I read a science fiction story as teenager, over 20 years ago, these are the details I remember:   Earth is controlled by an alien race who conquered it. The situation is really desperate, the technology gap is huge. Earth people became mostly slaves, sending materials to the home planet of the invaders.  The small resistance group on Earth succeeds to send a nuclear bomb to the invader's home planet, causing them to retreat from Earth after it caused major damage, maybe even destroyed the whole planet in a chain reaction of some kind.   I think this was written by Robert Heinlein, but not sure about it.  Can anyone help me remember what story this might be?
I saw this movie a while back. I don't remember how it starts, but from where I remember watching it, it may have not been too far from the start. Apparently, Earth has been conquered by some alien empire or something and humanity are basically cavemen being used as slaves. From what I remember, the main antagonist alien is seen taking one of the slaves to a room where a machine is used on him to make him smart; this is apparently a big no-no so the main antagonist and his sidekick have to keep it quiet. The idea was that by making one of the slaves smart, it could increase the work output of the others. Apparently the antagonist is using the slaves on Earth to gather gold bullion  which is apparently still very valuable to the aliens but he's doing it illegally (not the slave labor; that's apparently ok). The protagonist who had the machine used on him becomes the intermediary between the slaves and the aliens and begins teaching the other slaves. I remember him teaching them mathematics and I remember him saying that it was universally accepted (I think he may have been referring to algebra or trigonometry). At some point he becomes aware that they are slaves and organizes a plan to free not only his fellow slaves but the Earth. Some escape and find an old museum which has old flight simulators, and shows that humanity wasn't always a slave race and that it may have been modern times in which Earth was invaded (i.e. no lasers or starships). I think they also find Fort Knox as there is a huge collection of gold bricks and weapons. The protagonist comes up with a plan to destroy some sort of teleporter the aliens use to transport stuff to and from Earth, however that alone wont be enough as they could fight back, which will be bad for humanity, which is still undeveloped. So the plan also includes using the teleporter before destroying it to to transport and detonate a nuclear warhead on the alien home world which apparently cripples any attempt to immediately send a fleet but also as a show of strength. After executing their plan, the main antagonist is captured by the humans and as an insult is locked in a cage surrounded by the gold he sought. If I recall correctly the place is set to detonate as to destroy the precocious gold and that will be used against the aliens should they mobilize a fleet in the future (i.e. attack us and we destroy Earth's supply of gold). The antagonist's side kick for some reason I remember as a big black man from whom the antagonist had removed his hand at some point and also apparently the antagonist was cruel to him. After the antagonist is locked up, he is trying to appeal to his sidekick's loyalty, however the sidekick takes the humans' side, I'm also getting an image that apart from treating him kindly the sidekick's missing hand was restored.
Has 'Ubuntu Software' been renamed to 'Snap Store'? I updated Ubuntu last night (sudo apt get update &amp;&amp; sudo apt get upgrade) and to  my surprise this morning I didn't find the 'Ubuntu Software' app and there's a new entry called 'Snap Store' which when opened looks just like the old 'Ubuntu Software' app. So has 'Ubunu Software' been renamed to 'Snap Store'? And if yes, why? How does a phonon cause two electrons to attract each other and form a cooper pair? We know that like charges repel each other. But my professor claimed that two electrons can attract each other as well. What he said was that due to screening an electron travelling at some speed won't repel another electron, but that they will, in some cases, attract each other due to weak phonon exchange. What does that mean? What is phonon exchange? Do two electrons really attract each other? Accept Multiple Answers or Split Bounty among Several Users Often more than one person contributes to the community coming up with the final accepted answer to a question. However, it is only possible to accept a single answer. Restricting to one final answer does make sense for the sake of referencing that answer later, but in many cases that answer is the product of the input from several individuals. I would like to be able to decide how much of a bounty goes to different users, or some other mechanism to recognize the contribution of multiple users. Of course I could always upvote their previous answers, but this is really incorrect if their previous answers aren't the complete, final answer I've accepted.  