"Since" or "from"?
Proper usage of "since" and "from" with regard to duration of time
"Its" and "it's" - how to remember? What is a good mnemonic rule that an English learner can use to remember the difference between its (possessive adjective: a team has started its lunch) and it's (verb: it's raining)? Is trace of regular representation in Lie group a delta function? My major is physics. I need to use some tools in group theory, but I am really  confused by the trace in compact infinite groups. The following is my question:  In discrete group theory, the irreducible representation of identity group element $e$ is always an identity matrix. So the trace of $e$ under  regular representation is the order of the group : $\chi(e) = |G|$. I hope to get  similar result for Lie group. For example, SO(2) has infinite number of irreducible representations, $D^{(m)}$, where $m=0,\pm 1, \pm 2,\cdots $. All of them are 1-dimensional $D^{(m)} = e^{im\phi}$. Here $\phi$ is the rotation angle. For element $R(\phi)$ in SO(2), the trace in $m$th irreducible representation should be  $\chi(R(\phi))=e^{im\phi}$, if we sum all these traces up, we get the trace in regular representation. So what is the trace of $e$ in the regular representation ? It seems to be infinite. What are the benefits of modeling in one piece, or as separate parts? Is there any benefit of creating model in one piece or I can create separate pieces and just overlap them to create a visually joint part.  For example, the below image were made from two parts 1. Blade 2. Spinner  Is there any benefit to model them (e.g. extrude from the spinner) or it is actually ok to have them separated since visually I can achieve the same effect (See picture 2) I would like to insert the below mathematical symbol, it looks like a big Delta but different. Is there command to obtain a similar shape? How to install Oracle 18c (Enterprise Edition) on Ubuntu 18.04? This question is unanswered since Oracle 18c has been released. Except Ubuntu Linux platform, most of the other Linux platform supports Oracle 18c installation. I, myself, tested this on CentOS 7 and oracle 18c got installed without any glitch!  It is unfortunate that Oracle Corporation has not documented the installation procedure particularly for Ubuntu Linux platform, nevertheless one good thing is that the image file db_home.zip is a generic one, installable across all Linux platforms.    So how can I install Oracle 18c (Enterprise Edition) on Ubuntu 18.04? Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$ Can't plot with gnuplot on my Mac jQuery .on function for future elements, as .live is deprecated What are the most commonly used and basic Apache htaccess redirects? I want to construct a complex power series with the radius of convergence $R=1$ that diverges in:  1) $k$ points on the circle $\{|z|=1\}$.  2) countable number of points on the circle  I have already crafted series that converges on the whole circle and diverges on the whole circle.  Can anybody help with the problem?  Update: I have googled a series $\sum{\frac{z^{kn}}{kn}}$ that is an answer for 1). Though I still need help for the countable case. Why can two (or more) electric field lines never cross? The the title is self explanatory, I guess.  Why can two (or more) electric  never cross? What is time dilation really? Please will someone explain what time dilation really is and how it occurs? There are lots of questions and answers going into how to calculate time dilation, but none that give an intuitive feel for how it happens. The book says:     Concentration. Some spells require you to maintain concentration in order to keep   their magic active. If you lose concentration, such a spell ends.   So what happens if, for example, you are already concentrating on a spell, and cast Witch Bolt without concentrating. Would you get the initial arc of blue energy, or would it not even go off?  I am asking if you can cast a spell that says concentration without concentrating for an immediate effect. This would be useful to avoid interrupting your existing concentration. In essence, if you are concentrating on thing A (doesn't have to be a spell since other things need concentration), can you cast a concentration spell getting an immediate effect without losing concentration on thing A?  Since the definition of concentration is to keep the spell active (meaning it is already active) I would think that you would get the initial effect (if it had one) without the need to concentrate on it. How to determine $\int x^2 e^{-x^2}\mathrm dx$? I was wondering how to determine $$\int x^2 e^{-x^2}\mathrm dx?$$ I tried to move the exponential into the integrator, and apply integration by parts, but that will make the integrand more complicated. Thank you! In Windows 7, I know you can do Windows + Left to put a window in the left half of the screen.  Is there a feature that will do top and bottom? We have a few cases of chat accounts remaining without valid parent account:  and  for example. What should mods do when that happens:  delete the chat account notify the SE team so they can reattach or clean it up leave it as is: it's a normal situation Why aren't particles constantly "measured" by the whole universe? Let's say we are doing the double slit experiment with electrons. We get an interference pattern, and if we put detectors at slits, then we get two piles pattern because we measure electrons' positions when going through slits. But an electron interacts with other particles in a lot of different ways, e.g. electric field, gravity. Seems like the whole universe is receiving information about the electron's position. Why is it not the case and the electron goes through slits "unmeasured"?  Bonus question: in real experiments do we face the problem of not "shielding" particles from "measurement" good enough and thus getting a mix of both patterns on the screen? How do you get JavaScript/jQuery Intellisense Working in Visual Studio 2008? I thought jQuery Intellisense was supposed to be improved with SP1. I even downloaded an annotated version of jQuery 1.2.6, but intellisense will not work in a separate jscript file. I have the jQuery library referenced first on my web page in the &lt;head> tag. Am I doing anything wrong? How do the review limits work? I got the brand new Custodian badge today for reviewing posts. Inspired by that, I reviewed some more suggested edits. Now I ran into a limit:     You have no more suggested edit votes today; come back in x hours.   How is that limit calculated? I made 61 reviews today which seems to be some calculated limit.  I searched for an answer on meta but found nothing helpful. Cartoon in a world with magic stones wielded by four children which combine to become stronger, and can summon creatures Can you please help me find this animated show? There is a four member team with two boys and two girls. The boys can summon, with their stones, a rock golem (black wearing summoner) and a robot (orange wearing summoner). The two girls can summon something like a dragonfly (green wearing summoner, little girl) and the blue girl, I don't remember what she can summon.  I don't know where the animated show comes from.  By throwing the stone, they activate the stone's power. Each stone has different characters on it. When you don't match them correctly, you get a rebound effect.