A couple of years ago I read an interesting Wikipedia article about something called a "field-programmable gate array". The article made it sound like it's a box of logic gets which you can arbitrarily wire together to implement any kind of logic you want (but without needing thousands of discrete components).  Now, I had assumed this works something like a PROM. As in, you buy a die which has all the gates on it, with everything connected to everything, and then there's a glass window to the die, and you use one of those extremely expensive UV-laser writers to "burn" through the connections you don't want, resulting in the logic circuit you designed. (And maybe there's a version that's erasable too, like how CD-RW is somehow erasable.) Once you've "burned" your program into the chip, it behaves as if it were that actual combination of logic gates. (Because now it is that combination of logic gates!)  However, more recently I've been reading about this, and it appears this isn't how the technology works at all. A lot of recent articles talk about needing to send a "bitstream" to the FPGA at system power-up (and even the possibility of encrypting this bitstream to stop your competitors reading it). This makes it sound alarmingly like a FPGA isn't a hardware construct at all; it makes it sound like really it's just an ordinary microprocessor that's simulating your design in software.  In particular, that means a design programmed into an FPGA can never run any faster than the underlying microprocessor that's simulating it. Which kind of makes the entire endeavour sound... kinda pointless. I thought the whole point of an FPGA was to make custom logic that does stuff faster than you can do it in software. But all this "bitstream" stuff makes it sound like it is still software...  I'm a little confused here. How does an FPGA actually work?
I've seen a lot of people talking about FPGA's before and I know that it stands for field-programmable gate array but how does it work and what is the purpose of using an FPGA?
I'd like to remove my phone number from my iMessage account, but still have my phone enabled to receive messages sent to my email address (also used on iPad, Mac). Is there a way of doing this? Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous near $0$? If yes, find a constant for some interval containing $0$.   I think the answer is yes since I can find $L=1$ that satisfies Lipschitz continuity criteria in a interval close to $0$, am I right? "Looking forward to hearing from you" - May I omit "I am" at the beginning? At the end of a letter, is it correct to omit "I am" in this sentence?     I am looking forward to hearing from you   Then it will become:     Looking forward to hearing from you Every time i publish a new post i want to display an icon like a badge (NEW) and after a specific time it will disappear.  Lets say i publish a new post and i want to display that it is a new post. So i want to insert an icon that for example a star, in each new post in the blog list view into the metadata of the posts. Also i want to be removed after a specific time will pass. Lets say in one day or 24 hours the icon should be removed automatically.  How can i do this? Is there any bidirectional 5v-3.3v level shifter? Is there any IC that interfaces any 3.3V Input/Output to 5V Output/Input? I need it primarily for an Arduino Due but if there any bidirectional IC that works like that it would be great.  Some people advised me to use the SN74AHC125 and CD4050 ICs, but I don't understand how they work or how to interface with them. I am wondering if there is a modifier or tool that will essentially undo a subsurf or subdivide command. Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$? Question: If $R$ is a finite boolean ring, then show $R \cong \mathbb Z_2 \times \mathbb Z_2 \times \cdots\times \mathbb Z_2$.   I know that   $\mathrm{char}(R) =2$  $R$ has $2^k$ elements for some $k$  (this is because, if $p\neq 2$ is a prime with $p\mid|R|$, then there exists a non-zero $x \in R$ s.t. $px=0$ and $p $ is odd $\implies x=0$, contradiction).   Does this suffice to answer my question? Q: Will there be, or have there been, any “late blooming” students in the school who come into their magic potential as adults, rather than as children? By the way, I loved meeting you, and hearing you speak, when you came to Anderson's in Naperville. I can hardly wait until you tour again. JKR: Ahhh! I loved the event at Anderson’s. It was one of my favorites. That is completely true. No, is the answer. In my books, magic almost always shows itself in a person before age 11; however, there is a character who does manage in desperate circumstances to do magic quite late in life, but that is very rare in the world I am writing about. (src: )  Who was JKR referring to in “there is a character”? Clearly, it not a student; so the most obvious guess of &quot;Neville Longbottom&quot; is wrong – both due to “no” answer regarding the question itself, and the fact that Neville bloomed in his 6th/7th year, well before you can legitimately term “quite late in life”. Why would parametric statistics ever be preferred over nonparametric? Can someone explain to me why would anyone choose a parametric over a nonparametric statistical method for hypothesis testing or regression analysis?   