Can I Enter Italy in a valid visa and exit in another? I have a valid Italian schengen in an expired passport till the 19th September. Have a new Italian Schengen that starts on 20th September in the new passport. I have to travel on the 16th and be there till the 29th. The embassy infact issued visas back to back, but is this possible that I enter on one and exit on the other in a new passport?? please advice
Visiting Greece with back-to-back Schengen visas (One from Germany, other from Italy) I have a Schengen Visa issued by Germany, which expire on 11th Jan 2014, and I can remain in the zone till 11th Jan 23.59 PM. I have already visited Germany in the past with this visa, so I can travel whenever in Schengen zone directly from my country (Turkey).  I have a second Schengen Visa issued by Italy, which START on 12th Jan 2014, such that I can remain in Schengen zone from 12th Jan 00.00 AM onwards (I'm putting times to clarify which dates are inclusive).  I would like to travel to Greece with this visa: Entering the country on 6th January, and leaving the country on 19th January.  Is this allowed? Or do I have to leave the country first, and then re-enter through Italy?
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$. Alternative to itoa() for converting integer to string C++? I was wondering if there was an alternative to itoa() for converting an integer to a string because when I run it in visual Studio I get warnings, and when I try to build my program under Linux, I get a compilation error. Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$ Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$   I can not understand how to prove it. Please help me. How to remove selected commit log entries from a Git repository while keeping their changes? I would like to remove selected commit log entries from a linear commit tree, so that the entries do not show in the commit log.  My commit tree looks something like:  R--A--B--C--D--E--HEAD   I would like to remove the B and C entries so that they do not show in the commit log, but changes from A to D should be preserved. Maybe by introducing a single commit, so that B and C become BC and the tree looks like.  R--A--BC--D--E--HEAD   Or, ideally, after A comes D directly. D' representing changes from A to B, B to C and C to D.  R--A--D'--E--HEAD   Is this possible? if yes, how?  This is a fairly new project so has no branches as of now, hence no merges as well. Calculating Image boundary / footprint of satellite images using open source tools? Are there any drawbacks to legacy BIOS as opposed to UEFI? Are there any drawbacks to installing Ubuntu 13.10 (and soon 14.04) in Legacy BIOS instead of UEFI?  I have installed 13.10 64bit in Legacy by mistake and was just wondering if it would hurt anything to simply leave it there as is?  EDIT  Everything seems to be running just fine in Legacy and all my drivers work. I found a better proof for a theorem than a proof from a published paper. Is it possible for me to publish my proof with the same theorem citing that paper? Please allow using nested expressions when filtering with tags Please support the use of nested expressions like  and (or ) when searching.  Looking here, on meta, at questions tagged   and at questions found with +search +tag +boolean I didn't see any information on this topic. How do I customize the date/time display in GNOME Shell's top bar? Time indicator is shown as "%a %H:%M" in the center of the top bar.  How do I move it back to the right where it belongs, and make it include the full date and time ("%Y-%m-%d %s %H:%M")? Url decode UTF-8 in Python Recent movie involving dimensions and time travel/displacement It's a (relatively) recent movie about a kid whose scientist father is missing or presumed dead.  The kid experiences strange situations (e.g., books from a case fall off).  In the end, it was the father the one that was throwing those books to draw the attention of the kid.  Does anyone know the name of this film? During Winterbash 2014, there was a hat called , which was earned by giving an answer scoring 5 or better to question that had a score of −3 or worse at the time of answering and later rose to a score of +3 or better.  I’ve already shared the . Those cases give me a great deal of confidence that this would be a challenging badge trigger that would produce good behavior with a minor tweak. Here are the Red Barons earned on other sites:    (Logan Maingi) Mathematics  (Mike Miller) Mathematics  (Hugo) English Language and Usage  (tchrist) English Language and Usage  (Mr. Shiny and New 安宇) English Language and Usage  (Darth Satan) Science Fiction and Fantasy  (DVK) Science Fiction and Fantasy  (rolfl) Code Review  (Heslacher and Hosch250) Code Review  (Edward) Code Review  (janos and Manny Meng) Code Review  (Mark Mayo, Rory Alsop and MeNoTalk) Travel      (DJClayworth) Christianity  (McMagister) Puzzling   Looking through the timelines, I’m convinced that the answerer’s votes should be excluded from the pre-answer question score calculation. Doing that would have reduced the number of Red Barons to 16 across the network. However, the cost of making a badge harder to obtain is worth the benefit of avoiding giving people an incentive to manipulate question scores¹.  