How did the Master return in season 8? Any classic Whovian will know that the Master is never dead, just renegotiating his contract with life.  I just want to know how the writers justified his return as the Mistress in season 8.  What in-universe reason is there behind the Master's return?
How did this character come to be in the Nethersphere? How is it that       The Master   Came to be in the Nethersphere?  The last time we saw him      He died and refused to regenerate.  The Doctor even cremated his body.   So, given what previously happened to him, how was he now able to      Regenerate as Missy and take over the Nethersphere?
I have been working on the following problem:     For a given $c\in \Bbb Z^+$, find $a,b \in \Bbb Z^+: c=a^2-b^2$.   I have already figured out and proved a number of things:   A way to directly determine if a particular instance is solvable:  $\exists a,b \in \Bbb Z^+: c=a^2-b^2 \iff c \not\equiv 2 \mod 4$ An upper bound on the values for a (and b): $b \lt a\le\lfloor\frac{c-1}{2}\rfloor$ And a simple algorithm to find a solution:     $$ \begin{align*}  (a_0, b_0) &amp;= (0, 0) \\  (a_{n+1}, b_{n+1}) &amp;= \begin{cases}   (a_n+1, &amp;b_n&amp;)&amp;\text{if } a_n^2-b_n^2 &lt; c\\   (a_n, &amp;b_n+1&amp;)&amp;\text{if } a_n^2-b_n^2 &gt; c\\  \end{cases} \end{align*} $$   This can be iterated until a solution is found or the upper bound is reached.   I am currently trying to work out a more direct way to find an answer, but I have been unable to figure out any other ways to approach the problem.  How can I more directly find values for $a$ and $b$ for a given value of $c$? Duplicate typeset index entries Scientists have found mammoth blood, and are planning to   How does one go from having its blood to a full blown living mammoth? Is it possible?    Why does it matter if the blood is frozen or not? Suppose one found dinosaur blood, could one clone a dinsosaur (as in say 'Jurassic Park')? How do I install .run files? My PC has both Ubuntu and Windows 7 installed. I have installed all my drivers in Windows like Nvidia graphics, motherboard etc. Shall I install them in Ubuntu too?  I looked on the web for my Nvidia drivers and I have found a .run file. How could I install it on my Ubuntu? Change bounding box of math glyphs in LuaTeX I'm trying to use the Garamond-Math font in LuaTeX (despite the documentation saying I should use it with XeTeX only :-). It's working more or less OK with LuaTeX, except for some unfortunate glyph combinations, mostly at the end of inline math, such as “where $T$ is the period”.  I used \fbox to draw the bounding box of the glyph and noticed that the bounding boxes are different in LuaTeX:        and in XeTeX:        In XeTeX the glyph fits almost entirely in the bounding box, but in LuaTeX it overshoots far too much.  I'm not a font guy, so I have no idea why this happens. I thought the bounding box was a property of the font, so in my imagination the result should be the same. Thus the first question is: what actually happens that the bounding boxes are different?  The second question, in the title, is: can I change the bounding box of specific glyphs (using LuaTeX) so that the output looks more like XeTeX's?  I tried manually adding some spacing after the glyphs, but this looks hideous and will go down the drain if I happen to change the font or engine, so I'd really like not to do that. I also tried using the italic correction \/ but it seems to have no effect in math.  Here's the code to produce the pictures above:  \documentclass{standalone} \usepackage{unicode-math} \setmathfont{Garamond-Math.otf} \begin{document} \fboxrule=1sp \fboxsep=0pt In Lua\TeX{} this \fbox{$T$} looks horrible, but the \fbox{$X$} looks OK. \Huge\fbox{$T$}\quad. \end{document}   I'm using TL 2018:  This is LuaTeX, Version 1.07.0 (TeX Live 2018)  (format=lualatex 2019.3.29)  13 APR 2019 12:43  restricted system commands enabled. **test.tex (./test.tex LaTeX2e &lt;2018-12-01&gt; Lua module: luaotfload-main 2019-02-14 2.96 luaotfload entry point If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$? Let $S = \bigoplus_{n\ge 0} S_n$ be a graded commutative ring. Let $f$ be a homogeneous element of $S$ of degree $&gt; 0$. Let $S_{(f)}$ be the degree $0$ part of the graded ring $S_f$, where $S_f$ is the localization with respect to the multiplicative set $\{1, f, f^2,\dots\}$. Suppose $S$ is finitely generated algebra over $S_0$. Then $S_{(f)}$ is a finitely generated algebra over $S_0$. How to isolate the text from a bitmap logo? I have been given a logo from a client that they want me to 'extract' or 'cut' the text out of and use just the text with a transparent background to fit with the design ethos of their marketing.   