Am an Indian Citizen travelling to Ireland with an Irish visa via LHR so would I need a transit visa at London Heathrow airport?
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.
Gradient of $a^T X b$ with respect to $X$ How can I find the gradient of the term $a^TXb$ where $X$ is a $n \times m$ matrix, and $a$ and $b$ are column vectors.  Since the gradient is with respect to a matrix, it should be a matrix.  But I do not have a clue on how to derive this gradient.   Any help ? I've been trying to understand how the second order derivative "formula" works:  $$\lim_{h\to0} \frac{f(x+h) - 2f(x) + f(x-h)}{h^2}$$  So, the rate of change of the rate of change for an arbitrary continuous function. It basically feels right, since it samples "the after $x+h$ and the before $x-h$" and the $h^2$ is there (due to the expected /h/h -> /h*h), but I'm having trouble finding the equation on my own.  It's is basically a derivative of a derivative, right? Newtonian notation declares as $f''$ and Leibniz's as $\frac{\partial^2{y}}{\partial{x}^2}$ which dissolves into:  $$(f')'$$ and $$\frac{\partial{}}{\partial{x}}\frac{\partial{f}}{\partial{x}}$$  So, first derivation shows the rate of change of a function's value relative to input. The second derivative shows the rate of change of the actual rate of change, suggesting information relating to how frequenly it changes.  The original one is rather straightforward:  $$\frac{\Delta y}{\Delta x} = \lim_{h\to0} \frac{f(x+h) - f(x)}{x + h - x} = \lim_{h\to0} \frac{f(x+h) - f(x)}{h}$$  And can easily be shown that $f'(x) = nx^{n-1} + \dots$ is correct for the more forthcoming of polynomial functions. So, my logic suggests that to get the derivative of a derivative, one only needs to send the derivative function as input to finding the new derivative. I'll drop the $\lim_{h\to0}$ for simplicity:  $$f'(x) = \frac{f(x+h) - f(x)}{h}$$  So, the derivative of the derivative should be:  $$f''(x) = \lim_{h\to0} \frac{f'(x+h) - f'(x)}{h}$$  $$f''(x) = \lim_{h\to0} \frac{  \frac{ f(x+2h) - f(x+h)}{h} - \frac{ f(x+h) - f(x)}{h}  }{h}$$  $$f''(x) = \lim_{h\to0} \frac{  \frac{ f(x+2h) - f(x+h) - f(x+h) + f(x)}{h}  }{h}$$  $$f''(x) = \lim_{h\to0} \frac{  f(x+2h) - f(x+h) - f(x+h) + f(x)  }{h^2}$$  $$f''(x) = \lim_{h\to0} \frac{  f(x+2h) - 2f(x+h) + f(x)  }{h^2}$$  What am I doing wrong? Perhaps it is the mess of it all, but I just can't see it. Please help. How do I set a user environment variable? (permanently, not session) This is irritating me. I seen several suggestions (all using different files and syntax) and none of them worked.  How do I set an environment variable for a specific user? I am on debian squeeze. What is the exact syntax I should put in the file to make ABC = "123"? Why is cpu_idle called as the last function of the start_kernel routine? I'm reading the  function in /init/main.c.  The last function called in start_kernel is rest_init, and at the end of rest_init, cpu_idle is called.   Why is it called as the last function of the start_kernel routine, and what does it do? Is it possible to get the data off of the hard drive of a PlayStation 3 that has crashed? I have already voided the warranty so I am not worried about that and I have access to quite a few tools.   I have a new PlayStation and a few saves that were not backed up. I am not worried about them but if it is possible I would love to get it moved over.   The old PlayStation will not turn on at all and I think I am going to have to pull the drive. My main concern is if I am able to transfer the files without running into any issues. I have heard that some of the stuff is specific to each PlayStation, is that true? What is the lowest level of mathematics required in order to understand how encryption algorithms work? What mathematical fields of knowledge would be required in order to get a good understanding of encryption algorithms?   Is it basic algebra, or is there a "higher education" mathematical field dedicated to encryption? I know there is the cryptography field, but what is the subset of knowledge required for cryptographers? Edit a truetype font I'm trying to find a free tool (on windows ) that would enable me to change some settings on a TrueType font. Specifically, I'm trying to fix the following errors:  E1311 The macStyle bold bit doesn't match the name table's font subfamily string macStyle bold bit is set, but subfamily is Regular  W2000 The subfamily string is inconsistent with the style of the font OS/2.fsSelection bold bit is set, but subfamily string = 'Regular'  I can do that with fontographer, but would prefer to use something free.  