I am traveling to Amsterdam and then Dusseldorf and Brussels for about 20 days. My Schengen visa expires one week after the date of entry. Is this allowed, or should I apply for another Schengen visa?
I'm from Tunisia and I got a Schengen visa from the Austrian Embassy for  28 days, the “duration of stay”, and the number of entries is 1. But the validity of the visa is from 02/08/2015 to 13/09/2015.  Do I have to stay only 28 days, for example from 02/08/2015 to 29/08/2015 or can I stay there until 12/09/2015 ?  And if I have got to stay only 28 days, then can I choose the days of stay, that's mean can I stay in Austria for example from 09/08/2015 to 05/09/2015?
On Ubuntu 12.04 LTS on a Dell Vostro 2420 laptop, each time I start Ubuntu, the screen brightness is set to the maximum level, which gives a high glare. (I have recently installed Ubuntu on the laptop, but did not change any default settings related to brightness, IIRC.) I am currently lowering the brightness manually each time after starting, using the System Settings icon on the left of the screen. Looking for a permanent way to set it to a lower value. What is a serialVersionUID and why should I use it? Eclipse issues warnings when a serialVersionUID is missing.       The serializable class Foo does not declare a static final   serialVersionUID field of type long   What is serialVersionUID and why is it important?  Please show an example where missing serialVersionUID will cause a problem. Is it possible to write a Ping class in C# that will run within Windows 8 Metro environment? How to Measure Luck vs Skill in Games? Will be glad for a little hint: let x and n be positive integer such that $1+x+x^2+\dots+x^{n-1}$ is a prime number then show that n is prime Why does QgsSpatialIndex.nearestNeighbor(point, 1) sometimes return 2 lines? I'm trying to get the closest line to a point using PyQGIS in a plugin. The active code file is this:   When I request the closest line (only 1)  nearestIds = self.spIndex.nearestNeighbor(self.feat2.geometry().centroid().asPoint(),1)   I sometimes get a list with two lines and the first one is not the closest but as far as I can see the second one is. Why is this?   Does QgsSpatialIndex use only boundingboxes for lines? How do I get the real closest line always, not only most of the time? How do I enable hardware virtualization technology (VT-x) for use in Virtualbox? One of the new search hints is wrong How do I pre-populate a jQuery Datepicker textbox with today's date? I have a very simple jQuery Datepicker calendar:  $(document).ready(function(){     $("#date_pretty").datepicker({      }); });   and of course in the HTML...  &lt;input type="text" size="10" value="" id="date_pretty"/&gt;   Today's date is nicely highlighted for the user when they bring up the calendar, but how do I get jQuery to pre-populate the textbox itself with today's date on page load, without the user doing anything?  99% of the time, the today's date default will be what they want. Varying behavior for possible loss of precision Is the double-slit experiment typically carried out in a vacuum? It is my understanding of the double-slit experiment that when a measuring device is activated, to measure which of the two slits a particle is travelling through, this measuring is responsible for a different outcome than when the device is left off. When the device is left off particles leave an interference pattern, suggesting a single particle (or its wave) interferes with itself; when the device is activated no interference pattern is left, and particles are observed to travel through a single slit.  Now, does all this imply that this experiment is typically carried out in a vacuum? If not, how is it that interaction with other particles in the environment of the experiment's set-up are not already influencing the outcome, regardless of whether the measuring device is on or left off?  This question may very well be a very naive one, due to my very limited understanding of particle interaction, vacuums and/or physics in general. If so, I would appreciate a brief, layman's, overview of where my understanding of the different subjects at play here is likely to be lacking. This is a Putnam Problem that I have been trying to solve (on and off) for two years, but I have failed. I am in Calculus BC. This problem comes from the book "Calculus Eighth Edition by Larson, Hostetler, and Edwards". This problem is at the end of the first section of the chapter 8 exercises. Here's the problem:  Evaluate $$\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$$  Please. Any help is very much appreciated. So are solutions. Thank you!  Edit: I like the solution given, but I was interested to see if there is any other way of doing the problem? I'm excited to see the results. Is the orbit in Schwarzshild metric a path with maximal proper time? In curved spacetime particles follow timelike geodesics, which should have maximal proper time (at least locally). I thought this path usually corresponds to a global maximum, and there are only strange exceptions. Propably I was wrong, or I really don't understand something, because it doesn't seem to be true for the case of orbitals in Schwarzschild geometry.  