What think you metaSOrs? Limit of sequences $V(n)$ and $U(n)$ How to troubleshoot unwanted white spaces smartly? Why is there a white space on the left side?  \documentclass{standalone} \usepackage{asymptote} \begin{document} \noindent \begin{asy} size(10cm,10cm); draw((0,0)--(100,100)); draw((0,100)--(100,0)); dot((50,50)); \end{asy} \end{document} Replace Builtin commands with Custom Commands for CMD.exe For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$  Oh, the exponential of a matrix is: $e^A=\sum_{i=0}^\infty\frac{1}{i!}A^i$    I thought I'd solved the $e^A$ form but I actually did something really silly, now I'm a little stuck.  If $A^k=I$ then $A^{k+1}=A$ and we have a cycle forming, so we will get:  $$\sum^{k-1}_{i=0}\sum^{\infty}_{j=1}\frac{1}{(kj+i)!}A^i$$  (Or something like this form, I don't have paper to hand and just spotted that now)  Is this what the question wants? It doesn't use the 2x2 property.  I believe the answer lies in finding an expression for the inner summation, I can do this for two terms (think of $e+e^{-1}$ all the odd power leave) How to install the OS with a new Hard drive? Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$ I had an example in the book given as follows:        Find the minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$ .       Solution:  $~~~~~$$(\sqrt{2}+\sqrt{3})^2=5+2 \sqrt6$      $(\sqrt{2}+\sqrt{3})^4=49+20 \sqrt6$       Then $(\sqrt{2}+\sqrt{3})^4-10(\sqrt{2}+\sqrt{3})^2+1=0.$       Thus $a=\sqrt{2}+\sqrt{3}$ satisfies $f(x)=x^4-10x^2+1$ over $\mathbb Q$.       Let $p(x)$ be the minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$.Then $(\sqrt{2}-\sqrt{3}),(-\sqrt{2}+\sqrt{3}),(-\sqrt{2}-\sqrt{3})$ are also roots of $p(x).$   So degree of $p(x)$ is atleast $4$.      But $f(a)=0 $ and $f(x) \in \mathbb Q[x] \implies p(x)$ divides $f(x)$ .      So $f(x)$ is minimal polynomial of $\sqrt{2}+\sqrt{3}.$   But I can't get the step  how are $(\sqrt{2}-\sqrt{3}),(-\sqrt{2}+\sqrt{3}),(-\sqrt{2}-\sqrt{3})$ also roots of $p(x).$   Kindly help with this. How to change from German to English in the File Manager in Ubuntu 15.10? My months and days in my File Manager are in German, how do I change that? On the photo you see 'Dez' : It means Dezember (German for December). I also saw one day Mittwoch (German for Wednesday). How do I change that German issue? This is only my File Manager and not completly but partially. Weird. Baire: Show that $f\colon \mathbb{R}\to\mathbb{R}$ is a polynomial in an open bounded set Let $f\colon\mathbb{R}\to\mathbb{R}$ be an infinitely differentiable function, and suppose that for each $x\in\mathbb{R},$ $\exists\  n=n(x)\in\mathbb{N}$ such that $f^{(n)}(x)=0$. For each fixed $n\in\mathbb{N}$, consider the sets $F_n=\{x\in\mathbb{R} : f^{(n)}(x)=0\}$ and let $I=[a,b]$ a finite closed interval.  Show that $$I=\bigcup_{n=0}^\infty(I\cap F_n).$$ Show that there is a non empty open set $A\subset I$ where $f$ is a polynomial.   My attempt:  If $x\in I$ then by hypotesis there is $n$ such that $f^{(n)}(x)=0$ then $x\in F_n$ so then $\bigcup F_n\supset I$ then $$I=I\cap\bigcup_{n=0}^\infty F_n=\bigcup_{n=0}^\infty(I\cap F_n).$$  Let $$B_k=\bigcap_{n=k}^\infty F_n.$$ I want to show that $I\cap B_k$ has non-empty interior for some $k\in\mathbb{N}$. Then there is $A\subset B_k$ and by Taylor's Theorem $f$ will be a polynomial. But I didn't know how to prove this. I tried using the following bigger set: $$B=I\cap\bigcup_{k=0}^\infty B_k=I\cap\bigcup_{k=0}^\infty \bigcap_{n=k}^\infty F_n.$$ I think that it suffices to show that $B^o\neq\emptyset$ maybe using the Baire's Theorem proving that $B$ is a not meagre set.   