Why Mystique can't do what Sentinels are doing?
Why would Mystique's DNA allow for Sentinels that can duplicate mutant powers?
What is the importance of the Diophantine inequality $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} > 1$? In Humphreys' book  Introduction to Lie algebras and Representation Theory(3rd printing, p.62), the Diophantine inequality $$\frac{1}{p} + \frac{1}{q} + \frac{1}{r} &gt; 1$$ appeared while classifying all Coxeter graphs of irreducible root systems. Under the assumption $p \geq q \geq r \geq 2 $, the possible triples turn out to be $(p,2,2), (3,3,2),(4,3,2),(5,3,2)$, which correspond to the Coxeter graph $\text{D}_{p+2}, \text{E}_6, \text{E}_7, \text{E}_8$, respectively.  It seems quite straightforward to solve the inequality in positive integers, but Humphreys said that      This inequality, by the way, has a long mathematical history.   without further comment. So I want to know if this Diophantine inequality has any important significance, or if it has appeared in other context (maybe relevant history) before. I have a Mac that runs Snow Leopard and I intend to upgrade it to Mountain Lion and sell it on ebay. However, I only have one hard-drive, and I'm sure I can't use something in my OS to delete my OS and all user data.  Is there something for this that's built into the firmware that I can do on boot, or otherwise?   I have source code on my Mac for multiple corporations' proprietary software and I can't risk somebody gaining access through the use of any sort of disk recovery tool. I plan to use a 7 pass erase rather than simply deleting the directory. Is there a way to resolve probability of an event, given another event that never happens? Mathematically speaking the problem is:  Given that $P(B) = 0$,  $$P(A|B)=\frac{P(A \cap B)}{P(B)} = \frac{0}{0}$$  Is this probability vacuously $0$ of $1$? Can we show that it's one or the other? ++ is dangerous for C programmers How to use `ybar interval` without skipping the last value What is the expected minimum euclidean distance between $N$ points uniformly and independently chosen on the shell(sphere) of 3-D ball of radius $R$?   Note that the expected minimum distance might be difficult to compute, so a good lower bound is also fine.   My approach  I take the approach similar to this   .   Suppose we put $N$ circles of radius $r$ uniformly on the surface of the ball. Therefore we could compute the expected minimum distance by the following expression \begin{align} E[D]=\int_0^\infty P(D&gt;t) dt. \end{align}  So, it remains to compute  $P(D&gt;t)$. Actually, since we are after a lower bound on  $E[D]$ it is enought to give a lower bound on $P(D&gt;t)$.  Let $S_i$ be the event that the pair of circles does not intersect which should be given by \begin{align} P(S_i) =  \frac{ Surf(R)-Surf(r)}{Surf(R)}= 1-\frac{  \pi r^2}{ 4\pi R^2}=1-\frac{ r^2}{ 4 R^2} \end{align}  Now the probability that euclidean minimum distance $D$ between $N$ balls is bigger than $t$ should be similar to  \begin{align} P[ D \ge t] \stackrel{?}{=}  P[ \cap S_i] \end{align} However, I think we somehow need to converte from the geodesic distance to euclidean distance but I am not very sure how to do that? Chromium on Ubuntu 12.04. Youtube says:     This video is currently unavailable   I don't know why but this is the case for some videos, but not all. Well, most videos. And I don't know what's wrong.  Anyone help? I would like to configure a module () settings with drush. This is the variable:  addtoany_nodetypes: Array (     [about_us] =&gt; about_us     [contact] =&gt; contact     [page] =&gt; page     [legal] =&gt; 0     [webform] =&gt; 0 )   So that, for instance:  [page] =&gt; page [legal] =&gt; 0   becomes  [page] =&gt; 0 [legal] =&gt; legal   But I am rather new at drush and I am at a complete loss. Thanks for your time. What's the easiest way to run GUI apps on Windows Subsystem for Linux as of 2018? I searched around, and currently there are two methods suggested; installing an enhancement for Windows Subsystem for Linux and installing an XServer.  I want to know which method is the most hassle-free (easy to install AND to use), and which one is less memory-heavy.  I just want Synaptic and CMake. Why couldn't that be a builtin feature? I gave Google my phone number to verify it, not knowing that it would change it, and now my phone number is completely different? What have I done, and how do I unverify it and change my phone number back? Why don't digital cameras shoot video at full sensor resolution, or do continuous drive at video framerates? I can't seem to get these particular faces to take the UV Mapping. I selected the entire object, entered edit mode, hit U>Unwrap.   The rest of the mesh takes the uv wrapping, but not those faces for some reason.    