Schengen Visa Free Travel as Tourist (90/180) Immediately Following Long Stay (D Type Visa)
Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries?
Why are imported PDFs blurry in InDesign? ArcMap Attribute Table not seen when second screen disconnected from Main Computer? Solve recurrence relation $a_n = 3 a_{n - 3} + a_{n-1} + 2 n$ I am not able to solve the above recurrence relation which involves $n$. The initial conditions $a_0 = 1, a_1 = 2, a_2 = 3$, for $n \geq 0$. Please try to give closed form in terms of arbitrary $a_i \geq 1 $ for $i \geq 0$ Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$ Sphere rolling up a ramp In this question, I did energy conservation, with the states being the initial one and the one where it is at the top , and I got $$ .5 I w^2 + .5 mv^2 = mgh$$ However, in  the answer key they have done, $$ .5 mv^2 + .5 Iw^2 = .5 Iw^2 + mgh$$ Now why would the k.e be turned to p.e but not the rolling energy?? Possible Duplicate:          In  the following claim was mentioned:  $R/I \otimes_R M \cong M / IM$  So I tried to prove it. Can you help me finish my proof? Thanks!    We recall that $M \otimes_R -$ is a covariant right-exact functor that it is exact if $M$ is flat and we observe that the following is an exact sequence: $$ 0 \to IM \xrightarrow{i} M \xrightarrow{\pi} M / IM \to 0$$  $R/I$ is an $R$ module since $R/I$ is a subring of $R$ closed with respect to multiplication from $R$ but it is not necessarily flat hence we only get exactness on one side:  $$  (R/I) \otimes_R IM \xrightarrow{id \otimes i} (R/I) \otimes_R M \xrightarrow{id \otimes \pi} (R/I) \otimes_R M / IM \to 0$$  Then $$ \mathrm{Im(id \otimes \pi)} = (R/I) \otimes_R M / IM  \cong (R/I) \otimes_R M / \mathrm{Ker} (id \otimes i) $$  so we want to show two things:   (i) that $\mathrm{Ker} (id \otimes i) = \{0\}$. To this end let $r + I \otimes im \in (R/I) \otimes_R  IM $ and assume $ id \otimes i(r + I \otimes im ) = r + I \otimes im = 0 + I \otimes 0$. I'm not sure how to proceed from here.   (ii) and that $M /IM \cong (R/I) \otimes_R M / IM $  Can you help me? Thanks. I have a question about editing practices:  Does it look good to edit a question you have just answered?  For example: say I had just answered a question, then saw that the question had some minor formatting issues. Should I edit it? Does it turn up voters off when they see that I am answering a question I changed, possibly to better suit my answer? For example, the square can be described with the equation $|x| + |y| = 1$. So is there a general equation that can describe a regular polygon (in the 2D Cartesian plane?), given the number of sides required?  Using the Wolfram Alpha site, this input gave an almost-square: PolarPlot(0.75 + ArcSin(Sin(2x+Pi/2))/(Sin(2x+Pi/2)*(Pi/4))) (x from 0 to 2Pi)  This input gave an almost-octagon: PolarPlot(0.75 + ArcSin(Sin(4x+Pi/2))/(Sin(4x+Pi/2)*Pi^2)) (x from 0 to 2Pi)  The idea is that as the number of sides in a regular polygon goes to infinity, the regular polygon approaches a circle. Since a circle can be described by an equation, can a regular polygon be described by one too? For our purposes, this is a regular convex polygon (triangle, square, pentagon, hexagon and so on).  It can be assumed that the centre of the regular polygon is at the origin $(0,0)$, and the radius is $1$ unit.  If there's no such equation, can the non-existence be proven? If there are equations, but only for certain polygons (for example, only for $n &lt; 7$ or something), can those equations be provided? What does --shell-escape do? I stumbled upon an example, which needed to be compiled with the additional option --shell-escape. Using this option it worked just fine, but I'm curious:     Why or when is this option needed and what does it actually do? Did Emperor Palpatine know about Luke and Leia from the beginning? Did Emperor Palpatine know that Padme had given birth to twins while it was happening?  Was it his long-term goal to have Vader only discover his offspring later, at some "correct" moment? Is there any difference between Frequentist and Bayesian on the definition of Likelihood? Some sources say likelihood function is not conditional probability, some say it is. This is very confusing to me.  According to most sources I have seen, the likelihood of a distribution with parameter $\theta$, should be a product of probability mass functions given $n$ samples of $x_i$:  $$L(\theta) = L(x_1,x_2,...,x_n;\theta) = \prod_{i=1}^n p(x_i;\theta)$$  For example in Logistic Regression, we use an optimization algorithm to maximize the likelihood function (Maximum Likelihood Estimation) to obtain the optimal parameters and therefore the final LR model. Given the $n$ training samples, which we assume to be independent from each other, we want to maximize the product of probabilities (or the joint probability mass functions). This seems quite obvious to me.  According to , "likelihood is not a probability and it is not a conditional probability". It also mentioned, "likelihood is a conditional probability only in Bayesian understanding of likelihood, i.e., if you assume that $\theta$ is a random variable."  I read about the different perspectives of treating a learning problem between frequentist and Bayesian.   