Amazon Prime Instant Video? How can adding an infinite number of rationals yield an irrational number? For example how come $\zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}$. It seems counter intuitive that you can add numbers in $\mathbb{Q}$ and get an irrational number. How can the behavior of InterpolationOrder->0 be controlled? Why are `/dev/ptmx` and `/dev/pts/ptmx` not device files? says     On Linux, using devpts, there is no master device file. The process on the master end uses a file descriptor, which it gets by opening ptmx, but there’s no corresponding device node.   Did the author refer to /dev/ptmx or /dev/pts/ptmx?    Why are /dev/ptmx and /dev/pts/ptmx not device files? What types of files are they?  What is the difference between /dev/ptmx and /dev/pts/ptmx?  Thanks.  On Lubuntu 18.04  $ file /dev/ptmx  /dev/ptmx: character special (5/2) $ file /dev/pts/ptmx  /dev/pts/ptmx: character special (5/2)  $ sudo su  # stat -L /dev/fd/3 3&lt;&gt; /dev/pts/ptmx   File: /dev/fd/3   Size: 0           Blocks: 0          IO Block: 1024   character special file Device: 15h/21d Inode: 2           Links: 1     Device type: 5,2 Access: (0000/c---------)  Uid: (    0/    root)   Gid: (    0/    root) Access: 2018-11-21 13:39:10.544000218 -0500 Modify: 2018-11-21 13:39:10.544000218 -0500 Change: 2018-11-21 13:39:10.544000218 -0500  Birth: -  # stat -L /dev/fd/3 3&lt;&gt; /dev/ptmx   File: /dev/fd/3   Size: 0           Blocks: 0          IO Block: 4096   character special file Device: 6h/6d   Inode: 87          Links: 1     Device type: 5,2 Access: (0666/crw-rw-rw-)  Uid: (    0/    root)   Gid: (    5/     tty) Access: 2019-01-06 07:19:54.372098540 -0500 Modify: 2019-01-06 07:19:54.372098540 -0500 Change: 2018-11-21 13:39:30.372098540 -0500  Birth: - If light rays obey to the wave equation, why can they be thought as straight lines? I'm a newbie with physics but I'm wondering how a ray of light can essentially be represented. I have always known that a ray of light proceeds in a straight line until it encounters another object (or material) that refracts/reflects it. But a light ray should be part of an electro-magnetic wave, is this correct? If it is so, it should obey to the  and this doesn't seem to me to describe a straight line ray.  I'm having problems visualizing how light is emitted and how it relates with the wave equation. Can someone with a clear understanding of the problem explain it to me in simple terms? "Effect" vs. "Affect" I've noticed that some people use effect and affect interchangeably. What are the differences between these two and when are the proper situations to use each of them?