Why not use modulus for variance?
Why square the difference instead of taking the absolute value in standard deviation?
I'm trying to simulate a rope (that later might get pulled on the ends*) that interacts with some obstacles. So far I created a plane as the floor and a cube as an obstacle, and activated "collision" in the physics menu for both of them.   *(In the end the goal is simulating a .)  For modelling the rope, I tried using a long cylinder with enough subdivisions, and activate "cloth" in the physics menu. This resulted in the cylinder collapsing like a sleeve of a sweater, but I would like the cross section to remain roughly circular. Is there a way to directly avoid this?   Another approach I tried now was just using a a line made up of vertices and edges (with the idea of later adding modifiers to give it a thickness), but this just fell through all the collision objects as it has no faces. Is there good way to do this? To avoid printing single letters at varying sizes and measuring how far away I can see it from a distance is there a formula for determining what size font for a particular read distance? Is it better to take the midpoint between the ascender line and x-height or to go purely off of the x-height (since going purely off the ascender line could leave lowercase letters difficult to read)? How does vertical height play into this? Would I need to then figure the hypotenuse distance instead of a straight distance?  For example if I'm shooting for a 20' read distance but the sign is to be placed about 30' up should I use a distance of  35' instead of 20'?  I'm shooting for a 20' read distance for the headline and then possibly a 10' read distance for additional content depending on how it all fits on the active area. How do I debug permissions? How do I debug permissions in Drupal 7?  I use core reporting, error logs, devel module error logs, backtrace and node access permission block but sometimes it is not enough. What else should I check to find out why certain fields, views or blocks are not showing to a user?  I also found there is a  for reporting on permissions called  but it is not available for Drupal 7.  I am using various permission related third-party modules:   - devel node access 7.x-1.x-dev   - fast permissions administration 7.x-2.0  - organic groups access control 7.x-1.x   - profile2 group access 7.x-1.x-dev   - ur-node access 7.x-1.x-dev Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ . I'm looking for a simple proof that up to isomorphism every group of order 2p (p prime) is either $\mathbb{Z}_{2p}$ or $D_{p}$ (The Dihedral group of order 2p).  I should note that by simple I mean short and elegant and not necessarily elementary. So feel free to use tools like Sylow Theorems, Cauchy Theorem and similar stuff.  Thanks a lot! Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite? Why is log-of-sum-of-exponentials $f(x)=\log\left(\sum_{i=1}^n e^ {x_i}\right)$ a convex function for $x \in\mathbb R^n$? How to prove $f(x)=\log\left(\displaystyle\sum_{i=1}^n e^{x_i}\right)$ is a convex function?  EDIT1: for above function $f(x)$, following inequalities hold:  $$\max\{x_1,x_2,\ldots,x_n\}\leqslant f(x)\leqslant\max\{x_1,x_2,\ldots,x_n\}+\log n$$  and I have tried proving its convexity via definition of a convex function with above inequalities, but that didn't work.  EDIT2: I have posted my answers below. How can I customize the Ubuntu installer? WIth Vimeo Plus account, how to hide/remove the "play" button in the middle of an embedded video? nginx open reverse proxy? Somehow, and I'm not sure how, we have configured an nginx reverse proxy that is acting as an open proxy.  The log files tells us the matching requests are going against the following conf file:  map $http_upgrade $connection_upgrade {         default upgrade;         ''      close; }  access_log      /var/log/nginx/access.p.log; error_log       /var/log/nginx/error.p.log;  proxy_next_upstream     error timeout invalid_header http_500 http_502 http_503 http_504; proxy_buffers           8 32k; proxy_buffer_size       64k; proxy_http_version      1.1; proxy_set_header        Host            $host; proxy_set_header        X-Real-IP       $remote_addr; proxy_set_header        X-Forwarded-For $proxy_add_x_forwarded_for; proxy_redirect          off; proxy_set_header        Upgrade         $http_upgrade; proxy_set_header        Connection      $connection_upgrade;  server {         listen          80;         server_name     ~first.*\.second\.com;          location / {                 resolver                172.16.1.1 172.16.1.2;                 proxy_pass              http://$host;                 proxy_read_timeout      7200s;         } }  server {         listen          443;         server_name     ~first.