Where can I learn the rules of representation decompositions?
Comprehensive book on group theory for physicists?
Breaking of diffeomorphism invariance after fixing a background metric Can not find the tag library descriptor for “http://java.sun.com/jsp/jstl/core” Raise bounty on question I have this question here:  I chose 500 then before accepting decided that was too much and halfed it, but now I just want the answer so I'd like to raise it to 500 but I can't find how to it. Also it's just such an irritating problem that I'd give all my rep away if I could to the clever person who has the answer. It would be nice to have a few minutes after creating the bounty to be able to raise it. But for now could a mod or something please raise it for me to 500. Connecting multiple screens to the 2016 MacBook Pro with Touch Bar I'm thinking about buying the new MacBook Pro with 4 USB-C ports.  I want to attach two screens, mouse and keyboard and ethernet to the MacBook Pro while using the fewest number of USB-C ports possible.  So what I need is an adaptor with:   two DP or HDMI ports (or one DP port with daisy chaining support) two or more USB ports an ethernet port   Best case would be a hub to which all devices are connected with a single connection to the MacBook Pro, including power supply. Worst case if attaching the MacBook Pro to the devices would require me to use all four of USB-C ports.  Given the answers up to far, I can tell that:   Daisy chaining might or might not work with the MacBook Pro (since it requires DP1.2 which is supported by the graphics chipset, but it's uncertain if it's supported by the MacBook Pro itself) I can attach the monitors with two cables as a last resort, leaving me with two ports for the remaining peripherals.   What I still don't know:   Would daisy chaining work with a hub or does it require the first monitor to be directly attached to the MacBook Pro? Does some kind of hub exist supporting attachment of all listed devices with a single upstream connection to the MacBook Pro? What is reflection, and why is it useful?  I'm particularly interested in Java, but I assume the principles are the same in any language. What should I do when Ubuntu freezes? Why can't I catch Pokemon in Pokemon Go anymore? Why is there an "electric" potential drop across the resistor? An electric potential difference is created when two charges are separated. In a capacitor, there is a clear accumulation of opposite charges on the two separated plates, therefore work has to be done in moving an unit charge from one plate to another, against the electric field.   But, , a potential difference is created in a resistor due to the heat produced by the collision and increased lattice vibrations. So there is an energy loss across the resistor, yes, but how does this energy loss due to heat create an electric potential difference. In other words, do electrons accumulate on one or both sides of the resistor? If not, why should we do electric work in moving from one end of the resistor to another. If the difference in energy is not due to electric work, then that's not electric potential, is it? I followed the official step-by-step "Visual Studio Code and Unity" guide, but it seems I messed up something, because Intellisense doesn't see any Unity related stuff.  Like the MonoBehaviour class and its members (like .transform), or the Unity callbacks, like Start or Update. Minecraft launcher could not connect to server? What do I do? I looked at a similar question to mine and there was an answer saying to make sure Java is allowed past the firewall. So I checked and it already is. I've tried uninstalling and installing both Minecraft and Java but nothing has changed.  says that all services are fine, so what's going on? I bought a 2nd account to use as an alternative in-game account and now I can't log in.  (I cleared the email and password boxes for obvious reasons in this screenshot: security purposes) One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would collapse with the nucleus.  Now Schrödinger describes the electron as a wave function. His theory is able to describe all atoms (in contrast to Bohr's model), but how is the radiation problem solved? I understand that the wave has not an exact position in the time anymore. But the electron still "moves", so it has an acceleration anyway (because of vibrations or so).   Why is in this theory the electron not radiating anymore? And if it is, why doesn't the atom collapse? Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.    The problem can be solved by putting every element from $\mathbb{Z}_{11}$ and checking if there is any root.  $0^2 + 0 + 4 = 4 \\ 1^2 + 1 + 4 = 6 \\ 2^2 + 2 + 4 = 10 \\ 3^2 + 3 + 4 = 5 \\ 4^2 + 4 + 4 = 2 \\ 5^2 + 5 + 4 = 1 \\ 6^2 + 6 + 4 = 2 \\ 7^2 + 7 + 4 = 5 \\ 8^2 + 8 + 4 = 10 \\ 9^2 + 9 + 4 = 6 \\ 10^2 + 10 + 4 = 4 $   But this process is very long one. I am seeking a short method by which I can solve such problem.   Now suppose that it is reducible, then the factors should be linear. So how can we solve the problem based on this kind of observation? Any help will be great. Thanks. What does outputting to /dev/null accomplish in bash scripts? Do I need to tame my twitchy F5 finger? I just got this error message for the first time (I was getting this as the response to any request on the SE network for about the last five minutes, until now):     We're sorry...      There are an unusual number of requests coming from this IP address.   To protect our users, we can't process any more requests from this IP   address right now. We'll restore access as quickly as possible, so try   again soon. If you believe you have reached this page in error,   contact us.   As far as I know, I was not spamming SE or participating in DOS attack, and I find it unlikely that any of my office coworkers who share my IP address were doing so either.  Granted, I was pressing F5 a lot. But I've always pressed F5 a lot on SE, and have never gotten this message before. So my question is: Is it possible to get this error message simply by refreshing too much or too often? Or is that message reserved for a truly massive number of requests that are unlikely to be caused by one person refreshing a lot? (In the former case, I can't explain why I've never gotten it before; in the latter case, I can't explain why I just got it now). Limit distribution of infinite sum of Bernoulli random variables How do I split a string by a multi-character delimiter in C#? Are getters and setters poor design? Contradictory advice seen I have bought return tickets from London to Lille Europe on Eurostar. The trains on my outward and inbound journeys both stop at Calais Frethun.  Will Eurostar let me get on in Calais on the inbound? What about getting off at Calais on the outbound leg? I suspect leaving the train early is easier than getting on the train 'late'. Mrs Reed safe combination Mrs Reed forgets the number combination to her safe. The combination has $4$ numbers each is a $1$ digit number. The $4$ digits add up to $10$ and there are no zeros. How many times does Mrs Reed have to try to open her safe?  My attempt: ${9 \choose 3} = 84$ but the answer is $80$. In what cases I should skip 's in possessive case?