I'm using Photoshop CS6 and have tried using channels, magic wand and eraser but I can't get clean edges on the text.  I'm pretty new to Photoshop and any help appreciated. Why the CMB has not been dispersed so far? Imagine you have a box of black body radiation. What happens if you open the box for a long time? It becomes dispersed and no radiation remains in the box.   Now, apply this example to the Cosmic Microwave Background radiation. The CMB has been produced about 380,000 years after the Big Bang. Giving that the space is flat as many observations suggest, that radiation has been produced in a universe with no boundaries.   Now, my question is this: in these conditions, why that radiation has not been dispersed completely so far? It is true that the radiation has been produced everywhere in the space but giving that the space is infinite, why has not it been dispersed do far?   Calculations in the standard textbooks are done in such a way as if the CMB has been within a physical box, however expanding with the universal expansion. But, this is not the actual situation. The CMB has not been and is not enclosed by walls of a box, so it must have completely dispersed so far. What has prevented this to happen? What is the rule to convert the 'mm' notation to the 'optical zoom' notation? I searched a bit and found this one:  optical zoom = maximum focal length / minimum focal length   For example a 18-55mm lens would have a 3x optical zoom, and a 18-200mm lens would have a 11x optical zoom. Is that right? How can I run ssh-add automatically, without a password prompt? variable access outside of if statement How to access specific raw data on disk from java Cases environment compresses fractions? what should I do to stop the cases environment compressing the first line of the following? \begin{equation} \alpha_{mn} = \begin{cases} \frac{16\mu^2}{mn\pi^2\left[\pi^2(m^2/a^2 + n^2/b^2) - \mu^2\right]} &amp;\mbox{for } m \mbox{ and } n \mbox{ odd;}  \\ 0 &amp;\mbox{for } m \mbox{ or } n \mbox{ even;} \end{cases} \\[1ex] \end{equation}  I'm not sure to do tex on this site, but if anyone tries it they see the first case is compressed because it's a fraction. Young boy living on Mars discovers that his parents are robots Convergence of a Harmonic Continued Fraction How can I determine the height and the least number of generators of the ideal $ I=(xz-y^2,x^3-yz,z^2-x^2y) \subset K[x,y,z] $?      I tried to calculate the dimension of the vector space $I/I\mathfrak m$ with $\mathfrak m=(x,y,z)$, but I'm not able to find it.  I think the height is $2$, because the affine variety should be a curve, and also I know that the ideal is prime, so I need a chain $0\subset \mathfrak p \subset I$. Maybe $(xz-y^2)?$ Is it prime? Regular expression to match a line that doesn't contain a word I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "&lt;Regex for 'doesn't contain hede'&gt;" input   Desired output:  hoho hihi haha How to make a multiboot CD that will start a user-chosen ISO file I have many CD ISOs downloaded from the Internet. They are each about 100 MB in size and consist of repair/diagnostic programs and other tools. Some of them are Linux-based; others are based on DOS clones, like FreeDOS. I want to put all of the ISOs onto one bootable DVD, so that when I use the DVD, I will get a menu prompting me to select the ISO I want to boot. How can I do this? I've seen some rescue CDs that are combinations of other people's ISOs, but I have no idea how they were made.  Regarding bounty: I, a different person than the OP, have placed a bounty on this question for a solution that meets ALL of these criteria:  Is for DVDs (not flash drives!!!) Is free Works with any ISO file, regardless of original OS If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$ NSString question - rangeOfString method