I read a short story online a year or so ago. Told from an alien's point of view, they discover Earth and are so horrified by mankind's warlike nature they fire a weapon at Earth that will take a few centuries to hit us.  They then watch as we evolve beyond the middle ages and realize we're not that warlike. The scientists involved in creating the weapon kill themselves by 'Sealing their spiracles' I seem to remember.  It ends with humanity developing fast enough to stop the weapon, then sending a message to the aliens along the lines of "big mistake".
The story is basically told from an alien's point of view. Essentially they observed us from far off, deemed us as violent and a danger to the universe, and set course (asteroid or something) to kill us. They kept observing and saw all the art and beauty we created and realized we were actually not so bad, but by then they couldn't stop it. So it was sort of also an apology letter to Earth in the end.  First read it like a year ago online and I can't find any trace of it anymore, nor can I recall the site it was on. Anyone know what short story this is?
Dirichlet's problem in the unit disk is to construct the harmonic function from the given continuous function on the boundary circle. It is solved by the convolution with the Poisson kernel, and we know that the constructed function has uniform limit which is the given continuous function as $r\to 1$, and we can complexify the solution by taking the Schwarz integral formula. Now (in this very particular case) does the imaginary part has a uniform limit? If it does, why don't we prove the uniqueness of the solution by a simple application of the Cauchy integral formula? Here is the proof that I reckon to be reasonable(which is what I expose here to be criticised)  We construct the Schwarz integral, or $\frac{1}{2\pi}\int _{0}^{2\pi}\frac{\exp(it)+z}{\exp{(it)}-z}u(\exp{(it)})\mathrm{d}t$. This function is an analytic function in the interior unit disk, and is continuous in the closed unit disk(its closure). Let this analytic function denoted by $f$, and another analytic function that has the same uniform limit function on the circle be $v$. Then $u-v$ is an complex analytic function in the interior of the unit disk, continuous on the closure, with boundary value identically zero. An application of Cauchy's integral formula gives rise to the conclusion that $u-v$ in identically zero on the entire disk.   Another question being if the boundary function has finite jump discontinuities, what is the behaviour of the convolution with the Poisson kernel near the discontinuous points? Norm is sup of inner products (proof). Let $V$ be a vector space with an inner product $\langle.,. \rangle$ and associated norm $|| . ||$ Then:    Could I have a proof of this fact? I have a simple question.     over centuries / for centuries   what is the difference?  Thank you. I'm passing through Canada, on my way to somewhere else. I'm staying only a short time.   Is there a website, or some other way of find out out if I need a visa? Are global variables thread-safe in Flask? How do I share data between requests? Finite abelian group contains an element with order equal to the lcm of the orders of its elements I will quote a question from my textbook, to prevent misinterpretation:     Let $G$ be a finite abelian group and let $m$ be the least common multiple of the orders of its elements. Prove that $G$ contains an element of order $m$.   I figured that, if $|G|=n$, then I should interpret the part with the least common multiple as $lcm(|x_1|,\dots,|x_n|)=m$, where $x_i\in G$ for $0\leq i\leq n$, thus, for all such $x_i$, $\exists a_i\in\mathbb{N}$ such that $m=|x_i|a_i$. I guess I should use the fact that $|x_i|$ divides $|G|$, so $\exists k\in \mathbb{N}$ such that $|G|=k|x_i|$ for all $x_i\in G$. I'm not really sure how to go from here, in particular how I should use the fact that $G$ is abelian. How do I fork a process that doesn't die when shell exits? Jensen's Inequality implies convexity? Suppose $\phi$ is a real function on $\mathbb{R}$ such that $$\phi \Bigl(\int_0^1f(x)\,dx\Bigr)\leq \int_0^1 \phi(f)\,dx$$ for every real bounded measurable function $f$. Prove that $\phi$ is then convex.    This one is in Rudin's Real and Complex Analysis, page 74, and, to be quite honest, I am unsure what my first step to solve this problem should even be. To help think of a general methodology, I attempted this similar question, from page 71 of the same book:      Assume $\phi$ is a continuous real valued function on $(a,b)$ such that $$\phi\Bigl(\frac{x+y}{2}\Bigr)\leq\frac{\phi(x)+\phi(y)}{2}$$ for all $x, y\in (a,b).$ Prove that $\phi$ is then convex (the conclusion does not follow if continuity is omitted from the hypothesis).   