*\.second\.com;         ssl             on;          location / {                 resolver                172.16.1.1 172.16.1.2;                 proxy_pass              https://$host;                 proxy_read_timeout      7200s;         } }   The top-level conf file looks like this:  user nginx; worker_processes 8; pid /var/run/nginx.pid;  events {         worker_connections 4096;         # multi_accept on; }  http {      ##     # Basic Settings     ##      sendfile on;     tcp_nopush on;     tcp_nodelay on;     keepalive_timeout 65;     types_hash_max_size 2048;     # server_tokens off;      # server_names_hash_bucket_size 64;     # server_name_in_redirect off;      include /etc/nginx/mime.types;     default_type application/octet-stream;      ##     # Logging Settings     ##      access_log /var/log/nginx/access.log;     error_log /var/log/nginx/error.log;      ##     # Gzip Settings     ##      gzip on;     gzip_disable "msie6";      # gzip_vary on;     # gzip_proxied any;     # gzip_comp_level 6;     # gzip_buffers 16 8k;     # gzip_http_version 1.1;     # gzip_types text/plain text/css application/json application/x-javascript text/xml application/xml application/xml+rss text/javascript;      ##     # nginx-naxsi config     ##     # Uncomment it if you installed nginx-naxsi     ##      #include /etc/nginx/naxsi_core.rules;      ##     # nginx-passenger config     ##     # Uncomment it if you installed nginx-passenger     ##      #passenger_root /usr;     #passenger_ruby /usr/bin/ruby;      ##      include /etc/nginx/conf.d/*.conf;     #include /etc/nginx/sites-enabled/*;   }  what here is causing this? How to move 100 files from a folder containing thousands? I have a directory with thousands of files. How can I move 100 of the files (any files will do) to another location. My character has a bite attack from his race.  What happens if he gains another bite attack from class abilities or spells?  Does the damage increase?  Can he make more than one attack?  Or is it simply that only the better version applies?  I would prefer answers from a Pathfinder context but 3.5e is also acceptable. Is there a way to access an iteration-counter in Java's for-each loop? Is there a way in Java's for-each loop  for(String s : stringArray) {   doSomethingWith(s); }   to find out how often the loop has already been processed?  Aside from using the old and well-known for(int i=0; i &lt; boundary; i++) - loop, is the construct  int i = 0; for(String s : stringArray) {   doSomethingWith(s);   i++; }   the only way to have such a counter available in a for-each loop? Volumes of n-balls: what is so special about n=5? The volume of an $n$-dimensional ball of radius $1$ is given by the classical formula $$V_n=\frac{\pi^{n/2}}{\Gamma(n/2+1)}.$$  For small values of $n$, we have $$V_1=2\qquad$$ $$V_2\approx 3.14$$ $$V_3\approx 4.18$$ $$V_4\approx 4.93$$ $$V_5\approx 5.26$$  $$V_6\approx 5.16$$ $$V_7\approx 4.72$$ It is not difficult to prove that $V_n$ assumes its maximal value when $n=5$.   Question. Is there any non-analytic (i.e. geometric, probabilistic, combinatorial...) demonstration of this fact? What is so special about $n=5$? I also have a similar question concerning the $n$-dimensional volume $S_n$ ("surface area") of a unit $n$-sphere. Why is the maximum of $S_n$ attained at $n=7$ from a geometric point of view?   note: the question has also been  for those curious to other answers. uint color;  bool parsedhex = uint.TryParse(TextBox1.Text, out color);  //where Text is of the form 0xFF0000 if(parsedhex)    //...   doesn't work. What am i doing wrong? Word for the opposite of "hypochondriasis" What are character special and block special files in a unix system? I want to prove that the distance between incentre and orthocentre is $$\sqrt{2r^2-4R^2\cos A\cos B\cos C} $$here $r$ is inradius and $R$ is circumradius. I considered $\triangle API$ ($P$ is orthocentre and $I$ is incentre). I could find  $AP=2R\cos A$, $AI=4R\sin\frac{B}{2}\sin\frac{C}{2} $ and $\angle PAI=\angle \frac{B-C}{2}$. So applying cosine rule I got $$PI^2=4R^2+16R^2\sin^2\frac{B}{2}\sin^2\frac{C}{2} -16R^2\cos A\sin\frac{B}{2}\sin\frac{C}{2}\Bigg(\cos\frac{B}{2}\cos\frac{C}{2}+\sin\frac{B}{2}\sin\frac{C}{2}\Bigg)$$ How to proceed form here ? "This site is all about getting answers. It's not a discussion forum. There's no chit-chat." The  has this text:     This site is all about getting answers. It's not a discussion forum. There's no chit-chat.   It's probably an oversight and copied from the regular site tours. Can it be reworded/removed?  Right above that text, there's this:      So each community has a meta to discuss site-specific issues, and Meta Stack Exchange is for conversations about problems and ideas that affect the whole network.   Don't they contradict eachother? Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$? Let $A, B$ be similar $n \times n$ matrices over (say) $\mathbb{R}.$  Is it the case that $A+cI$ is similar to $B+cI$?    Here is an argument (which seems too good to be true...)  Since $A, B$ are similar, they have the same Jordan form. So we can write $PAP^{-1}=QBQ^{-1}=J$ for $P, Q$ invertible matrices.   Hence we have $P(A+cI)P^{-1}=PAP^{-1}+cI= J+cI.$ Similarly, we find $Q(B+cI)Q^{-1}=J+cI.$  Hence $A+cI$ and $B+cI$ are both similar to $J+cI$ and hence similar to each other.   Is this correct? Are there critical hits for spells? According to PHB p. 194 you always score a critical hit on any attack roll.  Does this rule also apply to magical attacks, e.g. the  spell?