Stopping overnight at London Heathrow - do I need an arrival visa and what kind?
London Heathrow airport - do I need a transit visa?
Do gravitational lenses work on gravitational waves? Do gravitational lenses work on gravitational waves? Could we get an Einstein cross of gravity? Is LED properly implemented in the constant current circuit? Once it is compiled, is there a difference between:  delegate { x = 0; }   and  () =&gt; { x = 0 }   ? How to find range $a_{75}$ of the term of the series $a_n=a_{n-1}+ {1 \over {a_{n-1}}} $ If $a_1=1$ and for n&gt;1$$a_n=a_{n-1}+ {1 \over {a_{n-1}}} $$ $a_{75}$ lies between (a) (12,15) (b) (11,12) (c) (15,18)  Now , in this question, I rewrote, $a_n-a_{n-1} = {1 \over {a_{n-1}}}$, to make a telescopic type and summed the terms to get $$a_n-a_{1}= {1 \over {a_{n-1}}}+ {1 \over {a_{n-2}}}...{1 \over {a_{1}}}$$ And as ${1 \over {a_{r}}} &lt;1$ for all r , I got $a_{75} &lt;76$ , but it's of no help as , the upper bound is much higher. I got no further ideas , on how to solve it, please help. A single word for someone who spends their wealth very foolishly Is there a general formula for finding the primitive of $$e^{ax}\sin(bx)?$$  I've done this manually with $a=9$ and $b=4$ using Euler's formulas. But it takes a bit of time. Is there a pattern here? Could I use a 1/2TB USB 2/3 external HDD with an XBox 360? wildcard * in CSS for classes first post between 12/26 and 1/1   Does that mean your very first post as a user should be made in those days?  Or that you should be the first user to post any post on a site starting 12/26?  Or something else?  The first option seems somewhat more likely but I'm not sure I'm parsing the description right. There has been talk of how to answer a negative question without ambiguity, most often with a qualifying phrase needed for clarification. (For example, "yes, I do"/"no, I don't.)  I've noticed that other languages have a single word to address a negative question on the contrary. In German, ja means yes and nein means no. Alternatively, doch is used to respond in the positive to a negative question, in essence meaning "No, I intend to do the opposite of what your question presumes."  Take for example the question, "You don't want to go to the movie then?" German speakers could simply reply, "nein" if they don't want to go or they would say "doch" if they did want to go; an unambiguously positive response to a negatively phrased question. No need for, "no, I actually would like to go" or "yes, I'll come actually". In French, the respective equivalents of ja, nein, and doch are oui, non, and si. I imagine many other languages contain this set as well.  I am wondering whether there was at one time an equivalent word in the English language that has since (unfortunately) disappeared. Any ideas? Recovering the data from a failed WD My Book NAS drive My Western Digital 500GB NAS drive (which is my main backup device) has recently broken. Windows can no longer use it as a network drive (using Map Network Drive), and the web-based control panel is INCREDIBLY sluggish, taking as much as 5 minutes to load a single page.  However, when it does load, it reports the Drive Status as OK, and has the correct disk usage values, which leads me to think the actual drive is OK, and it's the networking components that have failed.  I have checked the wires and router, and so it their isn't another point in the network causing the problem.  Is there any way to get the data back? It's a backup, so I still have about 80% of the data spread out across 3 computers (the only major loss being my music library, and I have the discs for a fair proportion of that).  However, it'd be much more convenient if I can get the data from the drive itself, as it is organised properly on the drive. A finite $p$-group cannot be simple unless it has order $p$ I am to trying to prove this theorem: A finite $p$-group cannot be simple unless it has order $p$.  I have this:   Let $G = P$ and $|G|=p$; then there exists $N$, a normal subgroup of $G$ by Lagrange's theorem, such that $|N| \mid |G|$ so, $|N|= |e| = 1$ or $|N| =  p$  If $|N|=p$ so $N=G$.  But I don't know how I can prove the part in the case of $|N|=|e| = 1$  Is my start correct? If $f$ is integrable then $|f|$ is also integrable Show that if $f$ is integrable on $[a, b]$ then $\lvert f \rvert$ is also integrable. Hint: Show that $$U (P , \lvert f \rvert) − L(P , \lvert f \rvert) ≤ U (P , f ) − L(P , f ).