How data flows through internet?
What exactly happens when you browse a website in your browser?
Restrictions on the variables for this identity are as follows: $a \geq m \geq 0$ and $n \geq b \geq 0$.  I have not gotten far with this, but these are my very rudimentary thoughts: We need to define a special element, somehow, and then carve up the $m + n$ remaining elements to be chosen out of the remaining pool of $a + b$ elements by writing $a + b = a - i + b + i$. From the $a - i$ pile, we choose $m$ things. From the $b + i$ pile, we choose $n$ things. My problem is, what is going on with this special element? How is it being defined so as to split things in this precise way?  A hint would be great for the moment. Inequality: $ab^2+bc^2+ca^2 \le 4$, when $a+b+c=3$. Let $a,b,c $ are non-negative real numbers, and $a+b+c=3$.  How to prove inequality $$ ab^2+bc^2+ca^2\le 4.\tag{*} $$    In other words, if $a,b,c$ are non-negative real numbers, then how to prove inequality $$ 27(ab^2+bc^2+ca^2)\le 4(a+b+c)^3.\tag {**} $$ $\color{gray}{\mbox{(Without using "universal" Lagrange multipliers method).}}$  Thanks! The portion of the tangent to any conic intercepted between the point of contact and the directrix subtends a right angle at the focus of the conic? I'm having a bit of trouble proving this with the propositional calculus rules.  $$p \lor (p\implies q)$$ Would someone mind helping me and showing which rules they've used with an explanation! Thanks! How to reset Canon 70D WiFi? When I go to the WiFi Settings in Camera (Canon 70D) all I see is:  Connection:   Exit Confirm Set Error Details (greyed out)   I can't recall the password or find any way to reset it. Some I found () say the Camera should say Infrastructure mode. Inside the Confirm Settings I can see on page 3 it shows:     Connect'n method: Camera access point mode   But again I see no way to change this.  On my Smartphone EOS Remote app there's a Connection Guide with completely different menus from what I'm seeing on the Camera.  Any idea how I can reset the WiFi Name and Password on the Canon 70D? Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$. $f(x)$ is a differentiable function and $g(x)$ is a double differentiable function such that $|f(x)|\leqslant 1$ and $f'(x)=g(x)$. If $$f(0)^2+g(0)^2=9$$ then prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)&lt;0$.  Attempt: Let us define a function $h(x) = g(x) g~'(x)$. Then $$h'(x) =  g(x)g''(x) + \left( g'(x) \right)^2 \tag 1$$ If we prove that for some $c \in (-3,3), h~'(c) &lt; 0,$ then $$g(c)g''(c) &lt;0 \tag 2$$ Also, $$\left|f(0)\right| &lt; 1 \implies f'(0) \in (-3,-2\sqrt 2 ) \cup (2\sqrt 2,3) $$ Could someone please advise me how do I move forward from here. Thank you very much for your help in this regard. The future of meta.stackoverflow and meta.stackexchange Historically this site, , has been the place to ask questions about not just Stack Overflow, but the functioning of the entire Stack Exchange (2.0) network, including Area 51 and stackexchange.com and careers.  (Yes, there was a , but that dealt with the old legacy Stack Exchange 1.0 sites. It was deprecated a while ago, and currently redirects here.)  Now that we've gotten many, many months under our belt from the SE 1.0 days, I think it's time that we gave Stack Overflow its own, true per-site meta, and moved the higher level network meta discussions to meta.stackexchange.com.  Over time, it's begun to bug me more and more that requests for Stack Overflow, the site, kind of get buried here on meta.stackoverflow under the avalanche of network issues. Retag requests, synonym requests, things truly specific to Stack Overflow, the site, not the network. This is unfair to our vastly largest and flagship Q&amp;A site, and it's unfair to the Stack Overflow users to mix their requests in with network level concerns.  It's also odd that Stack Overflow is the only network site without a proper, dedicated per-site meta, where its meta has its own reputation system not tied to the parent site in any way.  This is mostly a quirk of history more than anything else, and I believe it is now an appropriate time to split into two sites:   , a proper per-site meta for Stack Overflow with integrated rep , a global network meta with its own reputation system   Yes, this will be painful. But I believe it is a good, necessary, and healthy step both for the future of the network and the future of Stack Overflow.  