I can remember these details:    The ship is disintegrating because years ago it passed through a cloud containing organisms that are now eating through its hull Nobody is able to figure out how to get rid of the organisms It's a generation ship. The main characters were born there and are the latest of many generations who have never lived on a planet The ship is not going to make it to the new earth colony before it disintegrates The main characters encounter some other beings (can't remember details) that help them travel faster than light to arrive at their destination   I got this book at a school book fair when I was in maybe 6th or 7th grade (early 80s). I can't remember the author or the title, but would love to rediscover it and/or share it with my kids.   Thanks for your help!
In the late 1970s I bought a book at a school book fair (likely published by Scholastic) about a young boy who lived on a generational starship.  The ship was failing.  I remember some bit about an icey cold airlock.  One of the constellations (Cygnus) somehow took on actual fleshy form and manifested as a talking swan, which somehow helped the starships reach their destination.  Pointers?
Are there any tools that I can use to defrag my Windows partition from Linux? I'm able to get a list of the field types with the following code.  $defs = \Drupal::service('plugin.manager.field.field_type')-&gt;getDefinitions();   I want to get the field type of a specific field. How do I get it?  For example, I'd like to check if the field type of field_image is _image. Is there code similar to the following one?  $fieldType = \Drupal::service('plugin.manager.field.field_type')-&gt;getDefinition('field_image'); Prove that at most $2k+1$ independent sets form the set of vertices of a graph, where $k$ is the maximum degree. Increasing spacing between section number and title in the table of contents I'm using the simple ordinary \tableofcontents command to produce a table of contents, and I find that the resulting spacing between the section number and the section title is too small:    Can someone tell me how to fix this, please. My documentclass is memoir, if that matters. In C the following horror is valid:  myFunc() {   return 42;  // return type defaults to int. }   But, what about in C++? I can't find a reference to it either way...  My compiler (Codegear C++Builder 2007) currently accepts it without warning, but I've had comments that this is an error in C++. I was reading the following article by Mathew Might.  I saw the following the paragraph  What doesn't matter GPA? I don't care if it's 2.0 or 4.0. I won't even look at it. The school you went to? I'll judge you the same whether you went to Nowhere State U or a top-ten school. Transcripts? Never seen one. GREs? Irrelevant. Where you work/worked? Unless it's a research lab, it's not important. I don't think these items have much predictive capacity as to whether or not someone can complete a Ph.D.  Is Mathew Might telling the truth? For me it's very hard believe that GPA, GRE scores and undergraduate school don't matter. I used to think that they play an extremely important role in grad school admission. An image alt="" text should contain information about that image in the context of the page, so for instance if you have an article about cats on skateboards and then a photograph of the cat on his skateboard you'd probably give it the alt text of alt="Fluffy pulling some mad tricks on his pimped-out board".          &ndash; Wireframes created with   However, what should happen when that image is a link to a page (such as the Wikipedia cat page)?  I don't think there is any point using the title attribute here because screenreaders just ignore that when an alt attribute exists - the only people who would see the title attribute are mouse users who hover over the image, so that excludes keyboard only users too. It's not really any benefit to accessibility to include a title in this situation (Overall the title attribute is a bit useless really).  So, what should the image ALT text say in this case?   states:     Provide text alternatives for any non-text content so that it can be changed into other forms people need, such as large print, braille, speech, symbols or simpler language.    Therefore giving it the alt text of cat article page on Wikipedia is incorrect because that doesn't describe the image, neither does skateboarding cat image that links to the wikipedia article because the alt text should refer to the image itself, not the link associated with it. On our minecraft server, I've built a Nether portal in my basement. Which connected two-way (tested) to a location in the Nether.    