In my mind, it's like going for rafting and choosing a non-water resistant watch, because you may not get it wet. Why not use the tool that works on every occasion? How do I have a camera follow my object in Unity? I have an object that automatically moves by itself and I want the main camera to automatically follow it.(Like in games such as geometry dash and jetpack joyride)  This is the code for the automatic moving object in case it is needed:  using UnityEngine; using System.Collections; public class automove : MonoBehaviour { public static int movespeed = 5; public Vector3 userDirection = Vector3.right;    public void Update() {     transform.Translate(userDirection * movespeed * Time.deltaTime);  } }   So does anyone know any good scripts I could add to the main camera to follow this object that automatically moves? Thanks in advance! I've been trying to play with a rigid body simulations.  I prepared a project of a building made of domino tails. I've placed all objects very tight, but as soon as I start animation it looks like there was some tiny gap between objects, so they all fall down a little bit. For a high building it leads to a construction disaster as the whole building colapses.  Here is an example:  (I'd suggest to use 0.25x speed).  How can I fix it? If G is a group of order n=35, then it is cyclic I've been asked to prove this.   In class we proved this when $n=15$, but our approached seemed unnecessarily complicated to me. We invoked Sylow's theorems, normalizers, etc. I've looked online and found other examples of this approach.    I wonder if it is actually unnecessary, or if there is something wrong with the following proof:   If $|G|=35=5\cdot7$ , then by Cauchy's theorem, there exist $x,y \in G$ such that $o(x)=5$, $o(y)=7$. The order of the product $xy$ is then $\text{lcm}(5,7)=35$. Since we've found an element of $G$ of order 35, we conclude that $G$ is cyclic.   Thanks. Stopping to eat is tedious, is there any way to automate the process? While I've managed to optimize and automate almost everything, constantly having to stop and eat is annoying (I run around a lot, so I get hungry quickly). Is there any device or tool that will keep me well fed at all times without having to stop and feed? A line is drawn through the point $A(1,2)$ to cut the line $2y=3x-5$ in $P$ and the line $x+y=12$ in $Q$. If $AQ=2AP$, find the coordinates of $P$ and $Q$.  I found the lengths of the lines $AQ$ and $AP$ in terms of $x$ and $y$ and used $AQ=2AP$ to get this equation $11x^2-40x-16=0$  Working: $AP=\sqrt{(x-1)^2+(\frac{3}{2}x-\frac{9}{2})^2}=\sqrt{\frac{1}{4}(13x^2-62x+85)}$  $AQ=\sqrt{(x-1)^2+(-x+10)^2}=\sqrt{2x^2-22x+101}$  $AQ=2AP\Rightarrow \sqrt{2x^2-22x+101}=2\sqrt{\frac{1}{4}(13x^2-62x+85)}$  $\Rightarrow 2x^2-22x+101=13x^2-62x+85\Rightarrow 11x^2-40x-16=0$  Using the quadratic formula I found $x=4,x=-\frac{4}{11}$  I then substituted these values into the two equations in the question to get the coordinates $(4,\frac{7}{2}),(-\frac{4}{11},-\frac{15}{11})$ or $(4,8),(-\frac{4}{11},\frac{136}{11})$  But the answers in the book are $(4,\frac{7}{2}),(7,5)$ or $(\frac{2}{5},-\frac{19}{10}),(\frac{11}{5},\frac{49}{5})$  I don't know where I went wrong in my method.  Edit: Found some errors in my method and calculation.  Using $x=4$ in $2y=3x-5$ gives $P(4,\frac{7}{2})$  Line with points $AP$ has equation $y-2=\frac{\frac{7}{2}-2}{3}(x-1)\Rightarrow y=\frac{1}{2}x+\frac{3}{2}$  $Q$ lies on the same line. Therefore, the intersection between $y=\frac{1}{2}x+\frac{3}{2}$ and $y+x=12$ is the point $Q$. Working: $\frac{1}{2}x+\frac{3}{2}=-x+12\Rightarrow x=7$ Therefore, $y=-7+12=5$. Point Q has coordinates $(7,5)$.  But $x=-\frac{4}{11}$ is not the other $x$ coordinate of $P$ according to the answers in the book. I have no idea where I went wrong at this point. One of is followed by plural noun/pronoun and singular helping verb Excel multiple FIND formula I am no expert with excel so any help is appreciated!   I am trying to make one cell do multiple searches within another.  I know that to search one cell for a specific word you would use  =FIND(Blue,C2)   But I need to find multiple different words in one cell. Heres an example of what im trying to do:    I need to show all the allergens in the ingredients cell eg peanuts, gluten, milk, sesame seeds etc   How do I get the result to list all the allergens?   I know that I can do a single find function in separate cells and then concatenate them, but there must be a more simple way?  