Some things to discuss:   which questions should be migrated from here to meta.so? Obviously site-specific things like the retag-requests, and perhaps questions with the  tag. Anything that is 100% wholly specific to Stack Overflow and not generalizable to the rest of the network should be moved over. This may be a pretty small, narrow list of questions, and that's OK. Should we do some meta spring cleaning in our transition? Which questions / tags should be blown away as no longer relevant, referring to ancient versions of Stack Overflow or issues that have long since ceased to exist and aren't instructive for any future visitors? Your meta reps will generally be unaffected, except insofar as we delete for spring cleaning, or move site-specific things to meta.so. We still plan to have a distinct reputation system for the new meta.se site, just like here.   I do not have a timeline for this change, that is up to Jarrod and David to decide. It may be months away. However, we feel pretty strongly that this is something that we need to do to clean things up and pave the way for the future -- so I expect it will happen in the next few months, giving us lots of time to decide how we want to do it, per the above.  Update  . How large would the steam explosion at Chernobyl have been? So the  of the HBO series began to cover the  that led to them sending three divers into the water below the reactor to drain the tanks.  This occurred after the initial explosion that destroyed the reactor, and after the fire in the core had been put out. But at this point the decay heat and remaining fission reaction kept the core at more than 1200°C, causing it to melt through the concrete floors below the reactor.  And below the reactor were water tanks which contained 7,000 cubic meters of water (according to the TV show. If anyone has a real figure, I'd love to hear). When the lava of the melted core hit it, it would cause an enormous .  Finally, my question: About how large would this explosion have been? The character in the show says "2-4 megatons" (of TNT equivalent, I assume). I'm pretty sure this is absurd and impossible. But real estimates are hard to come by. Other sources vary wildly, some repeating the "megatons" idea, and others saying it would've "". This still seems crazy.  tl;dr:  I know a lot of it hinges on unknowns and the dynamics of the structures and materials involved, so I can simplify it to a constrained physics question:  Assuming 7,000 cubic meters of water instantly flashes to steam, how much potential energy is momentarily stored in that volume of steam occupying the same volume as the water did?  I don't know what to assume the temperature of the steam is. There were hundreds of tons of core material at temperatures near 1200°C, so worst case scenario you could assume all the steam becomes that temperature as the materials mix. Best case scenario, I guess we could assume normal atmospheric boiling point (100°C)? $$\frac{1}{z-\sin z}$$ $$\frac{1}{z(1-\frac{\sin z}{z})}$$  the laurent's transform is also used to simplify the function.  the residue is found a $\frac{2*36*2}{5}$ but the actual answer is given as $\frac{3}{10}$ the residue is given as The solution is incorrect and also the pole is of the order 3. How to load a taxonomy term with case-sensitive? I used this      $this-&gt;termStorage-&gt;loadByProperties(['name' =&gt; 'test']);   I got two terms: Test, test. I want to get only one: test  This is working without case-sensitive:       $this-&gt;termStorage-&gt;getQuery()-&gt;condition('name', 'test', '=')-&gt;execute();       \Drupal::database()-&gt;select('taxonomy_term_field_data', 't')       -&gt;condition('t.name', 'test')       -&gt;fields('t', ['name'])       -&gt;execute()       -&gt;fetchAll();       \Drupal::database()-&gt;query("SELECT name FROM taxonomy_term_field_data WHERE name='test'")-&gt;fetchAll(); Conditions: do not modify the original lists; JDK only, no external libraries. Bonus points for a one-liner or a JDK 1.3 version. Is there a simpler way than: List&lt;String&gt; newList = new ArrayList&lt;String&gt;(); newList.addAll(listOne); newList.addAll(listTwo); Short story about survivors on Earth after the atmosphere has frozen This is a short story I read maybe in the '80s.  Earth has been thrown away from the Sun, probably due to a very large object passing through the Solar System, and the atmosphere has frozen in layers. There is a small family - father, mother, two children, who live in a room they have made airtight by hanging many layers of material to slow the loss of air. They keep warm with a 'camp-fire'. The father goes out every day in a suit of some sort to find food and mine frozen oxygen. It ends when they are found by another, larger group of survivors.  Does anybody know the title and author? Inequality involving sides of a triangle How can one show that for triangles of sides $a,b,c$ that   $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} &lt; 2$$  My proof is long winded, which is why I am posting the problem here.   