This nether portal took me to an area in the nether which was a small cave. I dug upwards and surfaced close to a Nether Fortress. After clearing the fortress of Blaze spawners, I decided to 'move in'. So I went back to the portal, dismantled it, and reactivated in in a location in the Fortress.    The fortress would be within the same 128m radius I would assume as it's really close to the original place. Literally some steps to the surface, then a ladder up the nearest Nether Fortress bridge support.  Now, taking this portal back to my original doesn't work, I spawn deep underground in an Abandoned Mine Shaft.  I read somewhere that my Nether portal has found a 'better match' and this could be remedied by disabling the 'wrong' portal in the mine shaft.  However, upon multiple attempts, a new nether portal is dynamically created in the same area. See screenie for example. You'll see two 'stacked' portals on the left (from my different attempts at disabling) and then the current active one on the right.    My question is, how can I make sure these portals go to the correct place. Is it a matter of returning the portal to it's original location or am I stuck for returning to the basement? I am trying to grab the capital letters of a couple of words and wrap them in span tags. I am using  for extract and wrapping purposes, but it's not outputting anything.  preg_replace("/[A-Z]/", "&lt;span class=\"initial\"&gt;$1&lt;/span&gt;", $str) What's the section of the soundtrack used in the second episode of R2 at 8:00, after Kallen defeats a Knightmare and Lelouch gives new orders, called? How to set systemd for automatically force fsck disks after crash (hard poweroff)?  When I used sysvinit (in Arch Linux) as /sbin/init I used the hack: in the rc.local I create /forcefsck file; in the rc.local.shutdown I remove it. At boot-up rc.sysinit enable force fsck if /forcefsck exists.  How to do same in systemd? Maybe it has built-in facilities for automatic fsck after crush? Can a continuous function from the reals to the reals assume each value an even number of times? Why is negative times negative = positive? Question is :     Prove that the polynomial $p(x)=x^4-4x^2+8x+2$ is irreducible over the quadratic field $F=\mathbb{Q}(\sqrt{-2})$. [Hint : first use the method of proposition $11$ for the U.F.D $\mathbb{Z}[\sqrt{-2}]$(cf.Exercise $8$, Section $8.1$) to show that if $\alpha \in \mathbb{Z}[\sqrt{-2}]$ is a root of $p(x)$ then $\alpha$ is a divisor of $2$ in $\mathbb{Z}[\sqrt{-2}]$ . Conclude that $\alpha$ must be $\pm 1,\pm \sqrt{-2}$ or $\pm 2$ and hence show that $p(x)$ has no linear factor over $F$. Show similarly that $p(x)$ is not the product of quadratics with coefficients in $F$.]   What I have done so far is :  Suppose $\alpha \in\mathbb{Z}[\sqrt{-2}]$ is a root of $p(x)=x^4-4x^2+8x+2$ we would then have :  $p(\alpha)=\alpha^4-4\alpha^2+8\alpha+2=0\Rightarrow 2=\alpha(-\alpha^3+4\alpha-8)$  i.e., $\alpha$ is a divisor of $2$ in $\mathbb{Z}[\sqrt{-2}]$.  so, I have used the method of proposition $11$ for the U.F.D $\mathbb{Z}[\sqrt{-2}]$(cf.Exercise $8$, Section $8.1$) to show that if $\alpha \in \mathbb{Z}[\sqrt{-2}]$ is a root of $p(x)$ then $\alpha$ is a divisor of $2$ in $\mathbb{Z}[\sqrt{-2}]$  I do not understand why does he mentioned that $\mathbb{Z}[\sqrt{-2}]$ is U.F.D and all... I do not use that at all... It is unnecessarily confusing me or i am unnecessarily getting confused.. hint is actually misleading me :(  Now, I have to prove that $\alpha$ must be $\pm 1,\pm \sqrt{-2}$ or $\pm 2$  i.e., suppose I have $2=ab$ in $\mathbb{Z}[\sqrt{-2}]$ then, $N(2)=N(ab)\Rightarrow 4=N(a)N(b)$   i.e.,$N(a)=1\text{ or }2\text{ or } 4$ i.e., $p^2+2q^2=1\text{ or }2\text{ or } 4$ for $a=p+\sqrt{-2}q$   $p^2+2q^2=1\Rightarrow p=\pm 1 \Rightarrow a=\pm 1$ $p^2+2q^2=2\Rightarrow q=\pm 1\Rightarrow a=\pm\sqrt{-2}$  $p^2+2q^2=4\Rightarrow p=\pm 2\Rightarrow a=\pm 2$    Once I prove that those are the only divisors then I would consider :    $p(1)=(1)^4-4(1)^2+8(1)+2\neq 0$ $p(-1)=(-1)^4-4(-1)^2+8(-1)+2\neq 0$ $p(\sqrt{-2})=(\sqrt{-2})^4-4(\sqrt{-2})^2+8(\sqrt{-2})+2\neq 0$ $p(-\sqrt{-2})=(-\sqrt{-2})^4-4(-\sqrt{-2})^2+8(-\sqrt{-2})+2\neq 0$ $p(2)=(2)^4-4(2)^2+8(2)+2\neq 0$ $p(-2)=(-2)^4-4(-2)^2+8(-2)+2\neq 0$   So, no divisor of $2$ is a root..  