Friend recursively changed ubuntu filesystem permissions
What if I accidentally run command "chmod -R" on system directories (/, /etc, ...)
adding @2x to src above certain resolution on none retina devices I am trying to solve the following two problems:  1) Prove that the functions $\cos(z)$, $\sin(z)$ are surjective over the complex numbers.  2) Find all $z \in \mathbb C$: $cos(z) \in \mathbb R$ and find all $z \in \mathbb C$: $\sin(z) \in \mathbb R$.  For 1),I've tried to prove it for the function $\cos(z)$ (I suppose the other one is analogue)  so I've used the fact that $\cos(z)=\dfrac{e^{iz}+e^{-iz}}{2}$.  Let $w \in \mathbb C$, I want to show there exists $z \in \mathbb C : f(z)=w$, i.e., $\dfrac{e^{iz}+e^{-iz}}{2}=w$, multiplying by $2$ and then by $e^{iz}$ yields $e^{2iz}+1=2we^{iz}$ iff $e^{2iz}-2we^{iz}+1=0$.   I don't know if this approach is the correct one but here I've replaced $e^{iz}$ by $x$, so the solutions of the equation would be the roots of the polynomial $p(x)=x^2-2wx+1$, by the quadratic formula, I get that $x \in \{\dfrac{2w+w_0}{2},\dfrac{2w-w_0}{2}\}$, where $w_0^2=4w^2-4$.  Then, $e^{iz} \in \{\dfrac{2w+w_0}{2},\dfrac{2w-w_0}{2}\}$. At this point I got lost, I would like to explicitly show that $z$ exists and I can't see existence directly from the fact that $e^{iz}=\dfrac{2w+w_0}{2}$ or $e^{iz}=\dfrac{2w-w_0}{2}$.  First I thought of taking logarithm of both sides of the equation ir order to solve for $z$, but this is not a legitimate operation unless $e^{iz} \in \mathbb R$.   I couldn't go any farther.  For point 2) I have no idea what to do, should I use the identity $\cos(z)=\dfrac{e^{iz}+e^{-iz}}{2}$?  I would appreciate some help with the two points (specially with point 2), at least in 1) I could do something).   Btw, Happy new year! I have read questions about this, and people say that it is just to include the natbib package and the plainnat style. For some reason my references will not sort alphabetically. Any help on this would be much appreciated! I am really new to LaTeX ...  My commands:  \documentclass[a4paper,norsk]{article} \usepackage{amstext} \usepackage{makeidx} \usepackage{graphicx} \usepackage[comma,authoryear]{natbib} \usepackage[norsk]{babel} \usepackage[hmargin=3cm,vmargin=3.5cm]{geometry} \pagestyle{plain}  \begin{document}  \begin{thebibliography}{56}  \end{thebibliography}  \printindex  \bibliographystyle{plainnat}  \end{document} Escape a string for a sed replace pattern I am from a physics background and my mathematics is not very good, so pardon my insolence with the question.  Editing based on the comments : We know that $\pi$ in decimal (i.e. base 10) is transcendental. Is it possible to have a radix base in which $\pi$ can be rational in that base ?  PS : My question is in general for any transcendental number. Why didn't Escobar's hippos introduced in a single event die out due to inbreeding Today I read a  about how Pablo Escobar had once imported 4 hippos (1 male, 3 female) into his estate in Colombia for his private zoo. After his downfall, while other species were shipped out, hippos were considered too big to move and expected to not survive. However, to the surprise of all the hippos are thriving and are so numerous that there have been calls to cull them. From the report:  Numbers are projected to only get bigger. [Colombian biologist Nataly] Castelblanco and her peers say the population will reach over 1,400 specimens as early as 2034 without a cull - all of them descended from the original group of a male and three females. In the study, they envisaged an ideal scenario in which 30 animals need to be culled or castrated every year to stop that happening.  My understanding is that since there was only 1 male, the gene pool would be limited and lead to lot of inbreeding in the descendants. This would cause population to not explode because some individuals would be unfit to survive. Why has this not happened in case of hippos? Is it because there are 3 females (probably unrelated to each other) which keeps gene pool large enough? Or can mutations explain this phenomenon? Would results have been different if originally 2 females had been moved and only 1 retained? EDIT - I have just found that  is maybe less than 100 individuals which though big is not massive. EDIT2 - I have edited the question title to keep focus on the hippos although a general answer would be welcome. What happens when you target a "magical effect" with Dispel Magic? According to the well ordering theorem "". Whenever we have a well ordering on a set, it is not difficult to construct a new well ordering with a largest element. My question is:     For a given infinite set, can we find a well ordering on it such that there is no largest element? ArcGIS Serious Application Error I'm a complete novice to GIS and just began an Introductory course. I am having an issue when I try to access the Symbology tab on a layer. Specifically, when I click on the 'Categories' field and 'Unique Values' subfield, ArcMap crashes and comes up with a report window to send to ESRI. The message is      ArcGIS for Desktop has encountered a serious application error and is   unable to continue.   