Affordable lenses for nightscape photography (nikon d5300)?
What lens characteristics are important in star photography?
How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$? Could you provide a proof of Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$? Differentiation operator and eigenvalues Let $V = \{p(x) \in F[x] \ | \ \deg(p(x)) \le n\}$. Let $T : V \to V$ be given by differentiation, in essence $$T(p(x)) = p'(x)$$ It seems to me that the only eigenvalue that can exist is $\lambda =0$, since the given operator lowers the degree of any given polynomial and hence makes it impossible for a constant multiple of a polynomial to be equal to the polynomial's derivative. Is my claim correct? is it possible to redefine { and } in C? Localisation is isomorphic to a quotient of polynomial ring I am having trouble with the following problem.      Let $R$ be an integral domain, and let $a \in R$ be a non-zero element. Let $D = \{1, a, a^2, ...\}$. I need to show that $R_D \cong R[x]/(ax-1)$.    I just want a hint.  Basically, I've been looking for a surjective homomorphism from $R[x]$ to $R_D$, but everything I've tried has failed. I think the fact that $f(a)$ is a unit, where $f$ is our mapping, is relevant, but I'm not sure. Thanks Possible point location algorithm Configuring ADB for Nexus 4 on Ubuntu 11.10 I'm using python\pyodbc and would like to access the second result set of a stored procedure. As near as I can tell, pyodbc does not support multiple result sets. Additionally, I can't modify the stored procedure. Are there any options to access the second result set using SQL or some other work-around? Perhaps create a second stored procedure that only returns the second result set of the first? Variation on Vandermonde's identity How can you show that $$ \binom{2n}{n}^2 = \sum_{m=0}^{n} \binom{2n}{2m} \binom{2m}m \binom{2n-2m}{n-m} $$?  I was fooling around with random walks, and apparently both expressions are supposed to be the number of unweighted random walks on a 2D square lattice of $2n$ steps that ends at the origin.  Whole thing reminds me of Vandermonde's identity but I can't it. Any hints? Greek numbering Did all Headmasters get a portrait in Hogwarts? Organize uploads by year, month and day I have seen that the new  shows off H.265/HEVC playback, the successor of H.264. I wonder how I may get this support in Linux. Is there a need to install a codec specific for this format? How? Kids' fantasy movie from the 80s or 90s? Dell Latitude E7270 This option, which was present in the "Mouse and Touchpad" settings panel in previous versions, is for some reason absent in 16.04 LTS. Does anyone know why this is, and/or how to fix it? Thanks. Uk visa refused as self employed How to use sed to replace only the first occurrence in a file? I would like to update a large number of C++ source files with an extra include directive before any existing #includes. For this sort of task, I normally use a small bash script with sed to re-write the file.   How do I get sed to replace just the first occurrence of a string in a file rather than replacing every occurrence?  If I use  sed s/#include/#include "newfile.h"\n#include/   it replaces all #includes.   Alternative suggestions to achieve the same thing are also welcome. "To like for somebody/something to be something" vs. "to like somebody/something to be something" Find all integer solutions to $x^2+y^2+z^2=2xyz$ Enroll Apple Developer Program under 18 I've seen a lot of questions like this throughout the web but they're mostly from 2 or 3 years ago, so I decided to ask to have some updated answers.   I'm 16 and I want to start publishing and using the benefits that comes with the Developer Program. In the legal agreement says that I should be over 18, and I'm not so, i can't do it. I've contacted the apple developer support and they told me that I should use a account in my father's name. We reside in Brazil. With that, I had some doubts:   Will the name on the App Store be mine or my father's? In the future, when I'm 18, this account can be transferred to my name?   Besides that, if someone has any advice or (legal) workaround I'd appreciate it, thanks