Grouping sums in Excel
Calculating the average of variably sized blocks of numbers within a column?
Can Hydrogen Fusion via CNO Cycle Occur in First Generation Stars CNO cycle requires the presence of carbon, nitrogen and oxygen to undergo hydrogen fusion. Does this mean that for first generation stars, no matter how big they are, can't undergo hydrogen fusion by CNO cycle because there is no carbon, nitrogen and oxygen present?   I can't seem to find any website which mentions this. All they say is if a star is large enough, it will undergo hydrogen fusion via CNO cycle, they don't specifically mention it having to be a second generation star. So, through typing several commands I've found that there's not only ls, but l and la too. There doesn't appear to be any man entries on Ubuntu 12.14. They all appear to do similar things with minor differences:  $ ls app        config     CONTRIBUTING.md  doc       Gemfile       Guardfile  LICENSE  MAINTENANCE.md  Procfile  Rakefile   script  tmp     VERSION CHANGELOG  config.ru  db               features  Gemfile.lock  lib        log      PROCESS.md      public    README.md  spec    vendor $ la app      CHANGELOG  config.ru        db   features  Gemfile       .git        Guardfile  LICENSE  MAINTENANCE.md  Procfile  Rakefile   .rspec  .secret     spec  .travis.yml  VERSION .bundle  config     CONTRIBUTING.md  doc  .foreman  Gemfile.lock  .gitignore  lib        log      PROCESS.md      public    README.md  script  .simplecov  tmp   vendor $ l app/       config/    CONTRIBUTING.md  doc/       Gemfile       Guardfile  LICENSE  MAINTENANCE.md  Procfile  Rakefile   script/  tmp/     VERSION CHANGELOG  config.ru  db/              features/  Gemfile.lock  lib/       log/     PROCESS.md      public/   README.md  spec/    vendor/   Just as a bit of trivia, are there more of these and what do they do? Is here any place to find this out? Unfortunately, google searching these commands gets ignored because they're so short. A coin with heads probability $p$ is flipped $n$ times. A "run" is a maximal sequence of consecutive flips that are all the same. For example, the sequence HTHHHTTH with $n=8$ has five runs, namely H, T, HHH, TT,H. Show that the expected number of runs is  $$1+2(n-1)p(1-p).$$  I have tried to use some generating function on this but calculus got pretty messy and didn't work. What cd/dvd burning software should I use? I have tried countless cd/dvd burning software on ubuntu 12.04 and none of them work for me,  any ideas guys?   I've tried tovidgui, bombono dvd,and mestelix, they are all so very confusing is there any program like dvdflick that is just straight to the point? \hfill \break does not work Does "no larger than" imply shapability? Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics? My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect? How does this wiring work? I have a Trane XV90 and XL 14i. The wiring looks a little strange as in the picture bellow.                    _____________                   |           |   BK W2  W1   R  G  Y  B/C  YLO O     |___||   |__|  ||   |          |   |     ||   |_____>|----------|         |   |     ||_________>|other wire|         |   |     |           ------------         V   V     V     ---------------     |thermostat   |     ---------------  The R and G are jumpered together and the G wire is connected on the board  but is actually not connecting to the thermostat on the other end. So people told me that means the furnace fan is always on! (In my diagram above, I switched the location of Y and B/C to make diagram easier to draw. You can refer to the photo added below to see the details) My questions are the following  is the jumper between O and Y doing anything? I don't think I have heat pump I need to install Honeywell wifi thermostat and I am thinking of doing either one of the following:   remove jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  leave jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  remove jumper between R and G, connect G on control board to thermostat G, and finally have the spare wire to connect B/C and then thermostat C  leave jumper between R and G, does not connect G to thermostat,  and just use a spare wire to connect B/C on board to thermostat C   Can anyone comment on those plans? Thanks a lot! ${\rm Aut}(G)$ is cyclic $\implies G$ is abelian I would appreciate if you could please express your opinion about my proof. I'm not yet very good with automorphisms, so I'm trying to make sure my proofs are OK. Proof: Since ${\rm Aut}(G)$ is cyclic, ${\rm Aut}(G)$ is abelian. Thus for any elements $\phi, \psi \in{\rm Aut}(G)$ and some elements $g_i \in G$, $\phi\psi(g_1g_2)=\phi\psi(g_1)\phi\psi(g_2)=g_3g_4=\phi\psi(g_2)\phi\psi(g_1)=\phi\psi(g_2g_1)=g_4g_3$. Hence, $g_3g_4=g_4g_3\implies G$ is abelian. The proof seems to be quite straightforward, but I'd rather ask for advice. How to model the bottle threads? The picture show the threads I want to create on the highlighted object. Problem is I don't know how and tutorials really haven't helped much as most of them seem to be about creating a bolt. So I was hoping I could get some help on how to do this efficiently.While keeping the top flat like a water bottle. The picture shows the threads I'm after. Often more than one person contributes to the community coming up with the final accepted answer to a question. However, it is only possible to accept a single answer. Restricting to one final answer does make sense for the sake of referencing that answer later, but in many cases that answer is the product of the input from several individuals. I would like to be able to decide how much of a bounty goes to different users, or some other mechanism to recognize the contribution of multiple users. Of course I could always upvote their previous answers, but this is really incorrect if their previous answers aren't the complete, final answer I've accepted.  What think you metaSOrs? What websites or other resources do users of Blender have available to them to report bugs or problems with the program?  I would like to get this issue cleared in Q&amp;A format so that we can link new users with bug-report-style questions to this post. GUI to CLI command translator Is there any application (or sequence of commands) for this function: seeing the result of the actions, while using a GUI interface, being automatically translated into a Terminal (or similar CLI environment) on the same machine.  I saw this in action long years ago in VBA for Applications (for example the Macros in Excel). I wonder if there is same function in Linux. Breakthrough at the Large Hadron Collider -Leptoquarks skepticism? question about the limit $\lim_{h\to0}\frac{\arcsin(x+h)-\arcsin(x)}{h}$ This image is what's supposed to look like in Edit Mode/Object Mode(although I still can make these screenshots even after the update by pressing F12 which is rendering) but the following is what my donut looks like now in Blender.  It shows no shadows and colors. The only thing I did is updating blender to 2.81 from 2.80. And I don't know what but something seems off with blender. Sometimes I can't click any objects so I just pressed tab and then now it's all clickable. Seems like I was in edit mode, but to me, it looked exactly like object mode. I don't know what is wrong with it. How do I make my colors show up again? TexShop will not compile without trashing aux files after every error I have a couple of LaTeX files with the same problem. If I produce an error, fix it, and then try to compile a pdf, I get the following error.  )Runaway argument? {{ ! File ended while scanning use of \@newl@ablel. &lt;inserted text&gt;                 \par l.90 \begin{document}   If I then click on the console or trash my .aux file, it compiles fine. Any thoughts on what is going on and how to prevent this annoying extra step? Could gravity accelerate light? In what order should you do linear regression diagnostics? In linear regression analysis, we analyze outliers, investigate multicollinearity, test heteroscedasticty.   The question is:  Is there any order to apply these? I mean, do we have to analyze outliers very firstly, and then examine multicollinearity? Or reverse?    Is there any rule of thumb about this? With the enthusiastic question of "Who wants ice-cream?", what is the more correct response?         (Not) I.   (Not) me.      Neither response is a sentence. The first response of "(not) I" sounds stuffy, like it should be followed with an indignant sniff. The second sounds like American idiom and acceptable for casual speech.    What do you say?