Resource recommendations on Renormalization Group Flow
Suggested reading for renormalization (not only in QFT)
Crossfading Video AND Audio with ffmpeg This Super User answer  has got me so far, but now that I have tried many solutions and seen every SO link out there, it's time to ask you all for help.  I am trying to crossfade 2 videos that are 10 seconds each in ts format with audio and video at the same time.   The steps are:   Add complex filter black screen Fade out video 1 after 9 seconds, with 1 second fade duration Fade in video 2 at 9 seconds, with 1 second fade duration Trim black filter output to 19 seconds   This works fine for just video alone, but when I attempt to add audio, I can't get past this error message:     Output pad "default" with type audio of the filter instance "Parsed_asetpts_4" of asetpts not connected to any destination   It appears I'm not connecting the audio output properly. I think I need to alter the [over] lines to include audio. But how do I do this?  `ffmpeg -i vid1.ts -i vid2.ts -f lavfi -i color=black -filter_complex \ "[0:v]format=pix_fmts=yuva420p,\ fade=t=out:st=9:d=1:alpha=1,setpts=PTS-STARTPTS[v0];\ [0:a]\ afade=t=out:st=9:d=1,asetpts=PTS-STARTPTS[a0];\ [1:v]format=pix_fmts=yuva420p,\ fade=t=in:st=0:d=1:alpha=1,setpts=PTS-STARTPTS+9/TB[v1];\ [1:a]\ afade=t=in:st=0:d=1,asetpts=PTS-STARTPTS+9/TB[a1];\ [a0][a1]amix=inputs=2;\  [2:v]scale=720x406,trim=duration=19[over];\ [over][v0]overlay[over1];\ [over1][v1]overlay=format=yuv420[outv]" -vcodec libx264 -y -map [outv] final.ts` Most useful additions in KOMA-Script? (Background: I'm a beginner who will mostly use LaTeX for university articles and reports, but no math. Also, as I reside in Canada, the German typography conventions, which I understand KOMA-Script supports better than LaTeX, are less relevant).  I've read that the KOMA-Script package has a lot of improvements for the default document classes. Yet the 's length, about 250 pages, is somewhat daunting. I plan to read the chapters I'm interested in anyway but it'd be useful to have some pointers about low hanging fruits. I searched the site and  answers say KOMA-Script adds improvements but do not delve into details.  I'll ask this as a community wiki topic and, since the audience of this site is international, feel free to mention German typography if KOMA-Script is better there. Attempting to create a tag wiki when a user has hit the suggested edit limit should alert the user that no more edits can be suggested at this time I ran into an issue on Gaming.SE where I attempted to create a tag wiki and wiki excerpt for a tag which did not have one already while I already have the maximum of five suggested edits in the queue.  Navigating to the tag page for the  provides a link to  for this tag. This link redirects to the  for this tag, without telling me that I can't submit an edit because I've reached the maximum number of suggested edits. Instead of silently redirecting, the page should alert me that I can't suggest any more edits until my suggestions are reviewed. How do I quickly switch between weapons and spells? When  I see him quickly change his weapons and spells during combat. When he later goes inside his items, you can see a second smaller arrow next to the weapon that you can quickly change to in combat. How can I set such an alternative so that I can quickly switch weapon?  The screen doesn't seem to intuitively explain what key I need to use to do that... Merge files based on matching of first column I have two files: File1  ARS-BFGL-BAC-10975 0.9303 688423261 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11025 0.9092 688423261 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11044 0.9626 688423261 2 01/04/2015 0.9983763305 ARS-BFGL-BAC-11193 0.9544 688423261 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-10975 0.9303 688423263 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11025 0.9092 688423263 1 01/04/2015 0.9983763305 ARS-BFGL-BAC-11044 0.9626 688423263 2 01/04/2015 0.9983763305 ARS-BFGL-BAC-11193 0.9544 688423263 1 01/04/2015 0.9983763305   File2:  ARS-BFGL-BAC-10975 10 21225382 ARS-BFGL-BAC-11025 10 84516867 ARS-BFGL-BAC-11193 1 29303546   Desired output  ARS-BFGL-BAC-10975 0.9303 688423261 1 01/04/2015 0.9983763305 10 21225382 ARS-BFGL-BAC-11025 0.9092 688423261 1 01/04/2015 0.9983763305 10 84516867 ARS-BFGL-BAC-11193 0.9544 688423261 1 01/04/2015 0.9983763305 1 29303546 ARS-BFGL-BAC-10975 0.9303 688423263 1 01/04/2015 0.9983763305 10 21225382 ARS-BFGL-BAC-11025 0.9092 688423263 1 01/04/2015 0.9983763305 10 84516867 ARS-BFGL-BAC-11193 0.9544 688423263 1 01/04/2015 0.9983763305 1 29303546   So file 1 has many more rows than file 2. I only want to keep rows in the output that are in file 2 based on column1.   