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| Euler Quote | Reply | This message was updated on 10/31/2006 11:54:01 PM by Euler | Anomalies, please read! posted on: 10/31/2006 11:50:37 PM Hey, I don't know if you remember me since I haven't been here for a while, but I have a question that I thought you would be able to answer. I am looking at a proof of the volume formula for the unit ball in n-dimensions for some UG research I am doing, and I completely understand everything except one point. The author begins by describing points in R^(n+1) as (x,y) where x belongs to R^n and y belongs to R. And, of course, by definition, the unit ball in R^(n+1) is defined as B={x1,x2,...,x(n+1) | ||xi|| <= 1}. Then the author defines a subset of R^(n+1) as D={(x,y) | |x|^2<y}. Do you know where he came up with this subset, and if it has a relation to the def. of the unit ball (as I suspect)?? Any help would be greatly appreciated, so thanks ahead of time! |
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Anomalies
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Anomalies, please read!
replied on: 11/1/2006 6:54:31 AM What I suggest you do is work out what these thing are for R^2. B is what is known as the closed ball centred at p = 0, of radius 1. You have picked the metric ||x-p||. That I understand. D I think is the open disk. But that would read something like D = {(x,y) \in R^n+1 | |x|^2 + |y|^2 < R} |
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Euler
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Anomalies, please read!
replied on: 11/5/2006 1:52:27 PM Alright, I think I see what you are saying. Because the author is using points (x,y) where y is the radius, and the metric being considered is ||x-p||, which in this case is ||x-0|| or just ||x||, then the open ball would be defined by the set B={(x,y) | |x-0|<y}, and so a subset of B could be defined as, D={(x,y) | |x|^2 <y}, since all of these points are contained within B. Alright thanks!! |
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Euler
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Anomalies, please read!
replied on: 11/12/2006 12:24:46 AM Hey, I have another question for you. If I have a set S, the power set of S, and a subset of S, denoted by G, then I define sigma(G)=the set of all sigma-fields F, such that G is contained in F. How can I show that sigma(G) is contained in P(S), if G is countable? |
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Anomalies
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Anomalies, please read!
replied on: 11/12/2006 12:41:45 PM I don't know, I know very little about formal set theory. |
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jehovah0121
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Anomalies, please read!
replied on: 11/12/2006 8:40:04 PM My gosh! I've forgotten all about so called sigma field, otherwise I might be able to offer some help. |
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Euler
Quote | Reply | This message was updated on 11/16/2006 9:00:42 PM by Euler |
Anomalies, please read!
replied on: 11/16/2006 8:55:02 PM Hey anomalies, have you done any work with 2-Hilbert spaces? |
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Anomalies
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Anomalies, please read!
replied on: 11/17/2006 7:17:03 AM I know a little about Hilbet spaces. |
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Euler
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Anomalies, please read!
replied on: 11/17/2006 10:27:29 AM Yeah, but what about 2-Hilbert spaces, which are basically Hilbert spaces consisting of hilbert spaces. The only reason I ask is because I was at a math-physics seminar the other day, which discussed the application of these 2-hilbert spaces, and some category theory, to quantum gravity. |
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Anomalies
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Anomalies, please read!
replied on: 11/18/2006 2:51:19 AM I don't know what 2-Hilbert spaces are. It sounds like they may be like Fock spaces which are like a collection of Hilbert spaces. |
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Euler
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Anomalies, please read!
replied on: 11/18/2006 8:59:10 PM Yeah, I looked into Fock spaces, and it does look pretty similiar- so do you know much about these spaces? |
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Anomalies
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Anomalies, please read!
replied on: 11/19/2006 4:43:56 AM Fock spaces are a bit like a "pile" of Hilbert spaces. They are infact Hilbert spaces themselves and so the mathematics litriture tends not to talk about them. |
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Euler
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Anomalies, please read!
replied on: 11/22/2006 2:57:24 PM Yeah- that's what he was talking about at the seminar. Basically using a hilbert space, whose "vector components" were made up of Hilbert spaces. And this was done in order to categorize the spaces, thereby making the morphisms between them better, so that you could work them out and then decategorize them, to get a new relation back. And then all of that was applied to quantum gravity. It was really interesting, and I was just wondering if you had seen anything like this- since you work with mathematical physics yourself. |
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Anomalies
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Anomalies, please read!
replied on: 11/23/2006 2:11:21 AM I have not looked at Hilbert spaces and Fock spaces for a while. Even then it was just the basic stuff from topology and vector spaces. |
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Euler
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Anomalies, please read!
replied on: 11/26/2006 9:28:30 PM So what kind of spaces, if any, would dyou be interested in when looking at supersymmetry? |
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Euler
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Anomalies, please read!
replied on: 11/26/2006 9:32:21 PM Also, what do you know about the radon transform? |
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