To wrap up, the hat seemed to have encouraged a number of great answers and rescued some questions that would otherwise have been lost to time. My outstanding questions are:   Were there any problems on questions where people were attempting to earn the hat, but failed? (Or any other problems I didn’t observe.) If not, should we  or create a new badge? If we create a new badge, what should it be called?   I’m especially interested in feedback that counters my own bias in favor of this idea. If I’m missing any problems, I’d like to know about them now.    ¹ Several questions were downvoted, answered, edited (sometimes trivially)  and upvoted by the user who earned the hat. How many Shutter Clicks on a New Camera considered normal?    I purchased a quotes new Nikon D750 and checked the shutter count and it has 264 Shutter Clik count on it.    Is that suspect of a returned purchase or used camera? Do opposite categories always exist? Deleted users who created a synonym are listed as "anon" in the tag synonyms list While browsing the  I came across the synonym [vote-to-close] -&gt; [closing] in which the creator is listed as &quot;anon&quot; — the username is not hyperlinked, just like how the user IDs of deleted users are listed in other places like in the list of close voters of a question, etc.  If this really were a deleted user, then I would have expected their user ID to be shown, and not &quot;anon&quot;. So, I checked using  for data on the tag synonym. And sure enough, it shows that the deleted user with the ID 147263 created the synonym. To double-check, I looked up the  and came across a bunch of synonyms created by &quot;anon&quot;. Checking with , these were all created by the now deleted user with the ID 80. Similarly, in the  there are several created by &quot;anon&quot;, but  says that these were created by the now deleted user with the ID 54262.  Feature request: Show the user ID of the tag creator under the &quot;Creator&quot; column in the list of tag synonyms if the user is deleted, to be consistent with how posts and actions by deleted users are attributed everywhere else. Endow $S^3$ with its standard smooth structures from the stereographic projections, i.e. $$\chi_1:S^3 \setminus \{(0,0,0,1) \} \to \mathbb{R}^3, \chi(x,y,z,t) = \frac{1}{1-t}(x,y,z) $$ and $$\chi_2: S^3 \setminus \{(0,0,0,-1) \}   \to \mathbb{R}^3, \chi_2(x,y,z,t) = \frac{1}{1+t}(x,y,z).$$   Do the same for $S^2$, call the charts $\eta_1, \eta_2$ (in the same order as the ones for $S^3$). Now, consider the complex projective space $\mathbb{C} \mathbb{P}^1$ endowed with the smooth structure given by the charts $\{(U_0, \varphi_0), (U_1, \varphi_1)\},$ $$U_0 = \{[z_0:z_1] \ \mid \ z_0 \neq 0 \} \text{ and } U_1 = \{[z_0: z_1] \ \mid \ z_1 \neq 0 \},$$ where $[x:y]$ represents the complex line through the point $(x,y)$ and $0$ in $\mathbb{C}^2$, and $$\varphi_0([z_0: z_1]) = \frac{z_1}{z_0} \text{ and } \varphi_1([z_0: z_1]) = \frac{z_0}{z_1}. $$   Now define the Hopf maps: $$h: S^3 \to S^2, h(x,y,z,t) = (x^2+y^2-z^2-t^2, 2(yz-xt), 2(xz+yt)) $$ and $$H:S^3 \to \mathbb{C} \mathbb{P}^1, H(x,y,z,t) = [(x+iy):(z+it)]. $$  Is there an easier way to prove that $h$ is a well-defined smooth submersion and that $H$ is a smooth submersion (with respect to the respective smooth structures)? By this I mean we can of course compute $\eta_i \circ h \circ \chi_j^{-1}, \forall i,j \in \{1,2 \}$ and $\varphi_k \circ H \circ \chi_l^{-1}, \forall k,l \in \{1,2 \}$ and prove that they are smooth (in the classical real-analysis sense) and that they are submersions, but this is a very tedious process. So, are there easier ways to do this? Will this maybe be easier if we switch the smooth structure of the unit spheres from stereographic projections to, say, normal projections (though we increase the number of combinations of charts to verify from 4 to 48), since they induce the same smooth structure? How to reduce space between image and its caption? Can I take clear night sky photographs with my smartphone? is it possible to take clear night sky shots with stars/ planets visible from Redmi Note 4? what settings do I use? when I try to take it just comes black, unless on full moon day with HDR, though stars like Orion's belt won't get captured. Would using a telescope make celestial objects much clear to capture? Preserving signatures of decorated functions Suppose I have written a decorator that does something very generic. For example, it might convert all arguments to a specific type, perform logging, implement memoization, etc.  