I have tried join but I cant get it to work right-it will tell me my files are not sorted  join -j 1 -o 1.1,1.2,1.3,1.4,1.5,1.6,2.2,2.3 &lt;(sort -k1 file1) &lt;(sort -k1 file2)   Preferably I would prefer an awk command. File 1 will be very large. I have tried   awk 'FNR==NR{a[$1]=$2 FS $3;next}{ print $0, a[$1]}' file2 file1 &gt; output   Any help would be much appreciated. Thanks  Sorry I cant comment below but just to clarify file not all rows in column1 in file 1 will be in file2.  The awk command  awk 'FNR==NR{a[$1]=$2 FS $3;next} $1 in a {print $0, a[$1]}'    will only keep the amount of rows there is in file 2. But ideally what I want is were for expample ARS-BFGL-10975 is repeated twice (realistically way more) to appear twice in my output.  Thanks for the help so far Convert all text from uppercase to lowercase and vice versa? Prove that if 51 positive integers between 1 and 100 are chosen, then one of them must divide another. Given $51$ integers $a_1, a_2, \ldots, a_{51}$ satisfying $1 \leq a_i \leq 100$. Prove that there exist $i$ and $j$ such that $a_i \mid a_j$.   I'm a little unsure how to approach this problem. Thanks for any help. Let $\mathbb{S} = \{ (X,Y,Z) \in \mathbb{R}^3 :X^2 + Y^2+Z^2=1\}$ denote the Riemann sphere. The following problem is taken from Gamelin "Complex Analysis" chapter one:     What is the image of the spherical cap $ C := \{(X,Y,Z) \in \mathbb{S} : A \leq X \leq 1\}$, where $A$ is some fixed real number between $-1$ and $1$, under the stereographic projection $ \pi(X,Y,Z) = \frac{X+iY}{1-Z}$?   Here is my work so far:  ( The case $A=1$ is trivial, so assume $A &lt;1$)  We want to find $\pi(C) = \{z \in \mathbb{C} \mid \exists(X,Y,Z) \in C: \pi(X,Y,Z) = z \}= \{z \in \mathbb{C} \mid \pi^{-1}(z) \in C\}$, where the last equality holds by $\pi$ being a bijection. Write $z=x+iy$.  Here, $ \pi^{-1}(z) \in C\iff A\leq \frac{2x}{1+x^2+y^2} \leq 1 \iff (\star) :A \leq \frac{2x}{1+x^2+y^2}$, since the inequality $2x \leq 1+x^2+y^2$ holds for all $x,y \in \mathbb{R}$.  $A=0$: $( \star)$ reduces to $ 0 \leq x$, so in this case the image is $\{z \in \mathbb{C} \mid \Re(z) \geq 0 \}$.   $A &gt;0$: Since $A \neq 0$ in $(\star)$ we have,  $ \frac{2x}{1+x^2+y^2} \geq A \iff Ax^2-2x+Ay^2+A \leq 0 \iff (x-\frac{1}{A})^2 +y^2 \leq \frac{1}{A^2}-1$. Thus the image is the interior and boundary of the circle centered at $\frac{1}{A}$ with radius $\sqrt{\frac{1}{A^2}-1}$. Note $\frac{1}{A^2}-1 \geq 0$ as $A \in (0,1)$.  $A &lt;0$ : By symmetry and the above, here the image is $ \mathbb{C} / \{ $ interior and boundary of circle centered at  $  \frac{1}{A}$ with radius $\sqrt {\frac{1}{A^2}-1} \}$.  Is my working correct? Many Thanks! How do i install drush for a drupal site which is on shared hosting? Commenting out multiple lines of code, specified by line numbers, using vi or vim I have learned from  that it is possible to use vi/vim to comment out a specified range of line numbers.  For example, suppose I have the following bash script:  #!/bin/bash  This is my very very great script   Now suppose that I want to comment out line numbers 6 through 8 (which contain the words very, very, and great) using the # comment character.  In vi/vim, I can simply type :6,8s/^/# to obtain the following:  #!/bin/bash  This is my #very #very #great script   which comments out lines 6 through 8.  My question is, is it possible to type a similar one liner that will remove the # comment character from lines 6 through 8 (but not any other commented lines in the file)?  Having said this, I realize that there is some debate about whether I am actually using vi or vim.  In practice, I open a file script.sh with the command vi script.sh.  Also, when I type the command which vi, I obtain /usr/bin/vi.  Nevertheless, when I simply type vi and press Enter, I obtain this:  ~                              VIM - Vi IMproved ~ ~                               version 7.2.330 ~                           by Bram Moolenaar et al. ~                 Vim is open source and freely distributable ~ ~                           Sponsor Vim development! ~                type  :help sponsor&lt;Enter&gt;    for information ~ ~                type  :q&lt;Enter&gt;               to exit ~                type  :help&lt;Enter&gt;  or  &lt;F1&gt;  for on-line help ~                type  :help version7&lt;Enter&gt;   for version info   which seems to suggest that I'm actually using vim.  I am accessing a remote Ubuntu Linux cluster using SSH from my PC.  