I remember reading a young adult novel in the '90s about a girl traveling on a spaceship. If I recall correctly, there's a dangerous race of aliens who can disguise themselves as humans, and she discovers that one of them is on the ship with her. She somehow ends up inside the walls of the spaceship, I believe in order to spy on the alien, and I think it ends up pursuing her through the walls toward the end of the book. Anybody know what it could be?
I read this book once when I was in middle school. A girl solves a murder or a mystery on a spaceship. It was a thin paperback books.   All I can remember is that there was an alien, and there was a movie star or actress or famous makeup artist on the ship traveling with another woman. By the end of the book the murderer was the woman the actress was traveling with who forced her to use her makeup skills to disguise her, and she was really some kind of alien.
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 $c$? How do the Azkaban escapees get their wands back? Sirius Black and a few Death Eaters escape Azkaban and seem to operate after that with their wands intact.  How come?  If a mere expulsion from Hogwarts entails wand destruction (as happened with Hagrid), shouldn't an Azkaban sentence entail the same?  And even if we imagine that the perceived impossibility of escape from Azkaban made it seem unnecessary to destroy the wand, this would apply to Sirius but not to Death Eaters.  PS: Two comments suggested that the escapees acquired new wands. It would be nice to have a more definitive answer than just a suggestion or a list of possibilities. Thanks.  PPS: Returning the personal property to a released prisoner is one thing, but the wand is a different matter: this is usually the tool of the crime, and I don't see how it can be argued that it should be returned and not destroyed. Again, Hagrid had his wand destroyed and he was not even sentenced to Azkaban.  PPPS: Maybe wand destruction is only done for non-fully-qualified wizards? So, I understand that for a NPN transistor to work the emitter-base junction needs to be forward biased and the collector-base junction needs to be reverse biased.  I understand how current flows from the emitter to the base when forward biased, but I can't seem to wrap my head around how it flows from the emitter, through the base, and into the collector.  From what I understand about the depletion region of a PN junction diode, when forward biased, the electrons in the N-type material are repulsed by the negative charge of the supply (say a battery) and the holes in the P-type material are repulsed by the positive charge from the supply, thus narrowing the depletion region and allowing electrons to flow from the N region to the P region.  I also understand that the holes and electrons are attracted to the source charges when reverse biased, widening the depletion region and blocking any electrons from flowing.  What I don't understand is what happens to the depletion region of the collector-base junction that allows electrons to flow from the emitter to the collector even though the collector-base junction is reverse biased.  Take a simple common emitter circuit for example.  I apparently am not cool enough to post pictures yet so you'll have to use your imagination.  So pretend we have the base connected to the positive terminal on a 1v battery (Vbb).  The collector is connected to the positive terminal on a 10v battery (Vcc).  The emitter and both negative terminals are connected to ground.  Also pretend that there is some kind of current limiting.  How does current get from the emitter through to the collector?  I can see how they are at different potentials, but I don't understand how this overcomes the reverse biasing of the collector-base junction.  Can anyone tell me what actually happens at the junction to allow current flow and how changing Vbb will affect that current? How do you link to applications in the Android market? When posting app links, I'm always using a link on Cyrket or AppBrain -- becuase I can't get a link to anything in the official Android Market.  But I have seen some links out there for use w/ Android itself ( ''market://'' protocol ):  market://details?id=de.schildbach.oeffi   (as seen @ )  Is it possible to web-link to apps in the Market so that a non-Android user can link to the appropriate Market page in a non-Android web browser? sort but keep header line at the top I am getting output from a program that first produces one line that is a bunch of column headers, and then a bunch of lines of data. I want to cut various columns of this output and view it sorted according to various columns. Without the headers, the cutting and sorting is easily accomplished via the -k option to sort along with cut or awk to view a subset of the columns. However, this method of sorting mixes the column headers in with the rest of the lines of output. Is there an easy way to keep the headers at the top? Suppose I am given a morphism of schemes $f: X \longrightarrow Y$ and suppose that for any point $y \in Y$, $\kappa(y)$ denotes the residue field. I would like to show that the fibered product $$X \times_{Y} \text{Spec}(\kappa(y))$$ is homeomorphic to the preimage $f^{-1}(y)$ in the induced topology.  