$$ I have: $$U (P , \lvert f \rvert) \ge U (P , f )$$ and $$ L(P , \lvert f \rvert) \ge L(P,f)$$ Thus, $$U (P , \lvert f \rvert) − L(P , \lvert f \rvert) ≤ U (P , f ) − L(P , f ).$$ I have always believed that it was ok to replace a capacitor with a slightly higher voltage rated one. eg 16v with 25v.Going higher than this would risk the capacitance value being out at the working voltage. However I just read the following quote from this       Electrolytic capacitors are non-ferroelectric with a very low dielectric constant. Their capacitance is derived from a very high surface area and nanometer thick dielectric layers. Their capacitance is not a function of applied voltage.‐Design Solutions For DC Bias In Multilayer Ceramic Capacitors (August 2010 Electronic Engineering Times)   So does this rule not apply to aluminum electrolytics? Eg will I have no issues replacing an electrolytic 25v 100uf with a 50v 100uf assuming both are low esr, similar footprint and good quailty? "Single ampersand used with wrong catcode" error using tikz matrix in beamer Eclipse doesn't start on Ubuntu 18.04 Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer? errors upgrading from 14.04 to 16.04 about Unknown Multi-Arch type for compiz, libkf5akonadisearch-bin packages I'm trying to upgrade my 14.04 machine to 16.04 using do-release-upgrade. After downloading the package lists for wily, I see the following errors:  Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-min Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-min Unknown Multi-Arch type 'no' for package 'libkf5akonadisearch-bin' Ignoring Provides line with DepCompareOp for package php-psr-http-message-implementation Ignoring Provides line with DepCompareOp for package php-psr-log-implementation Ignoring Provides line with DepCompareOp for package php-math-biginteger Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python-cffi-backend-api-min Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-max Ignoring Provides line with DepCompareOp for package python3-cffi-backend-api-min Unknown Multi-Arch type 'no' for package 'libkf5akonadisearch-bin' Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' Unknown Multi-Arch type 'no' for package 'compiz-core' Unknown Multi-Arch type 'no' for package 'compiz-gnome' You may want to run apt-get update to correct these problems   It then proceeds to abort the installation. The suggested run of apt-get update doesn't seem to do anything. Googling for the above error messages yielded others having similar problems when upgrading to other, previous releases, although I've not come across any apparent fixes. It's suggested that an apt upgrade could fix the problem, but I don't see a way to easily do that (it's up to date with the latest trusty package).  What should I do in order to upgrade directly to 16.04? QTimer can only be used with threads started with QThread Why do students go for a PhD even when chances of getting academic jobs on its completion are slim? This is in reference to my question: .  I was told in the answer of the above linked question that chances of landing a job as an assistant professor in Mathematics are quite slim. Very few people will actually get a permanent position in academia.  An article of 2014 shows only 0.5-3% of PhD graduates will actually get a job as an Assistant Professor.  But I have two questions:        Why do so many people still apply for a PhD in some reputed institutes in India even knowing the harsh reality? I found there are 1500 applications for four PhD scholarship positions.          One answer says that people move to industry, but I still don’t understand how after doing a PhD in suppose differential geometry or algebraic geometry one can do a job in industry if he/she gets no position as an assistant professor.   Will one be satisfied to do some managerial work in some Consultancy firm after doing a PhD in Mathematics?      Are people jobless after a PhD?   Completion of a PhD requires so much effort. So why is there no value after doing it?      NOTE:  In the most up-voted answer below it has been said that many who enroll for  a PhD don't even wish to pursue an academic career.  I have been asking my seniors who are currently pursuing a PhD or are in the verge of completing their degree or who have completed it. They said that they all want to be Professors in some Universities and want to be involved in research because that is the dream job for them.  I am obviously talking about PhD in Mathematics