Why am I being asked to pay for iPhoto when I already have it?
Just upgraded to Mountain Lion and I have to buy iPhoto again?
Cauchy-Riemann equations in polar form. Show that in polar coordinates, the Cauchy-Riemann equations take the form   $\dfrac{\partial u}{\partial r} = \dfrac{1}r \dfrac{\partial v}{\partial \theta}$ and $\dfrac{1}r \dfrac{\partial u}{\partial \theta} = −\dfrac{\partial v}{\partial r}$.      Use these equations to show that the logarithm function defined by   $\log z = \log r + i\theta$ where $z=re^{i\theta}$ with $-\pi&lt;\theta&lt;\pi$ is holomorphic in the region $r &gt; 0$ and $-\pi&lt;\theta&lt;\pi$.   What I have so far:   Cauchy-Riemann Equations: Let $f(z)$ = $u(x, y)$ +$iv(x, y)$ be a function on an open domain with continuous partial derivatives in the underlying real variables. Then f is differentiable at $z = x+iy$ if and only if $\frac{∂u}{∂ x}(x, y)$ = $\frac{∂ v}{∂ y}(x, y)$ and $\frac{∂u}{∂ y}(x, y)$ = −$\frac{∂ v}{∂ x}(x, y)$. So we have $f'(z)= \frac{∂u}{∂ x}(z) +i \frac{∂ v}{∂ x}(z)$. Let $f(z)$ = $f(re^{iθ})$= $u(r,θ)$ +$iv(r,θ)$ be a function on an open domain that does not contain zero and with continuous partial derivatives in the underlying real variables. Then f is differentiable at $z$ = $re^{iθ}$ if and only if $r \frac{∂u}{∂r}=\frac{∂ v}{∂θ}$ and $\frac{∂u}{∂θ}$ = $−r \frac{∂v}{∂ r}$.  Sorry, if this is not very good. I just decided to start learning complex analysis today... Can abilities with a [Click] cost be used during a run? Some abilities have a [Click] cost to them, such as Crypsis' ability to add a virus counter to it.  Does it count as a "paid ability" for the purposes of the ? I.e. could I, mid-run, add a virus counter to Crypsis for the cost of one [Click]? $\operatorname{Hom}(X \times Z, Y) \cong \operatorname{Hom}(X, \operatorname{Map}(Z, Y))$ is not true in $\textbf{Top}$ I read that in the category of topological space it is not true that $\operatorname{Hom}(X \times Z, Y) \cong \operatorname{Hom}(X, \operatorname{Map}(Z, Y))$ for every $X, Y, Z$ topological spaces. In particular, I read that this does not work when $Z = \mathbb{R} \setminus \{ 1/n \mid n \in \mathbb{N}\}$. This was not explained, i.e. there was no example.   I am looking for an example or – maybe better – just a hint.  EDIT   $\operatorname{Map}(Z, Y)$ is endowed with the compact-open topology $\cong$ means just bijection; i.e. there is already an obvious bijection as sets, but the claim is that (I think) sometimes the "output function" is not continuous How do I get the source code for eglibc in a format that will allow stepping through the source with gdb?    I have tried using apt-get source libc6-dev and that works for getting the source code, but I think that since the pre-processor directives were not applied that the line numbers that gdb has does not match with the source I downloaded. This makes it less useful when trying to step through the source and look at how functions in libc are working. I have a large table that is already partitioned by an identifier (CustomerId). I have created new customers, and want to add new partitions to the table, and want to confirm the correct way to do this. My predecessor set this up and is no longer available so I cannot confirm.  There are currently partitions for 60 distinct CustomerIds (let's say 1-60), and a filegroup and file for each. I have created new filegroups and files for the new customers (61-68) and need to partition the existing data already in this table. So, the data that's already in the table, with customerId 61-68 needs to be moved into separate partitions.   I tried to use the partition wizard, but couldn't find an option for what I wanted. As far as I can tell, I need to run something like:  ALTER PARTITION SCHEME PS_Details  NEXT USED Filegroup61 ALTER PARTITION FUNCTION PF_Details ()  SPLIT RANGE (61)   I'm looking for someone to point me in the right direction as to best practice for this sort of thing. Do I take the data out of the table, into a new table stored in the Filegroup61 then switch the partition in? Not really sure how to approach this. Cauchy-Product of non-absolutely convergent series While grading some basic coursework on analysis, I read an argument, that a Cauchy product of two series that converge but not absolutely can never converge i.e. if $\sum a_n$, $\sum b_n$ converge but not absolutely, the series $\sum c_n$ with $$c_n= \sum_{k=0}^n a_{n-k}b_k$$ diverges.  