Here is an example:  def args_as_ints(f):     def g(*args, **kwargs):         args = [int(x) for x in args]         kwargs = dict((k, int(v)) for k, v in kwargs.items())         return f(*args, **kwargs)     return g  @args_as_ints def funny_function(x, y, z=3):     """Computes x*y + 2*z"""     return x*y + 2*z  &gt;&gt;&gt; funny_function("3", 4.0, z="5") 22   Everything well so far. There is one problem, however. The decorated function does not retain the documentation of the original function:  &gt;&gt;&gt; help(funny_function) Help on function g in module __main__:  g(*args, **kwargs)   Fortunately, there is a workaround:  def args_as_ints(f):     def g(*args, **kwargs):         args = [int(x) for x in args]         kwargs = dict((k, int(v)) for k, v in kwargs.items())         return f(*args, **kwargs)     g.__name__ = f.__name__     g.__doc__ = f.__doc__     return g  @args_as_ints def funny_function(x, y, z=3):     """Computes x*y + 2*z"""     return x*y + 2*z   This time, the function name and documentation are correct:  &gt;&gt;&gt; help(funny_function) Help on function funny_function in module __main__:  funny_function(*args, **kwargs)     Computes x*y + 2*z   But there is still a problem: the function signature is wrong. The information "*args, **kwargs" is next to useless.  What to do? I can think of two simple but flawed workarounds:  1 -- Include the correct signature in the docstring:  def funny_function(x, y, z=3):     """funny_function(x, y, z=3) -- computes x*y + 2*z"""     return x*y + 2*z   This is bad because of the duplication. The signature will still not be shown properly in automatically generated documentation. It's easy to update the function and forget about changing the docstring, or to make a typo. [And yes, I'm aware of the fact that the docstring already duplicates the function body. Please ignore this; funny_function is just a random example.]  2 -- Not use a decorator, or use a special-purpose decorator for every specific signature:  def funny_functions_decorator(f):     def g(x, y, z=3):         return f(int(x), int(y), z=int(z))     g.__name__ = f.__name__     g.__doc__ = f.__doc__     return g   This works fine for a set of functions that have identical signature, but it's useless in general. As I said in the beginning, I want to be able to use decorators entirely generically.  I'm looking for a solution that is fully general, and automatic.  So the question is: is there a way to edit the decorated function signature after it has been created?  Otherwise, can I write a decorator that extracts the function signature and uses that information instead of "*kwargs, **kwargs" when constructing the decorated function? How do I extract that information? How should I construct the decorated function -- with exec?  Any other approaches? We all know some curves can be described by $y=f(x)$ and some surfaces can be described by $z=f(x,y)$ However, there exists curves and surfaces which cannot be described by those, such as a circle and a sphere. Therefore, we introduce parameterized vector equations, which can describe them. For example, circle: $\vec r(t)=r\cos(t)\hat i+r\sin(t)\hat j$ sphere: $\vec r(u,v)=\rho\cos(u)\sin(v)\hat i+\rho\sin(u)\sin(v)\hat j+\rho\cos(v)\hat k$ However, all curves described by $y=f(x)$ and  $z=f(x,y)$ can be parameterized. For curves, $$\vec r(t)=t\hat i+f(t)\hat j$$ For surfaces, $$\vec r(u,v)=u\hat i+v\hat j+f(u,v)\hat k$$ Therefore, I think this suggests the set of all parameterized surfaces (or curves) is the super-set of the set of all surfaces (or curves) described by $z=f(x,y)$ (or $y=f(x)$). Is that correct? Now, here comes the the real challenge. A curve can also be described by an implicit function $f(x,y)=0$ and a surface can also be described by an implicit function $f(x,y,z)=0$ I have 3 questions regarding this.   Can all surfaces (curves) described by an implicit function be parameterized? (If yes, then what is the general way?) Can all surfaces (curves) described by parametric vector equations be represented using implicit function? (If yes, then what is the general way?) Compare the set of all parameterized surfaces (curves) and the set of all surfaces (curves) represented by implicit function. (which is which super-set?)   Sorry for the use of nontechnical terms. I use them because I don't know the technical ones. I have only started learning vector calculus last year in university.  EDIT: I think my question is not too clear, so I will give an example of writing the surface $f(x,y,z)=0$ into $\vec r(u,v)$ We want to parameterize a sphere. $$x^2+y^2+z^2-\rho^2=0$$ Let $x=\rho\cos(u)\sin(v)$, $y=\rho\sin(u)\sin(v)$, $z=\rho\cos(v)$, $$\rho^2\cos^2(u)\sin^2(v)+\rho^2\sin^2(u)\sin^2(v)+\rho^2\cos^2(v)-\rho^2$$ $$=\rho^2\sin^2(v)(\cos^2(u)+\sin^2(u))+\rho^2\cos^2(v)-\rho^2=\rho^2-\rho^2=0$$ I want to know if there is a general way of finding $x=x(u,v)$, $y=y(u,v)$ and $z=z(u,v)$ for any given $f(x,y,z)=0$