Thus $p(x)$ do not have a root in $\mathbb{Z}[\sqrt{-2}]$  suppose I have something like :  $$x^4-4x^2+8x+2=(x^2+ax+b)(x^2+cx+d)=x^4+(a+c)x^3+(b+d+ac)x^2+(ad+bc)x+bd$$  But then, $bd=2\Rightarrow \text { b,d  are  a divisors of 2 in $\mathbb{Z}\sqrt{-2}$}$  But then we have seen that only divisors of $2$ in $\mathbb{Z}\sqrt{-2}$ are $\pm 1,\pm \sqrt{-2}$ or $\pm 2$  So, only possibilities are   $x^4-4x^2+8x+2=(x^2+ax\pm 1)(x^2+cx\mp 2)$ $x^4-4x^2+8x+2=(x^2+ax\pm \sqrt{-2})(x^2+cx\mp \sqrt{-2})$   But these are not possible...  This only tells that $p(x)$ is irreducible in $\mathbb{Z}[\sqrt{-2}]$ but then how do i show this is irreducible in $\mathbb{Q}(\sqrt{-2})$ I was expecting gauss lemma to help but it only works for integers and rationals...  So, please help me to clear this..  Thank you...   P.S : Proposition $11$ is Rational root theorem and Exercise $8$ is that ring of integers of $\mathbb{Q}(\sqrt{-2})$ is an Euclidean domain. Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.  Proof.  Surpose that: $\phi : (A, +) \rightarrow  \mathbb{Z} $ is an isomorphism. Then there is some $r∈A $ such that $ϕ(r)=1_\mathbb{Z}$. We have $$ 1_\mathbb{Z}=ϕ(r)=ϕ(2(r/2))=2ϕ(r/2)$$  or equivalently that $ϕ(r/2)=\frac{1}{2}$. But this is not in $ \mathbb{Z}$, so there can be no such morphism.  Is my proof above correct? Thanks How do I deal with NAs in residuals in a regression in R? Why is compactness so important? I've read many times that 'compactness' is such an extremely important and useful concept, though it's still not very apparent why. The only theorems I've seen concerning it are the Heine-Borel theorem, and a proof continuous functions on R from closed subintervals of R are bounded. It seems like such a strange thing to define; why would the fact every open cover admits a finite refinement be so useful? Especially as stating "for every" open cover makes compactness a concept that must be very difficult thing to prove in general - what makes it worth the effort?  If it helps answering, I am about to enter my third year of my undergraduate degree, and came to wonder this upon preliminary reading of introductory topology, where I first found the definition of compactness. I have 2 columns in Excel: the first contains a list of employee names who perform function A, and the second contains a list of employee names who perform function B.  What I want is to identify, in one cell, if there is one employee whose name appears in both the first and second columns. It does not have to show which name(s) appears in both columns, it just needs to identify IF there are any names that appear in both columns. I understand that division by zero isn't allowed, but we merely just multiplied $f(x) = 1$ by $\frac{x-1}{x-1}$ to get $f(x) = \frac{x-1}{x-1}$ and $a\cdot 1 = 1\cdot a = a$ so they're the same function but with different domain how is this possible?  Or in other words why don't we simplify $f(x) = \frac{x-1}{x-1}$ to $f(x) = 1$ before plotting the points. Is it just defined this way or is there a particular reason ?  Note: my book says the domain of $f(x) = 1$ is $\mathbb{R}$ and the domain of  $f(x) = \frac{x-1}{x-1}$ is $\mathbb{R}$ except $1$. It is commonly stated that there are four fundamental forces, or interactions, in nature. It is natural to consider which of those is responsible for the normal force we meet in elementary physics. What is the nature of the force exerted on a body by the floor on which it rests?  Of the four forces, the only one that seems relevant is the electromagnetic force, and I always assumed the repelling force in question is ultimately the EM one. The Wikipedia article on  seems to agree:     Molecular and quantum physics show that the electromagnetic force is the fundamental interaction responsible for contact forces.    An alternative explanation is that the force results from Pauli's Exclusion Principle; however, reasonable as it may seem, it doesn't seem to answer the question of what force is actually at play here. The exclusion principle isn't a force, or at least it's not normally described as such.  I've recently come across a rather forcefully presented argument that states that the normal force is a macroscopic force that is not directly reducible to the EM force, or to any of the other forces; rather, it does indeed result from Pauli's Exclusion Principle by way of interaction of electron wave functions. The argument further claims that attempts to correct the Wikipedia article have met with the usual "source needed" objections, and that this topic is either misunderstood by or poorly covered in the standard texts.  (The argument can be found ).   Which way is it?