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If you like electrodynamic problems with solutions and their connections to current research, please visit www.problemsinelectrodynamics.com


Jan
2
comment Eigenfunctions of the Helmholtz equation in Toroidal geometry
Dear Shuhao, thanks for your answer, although my thanks is quite late. Thanks for your argumentation and calculation. Most valuable, though, seems to be the reference to Boyer et al., Nagoya Math. J. 60 (1976) you provided and therein, P. Morse and H. Feshbach, "Methods of Theoretical Physics", a must-have.
Apr
28
comment A Projection Problem in Functional Analysis - Uniqueness of a Solution
I wanted to know if a certain approach I was using in some paper (arxiv.org/abs/1107.4934) was unique :)
Apr
28
comment A Projection Problem in Functional Analysis - Uniqueness of a Solution
Thank you oenamen for your answer!
Dec
7
comment Stochastic interpretation of Einstein Equations
Dear @Jon, thank you very much for your answer! Since I think the generalization to a four-dimensional Pseudo-Riemannian manifold is challenging, I appreciate your insightful two dimensional approach very much. Greets
May
2
comment Is there a definitive guide to speaking mathematics?
Very nice question @Michael and very nice idea for a program! If you can come up with something, this will greatly help a lot of people! Greets
Jan
21
comment A Projection Problem in Functional Analysis - Uniqueness of a Solution
@JonasT: Thank you for your thoughts! By the dual I mean it in the sense as in the Dirac notation, en.wikipedia.org/wiki/Bra-ket_notation . What you meantion in your second comment is exactly the problem. If $\alpha$ and $\beta$ are just constants (as I might not have pointed out very direct), taking the Fourier transform and dividing, they will be functions... This is one thing I am puzzled with :) Greets
Jan
20
comment Fourier Transform of an unsteady function
Thank you for the further clarification.
Jan
19
comment Fourier Transform of an unsteady function
@loenbloy: Thank you for your fast response. I think the three given ones make a pretty decent picture of the situation, all from a slightly different perspective :) Greets
Jan
19
comment Fourier Transform of an unsteady function
Thank you for this answer and the additional information. I think there was a brain overflow in understanding where the $\delta$ comes from :) Greets
Jan
19
comment Fourier Transform of an unsteady function
Thank you again for the clarification! I now know that there is a difference in these two approaches :) Greets
Jan
19
comment Fourier Transform of an unsteady function
Thank you for your answer. I must admit that I never had any course on measure theory so I have to speculate that I really want to calculate the first version. Greets
Jan
19
comment Mathematical difference between white and black notes in a piano
Please, Rudi, it should be Helmhol t z. :)
Jan
18
comment Effect of curvature of spacetime on intrinsic geometric properties (under general relativity)
@Steven: Thank you for your further thoughts. First of all I have to state that the choice of a timeslice would be the gauge I was referring to - hence angles will depend on this choice. Second of all the author is referring to lines of sight - I would interprete these as light geodesics. So, to maybe find a compromise here: One could define such angles more generally but they would depend on the gauge. Is this along your lines of thought? Greets
Jan
18
comment Effect of curvature of spacetime on intrinsic geometric properties (under general relativity)
@Steven: Thank you for your thoughts - I am not sure if I get them correctly, though. Assuming you are in a dynamic spacetime you can go from A to B to C on some geodesic. How do you go to A from C? It wont be possible with respect to causality. So you will have to define an equivalence class of points A - but in a dynamical spacetime this construction will be due to a certain gauge - your angle will depend on this as well. I wanted to leave out these things for simplicity. Greets
Jan
18
comment Writing an Integral in Different Form?
@Willie Wong: Thanks you, I wrote small $n$'s if I remember correctly. Greets
Jan
18
comment Effect of curvature of spacetime on intrinsic geometric properties (under general relativity)
@Ronaldo: Now looking at the comments I think I have just done what you had in mind :) Greets
Jan
14
comment Eigenfunctions of the Helmholtz equation in Toroidal geometry
@Hans Lundmark: Thank you for the hint. I just found the book in our library and will have a look. Is this a classic like the Courant-Hilbert?
Jan
14
comment Eigenfunctions of the Helmholtz equation in Toroidal geometry
@Willie Wong: Thank you for the correction. Indeed, I mean it in this way. It seems to as if it is just a historic issue of applied mathematics that some "special" functions (trigonometric, Bessel etc) paved their way into standard textbooks. Nevertheless, do you know if there are implicit definitions of solutions available like the elliptic ones? If I remember correctly, the Greens function of the Helmholtz equation is normally constructed from eigenfunctions of the Laplace... Isn't an application of this procedure applicable here somehow?
Jan
14
comment Eigenfunctions of the Helmholtz equation in Toroidal geometry
@Hans: Thanks for pointing out to the error, I will correct it. And also thank you for the link. It really is a pitty that there is no reference given. Greets
Jan
13
comment Stochastic interpretation of Einstein Equations
@Willie Wong: Thank you again for your nice comments! You have a lot of knowledge about the structure of general relativity and the underlying geometrical and functional concepts and I enjoy reading your thoughts. So, for this question, the situations seems to be arbitrarily complicated - even though there might exist a corresponding stochastic process we simply don't know it yet :) You may consider posting your comments as answer, I would be glad to accept. Sincerely