Recent content by Hjensen

Perhaps I should clarify a few things. By ω I mean the least infinite ordinal, which is identified with \aleph_0. The idea I have of the two notions being different relies on intuition only. If anyone has a concrete example, you would make my day. Especially if you could include a reference to...

I'm a bit confused on the subject of transfinite induction. I've read that it is equivalent to usual induction on the ordinal number ω (presumably a proof of this can be found in a standard book on the subject - any suggestions?) Does anyone have an example of a case in which this isn't true...

Hello, I had a lecture in an elementary Calculus course today, and the professor used a method for classifying critical points which I can't see in my book (Calculus, a complete course, by Adams). Basically he had the function f(x,y)=x^2+2y^2-4x+4y. He found a critical point at (2,-1) -...

Thanks a lot - I get it now. Meanwhile, I've spotted another thing in my notes: It says that the 0.012Å also corresponds to 0.0268cm^{-1}. How can this be? This just looks like there should be a factor for the purpose of division? Is this the case, or is it something a bit more sophisticated...

I'm sure this is a rather simple calculation, but I just can't seem to get it right. During a recent lecture a professor gave an example concerning hyperfine-structure splitting. This is the essence of it: We're considering a Lithium-7 isotope, which exhibits a fine-structure splitting (due...

I have a question I need to resolve before my exam on thursday. It relates to the following result: Let N be a normal subgroup of G, and let K be any subgroup of G containing N. Then K/N is a subgroup of G/N. Furthermore, K/N is normal in G/N if and only if K is normal in G. The first part...

Thanks a lot guys. I'll look into that.

I am taking a course on Hilbert spaces and we're using Walter Rudins "Real and complex analysis", which I am generally very happy about. However, I don't think the section about orthonormal sets (page 82-87) is that nice. In particular, I would like to see a different approach to the theorem...

I did have a look at Wikipedia before writing here. However, all it states is that BV functions have uses in mechanics, physics and chemical kinetics. I would have liked something a bit more specific. As for the book, it goes through the theory of BV - which I am already familiar with - but I...

I am reading about a branch of mathematics which does not allow separable spaces. The author of the text gives the space of functions of bounded variation as an example of a non-separable space, which is fine - except for the fact that he goes on to claim that "this space is relevant to both...

Edit: Rubbish.

I'm taking a course on Hilbert spaces, but this falls more into the category of linear algebra. If we consider V, the space of polynomials with complex coefficients from \mathbb{R} to \mathbb{C}. Then, for f,g\in V, define (f,g)=\int_{0}^{\infty}f(x)\bar{g(x)}e^{-x}dx I'm asked to find the...

Thank you for your help, I'll get on it later today.

I'm on a course which is currently introducing me to the concept of Hilbert spaces and the professor in charge was giving examples of such spaces. He ended by considering V, the space of polynomials with complex coefficients from \mathbb{R} to \mathbb{C}. He then, for f,g\in V, defined...

That's what I thought. I thank you for all your patience and insight. I'm just a chemist trying to make it in the world of physics, so I salute people like you. :)