It looks normal in solid mode.     Does anyone know what could be causing this? Is it possible to run Microsoft Office 2010? I am in doubt as to whether the subject-verb agreement of the second sentence of this paragraph is correct :  Unfortunately, there is no such thing as the ideal home workshop because most people are limited by the space available and by their budget. However, the information and diagram here acts as a guide to help you formulate a sensible workshop layout and a machinery “wish list”.  I suppose if the compound subject is seen as a single unit, then the sentence can be considered as correct. A little further in the same book, another sentence has a singular verb with a compound subject :  Alternatively commandeer a garage, or build yourself a substantial workshop if outdoor space and permission allows – however, do consider the impact of machinery noise on your neighbours.  Can &quot;outdoor space and permission&quot; be seen as one thing, or would this be considered a mistake ? product of two uniformly continuous functions is uniformly continuous Suppose that $f$ and $g$ are uniformly continuous functions defined on $(a,b)$. Prove that $fg$ is also uniformly continuous on $(a,b)$.   My attempt: Since $f$ is uniformly continuous on $(a,b)$, for all $\epsilon&gt;0$, we have $\delta_f(\epsilon)&gt;0$ such that for all $x,y \in (a,b)$, $|x-y|&lt;\delta_f$, $|f(x)-f(y)|&lt;\epsilon$  Since $g$ is uniformly continuous on $(a,b)$, for all $\epsilon&gt;0$, we have $\delta_g(\epsilon)&gt;0$ such that for all $x,y \in (a,b)$, $|x-y|&lt;\delta_g$, $|g(x)-g(y)|&lt;\epsilon$  Notice that $$|f(x)g(x)-f(y)g(y)|=|f(x)g(x)-f(x)g(y)+f(x)g(y)-f(y)g(y)| \leq |f(x)||g(x)-g(y)| + |g(y)||f(x)-f(y)|$$  Here I don't know how to bound $|f(x)|$ and $|g(y)|$. I have proven that uniformly continuous functions preserve boundedness of an interval , i.e. $f$ is bounded on $(a,b)$. Can anyone help me? Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge? Does the following series converge or diverge? $$ \sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}} $$ The methods I have at my disposal are geometric and harmonic series, comparison test, limit comparison test, and the ratio test. An elementary question regarding a multiplicative character over finite fields Reading Chapter 2 of Koblitz's Introduction to Elliptic Curves and Modular Forms, I got stuck on the following question. I would like to proceed my reading, so I would appreciate any hint to this. I have no background in Algebraic Number Theory, but if someone explains in that language, I would like to see it and learn it as much as I can at this moment. References will also be appreciated!  Let $q$ be a power of prime $p$ such that $q \equiv 1 \mod 4$ and $p \nmid 2n$.  Question. Let $\chi_{4} : \mathbb{F}_{q}^{*} \rightarrow S^{1}$ be the character of order $4$, show that $\chi_{4}(-4) = 1$.  The hint in the book says we may show that $\chi_{4}(4) = \chi_{4}(-1) = 1$ for $q \equiv 1 \mod 8$ and $\chi_{4}(4) = \chi_{4}(-1) = -1$ for $q \equiv 5 \mod 8$.  If $q \equiv 1 \mod 8$, then $\chi_{4}(4) = \chi_{4}(2)^{2} = \chi_{2}(2) = \pm 1$, where $\chi_{j}$ denotes the character of order $j$. So I think $2$ must be quadratic residue in this case, but I cannot figure out why. Is this true?  If $A$ and $B$ are sets, then $A=\emptyset $ if and only if $B = A \bigtriangleup B$.  If $A=\emptyset$ then $B=\emptyset$ too?  Could someone help me please? How to invoke a system call via syscall or sysenter in inline assembly? MicroSD card is set to Read-only state. How can I write data on it? I have a MicroSD card reader in my notebook. When I insert a MicroSD memory card into it, I can't write any data on it - it's read-only. The same thing happens when I try to do it under root. And I can't change the permission policy for it. This problem happens for all microSD cards (I've tested 2 cards). I've encountered it on Ubuntu 12.04 LTS, now I'm on Ubuntu 12.10, the problem is still on it's place. When I try to insert such a "read-only" card in my mobile phone, everything's OK and I can write data on it. So, can anybody tell me, how can I write a data onto the card?  UPD: here's fdisk -l output:  Disk /dev/sdc1: 2013 MB, 2013135360 bytes 62 heads, 62 sectors/track, 1022 cylinders, total 3931905 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x00000000   Device Boot      Start         End      Blocks   Id  System   The file system of the card is msdos. As to me it's weird.   UPD2: I've found a small "lock" switch on my card adapter, and it turns out, that when I insert it in my notebook, it switches on. Perhaps, I have to find some glue or something to get that switch stuck...  UPD3: There was no glue near me, so I've decided to buy another card-reader.