I take it that the latter question is just a special case of the former (assuming $\phi$ is bounded on $(a,b)$), so I attempted to solve the latter problem first. My attempt was to note that \begin{align*} \phi\big(\lambda x + (1-\lambda)y\big) &amp;\leq \phi\Bigl(\frac{2\lambda x + 2(1-\lambda)y}{2}\Bigr) \\ &amp;\leq \frac{1}{2}\Bigl(\phi\bigl(2\lambda x\bigr)+\phi \bigl(2(1-\lambda)y\bigr)\Bigr) \\ &amp; \leq \phi\bigl(\lambda x\bigr)+\phi\bigl((1-\lambda)y\bigr) \end{align*} with the latter inequality justified simply by applying the hypothesis again twice to the previous expression.   From here, however, I am stuck; I cannot justify "popping out" the $\lambda$ and the $(1-\lambda)$ in the last inequality via some bound afforded by the hypothesis and/or the continuity of $\phi$. How a Gmail username can be taken but not recognised simultaneously? Being at  I enter a desired username (without @gmail.com which is supposed), and I get error:     "That username is taken. Try another."   But when I try to login into Google with that xxx@gmail.com at  it fails with:     "Sorry, Google doesn't recognise that email."   How that can be?  P.S.: I want that username still. I know there is a ton of questions and answers about this topic, but none answers my question sufficiently.  Let's say I have a viewport view that I want to render in Cycles. Pressing ALT CTRL Numpad 0 aligns the camera to this view, but it does not solve the whole problem. The thing is, I want PRECISELY this view on the render, preferably in one click, without manually moving the camera back-and-forth, changing sensor sizes etc. fiddling that will remove the unwanted border that appears and blocks the viewport partially. This whole activity wastes a lot of precious time especially if you do this 10 times a day.  What this dream action should do:   match the render resolution (proportions) to the resolution of the current view (can the resolution of current view be read by a Python script?) make the entire view the camera view, without any borders, passe-partout etc. by automatically maneuvering sensor sizes etc. whatever is necessary to make it exactly the same view, the same camera lens angle.   Is it possible to write such a script that would do it all in one click? Can I tap a creature with summoning sickness to pay "tap an untapped creature you control" costs? OneDrive for Windows 10 - Remove logged out account I'm following the , but on launching the upgrade tool I get this response:  Checking for a new ubuntu release No new release found   Am I doing something wrong? Is there a workaround? I have read a lot about the SB-800/SB-900 but I am on a low budget (around ~120$). Is there an external flash that I can have to start learning to use it? I do not need TTL compatibility so it can be an older model. I have a Nikon D5000. Is there any way to tell Google to use a particular account for all Google services by default? I typically use 2 Google accounts simultaneously in my browser. So whenever I fire up any Google service like Google Maps or YouTube or Google Search, it uses one of the accounts. The problem is that I don't want that account to be used and no matter how many times I switch the account for these services, they seem to default to same account.  Is there any way to tell Google to use a particular account for all Google services by default?    I am not talking about using Google account to sign in to third party websites. I am talking only about Google's own services.  I am using Chrome if anyone is going to suggest client-side solution. User systemd PulseAudio service Not much else to this question: I would like to know what I need to create a PulseAudio systemd service to be run with systemd --user.  I've tried a few different things, including various user services from Google, but I can't get it set up just right between dbus and everything else required for it.  Update: It seems to work ok with graphical sessions, but I'm still having some inconsistancy with dbus when logging in through console.  But PulseAudio is starting rather reliably, so I'm not overly concerned. Change Recycling Bin Location I have a SSD as a primary hard drive, and one HDD for storage. I want the recycling bin to be on the HDD. I want is so that even if I delete files from the SSD the end up on the HDD's recycling bin. What is the proper way of going about this? "turn down the volume" or "turn the volume down" - phrasal verb structure I'm learning about phrasal verbs, but I'm not sure if I'll use them correctly. Which one of the following phrasal verb uses correct:  -I don't know how to turn down the volume? -I don't know how to turn the volume down?  I always think that they're same, but lately I feel like there must be a rule how to use them correctly, or perhaps they get different meanings? Why is the voltage across a capacitor and the current across an inductor continuous? Is Morocco currently safe to visit despite the Ebola outbreak? I'm travelling to Morocco over the Easter period, and while I am aware that the current Ebola outbreak is mainly in Guinea, Liberia and Mali, and would have to cross the Sahara to get to Morocco, is it wise for me to go to Morocco at this time?  What are some basic precautions I can take in the case that the Ebola virus travels to Morocco?