Let $G$ be a compact Lie group assumed to be a subgroup of $U(n)$. Also, let $T$ be a maximal torus of G. Then there exists a basis $\{v_1, \ldots ,v_d\}$ of $\mathfrak{g}$ for which
$${\rm Ad}_{g_0^r}(v_{2k-1}) = \cos(r\theta_k)v_{2k-1} + \sin(r\theta_k)v_{2k}$$
$${\rm Ad}_{g_0^r}(v_{2k}) = -\s...
@robjohn Yeah, that worked very well, thanks! :) I'm visiting main every other day, so I see those messages, but I won't be on chat that often. I just thought I might say hi, while I have a few minutes to spare.
@robjohn I'm trying to get one or two preprints finished in the next two months (I still haven't decided if I'm going to make one or two parts out of the text). It's some stuff in abstract harmonic analysis, amenability, representation theory and a little homology theory. Nothing too deep, as usual.
@Gigili I missed you too... Unfortunately I won't be able to stay for too long and I probably won't be back more than once or twice till July at least.
@robjohn As I said, I shouldn't stay here for too long today, so I'm about to go again... Thanks again for the ping (and think about solving it without straightedge or with Bézout) :) See you soon!
@Jordan in a manner of speaking $\mathrm{d}y$ is the infinitesimal change in $y$ that happens when the infinitesimal change $\mathrm{d}x$ is made to $x$.
@Jordan The actual definition is as a limit of these changes as $\mathrm{d}x\to0$
there are too many weird rules in differential equations, you can't just solve the problem you have to know all these tiny rules that are never explained properly
Hi @robjohn, I posted a question and it was answered, but I am still slightly confused, partially because a client is telling me one thing and the answer is telling me another.
@Jordan Do you need to compute the hydrostatic force on the rectangle by a Riemann Sum or a Riemann integral is acceptable? math.stackexchange.com/q/157567/752
yeah, basically I posted the question already and it was answered, but the problem I have is that based on the answer, I come up with a difference answer, but a client is telling me it should be something else.
to give a small background in case your curious on what this is about: online travel agencies add fees to hotel prices that customers aren't supposed to pay, so the hotel has to adjust the value, for example removing a 10% and then a 20% VAT tax
@Gigili what did you mean by "You're quite right about. It's about "devide" and just mentioned the name at the end. I'm not sure how it's going to help the reader! (honestly I see no relevance between evenly and exactly) "
if the client insists it is 189, how do you refute something like this?
I can look at it another way, since they client wants to get back to 189 and is doing it by removing 10% and then 20%, the original value had to be the 189 plus the 10% and 20%
if you add 10% to 189 and then a compound 20%, what should you get?
I will still give a better background, I believe when a customer books a hotel room through an online travel agency, they are charged 189, but the OTA adds a 10% fee and 20% compound fee to the the value that they hotel will pay, so the hotel needs to adjust the value for the customer by removing the 10% and 20% values.
@xaisoft Dividing by 1.2 is the same as saying the value in the numerator will be 120% of the resulting fraction. It is not the same as removing 20% of a number (which would be equivalent to multiplying by 80% as you did).
@xaisoft However, this background indicates that if the original price is P, and then a 10% fee is added (giving a 1.10 P price), and then 20% is compounded on top of that, the result is 1.20 x 1.10 x P. To 'undo' this to find the original price as if no fees had been added, you have to divide by 1.1 and by 1.2.
@xaisoft I'm trying to understand the chronology here. Are you saying that the hotel agency is going to pay the 10% compouned by 20% fee, the original price is 189, and what the price would be after adding the fees has not yet been calculated, so that's what you're trying to calculate?
@anon - I think so. I will try to explain better. A customer booked a one night hotel room for 189. The 189 is marked up 10% and another 20% compound which the customer is not responsible for, so it has to to removed. The hotel is saying that the value after the markup's is 252 and they need to get back to 189 via (252 * 0.9) / 1.2
That's incorrect, that reverses the process of a 20% fee compounded on top of a 1/0.9 fee (bleh, edits). However what confuses me is why anyone needs to "get back" at all: If both the initial price and the marked up value are already known and agreed upon, what's there left to do?
The issue is that multiplying by 0.9 is not the same as dividing by 1.1
@anon - it is weird but that part just has to do with what the customer sees on an invoice, if they see 252 after they booked for 189, they will freak out
But then why do you have to do a calculation to go back to 189 if you already know the price before markup was 189, and so does the customer? Seems rather pointless.
I agree, but I am not 100% sure if they know the initial 189, it hasn't been made clear
i think one of the reasons is because the hotel property management system automatically adds these fees in, so for example, let's say a fee of 100 comes in and they need to add 10%, the PMS will add 10% on top of 110 which is incorrect
"You do realize there's a reason they're called open right? =) One needs a very vast amount of machinery before tackling any of those. It is great you're interested, but I think it is more down-to-earth to start with the basics. ;) "
"I'm not referring to the open problems that are well-known like for example Goldbach's Conjecture. I'm referring to unexplored areas suitable for a high school student interested in obtaining new results. "
"I see. I don't know about that. Open problems in high school level wouldn't be of relevance, methinks. Doesn't any of what I wrote call your attention? What do you know about number theory? " (Me)
I really despise word problems, they are false-creativity that is forced onto you. You can't actually get creative in the answer you just have to follow an incredibly rigid method from the example problem and previous problems
@AnunayKulshrestha well just take a look at this, this, and if you have a library look at this and see if anything is at about your level of understanding.
the problem with open problems in number theory is that most of the results that are easy to obtain have been obtained.
and while most of the problems are easy to state they aren't easy to prove.
