I am about to buy MacBook Air from Kuwait, and I wonder if I can purchase warranty from Canada since am living in Canada and am a student of a University there?
I'm about to travel to the US, where iPods / AirPods / iPhone are much cheaper than in my country.   I wonder if Apple's warranty is international, and/or what warranty coverage exists when I return to my country.  Where can I understand what Apple Warranty covers in the US when products leave the US?
Calculating the total number of surjective functions It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? Why is the triangle inequality property important for metric spaces? There is a property in the axiomatization of metric space: $d(x,z)\le d(x,y)+d(y,z)$. I understand that property applies well when it come to the measure of distances among points. However, that property seems to be irrelevant in the definitions of continuity, open set and some other key concepts.  My topology book says that it is asserting "the transitivity of closeness", a vague term that loses me. So why is that property important? Why did the founders (if any) of topology consider it at the first place? And what if that property is missed? What does 1x1 convolution mean in a neural network? I am currently doing the Udacity Deep Learning Tutorial. In Lesson 3, they talk about a 1x1 convolution. This 1x1 convolution is used in Google Inception Module. I'm having trouble understanding what is a 1x1 convolution.  I have also seen  by Yann Lecun.  Could someone kindly explain this to me? On a systems level, I understand that as electrons are pushed into a wire, there is a net field and a net electron velocity.  And I've read that the net electron drift is slow.  But electricity travels through the wire, essentially at c, and I want to understand that mechanism.  My apologies if my question is poorly stated, I know bare bones undergraduate quantum theory circa 1990s but it doesn't explain the motion of electricity in detail.  Here's my conception, I'm hoping someone will fill in the holes, ha ha.  An electron moves into the wire.  It's got a kinetic energy.  After travelling a short distance, it spontaneously emits a photon, which hits another electron in a valence shell.  That electron then presumably does the same.  If this conception is simply wrong, please enlighten me.  The questions that arise:   Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way? If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be?  I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible? Why should a photon emitted by an electron be in the direction of travel?  Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction?  If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling. What is the mechanism by which electrons propagating increase the temperature of the material?  Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way?  Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon.  By how much is this slower than light, and what is the speed of each interaction? How to define orbital angular momentum in other than three dimensions? Essentially, all is in the title: Is it possible to compute the integral $$\int_1^{+ \infty} \frac{dx}{x^2(1+e^x)} \hspace{1cm} ?$$  I suspected some relation with a , but I was not able to find something explicit. How to find a generator of a cyclic group? Remove appx package for all users Fresh Windows 10 install. Somehow the MSN Weather app became corrupted. (Unable to launch) I removed the app with the following Powershell command:     Remove-AppxPackage -Package Microsoft.BingWeather_4.7.118.0_x86__8wekyb3d8bbwe   However, when running     Get-Appxpackage –Allusers   the package is still present. When I attempt to reinstall the app via the Windows Store, the download is skipped and the same corrupted package is installed.  I've tried restarting (many times) and using WSReset to no avail.  What can I do? Thank you! Positive operator has a positive spectrum? Let $T : \operatorname{dom}(T) \rightarrow H $ be a positive self-adjoint operator, is it then true that $\sigma(T) \subset [0,\infty)$? This is something that sounds natural and I guess that it is true. For bounded operator, this can be easily shown, but the only proof I know cannot be adapted to unbounded operator, so I was wondering if anybody here knows how to show this? What is the average number of deaths per episode? While watching Game of Thrones and seeing people being killed left and right, I began to wonder:  Just how many people die per episode (not just major characters but the minor characters as well)?   I'm just wondering about an average, but a list that mentions the number of deaths for each episode would be good too. Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$. I'm looking for some guidance in solving this. I have read through my text multiple times trying to find something similar to this and I'm coming up with nothing. I'm not really sure where to start on solving this problem.  The question simply states     Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.   I'm very new to binomial coefficients, and extremely lost. How does HOTP keep in sync? My understanding of  is that each password is unique and based on a counter.    $$PASSWORD = HOTP_1(K,C)$$  Where $C$ is an incremental counter.  What I wish to know, is how you keep the client and server in sync?  Looking at current systems (google authenticator), there appears to be no indication if the actual 'counter' number, but you can generate successive passwords at will.  What happens if, for example, the password you have generated uses $C = 5$, but the server is expecting $C = 3$?  Also, what is the 'integrity check' for?  Google cant seem to come up with a solution. Syntax highlighting in app differs from normal web view Sum of indepedent random variables and a constant Let $X_1$ and $X_2$ be independent Normal random variables with mean $\mu_1$ and $\mu_2$, and variances $\sigma_1$ and $\sigma_2$. Let $Y = X_2-X_1 + c$, where $c$ is a constant. For notational simplicity, let $Y = X' + c$, where $X' = X_2-X_1$ The moment generating function of a Normal random variable $X_n\sim N(μ_n,σ_n^2)$ is $$M_{X_n } (t)=\text{exp}\Big(μ_n t+\frac{σ_n^2 t^2}{2}\Big)$$ Then, $$M_{X'} (t)=\text{exp}\Big[t(\mu_1+\mu_2)+\frac{t^2}{2}(\sigma^2_1+\sigma^2_2)\Big]$$ Thus, by the uniqueness property of moment generating function, $X'$ is said to follow a Normal distribution with mean $(\mu_1+\mu_2)$ and variance $(\sigma^2_1+\sigma^2_2)$. How do I proceed from here to derive the following:  First, I want to establish that $Y$ is also a Normal random variable using the moment generating function. The constant $c$ bugs me, but I cannot ignore it. As per my understanding, $Y\sim N\big(c+\mu_1+\mu_2,\sigma^2_1+\sigma^2_2\big)$ (and I could be completely wrong). But I don't understand how to apply the moment generating function to prove that.  Secondly, I want to derive $P(Y \leq a)$, where $a$ is a constant. If I am not mistaken, $P(Y \leq a)$ can be written as $$P(Y \leq a)=\Phi\Bigg(\frac{a-X_2-X_1 + c}{\sqrt{2(\sigma^2_1+\sigma^2_2)}}\Bigg).$$ But how do I arrive at that.   Any help is high solicited and appreciated. When I use the MouseUp event, I can get it to fire with a mouse right-click. But MouseLeftButtonUp won't fire with either click!  &lt;Button MouseLeftButtonUp="btnNewConfig_MouseUp"  Name="btnNewConfig"&gt;     &lt;StackPanel Orientation="Horizontal"&gt;         &lt;Image Source="Icons\new.ico" Height="24" Width="24" Margin="5"/&gt;         &lt;TextBlock VerticalAlignment="Center"&gt;New&lt;/TextBlock&gt;     &lt;/StackPanel&gt; &lt;/Button&gt;   I know this is most likely something simple. Thanks for the help! how I can continue this limit resolution?  The limit is:   $$ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $$  This is that I have done:  I apply this test: $ \lim_{n \to \infty}{\sqrt[n]{a_n}} = \frac{a_{n+1}}{a_n} $  Operating and simplifying I arrive to this point: $$ \lim_{n \to \infty}{\frac{n^n}{(n+1)^n}} $$  I've done something wrong? Thanks! ConcurrentModificationException for ArrayList Non-https links to other StackExchange sites in User profile when using https Use of each and every Run MySQLDump without Locking Tables