More general Problem  Let $f$ be an infinitely differentiable function on $[0,1]$ and suppose that for each $x \in [0,1]$ there is an integer $n \in \mathbb{N}$ such that $f^{(n)}(x)=0$. Then does $f$ coincide on $[0,1]$ with some polynomial? If yes then how. I thought of using Weierstrass approximation theorem, but couldn't succeed. Answer: The proof is by contradiction. Assume $f$ is not a polynomial. Consider the following closed sets: $$ S_n = \{x: f^{(n)}(x) = 0\} $$ and $$ X = \{x: \forall (a,b)\ni x: f\restriction_{(a,b)}\text{ is not a polynomial} \}. $$ It is clear that $X$ is a non-empty closed set without isolated points. Applying Baire category theorem to the covering $\{X\cap S_n\}$ of $X$ we get that there exists an interval $(a,b)$ such that $(a,b)\cap X$ is non-empty and $$ (a,b)\cap X\subset S_n $$ for some $n$. Since every $x\in (a,b)\cap X$ is an accumulation point we also have that $x\in S_m$ for all $m\ge n$ and $x\in (a,b)\cap X$. Now consider any maximal interval $(c,e)\subset ((a,b)-X)$. Recall that $f$ is a polynomial of some degree $d$ on $(c,e)$. Therefore $f^{(d)}=\mathrm{const}\neq 0$ on $[c,e]$. Hence $d&lt; n$. (Since either $c$ or $e$ is in $X$.) So we get that $f^{(n)}=0$ on $(a,b)$ which is in contradiction with $(a,b)\cap X$ being non-empty. How to apply for a UK standard visitor visa as a family? Two of my friends are getting married. They're both huge Doctor Who geeks, and actually met through a DW RPG. Their wedding invitation contained a very subtle DW reference (you wouldn't have been able to tell unless you were very familiar with the show yourself.)   Doctor Who's been running long enough that there are quite a few nice quotes for basically every occasion in life. I was hoping someone would know a nice wedding-related one, or maybe one about love, that I could include in a wedding card? Is there something I can do from the terminal when a program freezes up and Ubuntu becomes unresponsive? Using Leibniz Integral Rule on infinite region I am trying to take the derivative with respect to $a$ of some function $I(a)=\int_{0}^{\infty}f(a,x)dx$.  I would like to make sure that I am using the  correctly.  Various web sources indicate a set of conditions that must hold for $f(x,a)$ and $\frac{\partial f(x,a)}{\partial a}$ when integration is done over infinite region.  From reading  (see Theorem 10.3 on page 13) the conditions that $f(x,a)$ and $\frac{\partial f(x,a)}{\partial a}$ must obey are:   $f(x,a)$ and $\frac{\partial f(x,a)}{\partial a}$ are continuous over $x\in[0,\infty)$ and around $a$ that we are interested in. There exists an integrable function (over $x$) $g(x)$ such that $|\frac{\partial f(x,a)}{\partial a}|\leq g(x)$. There exists an integrable function (over $x$) $h(x)$ such that $|f(x,a)|\leq h(x)$.   Integrable here means $\int_{-\infty}^{\infty}g(x)dx&lt;\infty$.  However,  seems to omit condition 3 above.  I am wondering which source is correct.  If there are "both correct", when is condition 3 necessary? Personal Hotspot not working over Wi-Fi on iOS 13 After upgrade to iOS 13 from 12.4, I noticed that personal hotspot isn't working anymore over Wi-Fi (via USB is ok).  Tested on two computers with Win7. The PC can connect to Wi-Fi, but no valid IP (IPv4) is assigned and no connection is working to internet. idempotents acting as local identities Let $R$ be a ring with unity (not necessarily commutative) and $I$ an ideal of $R$.  Suppose that for every element $a \in I$ there exists an element $c\in I$ such that $ac=a$. Note that $c$ is related to $a$. Now we have the following question:  Can we say that  for every element  $a\in I$ there exists an idempotent element $c\in I$ such that $ac=a$?    Of course we have many examples such that the answer is true for them but in general  we don't know. Why does the right leg's bone in my rig move when I move the left? For some reason, when I moved the left leg's bone, the right leg has also moved and the bone of the right leg doesn't control anything at all.  I think this is because I used Mirror to make the model, but I'm not sure I'm a complete beginner. The Python docs say:     re.MULTILINE: When specified, the pattern character '^' matches at the beginning of the string and at the beginning of each line (immediately following each newline)... By default, '^' matches only at the beginning of the string...   So what's going on when I get the following unexpected result?  &gt;&gt;&gt; import re &gt;&gt;&gt; s = """// The quick brown fox. ... // Jumped over the lazy dog.""" &gt;&gt;&gt; re.sub('^//', '', s, re.MULTILINE) ' The quick brown fox.\n// Jumped over the lazy dog.' How to keep rice in a biryani from burning and sticking together? The bottom part of my  Biryani always  gets burnt, rice always gets sticky but I want each grain separated. How can I prevent burning &amp; stickiness of rice?