Hard SciFi book, with nearly 2 dimensional life (on a neutron star) that goes zipping past earth. They see our sun and that sparks their interest in space (they evolve super-fast).  We send a spaceship, and eventually they communicate with us, reading our entire list of knowledge in just one or two of their generations. One of their tiny space-ships detects (and removes) cancer from a female human astronaut.  As their world leaves our system they give us 3 gifts - the first of which is removing tiny black holes from the core of our sun.
A book I once owned and read back in late-80's or early-90's that I have not been able to identify title &amp; author for:  It was a SF story concerning tiny native lifeforms, living on either a planetoid or possibly a dead/neutron star, that evolve at a seemingly accelerated time rate. Most of their story is told in the few days of observation (from orbit) by a human expedition to the planet, during which time-frame the race below progresses from stone-age tech level to being more advanced than the human observers, and eventually flying up to meet the humans in small advanced craft powered by micro-singularities... one of which accidentally 'disintegrates' the tip of a human scientist's nose in the process.
Prove $\int_{a}^{b}{f(x)dx}>0$. Let $f\ge0$ be integrable on $[a,b]$. Let $f$ be continuous on $x_0\in (a,b)$ and let $f(x_0)&gt;0$.   Prove $$\int_{a}^{b}{f(x)dx}&gt;0$$  It is easy to see it, graphically, because $$f\ge 0 \Rightarrow\int_{a}^{b}{f(x)dx}\ge0$$  and if $f&gt;0$ somewhere between $a$ and $b$, then the zone of $F$ between those point is "real" (positive) and $\ne 0$.  My problem is, how do I show it formally?  I would appreciate your help. What is the standard team composition for a conquest game? I'm very new to Smite, and I'm wondering if there is some kind of standard team composition in high level play, comparable to the top, jungle, mid, dual lane meta in LoL.  What are the roles, and where should they go to start the game? Why might one also use a blank constructor? I was reading some Java recently and came across something (an idiom?) new to me: in the program, classes with multiple constructors would also always include a blank constructor. For example:   public class Genotype {   private boolean bits[];   private int rating;   private int length;   private Random random;    public Genotype() {              //  &lt;= THIS is the bandit, this one right here     random = new Random();   }    /* creates a Random genetoype */   public Genotype(int length, Random r) {     random = r;     this.length = length;     bits = new boolean[length];      for(int i=0;i&lt;length;i++) {         bits[i] =random.nextBoolean();     }   }    /* copy constructor */   public Genotype(Genotype g,Random r) {     random = r;     bits = new boolean[g.length];     rating = g.rating;     length = g.length;      for(int i=0;i&lt;length;i++) {         bits[i] = g.bits[i];     }    } }   The first constructor doesn't seem to be a "real" constructor, it seems as though in every case one of the other constructors will be used. So why is that constructor defined at all? apt-get update only for a specific repository Create a directly-executable cross-platform GUI app using Python Difficulty in creating macro '\newcommand' for the beginning and end of frames in Beamer I can open Thunderbird but as soon as I click on any file thunderbird freezes. Went to tools can see first page of settings but thunderbird freezes.  Ran norton 360 &amp; rebooted too   Went to firefox website to download thunderbird Version 3.1.9 (3) program downloads and then freezes while norton checks for viruses....  Any suggestions? How to define a figure size so that it consumes the rest of a page? Sometimes I don't need to have a specific picture size, but for layout reasons I would like to scale the image so that the rest of the page is filled. How can I achieve that? Unsung hero dilemma This is partly related to  question.  I ran some queries on odata for my work on Stack Overflow, and I have found that my statistics are the following ones:  Accepted answers: 148 Zero score accepted answers: 36 Percentage of total: 24,3%  I probably fit the idea of the Unsong hero badge, as I've mostly been active in  questions, from when it only had around 200 Questions until now.  To get the badge I could either try to get one of my accepted answers downvoted once, that would give me a 25% accept rate; I could also delete 4 of my accepted answers with 1 or more score. That would also give me the badge, but this just seems wrong: You are actually encouraging me to either try to get a down-vote on a good answer, or delete good answers.  So, should I delete good answers to receive a gold badge?  Update: It's not that I care much if I get a badge or not, it's only a badge after all and not why I spend time on Stackoverflow anyways. But it's not ideal [read: problem] that I'm encouraged to delete accepted answers or try to get downvotes to achieve a badge. Reload activity in Android Derivative of the product of operators and Derivative of exponential I'm asked to show that  $$\frac{d(\hat{A}\hat{B})}{d\lambda} ~=~ \frac{d\hat{A}}{d\lambda}\hat{B} + \hat{A}\frac{d\hat{b}}{d\lambda}$$ With $\lambda$ a continuous parameter. Should I use the definition $$\frac{d\hat{A}}{d\lambda} ~=~ \lim_{\epsilon \to 0} \frac{\hat{A}(\lambda + \epsilon) - \hat{A}(\lambda)}{\epsilon}$$ applied to $\hat{A}\hat{B}$ like $$\frac{d(\hat{A}\hat{B})}{d\lambda} ~=~ \lim_{\epsilon \to 0} \frac{\hat{A}(\lambda + \epsilon)\hat{B}(\lambda + \epsilon) - \hat{A}(\lambda)\hat{B}(\lambda)}{\epsilon}$$ and do some algebra to get the RHS of the first equation, or I'm missing something? Another interesting derivative to pay attention to is: $$\frac{d}{d\lambda}\exp(\hat{A}(\lambda) )~?