The following is my attempt so far:  The question is obviously affine on the target, so without loss of generality we reduce to the case of a morphism $f: X \longrightarrow \text{Spec }A$. Then we have  $$ f^{-1}(\text{Spec }A) = \bigcup_{i \in I} \text{Spec }B_{i} $$ via morphisms $$ \phi_{i}: A \longrightarrow B_{i}. $$ We can then write, \begin{align*} f^{-1}(\text{Spec } A) \times_{\text{Spec } A}\text{Spec } \kappa(y) &amp;= \bigcup_{i \in I} \left( \text{Spec } B_{i} \times_{\text{Spec }A} \text{Spec }\kappa(y) \right) \\  &amp;= \bigcup_{i \in I} \text{Spec }  \left( B_{i} \otimes_{A} \kappa(y)  \right). \end{align*} Now let $\mathfrak{p}$ be the prime ideal of $A$ corresponding to the point $y \in \text{Spec } A$. Then $\kappa(y) = (A/ \mathfrak{p})_{\mathfrak{p}}$. Then for any of the $B$ (dropping the index for brevity), we have \begin{align*} B\otimes_{A} (A/ \mathfrak{p})_{\mathfrak{p}} &amp;\simeq B \otimes_{A} A / \mathfrak{p} \otimes_{A} A_{\mathfrak{p}} \\ &amp;\simeq B_{\mathfrak{p}} \otimes_{A} A / \mathfrak{p} \\ &amp; \simeq B_{\mathfrak{p}} / \mathfrak{p}B_{\mathfrak{p}} \end{align*}  Now the prime ideals in $B_{\mathfrak{p}} / \mathfrak{p}B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B_{\mathfrak{p}}$ containing $\mathfrak{p}B_{\mathfrak{p}}$. Further, the prime ideals of $B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B$ contained in $\phi(\mathfrak{p})B$. That is, we have \begin{align} \text{Spec }B_{\mathfrak{p}} &amp;= \{  \mathfrak{q} \subseteq B :  \phi^{-1}(\mathfrak{q})  \subseteq \mathfrak{p}  \} \\ &amp;=  \{ \mathfrak{q} \subseteq B : f(\mathfrak{\mathfrak{q}}) \subseteq \mathfrak{p}      \}. \end{align} Note that in the very last line we have abused notation slightly: There is not really any notion of being "inside" $\mathfrak{p}$ when it is being treated as a point in the scheme. So really we mean that $f(\mathfrak{q})$ is a point in the scheme whose corresponding prime ideal is a subset of $\mathfrak{p}$. Now as we said above, the prime ideals of $B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}$ are the following $$ \text{Spec }(B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}) = \{ \mathfrak{q} \subseteq B : f(\mathfrak{\mathfrak{q}}) \subseteq \mathfrak{p}      \text{ and } ???  \} $$ This is the point at which I get stuck. Ideally I would like to make some argument from the statement "Now the prime ideals in $B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B_{\mathfrak{p}}$ containing $\mathfrak{p}B_{\mathfrak{p}}$" to conclude that the question marks are the condition $\mathfrak{p} \subseteq f(\mathfrak{q})$. Could someone point me in the right direction as to how to get this condition?   Is the proof up until this point correct? Different sources online seem to do this many different ways, so it's difficult for me to check. Is it possible to recover an email that has been clicked "delete forever" in the trash folder? Is it possible to recover an email that has been clicked on "delete forever" in the trash folder? I have accidentally clicked delete forever for an email but now I need to recover it. Trying to manually sign android package with jarsigner.exe and install with adb.exe How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables? Given that $X,Y\stackrel{\text{i.i.d.}}{\sim}\text{Exp}$ with mean $\lambda(&gt;0)$ and $Z=\mathbf{1}_{X&lt;Y}$, what is $\mathbb{E}(X\mid Z=z)$ ?   We have $Z=1$ with probability $\Pr(X&lt;Y)$ and $Z=0$ with probability $1-\Pr(X&lt;Y)$.   But $\Pr(X&lt;Y)=\frac{1}{2}$ as $X$ and $Y$ are i.i.d. random variables.   Does this mean I can simply say that $Z\sim\text{Ber}\left(\frac{1}{2}\right)$ ?   Then, $\mathbb{E}(X)=\mathbb{E}(X\mid Z=0)\times\frac{1}{2}+\mathbb{E}(X \mid Z = 1) \times \frac{1}{2}$  $\implies2\lambda=\mathbb{E}(X\mid Z=0)+\mathbb{E}(X\mid Z=1)$.   But I cannot conclude anything from here. I couldn't find the conditional distribution of $X\mid Z$ either. Maybe I have to condition on another variable $U$ so that $\mathbb{E}(X\mid Z)=\mathbb{E}\,[\mathbb{E}(X\mid Z,U)\mid Z]$. Which livestock is the most efficient food source? Why use a z test rather than a t test with proportional data? When testing the difference between 2 proportions why do we use a z-test rather than a t-test?    Further, is there a simple way to conduct an omnibus test for significant differences between more than 2 proportions (in the form of percentages). Is there an equivalent to a one-way ANOVA for this?  I imagine that you could use logistic regression (assuming you have the original data for the proportions in the form of 0s and 1s) Are there other options? "Try and" versus "Try to"? Convergence of exponential Brownian martingale to zero almost surely Define the exponential Brownian martingale as $N_t = \exp\left\{a W_t - \frac12 a^2 t \right\}$ which is a martingale with respect to the natural filtration of $W$ which stands for a standard Brownian motion.  I now want to prove that $N_t \rightarrow 0$ a.s. for $t \rightarrow \infty$. As $N_t$ is a martingale it is by definition in $L^1$ hence Doob's martingale convergence theorem tells us that there exists a $N_\infty \in L^1$ such that $N_t \rightarrow N_\infty$ a.s., but how could I prove that $N_\infty \equiv 0$? Any help is greatly appreciated! Can I force WordPress to use  instead of ? I tried to follow the new Blender 2.8 tutorial from Blender Guru.   When entering "Sculpting" with the icing there were suddenly alot of holes in it. Why is this? List all the conjugate classes in the dihedral group of order $2n$ and verify the class equation.  The dihedral group is generated by two elements $r$ and $s$.   The order of $r$ is two since $r^2=e$ and $s$ is $n$ since $s^n = e$. And I know all elements can be produced as either $s^k$ or $rs^k$. How can I list all the conjugacy class? Setting print layout to portrait using QGIS 3? What is the concept of erasure in generics in Java? What is the concept of erasure in generics in Java? Rescuing/Compiling old TeX file starting with “\input amstex” I have come across an ancient (1995) LaTeX file which was (surely) once compliant, but now does not compile at all. Is there any way to rescue it?  My actual question is much more precise. I want a copy of the follow paper on the arXiv:    Downloading the pdf source produces something which looks like a document on a4 paper printed on US letter (the bottoms of some pages are cut off). However, if you download the TeX source from the arXiv, then it doesn't compile (even adding .tex, naturally). I'm using an up to date version of TeXshop on a mac. Network reputation graph becomes nervous when clicking quickly, backs away slowly