So when I was younger I got a series of books involving an astronomer with Kung fu abilities who discovers a rogue object orbiting Jupiter. Next, he and his team figure out that it has left Jupiter's orbit and is on a course to intercept Earth. In there somewhere is some Russian espionage, the astronomer seduces his intern, and then by the end of the first book the plan is to send the astronomer into orbit to check out the alien spaceship that is now orbiting Earth (I believe the spacecraft was specifically egg shaped and golden). He gets inside and everyone thinks that he dies when he runs out of oxygen, but there were three books I believe and in the second one they recover his body and it turns out that somehow he got self-replicating nanobots into his bloodstream that continuously repair his organs, to the point where he no longer needs to eat or sleep. It's been some time since I read this series, but I'd like to reread them if only I could remember what they were called or even just the author's name.
Upon realizing it is a sarcophagus, he decides to sacrifice himself (I think by disconnecting his air) and exist in it for eternity along with the original creature. It may have been in an old Omni magazine, or some other periodical. I thought it may have been in the anthology "Dead Astronauts" but I did not find the story in there.
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$ There should be a notification when a moderator reviews or looks at a post which you've flagged.  The notification could show the status (helpful, declined, disputed, or something else) of your flag.  Edit  The reason for doing this is so that you would be able to see when a post which you have flagged has received moderator attention, at which point you could go back to the post. This would be good, for instance, if:   you flagged a post for migration to another site; after migration occurs, you could answer the question, since  that only unanswered questions should get migrated you flagged a post for removal of spam or otherwise nonconstructive content, and the content removal has to be carried out in batches Is there any online resource that can tell me what visa rules are for passport holders of a specific country? When thinking about travelling, I often have to think about a place to visit, and then look up visa rules for that particular country. This can be a fairly painful process because official government sites can often be hard to find, and advice on (say) guidebooks or Wikitravel tends to be generic.  Is there any resource where I can enter my nationality/residency, and then look up a list of visa rules for various countries? From question . You have to use \r when replacing text for a newline, like this  :%s/%/\r/g   But when replacing end of lines and newlines for a character, you can do it like:  :%s/\n/%/g    What section of the manual documents these behaviors, and what's the reasoning behind them? Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem. If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $ Solving $(z+1)^5 = z^5$ The default is that clicking on the folder in the unity dock opens the home directory.   Since there are shortcuts for all the sub-folders of the home directory in the sidebar already, I'd prefer the default directory to move to a different location (~/Documents).  How can I achieve this? How can I create an empty file from the command line? Dirac's remark that inspired Feynman when formulating path integral When Feynman was trying to formulate  of quantum mechanics, he was inspired by Dirac's remark which roughly states that $e^{i\frac{S}{\hbar}}$corresponds to the transition amplitude, where $S$ is the action.   I'm wondering what was Dirac's original argument behind this statement. Why Are Ethernet/RJ45 Sockets Magnetically Coupled? As the title says really, why do ethernet sockets need to be mag-coupled? I have a basic understanding of electronics, but mostly, I can't figure out the right search terms to google this properly. Why is it so hard to find the roots of polynomial equations? The question that follows was inspired by  question:  When trying to solve for the roots of a polynomial equation, the quadratic formula is much more simple than the cubic formula and the cubic formula is much more simple than the quartic formula.    That the general solutions to various polynomial equations are so complex and difficult to derive seems to suggest a fundamental limitation in the problem solving capabilities of the mathematical machinery. Does this intuition of mine make any sense? What should I make of it? Why is it that with each successive degree in a polynomial equation, the solution becomes so much more complex? Can I gain some intuition about what makes finding the roots so hard? According to the : "there is no general algebraic solution—that is, solution in radicals— to polynomial equations of degree five or higher." What is so special about the quintic that makes it the cut-off for finding a general algebraic solution? In what kind of rings a divisor of a product is a product of divisors? In a , if $a|bc$, then $a$ can be written as $a = a_1a_2$ so that $a_1|b$ and $a_2|c$.  Is this property of a commutative ring strictly weaker than the property of being a UFD?  