Review seems to need to be refreshed
Wrong posts number on Review section
How do we know that $F = ma$, not $F = k \cdot ma$ It seems intuitive that $a\; \propto \frac{F}{m}$, as the greater the force that is applied on an object, the greater its acceleration will be. Inversely, the greater the mass of the object, the slower the acceleration will be.  However, when rewriting proportions as equations, you must introduce a constant of proportionality, and in this case of a direct proportion, if $a \propto \frac{F}{m}$ then when rewriting as an equation you will have $$a = k\cdot\frac{F}{m}$$  In order to get the standard formula $F = ma$ this constant must be $1$. However, how do we know that this is the case? How do we know that the constant isn't $2$ and the formula $F = \frac{1}{2}ma$, for instance? Polynomial divisibility is unchanged by coeff. field extension I would like to verify the validity of the following line of thought:  Let $K \subset E$ be a field extension. Let $K[x]$ be the polynomial ring over $x$ and denote $K(x)$ its field of quotients (the rational functions over $K$).  Now assume $f(x)=g(x)h(x)$ with $f(x),g(x) \in K[x]$ and $h(x) \in E[x]$ and all $f$, $g$, $h$ are different than zero. Then $\frac{f(x)}{g(x)} = h(x)$ in $E(x)$. So $h(x) \in K(x)$. But $h(x)$ is a polynomial, so $h(x) \in K[x]$.  Is there any other simpler argument than that?  Added:  Let me be more specific. Let $x^p - a \in K[x]$, with $p$ being prime and $char(K)=p$. Let $b$ be the unique root of $x^p - a$ in its splitting field $K(b)$. Then $x^p - a=(x-b)^p \in K(b)[x].$ Let $m_b(x) \in K[x]$ be the minimal polynomial of $b$ over $K$. Then $m_b(x)$ divides $(x-b)^p$ and so $m_b(x)=(x-b)^l$ and $l$ is the smallest positive integer for which $(x-b)^l \in K[x]$. Let $p = lq+r$ where $0 \ge &lt;l$. Then $x^p-a=(m_b(x))^q (x-b)^r$. Can i conclude that $(x-b)^r \in K[x]$ and so $r=0$ by the minimality of $l$?  Thanks. I forgot the passcode for my iPad restrictions. How can I disable them? Is there a difference between "==" and "is"? Divergence of $\frac{ \hat {\bf r}}{r^2} \equiv \frac{{\bf r}}{r^3}$, what is the 'paradox'? I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2} \equiv \frac{{\bf r}}{r^3}$, now from the book, Griffiths says:  Now what is the paradox, exactly? Ignoring any physical intuition behind this (point charge at the origin) how are we supposed to believe that the source of $\vec v$ is concentrated at the origin mathematically? Or are we forced to believe that because there was a contradiction with the divergence theorem? Also how would the situation differ if $\vec v$ was the same vector function but not for a point charge? Or is it impossible? Manage SSH Users with MySQL backend What is a single word for a person who, as a habit, exaggerates a lot when relating information?   So for example, they relate something that happened but exaggerate so much that they are including clear falsehood and they are well known for doing that. In Java, is there any way to use the JDK libraries to discover the private classes implemented within another class? Or do I need so use something like asm? Learning Resources on Parsers, Interpreters, and Compilers I've been wanting to play around with writing my own language for a while now (ostensibly for the learning experience) and as such need to be relatively grounded in the construction of Parsers, Interpreters, and Compilers. So:   Does anyone know of any good resources on constructing Parsers, Interpreters, and Compilers?   EDIT: I'm not looking for compiler-compilers/parser-compilers such as Lex, Yacc and Bison... I just try to visualize some points using GeoServer to publish them as WMS and bind this WMS to my Openlayers website using the GeoServer internal Heatmap process to visualize it. I don't want to use the Openlayers Heatmap function.   But there seem to be some problems, look here:    I'm using this Openlayers implementation to bind my WMS URL:    Changing the params to:  params: {'LAYERS': 'test:points','TILED': true,'STYLES': 'heatmap'},   And using this as SLD to define the Heatmap:    Any ideas why this happens? Identify this story about a quickly healing woman Years ago I read a short story about a woman trying to commit suicide. However, because she had a extremely high rate of healing, her wounds were never fatal. The story ends with her being in the morgue after her heart was taken out for transplantation. Before a new heart could grow she was incinerated. The person who received her heart received the quick healing as well.  Does anyone know this story? Can I deploy Juju on Eucalyptus? Please let me know if I can deploy juju on Eucalyptus, if yes please provide me the configuration details which i need to edit on environments.yaml file. I've been wondering, what is the general form for the integral of $\sin(\cos x)$? I tried integrating it myself and couldn't, tried with Wolfram Alpha and it couldn't either. If you think about it conceptually, it should have a general form as it's graph if just like sin and cos, which both have general forms. If it doesn't have a general form, I'd like to know why. Thanks! Propose a privilege to sit in the 500 reputation mark As , the retag privilege serves a lot more confusion and a lot less of its benefit due to the suggested edit system. It must be done away with. It will be done away with. ♪  In light of this decided course of action, we're going to need a new snack for the road between "Create Tags" at 300 reputation and "Established User" at 1000 reputation. We'd like your help in thinking about some ideas on what would be a nice privilege to sit at this level. Since we're... a bit dry on our end.  