From the first chapter of The Half-Blood Prince (The Other Minister) the following things are known:   The Ministry finally realized that Voldemort was back. (End of The Order of the Phoenix)    Death Eaters were out in the open wreaking havoc on the Muggle and wizarding world .(Most probably on Voldemort's orders, in order for Voldemort to blackmail Fudge to give him access to the Ministry). Voldemort needed Dumbledore out of the way and had enlisted Draco for the job. Killing Amelia Bones (and maybe killing a few more people).   Apart from this, for the rest of the duration of the book, there is hardly any information about what Voldemort did for an entire year.  I know the book narration is from Harry's point of view but I am curious to know if there is any canon or any other interview/text by JKR where any details of Voldemort's activity during Harry's sixth year has been given?
We have no mention of Voldemort in Harry's sixth year. So, I was wondering- what could Voldemort have been doing?
Showing that $e^x > 1+x$ There is a nice property of normal spaces, namely, closed disjoint subsets can be separated by continuous functions into $\mathbb R$.   Then you ask yourself, what about Hausdorff spaces?, are all Hausdorff spaces completely Hausdorff?   Well, if we choose our separating space $X$, that is, the space such that for any Hausdorff $Y$ and any distinct $a,b\in Y$ there is some continuous $f:Y\rightarrow X$ with $f(a)\neq f(b)$, to be completely regular and Hausdorff, this cannot happen by an example of E. Hewitt, Hewitt’s Condensed Corkscrew, call it $\mathbb H$; as any continuous function from $\mathbb H$ into $\mathbb R$ is constant, and any Hausdorff completely regular space $X$ can be embedded into a product of closed intervals $\prod_{i\in I}[0,1]$, and thus any continuous $f:\mathbb H\rightarrow X\subseteq \prod_{i\in I}[0,1]$ is constant, as each $\pi_i\circ f$ is constant, so our candidate to be the separating space $X$ cannot even be $[0,1]$.  My question is, does there exist a Hausdorff space $X$ such that for all Hausdorff spaces $Y$, and any distinct $a,b\in Y$ there exists a continuous $f:Y\to X$ such that $f(a)\neq f(b)$?  Thanks. Blocking web sites with Windows Firewall Is it possible to use Windows Firewall to block specific web sites for all browsers? Question:  Is it possible to get multiple correct results when evaluating an indefinite integral?  If I use two different techniques to evaluate an integral, and I get two different answers, have I necessarily done something wrong?    Often, an indefinite integral can be evaluated using different techniques.  For example, an integrand might be simplified via partial fractions or other algebraic techniques before integration, or it might be amenable to a clever substitution.  These techniques give different results.  For example, looking over a few other questions on MSE:      From : evaluate $$ \int x(x^2+2)^4\,\mathrm{d}x. $$    Via the substitution $u = x^2+2$, this becomes $$ \int x(x^2+2)^4\,\mathrm{d}x       = \frac{1}{10}x^{10} + x^8 + 4x^6 + 8x^4 + 8x^2 + \frac{32}{5} + C.     $$ However, multiplying out the polynomial and integrating using the power rule gives $$ \int x(x^2+2)^4\,\mathrm{d}x       = \frac{1}{10}x^{10} + x^8 + 4x^6 + 8x^4 + 8x^2 + C    $$     From :  evaluate   $$ \int \frac{1-x}{(x+1)^2} \,\mathrm{d}x. $$    Simplifying the integrand using partial fractions then integrating gives $$ \int \frac{1-x}{(x+1)^2} \,\mathrm{d}x       = \frac{-2}{(x+1)} - \ln|x+1| + C.    $$ Via integration by parts, we get $$ \int \frac{1-x}{(x+1)^2} \,\mathrm{d}x       = \frac{x-1}{(x+1)} - \ln|x+1| + C.    $$     From : evaluate   $$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2\,\mathrm{d}x. $$    Using the substitution $u = \sec(\pi x)$, this becomes $$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2\,\mathrm{d}x       = \frac {\sec^2(\pi x)}{4\pi} + C.    $$ Using the substitution $u = \tan(\pi x)$, this becomes $$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2\,\mathrm{d}x       = \frac {\tan^2(\pi x)}{4\pi} + C.    $$ How can I install firmware-b43-installer driver if I can't connect to internet by wire? Create directory if it does not exist check if numbers from command line are powers of 2 I would like to use the same pipe for different applications, like in:  cat my_file | {   cmd1   cmd2   cmd3 }   Cmd1 should consume part of the input. Cmd2 should consume another part and so on.  However, each cmd eats more of the input then it read really needs due buffering.  For example:  yes | nl | {    head -n 10 &gt; /dev/null   cat  } | head -n 10   Outputs from line 912 instead of line 11.  Tee is not a good option, because each command is supposed to consume part of the stdin.   Is there a simple way to get this working? Hide Command Window of .BAT file that Executes Another .EXE File Is it (if at all) possible in Blender 2.6+?   If not, will future versions of Blender support it?  I see some old posts ( and ) saying that it is not possible. However, I found  referring to operators under  that allowed me to add sensors and controllers from python.  bpy.ops.logic.sensor_add(type='ALWAYS', object=my_obj.name) bpy.ops.logic.controller_add(type='LOGIC_AND', object=my_obj.name)   However I am not able to find any way to link them from python. I tried following (but did not work):  new_controller = my_obj.controllers[-1] new_sensor = my_obj.sensors[-1]   It throws AttributeError saying that object has no attribute 'controllers' :-/ Is is possible to convert a .vdi file into a .iso that can be burned to a cd or dvd and make it like an installer. Or Is it possible to convert virtual machines to physical environments? Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field I'm reading Galois Theory by Steven H. Weintraub (second edition), and finding that I'm at least somewhat short on the prerequisites. However the following proof looks wrong to me - am I misunderstanding something, or is it actually an incorrect proof?  Lemma 2.2.3. Let $F$ be a field and $R$ an integral domain that is a finite-dimensional $F$-vector space. Then $R$ is a field. Proof. We need to show that any nonzero $r \in R$ has an inverse. Consider $\{1, r, r^2, \cdots\}$. This is an infinite set of elements of $R$, and by hypothesis $R$ is finite dimensional as an $F$-vector space, so this set is linearly dependent. Hence $\sum_{i=0}^n{c_i r^i} = 0$ for some $n$ and some $c_i \in F$ not all zero.  It then goes on to show, given the above, that we can derive an inverse for $r$. However, if I consider examples like $r = 2 \in Q[\sqrt{2}]$, $r = \sqrt{2} \in Q[\sqrt{2}]$ or $r = 2 \in Q[X]/{&lt;X^2&gt;}$, the set $\{1, r, r^2, ...\}$ doesn't look linearly dependent to me. I do believe the lemma is true (and might even be able to prove it), but this does not look like a correct proof to me. Am I missing something? [Edit] Well yes, I am. Somehow I had managed to discount the possibility of any $c_i$ being negative, despite repeatedly looking at each fragment of the quoted text in an attempt to find what I might be misunderstanding. What's the scope of a variable initialized in an if statement? For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements? $L^p$ spaces and counting measure currently I am working on the following two exercises as a revision for my exam.  Let $\mu$ be the counting measure on $\mathbb N$.   Show that if $1 \le p &lt; s &lt; \infty$ then $f \in L^p$ implies $f \in L^s$ and $\|f\|_s \le \|f\|_p$. Show that if $f \in L^p$ for some $p \ge 1$ then $\lim_{s \to \infty} \|f\|_s = \|f\|_\infty$.   My attempts so far:   It is $f \in L^s$ iff $\sum_{k = 1}^\infty |f(k)|^s$ converges. Since $f \in L^p$ we know that $\sum_{k = 1}^\infty |f(k)|^p$ converges. Thus for any $\varepsilon &gt; 0$ there is $N \in \mathbb N$ s.t. \begin{align*} k \ge N \Longrightarrow |f(k)|^p &lt; \varepsilon \Longrightarrow |f(k)| &lt; \varepsilon^{1/p} \end{align*} We have $\forall k \ge N$ that $|f(k)|^s &lt; \varepsilon^{s/p}$. Originally I wanted to use the comparison test now, showing that \begin{align*} \sum_{k = N}^\infty \varepsilon^{s/p} &lt; \infty, \end{align*} but that does not work since \begin{align*} \sum_{k = N}^\infty \varepsilon^{s/p} = \varepsilon^{s/p} \underbrace{\sum_{k \ge N} 1}_{= \infty},  \end{align*} so I don't know how to go on here. Let $K := \|f\|_\infty$. We need to show that $\forall \varepsilon &gt; 0$ $\exists M \in \mathbb N$ s.t. \begin{align*} s \ge M \Longrightarrow \left|\left(\sum_{k = 1}^\infty |f(k)|^s\right)^{1/s} - K\right| &lt; \varepsilon. \end{align*} Choose $M$ s.t. $M &gt; p$. Then $s &gt; p$ and from part (i) we know that \begin{align*} \left(\sum_{k = 1}^\infty |f(k)|^s\right)^{1/s} \le \left(\sum_{k = 1}^\infty |f(k)|^p\right)^{1/p}. \end{align*} But how can I use this? Why is the sky dark at night? The question is the well-known      If there are so many/infinite stars, in every direction, why is it dark at night? Where goes all the light we don't see?    Discussing with a friend we found different answers.   The first (my friend's answer) is that given the fact that in a finite amount of time (in this case, the age of the universe), light can travel only a certain, finite, distance, we cannot see, if they actually exist, stars farther than such distance (about 13 billions of years, I guess). Then he states (or better, I got him notice he implicitly does this)  that within this radius there aren't enough stars to fill the night sky, and that's why we have darkness without sun's light.   The second answer (mine, or anyway the one I heard from a minutephysics YouTube video) is that despite of the big size of the observable universe, cosmological expansion red shifts most of the light out of the visible radiation range, so that the majority of light can't be seen by our eyes at night, while if we use, for example, an infrared camera, we should see a brighter sky, and lenghtening more and more the wavelength at which we observe the sky, we come to the uniform background radiation.  So my question is, what is the right answer? Is it one of the above-mentioned or even a third one?  EDIT: I've seen both answer may be acceptable, but what is the main contributing phenomenon? Confusing article status for journals of American Mathematical Society: "reviewing" AND "being handled by an editor" The web page of my article in the AMS editorial system for some three months says &quot;Article status: Reviewing&quot; and in the next line &quot;Your paper is being handled by an editor&quot;. I find this confusing as the &quot;reviewing&quot; status appears to suggest that the article is with the referee(s) rather than with the editor but this in turn seems to contradict the line &quot;Your paper is being handled by an editor&quot;.  Could someone with enough experience with AMS journals please explain how should one interpret the combination of &quot;Article status: Reviewing&quot; and the line &quot;Your paper is being handled by an editor&quot; at the article page? More broadly, which are the possible article statuses in the AMS editorial system?  Many thanks in advance. Solving Hardy Weinberg problems I really fail to understand Hardy-Weinberg equilibrium and can't find an easy enough source of information.  Can you help me to understand Hardy-Weinberg equilibrium?  My goal is to be able to solve the following kind of problem     In a population with two alleles for a certain locus, B and b, the allele frequency of B is 0.7. What is the frequency of heterozygotes if the population is in Hardy-Weinberg equilibrium? Backstory: I've been developing a game with LibGDX for the past two years, and I've seen it refactored more times than I remember.  I jumped on the iOS iKVM port as soon as it was released. But I've been struggling with it ever since in regards to cross platform networking.  Kryonet will not port over to iOS unfortunately. So it's either I ditch Kryonet, or lose a large chunk of my target audience (iOS Users)  My question for you is:  I noticed LibGDX has cross platform classes ready for sockets and HTTP Requests, but no documentation exists for these sockets at all.  Has anyone used these sockets at all in the past, and does anyone know how they work? Is there a way to turn option strict off for just a single line of code?    I'm doing some maintenance work and I need to "cheat" in just one place and I don't want to lower the standard for the entire file.