Type of friction on circular road
Direction of friction when a car turns
Friendly way to make previous large calculation results reusable in a new session Execute vs Read bit. How do directory permissions in Linux work? Why does the connection time out when connecting to a server? My friend had hosted a Minecraft server before and brought it back up today with my help. He and anyone in his LAN can connect. However we have had a few people try to connect, including me, and when we try to connect it gives the message:  Failed to connect to the server Connection timed out: connect  What does this exactly mean? How do we fix this? Why is polyploidy lethal for some organisms while for others is not? Random string that matches a regexp How do you reopen a closed question? How to find a point on a line at a given distance from a given point on the same line (given the equation of the line)? You are given a point P(x,y) on a line of equation ax + by + c = 0. I want another point, Q(a,b) on the same line which is at a distance d from P. There will be two points. I want to find both and know which side of P each one lies.  There are related questions in this forum, but I didn't get what I am exactly looking for. Sorry for beating around the bush, and thanks for any help... Please give me an elaborate explanation. Thanks once again!!! How many points in RSA, such that $m^e = m \bmod n$ For every RSA-cryptosystem, there exist some messages $m$, for which it holds that $m^e \equiv m \pmod n$ As to the question, how many such messages exist, this question has already been asked and answered here:  However, I do only understand the answer up to a certain point Suppose that $n$ is only 1 prime. Then it holds that the number of unconcealable messages is $\gcd(e-1, p-1)+1$ This is because in $m^e \equiv m \pmod  p$ , either $m = 0$ or $m \not= 0$. In the latter case $m$ can be expressed as $g^t$, where $g$ is a Generator in $\mathbb{Z_p}$ $g^{t*e} \equiv g^t \pmod p$ $g^{t(e-1) \bmod p -1 } \equiv g^{0 \bmod p -1} \pmod p$ $t(e-1) \equiv 0 \pmod {p-1} $ has exactly $\gcd(e-1, p-1)$  solutions, so the total number of unconcealable messages is, together with $m=0$ , $\gcd(e-1, p-1)+1$ When we now look at real RSA, which has two prime factors in its modulus, it holds that the number of unconcealable messages is $(\gcd(e-1, p-1)+1)\cdot(\gcd(e-1, q-1)+1)$ Why is that so? I suppose it has to do with CRT, but I just cant understand why. Isomorphism of centers of isomorphic groups Experimental Fractional scaling makes fonts dirty in Ubuntu 17.10 I updated to 17.10 from 17.04.   I activated the fractional scaling by running the following command.   gsettings set org.gnome.mutter experimental-features "['scale-monitor-framebuffer']"   Then, I changed 125% scale. The scale was changed, but the fonts and icons are so dirty.    The launcher icon and font in Google Chrome and other application except the system setting are dirty.  How can I resolve this problem?  For some reason, font in the system setting is not dirty... I'm working on a fairly big document that has a lot of graphs of functions- so far it has around 200, by the end it will have around 1500. I use pgfplots for each graphic, and the functions are pretty basic: exponential, rational, polynomial, and trigonometric.  Once I am happy with each graph, I don't necessarily need to see it every time I compile, and would like to minimize compilation time for future drafts. Naturally, the document is already chopped up into chapter files, but each chapter contains around 100 figures.  Having studied the pgfplots documentation, I haven't found a draft mode, but I'm interested in knowing if one could be created.    I'm envisaging something similar to the draft mode of the graphicx package, in which graphics are not included, and blank boxes are put in their place.  Some things I've considered:   the  documentclass; but with about 1500 figures, wouldn't this mean over-modulization?  tikzexternalize, but this still requires an initial 'monster' compilation to get the images externalized before the draft option could be invoked   Here's a MWE to play with  \documentclass{article} \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture}     \begin{axis}         \addplot {x^2};     \end{axis} \end{tikzpicture}  \end{document} I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this. It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth would be moving relative to the clock on the spaceship, and since time always dilates and never goes faster regardless of the direction of relative motion,  the clocks on earth should register less time than the clock on the spaceship.  Is this true? Whenever there is a fast-moving object such as a rocket do all clocks on earth really become slow?  If the rocket with the clock landed after moving at relativistic speed, would its clock and the earth's clock again show the same time since during its travel both appeared slow to each other?  Or is all this just an illusion, ie. the clocks just appear to be slow to each other but in actually run at normal speed, and neither is behind when the rocket actually lands? Prove $\gcd(a,b,c)=\gcd(\gcd(a,b),c)$ for $0\ne a,b,c\in \Bbb{Z}$. I tried solving it with sets but I sense there are some details I am missing. I would truly appreciate your reference. What could cause java.lang.reflect.InvocationTargetException? JavaScript editor within Eclipse Consider this equation :   $$\sqrt{\left( \frac{dy\cdot u\,dt}{L}\right)^2+(dy)^2}=v\,dt,$$  where $t$ varies from $0$ to $T$ , and $y$ varies from $0$ to $L$.  Now how to proceed ?   This equation arises out of following problem :   A cat sitting in a field suddenly sees a standing dog. To save its life, the cat runs away in a straight line with speed $u$. Without any delay, the dog starts with running with constant speed $v&gt;u$ to catch the cat. Initially, $v$ is perpendicular to $u$ and $L$ is the initial separation between the two. If the dog always changes its direction so that it is always heading directly at the cat, find the time the dog takes to catch the cat in terms of $v, u$ and $L$.  See my solution below :   Let initially dog be at $D$ and cat at $C$ and after time $dt$ they are at $D'$ and $C'$ respectively. Dog velocity is always pointing towards cat.  Let $DA = dy, \;AD' = dx$  Let $CC'=udt,\;DD' = vdt$ as interval is very small so $DD'$ can be taken straight line.  Also we have $\frac{DA}{DC}= \frac{AD'}{ CC'}$ using triangle property.  $\frac{dy}{L}= \frac{dx}{udt}\\ dx = \frac{dy.udt}{L}$  $\sqrt{(dx)^2 + (dy)^2} = DD' = vdt \\ \sqrt{(\frac{dy.udt}{L})^2 + (dy)^2} = vdt $  Here $t$ varies from $0-T$, and $y$ varies from $0-L$. Now how to proceed? Can we make the "expanded user card" privilege universal? Pursuant to discussion on the , several have asked how far they'll need to search to determine if a user has expressed their preferred pronouns. This requested feature could create an easy solution for that concern.  On sites where I've reached the  privilege level, users can hover over my picture to see a snippet of my profile:    This is where I've included my preferred pronouns, and where I see many others including them as well.  By making this feature universal, users could quickly and easily check for preferred pronouns without needing to navigate to another page. How to divide aleph numbers Forcing a SimpleXML Object to a string, regardless of context Let's say I have some XML like this  &lt;channel&gt;   &lt;item&gt;     &lt;title&gt;This is title 1&lt;/title&gt;   &lt;/item&gt; &lt;/channel&gt;   The code below does what I want in that it outputs the title as a string  $xml = simplexml_load_string($xmlstring); echo $xml-&gt;channel-&gt;item-&gt;title;   Here's my problem.  The code below doesn't treat the title as a string in that context so I end up with a SimpleXML object in the array instead of a string.  $foo = array( $xml-&gt;channel-&gt;item-&gt;title );   I've been working around it like this  $foo = array( sprintf("%s",$xml-&gt;channel-&gt;item-&gt;title) );   but that seems ugly.  What's the best way to force a SimpleXML object to a string, regardless of context?