$$ Get Last Friday of Month in Java Dealing with "Find out who's going to buy the croissants" On Stack Overflow at the moment, there is a popular question which is currently high in the Hot Questions feed:   So far it has been closed twice (once by the community and a moderator and once by a moderator alone) but re-opened twice by the community. It is clearly not a [so] Stack Overflow question. Reading between the lines, there could be a valid Software Engineering question there, but it would be a very basic one (at the fizz-buzz competency level) and looks more like a populist attempt to farm reputation than a serious question.  Worst of all, even though there are some interesting answers on this question, they are all going to be completely useless to future visitors to the site, since they will be completely undiscoverable. If the question were at least "What is the best fair distribution algorithm?" it would still be off-topic (primarily opinion based), but at least it might help someone once the topic falls off the Hot Questions feed.  Although this has turned into just a bit of fun, and I don't want to kill that, enough is enough. While this question is open, unlocked, and still seen as a valid question, it is setting a bad example for the whole Stack Exchange network.   questions like this, especially on the grandfather Stack Exchange site, devalue the work we are putting in on every other site by making it appear acceptable to re-open populist questions like this after two moderators have classified it as off-topic.  What should we do about this question?   Should it be left open? Power to the people? Closed and locked by a moderator? Migrated to another site? &hellip;or something else? When to use ''[verb] that'' I would like to know when to say think(s) that, say(s) that and mean(s) that and when to omit that. Good text on Clinical Trials? I'm an undergraduate statistics student looking for a good treatment of clinical trials analysis. The text should cover the fundamentals of experimental design, blocking, power analysis, latin squares design, and cluster randomization designs, among other topics.   I have an undergraduate knowledge of mathematical statistics and real analysis, but if there's a fantastic text that requires a bit higher level of statistics or analysis, I can work up to it. If i try to update node revision like this:  $node = node_revision_load(59); $node-&gt;set('publish_on', null); $node-&gt;save();   or simple save:  $node = node_revision_load(59); $node-&gt;save();   I have a PHP memory error, (i have 1gb allocated) If $A \in M_{n}(\Bbb{R})$ is an Upper triangular matrix with diagonal entries $1$ such that  $A \neq I$, then what can we say about the diagonalizability of $A$ ?  I know that if the matrix has distinct eigenvalues or the set of eigenvectors are linearly independent then the matrix is diagonalizable.  And that the eigenvalues of the triangular matrices are given by the diagonal elements like  and , but they work nocely if we had distinct elements on the main diagonal.  But in my case I have same value 1 on the main diagonal, how can I approach about the diagonalizability of the matrix? Differences in development between .NET and Mono has the following ability:     Whenever a creature you control with a +1/+1 counter on it dies, return that card to the battlefield under your control at the beginning of the next end step.   I had a number of creatures on the battlefield, including Marchesa herself, with one or more +1/+1 counters on them when  was played, destroying each creature on the board.  When Marchesa and several other creatures would be killed simultaneously,   Does Marchesa's ability trigger for herself? Does Marchesa's ability trigger for the other creatures under my control with +1/+1 counters?   In attempting to resolve the issue, we tried to look things up, leading to , which cites Rule 603.6d as proving that Marchesa's ability should trigger both for herself and for each other creature with +1/+1 counters.  Unfortunately, none of us could actually understand Rule 603.6d, aside from this example:     Two creatures are on the battlefield along with an artifact that has the ability Whenever a creature dies, you gain 1 life. Someone plays a spell that destroys all artifacts, creatures, and enchantments. The artifacts ability triggers twice, even though the artifact goes to its owners graveyard at the same time as the creatures.   The example certainly seems analogous to me, but without understanding the actual rule, rather than just the example, we weren't too sure.  A complete answer has to not only answer the question, but back up that answer with citation and explanation of the official rules on the matter. Why does unlocking the bootloader wipe phone?