Thanks Is there a way to show that $\sqrt{p_{n}} < n$? Is there a way to show that $\sqrt{p_{n}} &lt; n$?  In , I show that $f_{2}(x)=\frac{x}{ln(x)} - \sqrt{x}$ is ascending, for $\forall x\geq e^{2}$. As a result, $\forall n \geq 3$ $$\frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}}\leq \frac{p_{n+1}}{ln(p_{n+1})} - \sqrt{p_{n+1}}$$ Also (and as a result), $\forall n \geq 3$ $$ \frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}} &gt; 0$$ Or $$ \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$  According to  $$\displaystyle\smash{\lim_{n \to \infty }}\frac{\pi (p_{n})}{p_{n}/ln(p_{n})}=1$$ Or, $\forall \varepsilon &gt;0$, $\exists N(\varepsilon )$: $\forall n&gt;N(\varepsilon )$ $$1- \varepsilon &lt; \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; 1+ \varepsilon$$ Or $$1- \varepsilon &lt; \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$ As a result $\forall \varepsilon &gt;0$, $\exists N(\varepsilon )$: $\forall n&gt;N(\varepsilon )$ $$(1 - \varepsilon ) \cdot  \sqrt{p_{n}} &lt; \pi (p_{n}) = n$$  But this is not enough.  Interestingly,  is true iff function $f_{4}(x)=\pi (x) - \sqrt{x}$ is strictly ascending ($x &lt; y \Rightarrow f(x) &lt; f(y)$) for prime arguments.  If $f_{4}(p_{n}) &lt; f_{4}(p_{n+1})$ then $$\pi (p_{n}) - \sqrt{p_{n}} &lt; \pi (p_{n+1}) - \sqrt{p_{n+1}}$$ Or $$\sqrt{p_{n+1}} - \sqrt{p_{n}} &lt; \pi (p_{n+1}) - \pi (p_{n}) =1$$  And vice-versa, if $$\sqrt{p_{n+1}} - \sqrt{p_{n}} &lt; 1$$ Then $$-\sqrt{p_{n}} &lt; -\sqrt{p_{n+1}} + 1$$ Or $$\pi (p_{n})-\sqrt{p_{n}} &lt; \pi (p_{n}) + 1 -\sqrt{p_{n+1}} = \pi (p_{n+1}) -\sqrt{p_{n+1}}$$  So, if Andrica's conjecture is true then $\forall n \geq 3$ $$\pi (p_{n})-\sqrt{p_{n}} &gt; 0$$ Or $$\sqrt{p_{n}} &lt; \pi (p_{n})= n$$ Bash File Unable to locate package when new line is added When building a bash file to execute I keep getting an error after adding a new line. I have tried moving some lines around or removing some of the packages but it will results in the same error. In the file if I was to remove 3 and 4 it there will no longer be an error.   E: Unable to locate package &lt;package&gt;   The bash file looks like this   #!/usr/bin/env bash sudo apt update &amp;&amp; sudo apt install -y python3-pip build-essential python3-dev python3-setuptools gcc sshpass sudo apt-get install apt-transport-https lsb-release software-properties-common dirmngr sudo apt-get update   The output with the error  Hit:1 http://us.archive.ubuntu.com/ubuntu bionic InRelease Get:2 http://security.ubuntu.com/ubuntu bionic-security InRelease [88.7 kB]                                                   Hit:3 http://archive.ubuntu.com/ubuntu bionic InRelease                                             Get:4 http://us.archive.ubuntu.com/ubuntu bionic-updates InRelease [88.7 kB]         Get:5 http://us.archive.ubuntu.com/ubuntu bionic-backports InRelease [74.6 kB]                                       Fetched 252 kB in 1s (189 kB/s)     Reading package lists... Done Building dependency tree        Reading state information... Done All packages are up to date. Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package sshpass Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package dirmngr Hit:1 http://us.archive.ubuntu.com/ubuntu bionic InRelease Get:2 http://security.ubuntu.com/ubuntu bionic-security InRelease [88.7 kB]                                                   Hit:3 http://archive.ubuntu.com/ubuntu bionic InRelease                                             Get:4 http://us.archive.ubuntu.com/ubuntu bionic-updates InRelease [88.7 kB]         Get:5 http://us.archive.ubuntu.com/ubuntu bionic-backports InRelease [74.6 kB]                                       Fetched 252 kB in 1s (209 kB/s)     Reading package lists... Done How can I hide the jqgrid completely when no data returned? interaction between mathematical structures From a physicist's perspective there are several situations in which somehow arbitrary choices of mathematical structures can be made. One can describe a system from different perspectives, etc. without changing anything in the physical properties. (see gauge invariance, picture changing etc.) In the situation when these choices impose a mathematical structure one has limitations in the subsequent choices (are these limitations physical???). However, there are situations when this prescription does not hold. The best example is in this case the Black-Hole complementarity principle (if it is well defined in the first place). So, the question about how mathematical structures "interact" in a logical way is not a bad one. Again: what is the interaction between, say, locality and Hausdorff-ity in the case of a black hole? Or what is the true relation between metrizability and hausdorff-ity of a space in the context of a black hole? The question about how mathematical structures assigned (innocently) at some point interact in different situations is in my opinion a quite relevant one...