If so, does it have a name, or is it equivalent to some other well-known property? How to read "service --status-all" results I need to identify the currently running services but I can't figure out the results of running service --status-all, I mean what does ?, - and + mean ?  $ service --status-all  [ + ]  acpid  [ + ]  anacron  [ + ]  apparmor  [ ? ]  apport  [ ? ]  atieventsd  [ + ]  avahi-daemon  [ ? ]  binfmt-support  [ + ]  bluetooth  [ - ]  brltty  [ + ]  console-font  [ + ]  console-setup  [ + ]  cron  [ + ]  cups  [ + ]  cups-browsed  [ - ]  dbus  [ ? ]  dns-clean  [ + ]  friendly-recovery  [ - ]  grub-common  [ ? ]  irqbalance  [ - ]  kerneloops  [ ? ]  killprocs  [ + ]  kmod  [ ? ]  lightdm  [ - ]  lm-sensors  [ ? ]  mysql  [ ? ]  networking  [ ? ]  ondemand  [ ? ]  pppd-dns  [ - ]  procps  [ - ]  pulseaudio  [ ? ]  rc.local  [ + ]  resolvconf  [ + ]  rfkill-restore  [ + ]  rfkill-store  [ - ]  rsync  [ + ]  rsyslog  [ + ]  saned  [ ? ]  sendsigs  [ + ]  setvtrgb  [ ? ]  speech-dispatcher  [ - ]  sudo  [ + ]  timidity  [ + ]  udev  [ ? ]  umountfs  [ ? ]  umountnfs.sh  [ ? ]  umountroot  [ - ]  unattended-upgrades  [ - ]  urandom  [ + ]  virtualbox  [ - ]  x11-common   And would running this command with sudo make any difference ? I tried it and in my case it didn't make any difference, but may it differ in other setups ? Multiplicative nature of the separability degree In what follows, let $E / F$ be an algebraic extension, $h(x),f(x)\in F[x]$ polynomials, $h(x)$ irreducible.   Definitions.   We say $h(x)$ is separable if it has not repeated factors. We say $f(x)$ is separable if all its irreducible factors are separable. We say $\alpha\in E$ is separable over $F$, if its minimal polynomial over $F$ is. The extension $E/F$ is separable if all the elements of $E$ are separable over $F$. We define the field $$\newcommand\sclo{\operatorname{Scl}}\sclo_F E= \{\alpha\in E : \text{ $\alpha$ is separable over $F$ }\}$$ as the separable closure of $F$ in $E$. The separability degree of the extension $E/F$ is defined as $$[E:F]_s = [\sclo_F E:F].$$   Now, suppose the extension $E/F$ is finite.  My question is: how can one proof that with these definitions, if $B$ is an intermediate field of the extension $E / F$, then $$[E:F]_s = [E:B]_s[B:F]_s?$$  I know that the purpose of the separability degree is to count in how many ways we can extend certain injective homomorphism to an automorphism. If one starts defining separability degree this way, as done in the book by Lang, the result follows without much difficulty.  I wonder how to achieve it in this way. I originally read this book in the mid- to late '70s.   The premise was a bureaucracy whose job it was to manipulate events in human history by making the smallest possible change that would effect the desired outcome. Not time cops in the sense of going after law breakers.  The intent was to maintain a policy of non-interference as much as possible but when interference was warranted then to make the least possible change and to do so invisibly.  For example, they might take someone's keys off the dresser and put them just out of sight underneath the dresser where they plausibly might have fallen.  The subject would never know of the manipulation but would then be delayed getting out of the house and the ripples grew from there to avert a war or otherwise affect events on a large scale.  After reading that, whenever I would lose something - especially in an improbable way such as dropping a screw at my feet and then finding it on the other side of the room half an hour later - I would take some consolation in the thought that I had just averted some global catastrophe.  I was pretty scatterbrained as a kid (we call that ADHD nowadays) so I experienced this a lot.  Given that I've spent so much time pondering the ideas from the book, I'd love to re-read it. I'll like to add this functionality to the autocomplete widget in Entityreference field to show node ID next to the titles in the dropdown list. The reason behind the idea is to differentiate between multiple nodes with same title.  Example:    This is a title (3) This is a title (2) This is a title (1)   I know the node ID is shown once a selection is made but I like to show it in the dropdown list in order to pick the right node quickly based on the node ID. What does Morgoth look like? Is Morgoth, the original enemy in J. R. R. Tolkien's Middle-earth ever visually described? I envisage him as a bigger, meaner version of the physical Sauron, but I cannot find any reference in The Simarillion. Is there a place to see release dates for previous releases? Find the limit of $\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)$ I have to prove that      $$\Big[\log\Big(1+\frac 1{n^2}\Big)+ \log\Big(1+\frac 2{n^2}\Big)+...+ \log\Big(1+\frac n{n^2}\Big)\Big] \to \frac 12$$   I know that $$\log\Big(1+\frac 1{n^2}\Big)+ \log\Big(1+\frac 2{n^2}\Big)+...+ \log\Big(1+\frac n{n^2}\Big)= \\ =\log\Big(\frac {n^2+1}{n^2}\Big)+ \log\Big(\frac {n^2+2}{n^2}\Big)+...+ \log\Big(\frac {n^2+n}{n^2}\Big)=\\ =\log\Big(n^2+1\Big)+ \log\Big(n^2+2\Big)+...+ \log\Big(n^2+n\Big)-2n\log n$$  Doing some manipulation we get:           $$\lim_{n \to +\infty}\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)=\frac 12$$      How can I prove this limit?