What could be the problem? INNER JOIN ON vs WHERE clause So I am currently making a minecraft custom map (for 1.9). I want to make the player "say" something using /tellraw commands. I did figure out how to make the player name come up using /say commands, but still have no idea how to do it using the /tellraw command.  How do I do that? Open Safari / Google Chrome developer tools programmatically from JavaScript Name of component on output side cable of a DC power adapter? What is the name of this component (circled in red) of a charger?    What are the uses of this component? Resampling GeoTIFF images to same resolution using QGIS I have two geotiff images that I would like to resample the same resolution. If I use ArcGIS Desktop this is easy to do but how do I do this using QGIS? How can I transform the elliptic curve $E/\mathbb{C}$ of the form $$y^2=4(x-e_1)(x-e_2)(x-e_3)$$ with $e_1&gt;e_2&gt;e_3\in\mathbb{R}$ roots of $E$ into a Weierstrass-Form $y^2=x^3+ax+b$? I can understand this requirement for the old PPC RISC systems and even for x86-64, but for the old tried-and-true x86? In this case, the stack needs to be aligned on 4 byte boundaries only. Yes, some of the MMX/SSE instructions require 16byte alignments, but if that is a requirement of the callee, then it should ensure the alignments are correct. Why burden every caller with this extra requirement? This can actually cause some drops in performance because every call-site must manage this requirement. Am I missing something? Update: After some more investigation into this and some consultation with some internal colleagues, I have some theories about this:  Consistency between the PPC, x86, and x64 version of the OS It seems that the GCC codegen now consistently does a sub esp,xxx and then &quot;mov&quot;s the data onto the stack rather than simply doing a &quot;push&quot; instruction. This could actually be faster on some hardware. While this does complicate the call sites a little, there is very little extra overhead when using the default &quot;cdecl&quot; convention where the caller cleans up the stack.  The issue I have with the last item, is that for calling conventions that rely on the callee cleaning the stack, the above requirements really &quot;uglifies&quot; the codegen. For instance, what some compiler decided to implement a faster register-based calling style for its own internal use (ie any code that isn't intended to be called from other languages or sources)? This stack-alignment thing could negate some of the performance gains achieved by passing some parameters in registers. Update: So far the only real answers have been consistency, but to me that's a bit too easy of an answer. I have well over 20 years experience with the x86 architecture and if consistency, not performance, or something else concrete, is really the reason then I respectfully suggest that is a bit naive for the developers to require it. They're ignoring nearly three decades of tools and support. Especially if they're expecting tools vendors to quickly and easily adapt their tools for their platform (maybe not... it is Apple...) without having to jump through several seemingly unnecessary hoops. I'll give this topic another day or so then close it... Related Is sun revolving around certain mass in space with reference to some other galaxy? Are Newton's "laws" of motion laws or definitions of force and mass? If you consider  as laws, then there must be independent definitions of  and  but I don't think there's such definitions.  If you consider them as definitions, then why are they still called laws? What to look for in a starter-level off-camera flash? I have zero experience with flash and want to learn how to use it from zero, for example by following the Strobist blog.  What are the absolutely necessary specifications I should look for when shopping for a flash, and can I find something in a price range less than $200.00?  My camera is a Nikon DSLR. I was just wondering whether or not there have been mistakes in mathematics. Not a conjecture that ended up being false, but a theorem which had a proof that was accepted for a nontrivial amount of time before someone found a hole in the argument. Does this happen anymore now that we have computers? I imagine not. But it seems totally possible that this could have happened back in the Enlightenment.   Feel free to interpret this how you wish!