I am not using a Ubuntu Linux GUI. parallel thermostat I have a venter room heater in a cabin. It uses a milivo;t thermostat. I am hooking it up to a wifi thermostat using a relay and 24 volt power supply. My concern is that if the power goes off that the thermostat will not power the unit on. I currenty have a digital thermostat that controls the unit and works great. can I wire the current thermostat to the wifi in parallel so if power goes off it will still allow the heater to turn on. If I can how do I wire it? iOS Calendar Access Permission Dialog, force it to appear? I'm making a mini game (bomb squad) and the armor needs to be enchanted. I know that armor can be enchanted through command blocks and that is what I intend to do. I am wondering if it is possible to enchant armor twice in one command block or should I need multiple command blocks as I have done in the past? How did Newton discover his second law? I've always assumed/been told that Newton's 2nd law is an empirical law — it must be discovered by experiment. If this is the case, what experiments did Newton do to discover this? Is it related to his studies of the motion of the moon and earth? Was he able to analyze this data to see that the masses were inversely related to the acceleration, if we assume that the force the moon on the earth is equal to the force the earth exerts on the moon?   According to , the  reads:     Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.   Translated as:      Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.   My question is how did Newton come to this conclusion? I get that he knew from  the idea of inertia, but this doesn't instantly tell us that the change in momentum must be proportional to the net force. Did Newton just assume this, or was there some experiment he performed to tell him this? Reference - What does this regex mean? How can I get help on terminal commands? I often see things like     read man xyz   For more information read xyz's man page.   see info xyz    so I wonder:   How can I get help on terminal commands generally? What exactly are these man and info pages?   How can I find and view them? Retrieving minimum width that contains specified fraction of all values I'd like to find the min/max boundaries of a sliding window of minimum size that contains a certain fraction of the total number of elements in an array or collection of numbers.   Example: taking integers to make it easier to explain, say the proportion of elements that we're looking for is 50% on this array:  [1,1,2,3,3,3,3,3,3,4,5,6,7,8,9,10]  The mystery function would return something like ( 2, 4 ), meaning that the minimum value is 2 and the max value is 4 (let's assume it's inclusive and note that these are VALUES, not indices). That little window contains 8 of the 16 values and it's only 2 units wide, the narrowest such window that contains half the number of values.  Note: the quartiles are [1,1,2,3], [3,3,3,3], [3,4,5,6], [7,8,9,10] so they are NOT what I'm looking for.  I can code it...may take some time to get it nice. Hopefully somebody has run across it before. Does it have a name?  Is there an existing method that somebody knows about?  I am interested in Python implementations.   UPDATE:  Thanks to Glen_b who gave the names 'short-half' and 'shortest interval' I was able to come up with this: Circuitikz symbols in TikZ circuit library Some time ago, I asked about . wh1t3 wrote: "However, as far as I know there is nothing the circuitikz package does that the TikZ circuit library can't."  So if it is true that the tikz library is more powerful, how do I get all the symbols described in the  using the TikZ circuit library?  Especially I am missing the symbols for ammeters and voltmeters. Good abstract algebra books for self study Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, however, the self written syllabus was not self study friendly (good syllabus overall though).  The course was split up into 3 parts, group theory, ring theory and field theory. As a computer science major we only had to study the first 2.  Now that I passed the exam for this course I want to study the field theory part ( which covers Galois theory, etc).  So, now I want to ask whether any of you know any good books on abstract algebra, which lift off at basic ring theory and continue to more advanced ring theory and to finite fields, Galois theory, ...  Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition).  Thanks in advance! Where should looking-for-resources questions go? Questions like looking for css templates, blog templates, icons ... In general, resources (let's leave the licensing terms aside for now) which you might need when building a project of your own. Where should those questions go?  They're definitely not on-topic on Stack', SuperUser maybe although I doubt it. Webapps? Hmm, probably not.  Is there a place where they would be on-topic on the SE network?