Can I add my remaining Schengen days to my new 90 days?
How does the Schengen 90/180 rule work?
I usually disconnect my cellphone from the charger some time after it's fully charged because I'm afraid the battery could lose capacity over time if I don't. However, I believe modern electronics should be able to handle this kind of scenario and automatically stop charging the battery once it's full. Does this apply to modern Android phones? Or do I need to continue disconnecting it all the time? Android OS without Google Services? Collection of clopen sets form a base for a countable completely regular space I have $X$ as a countable, Tychonoff space, and I want to show that the collection of clopen subset of $X$ form a base for the topology on $X$.  Can I first just define a base $\mathscr{B}$ of X, let $x\in X$ and $E \subset X$ is closed such that $x\notin E$. So $x\in X-E$, which is open.   I also noticed that the interval $[0,1]$ is uncountable. Can I define a function $f: X\to [0,1]$, then f is onto. Do I need to show that $f$ continuous next? Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$ I'm working in C, and I have to concatenate a few things.  Right now I have this:  message = strcat("TEXT ", var);  message2 = strcat(strcat("TEXT ", foo), strcat(" TEXT ", bar));   Now if you have experience in C I'm sure you realize that this gives you a segmentation fault when you try to run it. So how do I work around that? Accidently deleted /usr/lib, how do I restore it? Proving $\sup B=\inf A$ Let $A$ be a nonempty and bounded below, and define $B= \{b\in \mathbb{R}: b$ is a lower bound for $A\}$. Show sup$B$ = inf$A$.   So far I have: Let $A$ be nonempty and bounded below. This implies $\exists l \in A, \forall a \in A, l\leq a$ and $l =$ inf$A$. Let $B = \{b\in \mathbb{R}: b$ is a lower bound for $A\}$ and let $M=$ sup$B$. This implies $\exists b\in B, \forall b \in B, b\leq M$. By definition of $B$, we know inf$A \in B$. Since $b\leq$ sup$B$, with sup$B$ the largest element in $B$, we have inf$A \leq M =$ sup$B$, so inf$A \leq$ sup$B$.  I realize I have to prove that sup$B \leq$ inf$A$ to get that sup$B$=inf$A$. I am having trouble doing so.   Part B: Use (a) to explain why there is no need to assert that greatest lower bounds exist as part of the Axiom of Completeness. Plot Option Precedence while combining Plots with Show[] Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ Evaluate $$\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$$  We can write as $\displaystyle\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ $$= \lim_{n \to \infty}\left[\frac{(n +1)(n+2) \cdots (n+n)}{n^n}\right]^{\frac{1}{n}} = \lim_{n \to \infty}\left[(1+\frac{1}{n})(1+\frac{2}{n})\cdots (1+\frac{n}{n})\right]^{\frac{1}{n}}$$  I have used this result if $\{a_n\}$ is a sequence of positive term which is convergent to $l$ and $b_n = (a_1. a_2 . \cdots a_n)^{1/n}$ ,thhen $b_n$ converges to $l$  here $a_n = 2$, but i think it is not right,how to use this result in this question. Give me hint how to proceed . Thank you Add custom command in the open with dialog? In earlier versions of Ubuntu (10.10-) there was an option in the "open with" tab in the properties window, to add a custom command to open a file. However, this is no longer the case in Ubuntu 11.10. Is there any way that I can add these file type associations with a command of my choice rather than the applications detected by the system. How do I enable or disable Apport? Prove that $(x^2 + x+2)$ ideal is a maximal ideal in $F_3[x]$ ring.  I know the theorem about factor rings and fields     B ideal from A ring is maximal iff A/B factor-ring is a field   How can I use the theorem here? Countable union of countable sets(ZF) How to parse JSON in iOS App How to check if list item already exist when adding it with how to check Title( Country) if exists in the list. if exists it is necessary to do the update if not it is necessary to add it ?  function AddListItem() {      var listTitle = "Test";     //Get the current client context       context = SP.ClientContext.get_current();     var airportList = context.get_web().get_lists().getByTitle(listTitle);          //Create a new record       var listItemCreationInformation = new SP.ListItemCreationInformation();     var listItem = airportList.addItem(listItemCreationInformation);      //Set the values      var country= $("#Country").val();     var client= $("#Client").val();     // var nb1 = $("#nb1").val();      // var nb2 = $("#nb2").val();       // var nb3 = $("#nb3").val();      // var nb4 = $("#nb4").val();       // // var nb5 = $("#nb5").val();        listItem.set_item('Country', Country);     listItem.set_item('Client', Client);     listItem.update();     context.load(listItem);     context.executeQueryAsync(AddListItemSucceeded, AddListItemFailed); } function AddListItemSucceeded() { } function AddListItemFailed(sender, args) {     alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace()); } Is torque as fundamental a concept as force? I used to think that torque and force were equally “fundamental”. In other words, my understanding was that we usually use Cartesian coordinates in many common problems because it is a convenient system, so as a result instantaneous forces which act in straight lines seem “easier” mathematically but torques require some extra “baggage”. This baggage includes typically teaching that torque is defined in terms of force.  But if say we happened to choose polar coordinates for the problem the situation would appear the other way around. So it would be arbitrary if we chose to define forces in terms of torques instead.  But later on I learned that angular momentum is conserved independently of regular linear momentum (IIRC). Given the definitions of force &amp; torque as derivatives of momentum, this makes it seem much less certain that one should define either torque in terms of force or vice versa — it gives the impression they are more distinct than it first seemed.  That said, as far as I know a lot of physics is about defining &amp; describing “fundamental forces” — not “fundamental torques”.   So is choosing to use either force or torque as the basis of laws &amp; problems arbitrary? Or is there an actual fundamental rationale to when one or the other should be used? Derive Variance of regression coefficient in simple linear regression How does an accelerating charge radiate electromagnetic waves? Mass dropped on a spring I thought this would be a particularly simple problem but it is turning out to be quite the opposite. I am sure I am doing a very simple mistake.   The problem statement is that there is a mass which is just barely kept on the spring (help by the force equal to the weight of the spring) such that the spring is uncompressed. As soon as I let the object go, it will compress the spring and come to rest at some height. The energy stored in the spring will be equal to the difference in the potential energy at the two height of the spring (compressed and uncompressed),  $$mgh_i -mgh_f= 1/2 kx^2$$ Furthermore, the compression of the spring would just be the difference in the $h_f -h_i$. This gives me two roots for compression,  $$ x=0 $$ And the second would be, $$ mg=1/2kx $$ But then by this, $kx=2mg$ and $kx$ is force by Hooks law, but then does it means that the force compressing the spring is twice the weight of the object? That sounds odd. I was expecting I would just recover Hooks law but I guess I am doing something wrong here. But I am not sure what that is.   Any help will be much appreciated.  P.S. This is not a homework problem. We are designing a project for our school.  Thanks for your time. My dad has an old Sears KS-2 + 50mm f/1.7, which from a bit of research seems to use a Pentax K-mount.  I've looked around a bit and found a , which says it supports af-confirmation, and costs ~$30 US.  Has anyone tried using an adapter ring like this, and if so, would you recommend doing so?  I am perfectly happy with shooting manual, but I'm curious about the quality of older lenses.  I'm assuming that if I use older primes the optical quality will be fine, and it looks like the build quality of the older lenses is much better that similarly priced new lenses.