Formalizing Quantum Field Theory
Rigor in quantum field theory
How do you prevent oatmeal from overflowing? Whenever I cook oatmeal (whether steel cut oats in a rice cooker or pan, or rolled oats in the microwave), it always overflows. How do you prevent this?   Do you just use a bigger container? Do you just take the pan off the heat or bowl off the microwave when it's about to overflow? I've also heard that if you put dried fruit or something like that along with the oatmeal while cooking, that helps prevent it from overflowing -- is this true? are two consecutive numbers relatively prime? Evaluating a PDF to find an unkown constant Evaluate the PDF to find K  $1 = \int_0^{\infty} \frac{k}{(1+x)^4}$  using u substitution I got:  $u=1+x$ and $du= dx$  $\int_0^{\infty} \frac{k}{u^4} \to \frac{k}{\frac{-1}{3} u^3}$   Since $u^4 du = \frac{u^{-4+1}}{-4+1}=$ $\frac{u^{-3}}{-3}$  which evaluating gives:  $1=\frac{k}{\frac{-1}{3(1+x)^3}} \vert_0^{\infty} \to \frac{-3k}{(1+x)^3} \vert_0^{\infty} = 0 -3k$   and $k= \frac{-1}{3}$  somehow though they came up with $\frac{-k}{3} \frac{1}{(1+x)^3}$ after integrating $\int_0^{\infty} \frac{k}{(1+x)^3}$   Was my approach correct to use substitution? Where does my work go wrong? My keyboard is typing by itself, could there be a ghost in it? The keyboard on my laptop seems to be typing by itself:   It sometimes types characters like 134, whether by itself or when I hit certain keys. Repeating characters may appear unexpectedly. The system volume may change by itself, or windows like the Print dialog or Web browser may appear.   This can happen without any input or as I type, and may occur more often when certain keys are pressed. Sometimes, the keyboard fails to respond altogether. This is happening regardless of the software involved.  Is there a ghost in my keyboard—is my keyboard broken?  A sample of text from the keyboard might look like this (normal QWERTY...ASDF...ZXC... sequence is expected):   QWERTYUIOPASDF)(G@*HKLZXCVBN QWERTYIOPASDFGL!#ZXCVB13 QWERTYUIOPASDFGHJKLZXCVB!#N qwertyu41iopasdf19g13h28j113k4113zxcvb4n qwerty4u1iopasdf0g7h1jklzxcvb13m qwert13uuuuuuuuuuuuuuuiopasdf87091134ghhhhhhhhhhhhhhhhhhhhhhh13jk13zxcvb14      This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. Disable the default app key (super+num) functionality on Ubuntu 17.10 and later I like to switch workspaces via Super+Number. But unfortunately the default behavior in Ubuntu for Super+Number is to select applications from the dock.   Is it possible to disable that functionality? I've tried overriding the keyboard shortcuts but it doesn't appear to be working. I'm trying to go into an irb session with specific environment variables from a file with this command:  $ env $(cat env.sh) irb   But when I try press Tab after I type env. to complete it, I get this following error:  $ env $(cat env.-bash: unexpected EOF while looking for matching `)' -bash: syntax error: unexpected end of file   Another interesting thing is that if I'm logged in as root, this error does not occur.   Here's the output of find ~ -uid 0:  $ find ~ -uid 0 /home/(redacted)/.rpmdb /home/(redacted)/.rpmdb/Group /home/(redacted)/.rpmdb/Conflictname /home/(redacted)/.rpmdb/Installtid /home/(redacted)/.rpmdb/Sha1header /home/(redacted)/.rpmdb/Providename /home/(redacted)/.rpmdb/__db.002 /home/(redacted)/.rpmdb/Requirename /home/(redacted)/.rpmdb/Sigmd5 /home/(redacted)/.rpmdb/__db.001 /home/(redacted)/.rpmdb/Obsoletename /home/(redacted)/.rpmdb/.dbenv.lock /home/(redacted)/.rpmdb/Name /home/(redacted)/.rpmdb/Basenames /home/(redacted)/.rpmdb/Triggername /home/(redacted)/.rpmdb/Packages /home/(redacted)/.rpmdb/Dirnames /home/(redacted)/.rpmdb/__db.003   Can anyone explain to me why this is happening and if so, how do I fix it in when I'm not a root user? I'm making all my diagrams in SVG format using Inkscape and then I export them to some other format (e.g. PDF, EPS or PNG). I wrote a short script that does this for me automatically, but I'd like to avoid this step, if possible --- sometimes the conversion from SVG converts the text labels into vectors, and that's annoying. Hence the question:  Is there a way to include SVG diagrams directly without conversion to an intermediate format?  Package suggestions, or instructions for specific LaTeX distribution are welcome. Tips and personal experience on which tools you have found to be working reliably would be also appreciated. 'innerText' works in IE, but not in Firefox How can I change an element's class with JavaScript? How can I change the class of an HTML element in response to an onclick or any other events using JavaScript? Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective Let $f: A \rightarrow B$ be a function. How can we show that for all subsets $S$ of $A$, $S \subseteq f^{-1}(f(S))$? I think this is a pretty simple problem but I'm new to this so I'm confused.  Also, how can we show that $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective? Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$ Need to find $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ Where $a_1\ge\dots\ge a_k\ge 0$  I thought about Cauchy Theorem on limit $\lim\limits_{n\to\infty}\dfrac{a_1+\dots+a_n}{n}=\lim a_n$ and something like what happen if all $a_i=0$ or $a_1=\dots=a_k$, but may be something I am thinking wrong?  