Human & Alien captured, observed by higher beings
Human vs. alien to avoid extinction by omnipotent being
I'm currently reading Evans' PDE book. In it he claims that for $f \in C^2_c(\mathbb{R}^n)$ $$\frac{f(x + he_i) - f(x)}{h} \to \frac{\partial}{\partial x_i}f(x)$$ and $$\frac{\frac{\partial}{\partial x_i}f(x + he_j) - \frac{\partial}{\partial x_i}f(x)}{h} \to \frac{\partial^2}{\partial x_jx_i}f(x)$$ uniformly as $h \to 0$.  My question is why must the convergence be uniform?  Thanks in advance. HTML favicon won't show on google chrome Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite. I have seen another post for this same question but it never got an answer. Since I am fairly new, I can't comment on other's posts, therefore I am creating a new one. The question states:  If a, b, and c are positive integers, prove that if $(a + b + c) | (a*b*c)$, then $a+b+c$ is composite.  I do not really know how to approach this.  The link to the post with the same question is: Paucity of words for relationships Someone who just thinks they know what they're talking about How can you prove that a function has no closed form integral? Typesetting long division with tabular and overlining repeating part Grammatically, what is "It" in the following sentence? I'm currently working at a private academy in Korea, and my boss just asked me a real head-scratcher.   In the sentence:     It doesn't have to be hot and humid for players to lose too much water from their bodies.    I'm aware that "It" is a subject pronoun replacing "The weather." Besides that, however, I'm unsure.   Is it a false subject? I wouldn't think so since it's a pronoun. Is it some crazy kind of indirect object?  Anyway, thank you all for your help! Prevent Photos app on OSX from launching when plugging in device How to make a VGA monitor display a white screen at all time? Selecting the right crank length What is the best way to determine the correct crank length for my height and more specifically my leg length? I am trying to figure out how to add a Lightning Web Component to a Lightning tab.  I have it on the Home Page, but I would like it to be on its own tab.  I feel like there should be an option to expose it to the Lightning tabs.  When I am in the Tabs section, I don't see my LWC listed. MCMC in a frequentist setting I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM algorithms. Are there more frequentist problems where MCMC is used? Prove that if the identity is written as the product of $r$ transpositions, then $r$ is an even number Theorem. If the identity is written as the product of $r$ transpositions, $id=τ_1τ_2\dots τ_r$, then $r$ is an even number. Proof. We will employ induction on $r$. A transposition cannot be the identity; hence, $r &gt; 1$. If $r = 2$, then we are done. Suppose that $r &gt; 2$. In this case the product of the last two transpositions, $τ_{r−1}τ_r$, must be one of the following cases: $(ab)(ab) = id\\ (bc)(ab) = (ac)(bc)\\ (cd)(ab) = (ab)(cd)\\ (ac)(ab) = (ab)(bc),$ where $a$, $b$, $c$, and $d$ are distinct. The first equation simply says that a transposition is its own inverse. If this case occurs, delete $τ_{r−1} τ_r$ from the product to obtain $id=τ_1τ_2···τ_{r−3}τ_{r−2}$. By induction $r − 2$ is even; hence, $r$ must be even. In each of the other three cases, we can replace $τ_{r−1} τ_r$ with the right-hand side of the corresponding equation to obtain a new product of $r$ transpositions for the identity. In this new product the last occurrence of $a$ will be in the next-to-the-last transposition. We can continue this process with $τ_{r−2} τ_{r−1}$ to obtain either a product of $r − 2$ transpositions or a new product of $r$ transpositions where the last occurrence of $a$ is in $τ_{r−2}$. If the identity is the product of $r − 2$ transpositions, then again we are done, by our induction hypothesis; otherwise, we will repeat the procedure with $τ_{r−3}τ_{r−2}$. At some point either we will have two adjacent, identical transpositions canceling each other out or $a$ will be shuffled so that it will appear only in the first transposition. However, the latter case cannot occur, because the identity would not fix $a$ in this instance. Therefore, the identity permutation must be the product of $r − 2$ transpositions and, again by our induction hypothesis, we are done. Question: That is the proof written in the book, but unfortunately after more than $10$ times reading I don't understand the last two paragraph (i.e., from &quot;In each of the other three cases&quot;). Is there another simpler proof or could someone please clarify what is going on? Thank you. What's the simplest SQL statement that will return the duplicate values for a given column and the count of their occurrences in an Oracle database table?  For example: I have a JOBS table with the column JOB_NUMBER.  How can I find out if I have any duplicate JOB_NUMBERs, and how many times they're duplicated? I have a directory where daily subdirectories are created, literally named according to $date. How can I delete folders and their contents that are older than 7 days according to the YYYYMMDD in the file name and not the metadata date? Say I have (skipped some for brevity):  20170817 20170823 20170828 20170901   I would end up with the following folders (which those should keep):  20170828 20170901   I created a variable that holds the date 7 days ago: dt_prev=$(date -d "`date`-7days" +%Y%m%d)  My thought was to ls -l a list of these folder names and compare row by row, but this involves cleaning that list, etc., and I figure there has to be an easier way. Why do light sources appear as stars sometimes? See for example this photo:    From my experience, the longer the exposure the stronger can this effect be observed. Is this correct? Are there any other factors that influence the creation of these stars (is there a better word for it, by the way?) And what exactly does technically happen? Google Chrome automatically adding websites to my list of search engines? I have noticed that certain websites (e.g. Stack Exchange sites, Dell, etc.) are automatically added to my list of search engines in Google Chrome.   They even add a keyboard shortcut to their entry. Here are some examples:   Dell: Keyboard -> Dell.com Stack Exchange Web masters: Keyboard -> webmasters.stackexchange.com Reuters: Keyboard -> reuters.com   Q1: Is this the default behavior in Chrome? (to let websites add themselves to the list of search engines?)  Q2: Is it possible to disable this behavior in Chrome?   Note: I'm running the latest version of Chrome: 11.0.696.57 on Windows 7 64, and I only have one extension installed: Google URL shortener. About embryonic and genetic evidence of evolution? My question here is about evidence for evolution from Embryology and from Genetics.  Mammals do have similar Embryos, but is it the case that for each species there is an embryonic development that occurs in earlier species, has such relationship been observed? What I mean for example if we generally conceive of having species$Sp_1,Sp_2,...,Sp_n$ where each $ Sp_{i+1}$ being evolved from $Sp_i,$ then is it the case that the embryonic development stages of $ Sp_{i+1}$ contains some of the embryonic development stages of all of its ancestor species.  Similar question to 1 but regarding Genetics, is it the case that every species has a genetic thumbprint of its ancestors that lie there in the non-functional sections of its DNA, i.e. is it the case that all the genetic history of our evolution is recorded in the non-functional section of our DNA. So do human DNA have some portions of the DNA of some dinosaurs for example? Customizing tray/taskbar date display in Ubuntu with GNOME 3