UK VISA Refusal! Submitted All Necessary Documents! (Graduation Ceremony In London)
UK visa refusal on V 4.2 a + c (and sometimes 'e')
On the street, temperatures at night are about -5 &deg;С and about 8 &deg;C during the day. In the apartment it is about 25 &deg;C. So, there is condensation on the windows and I don't want to wipe the windows every time.  How do I prevent condensation on the balcony windows? I'm one of very few people at my company who does graphic work, and I do quite a lot of it. Headquarters doesn't quite get that graphics work requires different hardware than, for example, sales work, which is pretty much email/Excel/Powerpoint/web browser and that's it. So they give everybody the same low-end rental PCs to work on.  This was tolerable when we were all on XP.  Recently I got "upgraded" to a new computer, which happens every two years or so as leases expire. The catch: the new PC had the same Core 2 Duo processor that the previous one did, less RAM, it runs Windows 7 instead of XP, and all the Creative Suite applications have been upgraded from CS3 to CS5! I am the first in my office to get 7.  So now I am in a situation where I have the slowest machine in the office, yet I have to do the most demanding work. I got them to OK 2 more gigabytes of RAM, and I hoped that would solve the issues, but it just isn't helping that much at all. I actually have to reboot every day after lunch because the machine stops responding after wake if you leave it asleep for too long.  I am currently talking to Information Systems to see if I can get a capable machine, but it does not bode well for me. Can anyone share any performance optimizations for Win7 that I might be able to use?  Thank you very much in advance! SS Wirtinger Inequality: $\int_0^1 f'^2 \geq \pi^2 \int_0^1 f^2 $ I have a  basic question  Let $f$ be a $\mathcal{C}^1$  map  from  $[0,1]$ into $\mathbb{R}$ vanishing in $0$ and $1$. I want to prove that   $$\int_0^1 f'^2 \geq \pi^2 \int_0^1 f^2 $$  and to see when we have equality. Simple form validation Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$? Consider square matrices over a field $K$. I don't think additional assumptions about $K$ like algebraically closed or characteristic $0$ are pertinent, but feel free to make them for comfort. For any such matrix $A$, the set $K[A]$ of polynomials in $A$ is a commutative subalgebra of $M_n(K)$; the question is whether for any pair of commuting matrices $X,Y$ at least one such commutative subalgebra can be found that contains both $X$ and $Y$.  I was asking myself this in connection with frequently recurring requests to completely characterise commuting pairs of matrices, like . While providing a useful characterisation seems impossible, a positive anwer to the current question would at least provide some answer.  Note that in many rather likely situations one can in fact take $A$ to be one of the matrices $X,Y$, for instance when one of the matrices , or more generally if its  (so coincides with the characteristic polynomial). However this is not always possible, as can be easily seen for instance for diagonal matrices $X=\operatorname{diag}(0,0,1)$ and $Y=\operatorname{diag}(0,1,1)$. However in that case both will be polynomials in $A=\operatorname{diag}(x,y,z)$ for any distinct values $x,y,z$ (then $K[A]$ consists of all diagonal matrices); although in the example in  the matrices are not both diagonalisable, an appropriate $A$ can be found there as well.   I thought for some time that any maximal commutative subalgebra of $M_n(K)$ was of the form $K[A]$ (which would imply a positive answer) for some $A$ with minimal polynomial of degree$~n$, and that a positive answer to my question was in fact instrumental in proving this. However I was wrong on both counts: there exist (for $n\geq 4$) commutative subalgebras of dimension${}&gt;n$ (whereas $\dim_KK[A]\leq n$ for all $A\in M_n(K)$) as shown in , and I was forced to correct  in the light of this; however it seems (at least in the cases I looked at) that many (all?) pairs of matrices $X,Y$ in such a subalgebra still admit a matrix $A$ (which in general is not in the subalgebra) such that $X,Y\in K[A]$. This indicates that a positive answer to my question would not contradict the existence of such large commutative subalgebras: it would just mean that to obtain a maximal dimensional subalgebra containing $X,Y$ one should in general avoid throwing in an $A$ with $X,Y\in K[A]$. I do think these large subalgebras easily show that my question but for three commuting matrices has a negative answer.  Finally I note that  to the cited MO question mentions a result by Gerstenhaber that the dimension of the subalgebra generated two commuting matrices in $M_n(K)$ cannot exceed$~n$. This unfortunately does not settle my question (if $X,Y$ would generate a subalgebra of dimension${}&gt;n$, it would have proved a negative answer); it just might be that the mentioned result is true because of the existence of $A$ (I don't have access to a proof right now, but given the formulation it seems unlikely that it was done this way).  OK, I've tried to build up the suspense. Honesty demands that I say that I do know the answer to my question, since a colleague of mine provided a convincing one. I will however not give this answer right away, but post it once there has been some time for gathering answers here; who knows somebody will prove a different answer than the one I have (heaven forbid), or at least give the same answer with a different justification. Finding CPU usage of a service Because my laptop fan was spinning up for no reason, I had a look at the CPU usage and I see  svchost with 12.5% CPU, which is basically a full core.  