The primary guideline in deciding what kind of privilege to put here is acknowledging its position in the overall hierarchy of privileges. 500 reputation is an early-intermediate user, one who has started to really get the hang of the site and its function. It can be something that provides convenience in how they currently can act on the site, or it could be some new functionality that fits as an early ability (especially considering there's no new abilities until 2000 reputation's "Edit Everywhat" ability).  I look forward to hearing what creative ideas y'all can provide. If $R$ is a local ring and $M$ and $N$ are finitely generated $R$-modules such that $M\otimes N=0$ then how does it follow from Nakayama's lemma that either $M=0$ or $N=0$?    This is an exercise in Atiyah and Macdonald. The part I could not show in the hints is $({M{\otimes}_R N)}_{k}=0$ implies $M_{k}{\otimes }_{k} N_{k}=0$, where $k=R/\mathfrak m$ and $\mathfrak m$ is the maximal ideal of $R$. How to make cmd correctly display arabic script? Why were there so many spells cast in the movies without saying the words to the spell? From my memory of the last Harry Potter movie I saw, I've seen many wizards cast spells without saying the spell at all.  During the final battle in Hogwarts, many wizards just swung their wands and their enemies were knocked out. I am 100% sure about this!  The most remarkable spells were the ones that emit a green or red beam in the final battle of Harry Potter against Voldemort when they pushed their beams towards each other.  So, the question is, are they cheating? Because, unless there are wordless spells, they must say the words for a spell. $4$ letter words taken from the letters of CONCENTRATIONS How many words with or without meaning can be made from the letters of the word CONCENTRATIONS by taking $4$ letters at a time?  There are  $14$ letters total present in the word. $4$ letters can be picked in $14\choose 4$ ways. $4$ letters can be arranged in $4!$ ways. So ideally answer has to be ${14\choose 4} * 4!$. But I know this answer is wrong because some letters are repeating. How do I solve this then? I appreciate any help. I would like to know the purpose of nohup these days. I ask because I read this  Nohup is short for “No Hangups.” It’s not a command that you run by itself. Nohup is a supplemental command that tells the Linux system not to stop another command once it has started. That means it’ll keep running until it’s done, even if the user that started it logs out. The syntax for nohup is simple and looks something like this: nohup sh your-script.sh &amp; Notice the “&amp;” at the end of the command. That moves the command to the background, freeing up the terminal that you’re working in. Nohup works with just about any command that you run in the terminal. It can be run with custom scripts as well as standard system commands and command line utilities.  With using linux distributions such as SLES 11.4, or RHEL/CentOS 7.x, I can  remote log in to linux over the network via SSH run the simple program below, or any other, doing ./a.out &amp; log out of linux; type exit in the putty SSH terminal my sample program below, or any other including bash, csh, or tcsh shell scripts, run to completion just fine without the need for nohup typing exit in putty to close an SSH session, I would think that qualifies as a logout?  Is there any purpose or value with nouhup today?  Is it a kernel &gt;= 3.x thing? For however long I can remember (kernel &gt;= 2.6) I've never used nohup and have always just use &amp; with no problems. Can someone give me a practical scenario where nohup would be used? #include &lt;stdlib.h&gt; #include &lt;stdio.h&gt;  /*     sample C code, to print numbers to a file named zz.tmp     the numbers 0 to 29 over 30 seconds */  int main ( int argc, char *argv[] ) {    FILE *fp;    int i;     i = 0;    fp = fopen(&quot;zz.tmp&quot;, &quot;w&quot; );     while ( i &lt; 30 )    {       fprintf( fp, &quot;%d\n&quot;, i++ );       sleep( 1 );    }    fclose( fp );    return 0; }  mysleep.sh #!/bin/bash  sleep 1000  On Centos 7.7, optiplex pc login with keyboard &amp; mouse, my account is bash. I do nohup ./mysleep.sh and then control-z.  When typing jobs I see [1]+ Stopped nohup ./mysleep.sh A ps -ef | grep mysleep shows that process id existing, but if I close the terminal window via X in upper right corner, that process goes away so it seems nohup is not working? How to change sign text color in Minecraft? I have gone through every single website and video to try to make a sign with colored text, but nothing works. Can anyone help me to get a sign to say:  Place Block(dark blue and bold text)  I really want this for a map I am making and I need help.