So apparently I was “randomly selected to participate in an exclusive pilot project to evaluate a range of tools designed to help increase your article’s usage and citations”. *EXCLUSIVE* pilot project. Looks interesting. I’ll bite. At first pass, it looks interesting because you get to add other stuff to your article (like a lay-person’s explanation and other neat stuff like videos). The addition of other interesting stuff might be useful if this weren’t one of the most theoretical articles I’ve ever written. 😛
Ok, and then you can promote your article. To twitter. And facebook. REALLY? FACEBOOK?!?!?! Facebook is for bragging about your vacation, not for posting your scientific work. Anyways, they sent me an auto-generated email that I can use to spam my 90000 email contacts (because they were dying to know about Hankel integrals). In the spirit of not having all my friends, family, colleagues and students add me to theirauto-spam folder, I’ll just post it here instead.
Subject line: Are you using Fourier or Hankel transforms with the wave equation? This article can help.
My latest article has just been published, and I hoped you might be interested enough to take a look! Here’s a link:
Multidimensional wave field signal theory: Mathematical foundations
Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green’s functions in different coordinate systems.