Now, I'm aware that  svchost runs services and I know how to display the services it runs in Task Manager or Process Explorer ().  Now I know which services are run, but I don't know which service eats the CPU time. I could disable one service after another, but I don't really like doing this (it could break things that are currently in use and I could forget turning the service back on later).  Therefore I'd like to know whether it's possible to instruct Windows to run only one service per svchost the next time I boot my PC. While I might have the slight disadvantage of several processes, I could immediately find out which one it is and it would be a much easier decision of whether or not to stop or restart the service. I'm currently working on the following question:  "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist"  I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far, I have got $P \lor D$,  $P \Rightarrow \lnot a$,  $D \Rightarrow A$,  $D = A$  However, I cannot seem to make these prove the statement using natural deduction, any hints? Is there a way to have a copy of any message sent from a Gmail account sent to another address?  I've got any messages coming to my address copied to another (see  for one solution, setting up filters is another), but I haven't yet found a way to have outbound messages automatically copied.  Is there a way? Can we get an indication comments are hidden between the comments? Proof involving absolute value and maximums Given the definition for any real numbers a and b, the max function is   $\max\{a, b\} =  \begin{cases}                                    a \text{ if } a \geq b \\                                    b \text{ if } a &lt; b \\   \end{cases} $  Lemma: for any two real numbers $a\text{ and }b, a \leq \max\{a,b\}$ and $ b \leq \max\{a,b\}$.  Prove that for real numbers, $a, b$, and $x$, if a $\leq x \leq$ b then $|x| \leq \max\{|a|,|b|\}$.  So far, I have  $x \geq 0$ or $x &lt; 0$ by the law of trichotomy  Case 1: $x\geq 0$  $|x| = x$ by the definition of absolute value  and I'm not sure where to go from there. Any hints? How far can/should one press philosophical doubt? Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do)? Descartes used 'I think' as this fixed point where the skepticism abates, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy? Shapefile Naming conventions in ArcPy? I have shapefile named `band-tailed_pigeon.shp which is fine and no problem on displaying or geoprocessing on Desktop but in ArcPy when I try to merge some layes to it I am getting this error   ExecuteError: ERROR 000354: The name contains invalid characters Failed to execute (Merge).  I tried to do the proccess with a simple name like sample.shp which it works but I HAVE TO keep the same name as we are using them in several projects. Here is the code which I have FinaloutLocation = &quot;E:\\GIS\\Data\\Final\\band-tailed_pigeon.shp&quot; inFeaturesToMerge = [dissolve_1, dissolve_2, dissolve_3, dissolve_4, dissolve_5] arcpy.Merge_management(inFeaturesToMerge, FinaloutLocation) Calling a parent window function from an iframe In Avatar: The Last Airbender, Aang's eyes glow when he goes into the Avatar State. This seems to be the case with all Avatars, but Aang and the other airbending Avatars tattoos glow too.      Is there any reason for why airbending Avatars tattoos glow as well as their eyes? How can I limit ssh *remote* port forwarding? I need to limit which ports can be remotely 'ssh -R' forwarded by an user.  I know about permitopen option on authorized_keys, but as it says on man page it only limits local 'ssh -L' port forwarding  As discussed  a user would get the same with netcat or similar, but in this case user has no shell access  I also found  that talks about using selinux or LD_PRELOAD, but I never configured selinux before and can't find info on how to do that with LD_PRELOAD.  maybe someone have made a patch for openssh to implement that?  EDIT: I've found  so I guess it's not yet implemented Numbers to the Power of Zero I have been a witness to many a discussion about numbers to the power of zero, but I have never really been sold on any claims or explanations.  This is a three part question, the parts are as follows...    1) Why does $n^{0}=1$ when $n\neq 0$?  How does that get defined?  2) What is $0^{0}$?  Is it undefined?  If so, why does it not equal 1?  3) What is the equation that defines exponents?  I can easily write a small program to do it (see below), but what about in equation format?    I just want a little discussion about numbers to the power of zero, for some clarification.    Code for Exponents: (pseudo-code/Ruby)  def int find_exp (int x, int n){     int total = 1;     n.times{total*=x}     return total; } Can you set custom ringtones for contact groups? In iPhone, you can easily change the default ringtone (Settings → Sounds → Ringtone) and set a custom ringtone for individual people (Contacts → [some person] → Edit → Ringtone).   But can you set a custom tone for a group of contacts? (E.g. "family" or "workmates".)  I think that would be handy—and quite basic functionality, so to speak—but I couldn't find a way to do this through the iPhone UI. Is it possible at all (without jailbreaking)? Firefox application associations not working in the 'Downloads' window If a user is the type of person to consecutively get downvoted to potential negative reputation, so be it. What's the reasoning to maintain a minimum of one?  One reason that may justify this is of trying to not deter new users from the site who haven't read the FAQ and unknowingly and wrongly ask or answer a question. But most of us acknowledge this and not downvote in such a scenario.  So what's the reasoning behind this lower bound of 1? A single row background colour