What is the logic used in the program?
How to implement Bitcount using only Bitwise operators?
How to change the hostname of a RHEL-based distro? "[somebody]'s theme" vs "[somebody] theme" — Saxon genitive dillema When is it required to use 's in phrases like below (examples taken from Wikipedia)?   James Bond theme 007 theme Boba Fett motif Droids motif Yoda's theme ...   Are there any rules for eliding Saxon genitive?  How does the situation change if we have something instead of somebody? If I have Optimize iPhone Storage enabled on my iPhone and my phone storage is completely full, I understand that iOS will only store a low-res thumbnail of many of my photos on the device. (The full high-res version of the image will only exist in iCloud and on devices with Download and Keep Originals enabled.)  But when only thumbnails exist on the device, how does that work in relation to other photo apps on iOS? For example, do third-party cloud-based photo apps (like Google Photos, Dropbox's Carousel, or Amazon Prime Photos) have access to the full high-res images from the iCloud Photo Library? Or will they only see the low-res thumbnails in some cases? factorization of a^n+1? $\int f=0$ implies $f=0$ almost everywhere Let $f$ be nonnegative and measurable. Show that $\int f =0$ implies $f=0$ almost everywhere (except possibly on a set of measure zero).  My thoughts. Take a set E with $m(E) \neq 0$. Suppose $f \neq 0$ on E. That means $\int_E f \neq 0$. Since $f$ is nonnegative this implies $\int f &gt;0$. That contradicts the given information, so $f$ must be 0 almost everywhere. reCaptcha v1 is shutting down on March 31, but SEDE still uses it Spacing changes when using unicode-math range feature. Why? You can use the range feature of unicode-math to set the math font for a specific unicode slots or the macro accessing the glyph. I tried this with the sum sign &amp; Latin Modern, see my example:  \documentclass{scrartcl}  \usepackage{amsmath} \usepackage{unicode-math} % use unicode in math &amp; setup math fonts \setmathfont{Asana Math} %\setmathfont[range=\sum]{Latin Modern Math} % substitute Sum sign  \begin{document}  Notice the different sum sign $\sum$, as intended.   Notice also, the difference in spacing, not intended: \begin{equation}     \begin{bmatrix}         0           &amp; \frac{1}{2}   &amp; \frac{2}{3} \\         \frac{3}{4} &amp; 0             &amp; \frac{4}{5} \\         \frac{5}{6} &amp; \frac{6}{7}   &amp; 0     \end{bmatrix}     \begin{pmatrix}         A \\         B \\         C     \end{pmatrix} \end{equation} \end{document}   However, not only the sum sign, but also the spacing in the matrices changes. With Latin Modern commented out (as in the example):  With Latin Modern active (remove % before relevant line):  Why is that? BTW, I'm using Lualatex from TeXLive 2012. How to configure splash screen after plymouth I have configured my splash screen for plymouth - and it works perfectly. I've also configured the display manager (I'm using gdm). In between these two I get a very brief splash screen - a kind of swirl of multi-coloured ubuntu like colours. Where does this splash screen get set, and how do I change it?  Edit: Here is a video of my boot sequence, showing the screen in question: Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$ Evaluating the limit $\displaystyle \lim_{n\to\infty} \left[  \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$  I have a question about the following solution:  We may write it in the form:  $$ \frac{1}{n} \left[ \frac{1}{1+(\frac{1}{n})^2} + \ldots + \frac{1}{1+(\frac{n}{n})^2} \right] $$  Somehow I need to figure out that the limit is actually the Riemann sum of $\frac{1}{1 + x^2}$ on $[0,1]$ for $\pi = 0 &lt; \frac{1}{n} &lt; \ldots &lt; \frac{n}{n}$.  Can you explain to me to reach this conclusion? Consider this picture of sun beams streaming onto the valley through the clouds.    Given that the valley is only (at a guess) 3km wide, with simple trigonometry and the angles of the beams, this gives the result that the position of the light source is being a few tens of km away at most.   What is wrong with the analysis? I am superimposing CGI over video footage, and have run into a problem in making materials for objects that act as 'shadow catchers'.  Essentially I want a shader that is shadeless—like an emitter—but catches shadows and light from other objects. This is so I can reconstruct objects in footage so other objects in the scene interact convincingly with them.  Here's an overcomplicated diagram to illustrate my point:   (In this particular scenario, the problem could be glossed over by using RGB curves, but that is definitely not the case with more complicated scenes)  Isn't this a common situation? How to the real guys do it? Thank you.  (I am welcome suggestions of other ways of doing this.) Pass shell variable as a /pattern/ to awk Why doesn't this perpetual motion machine using the buoyant force work? Generalizing polygon file while maintaining topology in QGIS? I have a polygon Shapefile, which I need to generalize. How can I generalize the poligons and ensure that there are no topological errors like "slivers".   I already tried:   Vector -> Geometry Tools  -> polygones to lines Vector -> Geometry Tools  -> simplfy geometries ... here I can already see on the screen, that I am producing overlaps and gaps nevertheless now I try Vector -> Geometry Tools  -> lines to polgones   and here the program show an error and crashes Python: Uniqueness for list of lists Why does second pre-image resistance imply pre-image resistance I am studying hash functions. I can understand why collision resistance implies second preimage resistance, but I don't get why second preimage resistance should imply first preimage resistance. Could anybody be help me with this argument from Introduction to Modern Cryptography by Katz &amp; Lindell, please?   Collision resistance: This is the strongest notion and the one we have considered so far.  Second pre-image resistance: Informally speaking, a hash function is second pre-image resistant if given $s$ and $x$ it is infeasible for a probabilistic polynomial-time adversary to find $x' \ne x$ such that $H^s(x') = H^s(s)$.  Pre-image resistance: Informally, a hash function is pre-image resistant if given $s$ and $y = H^s(x)$ (but not $x$ itself) for a randomly chosen $x$, it is infeasible for a probabilistic polynomial-time adversary to find a value $x'$ such that $H^s(x') = y$. (Looking ahead to later chapters in the book, this essentially means that $H^s$ is one-way.)   [...] Likewise, any hash function that is second pre-image resistant is also pre-image resistant. This is due to the fact that if it is possible to invert $y$ and find an $x^\prime$ such that $H^s (x^\prime ) = y$ then it is possible to take $x$, compute $y = H^s (x)$ and invert it again obtaining $x^\prime$. Since the domain of $H$ is infinite, it follows that with good probability $x \neq x^\prime$. We conclude that the above three security requirements form a hierarchy with each definition implying the one below it. How to blacklist kernel modules? How do I disable loading of unnecessary kernel modules. Kernel 3.2.4 How can I integrate $$\ln \left( x+\sqrt{1+x^2} \right) $$   The problem is from IA Maron Calculus, Problem 4.3.17. The problem is under the heading 'Integration by parts'. I have tried it, but it just leads to 2 unsolvable integrals How do I install the latest OpenOffice? Understanding Group Permissions