Fontforge doesn't seem to work with this font, when saved it corrupts the cyrillic letters in the font. What does "Incompatible types: void cannot be converted to ..." mean? Do I keep my Windows installation if I install Ubuntu with Wubi, the Windows installer? How can I change some pages into document into landscape mode, while leaving the others in portrait mode (or vice versa)? Clarifying question on meaning of derivative of a linear transformation In my analysis class, my professor (and the textbook) reference the fact that $\mathbf{D}T(\bar{x}) = T$ for any $\bar{x} \in \mathbb{R}^n$ where $T \in \mathcal{L}(\mathbb{R}^n,\mathbb{R}^n) $. I'm wondering about the precise meaning of this statement. Is it that the differential of any linear transformation is also linear? Or is that the differential of any linear transformation is itself (and therefore also linear)? The second seems confusing to me because the derivative of a function is often not itself. For example, $f(x) = 2x$ is a linear transformation but $f'(x) = 2 \ne 2x$ for all $x \in \mathbb{R}$. Prove by induction that $n! > 2^n$ Suppose that when $n=k$  $(k\geq4)$, we have that $k!&gt;2^k$.  Now, we have to prove that $(k+1)!\geq2^{k+1}$ when $n=(k+1)$ $(k\geq4)$.  $$(k+1)! = (k+1)k! &gt; (k+1)2^k  \text{ (since }k!&gt;2^k)$$  That implies $(k+1)!&gt;2^k2$, since $(k+1)&gt;2$ because of $k$ is greater than or equal to 4.  Therefore $(k+1)!&gt;2^{k+1}$  Finally  we may conclude that $n!&gt;2^n$ for all integers $n\geq4$    Solved, thank you! Selected references without hyperlink When using the hyperref package, is it possible to tell LaTeX not to create a link for some references?  In my case the page number is displayed in the footer in  \fancyhf[FC]{\thepage\ of \pageref{pg:end}}   which is what I want. Unfortunately every single page in the document then has a link to the final page, which is a bit silly.  Any ideas on how to fix that? What is the easiest way to highlight the difference between two strings in PHP?  I'm thinking along the lines of the Stack Overflow edit history page, where new text is in green and removed text is in red. If there are any pre-written functions or classes available, that would be ideal. Given the following sentences:        I have even started using them in normal writing.   People can understand your writing better.      Are using and writing gerunds, verbs, or some other part of speech?  Context:  I am prefixing the words in some phrases with abbreviations. Some of the words are giving me trouble in classification. (The message is supposed to be an implicit proof of why adding prefixes to table names in a database is terrible. But I'd like to get it right.)  Here's the full set of sentences for your amusement. However, please restrict your comments to the stated question, for the most part.        com-Don't ver-Listen prep-To adj-Those adj-Other nou-People.    pro-You aux-Should adv-Always ver-Use nou-Prefixes prep-With pro-Your adj-Table nou-Names.    pro-I aux-Have adv-Even ver-Started ver-Using pro-Them prep-In adj-Normal nou-Writing.   com-See adv-How adj-Effective pr-It ver-Is?    nou-People aux-Can ver-Understand pro-Your nou-Writing adv-Better!      (where com means command verb)  This question is part of 3 related questions:     This question   It originally came from Explain how (or if) a box full of photons would weigh more due to massless photons Take for example  both at SO and SU. Now that there's , (new) users asking a LaTeX question should at least be informed that there is a new Stack Exchange site dedicated to TeX and thus increases their chance of an answer. This should happen before the question is actually posted and ideally offer the option to post the question directly there instead (without the need to copy-paste).  LaTeX is just an example, there's also , ,  etc., and it is obvious that this can only be decided on a case-by-case basis which is why I certainly do not suggest migrating questions automatically when these tags are used. But informing users of that possibility would probably help the SE network in general. Green is the most common circuit-board color because it has become an industry standard.  What I'm interested in is How the traditional "PCB Green" become a standard in the first place?   Were there any interesting historical reasons for the initial choice, or was it just a product of what one particularly successful company was doing that became the de-facto standard? Is there a streaming API for JSON? For the command   sudo apt-get update   I get following error:  W: Failed to fetch http://ch.archive.ubuntu.com/ubuntu/dists/maverick-updates/multiverse/binary-i386/Packages.gz   407  Proxy Authentication Required (The ISA Server requires authorization to fulfill the request. Access to the Web Proxy filter is denied. )   I am running Ubuntu 10.10 installed on Windows XP using VirtualBox. For Internet connections I am using proxy server with an authentication. I tried to use gnome-network-proxy tool to set proxy settings system-wide.   After that /etc/environment has been updated by http_proxy variable with the format http://my_proxy:port/, there were no authentication data.  I checked this with Firefox. Browser asked my for login and password and everything was working fine. It was unfortunately not the case for apt-get. I have also tried to do as described . Unfortunately it does not work.  May it be somehow related to the fact that a proxy is in a Windows domain, any ideas?  My proxy name is http-proxy. Is '-' a special character here?