Step 1: let $a=x+y$, $b=y+z$, $c=x+z$, and let $x+y+z=1$ to get   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}&lt;2$  Step 2: consider the function $f(x)=\frac{1-x}{1+x}$, and note that it is convex on the interval (0,1), so the minimum of   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}$  is reached when the function takes the extreme points. i.e. $x=y=0, z=1$.    But going back to the fact that this is a triangle, we note that $x=y=0 \implies a=0$ which is not possible, so the inequality is strict. I am studying elementary Algebraic Topology recently. I have seen that a topological space is identified with a group. We are telling the group as Fundamental Group. So every topological space $X$ and for any $x \epsilon X$ there is a fundamental group $\pi_1 (X,x)$. I have a question about the converse. If we consider any arbitrary group $G$, then does there exist a topological space $X$ and an element $x\epsilon X$ such that $\pi_1 (X,x)=G$? Why are Bitmap-Fonts used automatically? I have the following LaTeX-document:  \documentclass[a4paper,11pt]{article} \usepackage[utf8x]{inputenc} \usepackage[ngerman]{babel}  \usepackage[T1]{fontenc}  \title{Sample} \author{Litb}  \begin{document}  \maketitle  \begin{abstract}  This is a report about my praxis phase at the company foo bar which I enjoyed. \end{abstract}  \end{document}   Much to my frustration, compiling with pdflatex creates a document with Bitmap-fonts. The reader's font-list shows that it uses Type3 fonts.  If I remove the fontenc loading, then I get a PDF using vector-fonts, but I heard that I should keep it, for having native German Umlauts working.  Does anyone know how I can get vector fonts with T1, and why it keeps using bitmap fonts if I have that package-load line in it? A coin is tossed $n$ times. What is the probability of getting odd number of heads?   I started this chapter sometimes ago and faced in front of a tough problem. At first I started considering cases. Case-I : The probability of getting 1 head.Case-II : The probability of getting 3 head and so on. But there are many cases. So how can I solved this . Please help me. Thank you! What prevents photons from getting mass from higher order Feynman diagrams The Higgs boson and gluons have no electric charge and photons couple to charge, so there is no tree level interaction between them and photons.  But what prevents higher order diagrams from contributing a non-zero mass term to the photon, for instance    where a photon couples to some fermion (say an electron, or a top quark) which can interact with the Higgs field.   Or consider that same diagram but with quarks and a gluon interacting between them? Or any higher diagram with even more loops?  I have heard charge conservation depends on gauge invariance, which in turn depends on photons being massless.  So it appears the photon has no mass, and these diagrams must all cancel somehow.  So I'm hoping there is a very nice symmetry explanation for why they all disappear, but if I say "because of gauge invariance" that would be circular logic, so there must be another symmetry at stake here?     What prevents photons from obtaining a mass from high-order self-energy loop diagrams? What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$? Find a closed form expression for $$\sum_{r=0}^n \dfrac{(-1)^r}{\dbinom{n}{r}}$$ where $n$ is an even positive integer.  I tried using binomial identities, but since the binomial coefficient is in the denominator, I can't do much. Also, I'm seeking a non-calculus, elementary solution, if possible. Thanks. I understand that there is an upper limit. But why do you have to type at least 15 characters to post a comment? It is easy to work around it anyway (like adding dots or other useless things). Children’s books, one in space setting, the other in a jungle When I was little I remember getting these two books from the library.  Both books were paperback and flimsy.  The pages were wide.  Each book had full page illustrations with puzzles and mazes in them, but it was like you were immersed in this setting completely.  They were also like choose-your-own adventure books, but only in the way that you go through the book in a different order based on your results in the puzzles/games.    For example, there is a bridge to cross, or you can take this path.  If you choose to cross the bridge you go to page x.  On page x you have to pretend to cross the bridge but some planks are broken.  You can't skip more than a certain number of planks, but you also cannot "step" on a broken plank.  One book was in a jungle setting with rope bridges, alligators, quick sand, etc. The other was in space, with all kinds of aliens and weird stuff.  I have faint memories of these books but I REALLY want to track them down because I remember loving them.