The Schwarzschild metric is (with +--- signature)  $$ g_{\mu\nu} = \textrm{diag}\left(1-\frac{2GM}{r},-\left(1-\frac{2GM}{r}\right)^{-1},-r^2,-r^2\sin^2\theta\right) $$  An observer with fixed $r,\theta,\phi$ coordinates will age according to $d\tau_1 = \sqrt{g_{tt}}dt$. An observer, which orbits the center at the same constant radius with $\theta=\pi/2$ will age according to $d\tau_2 = \sqrt{g_{tt}-\omega^2r^2\sin^2\theta}dt$, so he ages slower during the same amount of coordinate time $dt$. If the two observers start from the same point, they will meet again after a full rotation of the orbiting observer, and the orbiting observer will age less. What I don't understand is that the orbit is the geodesic (if the angular velocity is set properly), so why didn't he age more? He should have been on the path with maximal proper time. I have been working on this exercise for a while now. It's in B.L. van der Waerden's Algebra (Volume I), page $19$. The exercise is as follows:     The order of the symmetric group $S_n$ is $n!=\prod_{1}^{n}\nu$. (Mathematical induction on $n$.)   I don't comprehend how we can logically use induction here. It seems that the first step would be proving $S_1$ has $1!=1$ elements. This is simply justified: There is only one permutation of $1$, the permutation of $1$ to itself.  The next step would be assuming that $S_n$ has order $n!$. Now here is where I get stuck. How do I use this to show that $S_{n+1}$ has order $(n+1)!$?  Here is my attempt: I am thinking this is because all $n!$ permutations of $S_n$ now have a new element to permutate. For example, if we take one single permutation $$ p(1,\dots,n) = \begin{pmatrix} 1 &amp; 2 &amp; 3 &amp; \dots &amp; n\\ 1 &amp; 2 &amp; 3 &amp; \dots &amp; n \end{pmatrix} $$ We now have $n$ modifications of this single permutation by adding the symbol $(n+1)$:  \begin{align} p(1,2,\dots,n,(n+1))&amp;= \begin{pmatrix} 1 &amp; 2 &amp; \dots &amp; n &amp; (n+1)\\ 1 &amp; 2 &amp; \dots &amp; n &amp; (n+1) \end{pmatrix}\\ p(2,1,\dots,n,(n+1))&amp;= \begin{pmatrix} 1 &amp; 2 &amp; \dots &amp; n &amp; (n+1)\\ 2 &amp; 1 &amp; \dots &amp; n &amp; (n+1) \end{pmatrix}\\ \vdots\\ p(n,2,\dots,1,(n+1))&amp;= \begin{pmatrix} 1 &amp; 2 &amp; \dots &amp; n &amp; (n+1)\\ n &amp; 2 &amp; \dots &amp; 1 &amp; (n+1) \end{pmatrix}\\ p((n+1),2,\dots,n,1)&amp;= \begin{pmatrix} 1 &amp; 2 &amp; \dots &amp; n &amp; (n+1)\\ (n+1) &amp; 2 &amp; \dots &amp; n &amp; 1 \end{pmatrix} \end{align}  There are actually $(n+1)$ permutations of that specific form, but we take $p(1,\dots,n)=p(1,\dots,n,(n+1))$ in order to illustrate and prove our original statement. We can make this general equality for all $n!$ permutations: $p(x_1,x_2,\dots,x_n)=p(x_1,x_2,\dots,x_n,x_{n+1})$ where $x_i$ is any symbol of our finite set of $n$ symbols and $x_{n+1}$ is strictly defined as the symbol $(n+1)$.  We can repeat this process for all $n!$ permutations in $S_n$. This gives us $n!n$ permutations. Then, adding in the original $n!$ permutations, we have $n!n+n!=(n+1)n!=(n+1)!$. Consequently, $S_n$ has order $n!$.  How is my reasoning here? Furthermore, is there a more elegant argument? I do not really see my argument here as incorrect, it just seems to lack elegance. My reasoning may well be very incorrect, however. If so, please point it out to me. Since it's Friday and others are playing games, here's another one to take us into the weekend.  Everyone knows about those Russian nesting dolls (called matryoshka dolls, I believe). A small doll nests inside a larger, which itself is inside a larger doll, and so on.   This game does the same with words. You start with a three-letter word, add a letter to make another word, and so on. Longest word wins. The catch? Each additional letter has to form a legitimate word.  Here's one to start you off:     bur   burr   burro   burrow   burrows     Good luck. Just freeze an application (suspend the CPU, save its state to disk) and 'defrost' it when I want to use it 4 weeks later. I would like to take the full citation of a reference in my BibTeX file and write commentary in-line after it.  A \fullcitation{id} command would be perfect.  I would like to use it as:  \fullcitation{id1}   This paper talks about A with applications to B.  \fullcitation{id2}   This paper considers how C affects A.  Whenever the \fullcitation{id} command appears, I want it to be replaced with the full reference, including authors, title, journal, and date.  Is this possible? failed to get D-Bus connection: Operation not permitted I'm trying to list services on my CentOS image running in Docker using  systemctl list-units     but I get this error message:  Failed to get D-Bus connection: Operation not permitted   Any suggestions what the problem might be? I came across the following question:    This can be easily flagged for too broad or opinion based, but I wonder on which stack-exchange site can one ask answers for such a question? how do I get my code to use the value of the $HOME variable? I'm trying to put together a generic script that will check the existence of several key directories for various users on different servers. Additionally, I want to leverage each user's $HOME variable.  For eg, let's say this were true:   on server 1: jdoe's home is /home/jdoe  on server 2: jdoe's home is /opt/jdoe2 server 3 hasn't been built yet; we won't know where they build his $HOME until the server is built. on server 4: mysql's home is /opt/home/mysql   This is what I have for my important directories (ordered from most to least impt):  $ cat mylist.txt $HOME/most_impt_dir1 $HOME/most_impt_dir2 $HOME/most_impt_dir3 $HOME/misc $HOME/junk   ...I want to find the most impt dir owned by this user.   Here's what I'm trying:  for i in `cat mylist.txt` do    if [[ -O $i ]] &amp;&amp; [[ -d $i ]]; then     echo "found it: $i"     break   else     echo "$i is not it."   fi  done   The above code does not work for anything in my list because it is literally checking for dirs beginning with $HOME. How do I get my code to use the value of the user's $HOME variable?