Maybe it is too simple but I am not getting it; please help. How to generate a random snowflake Is it safe to have laptop turned on 24/7? I was asked this question during an interview for a trading position with a proprietary trading firm. I would very much like to know the answer to this question and the intuition behind it.  Amoeba Question:  A population of amoebas starts with 1. After 1 period that amoeba can divide into 1, 2, 3, or 0 (it can die) with equal probability. What is the probability that the entire population dies out eventually? Android: No icon for Notification I use a cookieless sub domain static.example.com to serve all images, js, and css files. This static sub domain has as its root directory the same directory as the parent http://example.com. So static.example.com/index.php will result in calling the same file as http://example.com/index.php  Google has taken up indexing static.example.com and I need to stop this.  I can't modify robots.txt since it would apply to both domains. Webmaster tools allows "temporary" removal of a link, but this needs to be permanent.  I registered this static domain through google as a separate site from example.com, but this doesn't seem to buy me anything since I can't see a way to block crawling without using robots.txt - which would block it from the parent domain.  Any other ideas?  UPDATE  Found this conversation on   I am looking into whether it's possible to insert a META tag dynamically into the header of every page called on the static domain using php  CLARIFICATION  I am not putting any content on static.domain.com. There are NO webpages on it that are called - it only serves images. I have it redirecting to the same root directory as the main site for ease of coding image links (not every image is fed from the same image path).  Google got a hold of the static web root address - probably because .htaccess redirects to index.php if a file is missing and then crawled it. Now Google is showing the static version of the same pages with search results. redirecting openshift rhcloud domain to custom domain for SEO purposes Openshift application url: example.rhcloud.com  Custom domain: example.com  I came across this  and added the redirection rule. However, I can not access example.rhcloud.com now. My custom domain is www.example.com.  To avoid duplicate content problems, I tried this redirection.   Here is my .htaccess file:  RewriteEngine on   # Uncomment the following lines to force HTTPS #RewriteCond %{HTTP:X-Forwarded-Proto} !https  #RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [R,L]   # WordPress Defaults RewriteBase / RewriteRule ^index\.php$ - [L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule . /index.php [L]  # Redirect Https traffic to Http RewriteEngine on  RewriteCond %{SERVER_PORT} ^443$ [OR] RewriteCond %{HTTPS} on RewriteRule  ^(.*)$ http://%{HTTP_HOST}%{REQUEST_URI} [R=301,L]   # Redirect non-www to www RewriteEngine on  RewriteCond %{HTTP_HOST} !^www\. [NC] RewriteRule ^(.*)$ http://www.%{HTTP_HOST}/$1 [R=301,L]    # Redirect openshift rhcloud domain to custom domain RewriteEngine on  RewriteCond %{HTTP_HOST} ^example.rhcloud.com$ RewriteRule (.*)$ http://www.example.com/$1 [R=301,L]   Why is example.com not redirecting to ww.example.com? How do I fix this?  Also, I see that since I have https to http redirection and non www to www redirection, my blog has been loading slow. How can I reduce it to lesser number of rules?  Edit:  In chrome:   In Firefox:     The page isn't redirecting properly, Firefox has detected that the server is redirecting the request for this address in a way that will never complete.     This problem can sometimes be caused by disabling or refusing to accept cookies. Stack Overflow duplicated layer bug Originally posted on Stack Overflow:   Requirements to reproduce:  Windows 7 x64  Firefox 71.0 x64  Steps to reproduce:   Go to the ask question section Write something to the title field Start scrolling similar questions Change the title field Start scrolling the similar questions again Are units in English singular or plural? It's not consistent to leave an edit pending for approval (thus not making available for everyone else and locking its state) after a user who has those privileges have given his endorsement.   You could say why don't I improve the edit, but that makes no sense for something that is correct and it would not follow the "keep it simple" policy.  Update:  This is the current time line:   Someone who doesn't know about formatting makes a question. It's not legible A user without edit privileges amends the formatting. The correction is not visible, still not legible. I see the question and the pending revision and then cast my approval. It doesn't take effect yet, still not legible. Even for me if I didn't take care of copying the question source because it disappears from my own revision page!   I might agree that one's approval is indicative of both revision's quality and editor's competence. But we should retain that the main objective is to ask and answer questions. So, I propose this model:   Someone who doesn't know about formatting makes a question. It's not legible A user without edit privileges amends the formatting. The correction is not visible, still not legible. A user with edit privileges cast his approval. Revision takes effect. Although it keeps the pending approval (the Edit (1) button). If a second user with edit privileges cast a rejection, it also takes effect as a rollback.