Although we didn't have any theorem in the course stating something like this, it made me wonder if it was true. biblatex in a nutshell (for beginners) Why not to extend the set of natural numbers to make it closed under division by zero? Hair particles render not same as 3dView(Eevee) Hair particle renders are not same as in 3dView(Eevee). Hair is using Principle Bsdf shader and  camera is set to Orthographic. Force and turbulence fields are applied to it. How to resolve this? Will Unity allow making custom launcher icons from .desktop files or via menu editing system? (Right now the launcher doesn't give the option to "keep in launcher" on all programs.  For some programs I use, I have to make custom launchers or .desktop files.  For instance, daily blender builds are generally just folders with an executable.  In basic Gnome or KDE, I can make a new menu entry with the menu editing system. Then, I can also add it to Docky either from the menu or by dragging a .desktop file to it. Unity launcher doesn't support drag and drop, so thats not a bug or anything, but when I open a .desktop file, it has unpredictable results. Most time it will not have "keep in launcher". Sometime it will have a pinnable item without the .desktop's icon, and if I pin the item to the launcher, it will not call upon the program again after closing it. I've also gotten it to just work with a .desktop file for celtx. Area of intersection between two circles Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres of the circles? What is a good focal length for street photography? With a long lens you don´t disturb people but you are left "out of the scene", while with a short focal lens you are "inside the scene" but you may disturb people. What is a better alternative for street photography? How To: Execute command line in C#, get STD OUT results How do I execute a command-line program from C# and get back the STD OUT results? Specifically, I want to execute DIFF on two files that are programmatically selected and write the results to a text box. What hardware does Ubuntu Touch support? Find $f$ where $f'(x) = f(1+x)$ Let $f \colon \mathbb{R} \rightarrow  \mathbb{R}$ be a smooth function such that $$f'(x) = f(1+x)$$ How can we find the general form of $f$? I thought of some differential equations, but not sure how to use them here. Thanks. Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$. This seems to be a common exercise question, however I am having trouble with it. The hint is to use a map that associates the k-plane to its orthogonal complement. But I have not been able to show this as a diffeomorphism.   I was thinking of using the orthonormal basis and extending it to get a basis of $\mathbb{R}^n$, then using the remaining $n-k$ vectors to generate the orthogonal complement. Am I on the right path??How else should I approach this otherwise?? My technophobe mother returned from a European trip to discover she'd erased all but 15 images from a nearly full 2GB card. As I am the computer guy in the family, she posted the card to me and asked that I make something magical happen.  The photos were taken with and deleted by a Nikon Coolpix. (I don't know the model.)  I am a Linux guy, but there is a Windows Vista box at my disposal.  What is my best strategy to try to recover something? Using Ubuntu 11.10, how do I format an external or USB drive? I don't find an option to 'format' when I right click. In the new version, the drives don't come up on the desktop, but instead come on the Launcher. ArrayList vs List I saw this reply from Jon on :     If you want a single collection to   contain multiple unrelated types of   values, however, you will have to use   List&lt;object&gt;   I'm not comparing ArrayList vs List&lt;&gt;, but ArrayList vs List&lt;object&gt;, as both will be exposing elements of type object. What would be the benefit of using either one in this case?  EDIT: It's no concern for type safety here, since both class is exposing object as its item. One still needs to cast from object to the desired type. I'm more interested in anything other than type safety.  EDIT: Thanks Marc Gravell and Sean for the answer. Sorry, I can only pick 1 as answer, so I'll up vote both. How to programmatically close a JFrame