According to a source, for Bayesian inference, we have a priori $P(\theta)$, likelihood $P(X|\theta)$, and we want to obtain the posterior $P(\theta|X)$, using Bayesian theorem:  $$P(\theta|X)=\dfrac{P(X|\theta) \times P(\theta)}{P(X)}$$   I'm not familiar with Bayesian Inference. How come $P(X|\theta)$ which is the distribution of the observed data conditional on its parameters, is also termed the likelihood? In , it says sometimes it is written $L(\theta|X)=p(X|\theta)$. What does this mean?  is there a difference between Frequentist and Bayesian's definitions on likelihood??  Thanks.    EDIT:  There are different ways of interpreting Bayes' theorem - Bayesian interpretation and Frequentist interpretation (See: ). Can massive damage knock out rather than causing instant death? Suppose, as happened last night, a character intends to subdue rather than kill an opponent. She made a melee attack, hit, declared her intent to knock out. The damage roll was enough to reduce the opponent to zero and the remaining damage exceeded the opponent's maximum HP. Now we would seem to have two rules invoked:  Instant Death. Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum. (PHB p.197) Knocking a Creature Out. When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable. (PHB p.198)  So which rule takes precedence? Or is it neither? If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$ I was working my way through some number theoretic proofs and being a newbie am stuck on this problem :     If $(x, 4) = 2$ and $(y, 4) =2$, then $(x + y, 4) = 4$,     where $(a,b)$ denotes the greatest common divisor of $a$ and $b$.   My Solution  (Incorrect)   $x-4 = 2t$ $y-4 = 2p$ $x + y - 8 = 2(t+p) \Rightarrow x + y - 4 = 2f + 4 = 2(f+2)\Rightarrow 2$ divides $(x+y , 4)$   My Question:  My solution is definitely inadequate. Can someone help me out? Permalinks: custom post type -> custom taxonomy -> post I am having trouble working with WordPress rewrite rules, and could use some help.  I have a custom post type called _shows_.  All shows have a single custom taxonomy category _show-category_. A _show_ will never have more than one _show-category_.  I would like my urls to route in this manner:  www.mysite.com/shows/  =&gt;  archive-shows.php  www.mysite.com/shows/%category%/ =&gt; taxonomy-show-category.php  www.mysite.com/shows/%category%/%postname%/ =&gt; single-shows.php   So as a real world example, lets say we have a _show-category_ "Foo" and a _show_ post titled "Bar" that has "Foo" as it's _show-category_. I would expect my WordPress app to look like this:  www.mysite.com/shows/foo/ =&gt; shows all posts under the foo category www.mysite.com/shows/foo/bar =&gt; shows the indivual post   I try to avoid plugins when possible, but am open to any solution. How to prepare files for rsync on a case insensitive filesystem? I am transferring a large number of files on a HFS+ filesystem.  The files are currently on ext2 partitions.  I have conflicts due to case insensitivity of the target partition (HFS+).  I want to identify the files that have duplicates filenames once they are in lower case, and delete them if they are actually duplicates.  I also found that I will have duplicate folder names if I convert everyhing to lower case. Basically these hard drives contain years of unsorted data, and I happen to have this problem with folder names too.   Does this seem reasonable:  find . -type f | while read f; do echo $f:l; done | sort | uniq -d    $f:l is ZSH for convert to lower case.  Now I want to keep only one instance of each file that have duplicates. How to do this efficiently ?  I do not want to find files with duplicate content, unless they have the same lower case filename. I will deal with duplicates later. Why does evolution not make life longer for humans or any other species?  Wouldn't evolution favour a long life? How can i show that two $R$-modules of finite rank are isomorphic if and only if they have the same rank, i.e., $R^n \cong R^m$ iff $n=m$. What is a StackOverflowError? I know that the Windows copy dialog (in Windows&nbsp;XP) stores the copy in memory first, and it is still copying after the dialog closes, so the time is off, but why is the estimation of the time it will take to make a copy so inaccurate, even when memory copying has been disabled (in Vista and Windows&nbsp;7)? It seems so arbitrary! How does the whole copy procedure work, and why can't Windows estimate it correctly? Determine if two rectangles overlap each other? I am trying to write a C++ program that takes the following inputs from the user to construct rectangles (between 2 and 5): height, width, x-pos, y-pos. All of these rectangles will exist parallel to the x and the y axis, that is all of their edges will have slopes of 0 or infinity.  I've tried to implement what is mentioned in  question but I am not having very much luck.  My current implementation does the following:  // Gets all the vertices for Rectangle 1 and stores them in an array -&gt; arrRect1 // point 1 x: arrRect1[0], point 1 y: arrRect1[1] and so on... // Gets all the vertices for Rectangle 2 and stores them in an array -&gt; arrRect2  // rotated edge of point a, rect 1 int rot_x, rot_y; rot_x = -arrRect1[3]; rot_y = arrRect1[2]; // point on rotated edge int pnt_x, pnt_y; pnt_x = arrRect1[2];  pnt_y = arrRect1[3]; // test point, a from rect 2 int tst_x, tst_y; tst_x = arrRect2[0]; tst_y = arrRect2[1];  int value; value = (rot_x * (tst_x - pnt_x)) + (rot_y * (tst_y - pnt_y)); cout &lt;&lt; "Value: " &lt;&lt; value;     However I'm not quite sure if (a) I've implemented the algorithm I linked to correctly, or if I did exactly how to interpret this?  Any suggestions?