摘要:

A proposal is made that electromagnetic fields should be understood to be linear functionals operating on advanced fields, in order to justify their jump conditions. Our advanced field is literally a test function, as in the theory of generalized functions, and is interpreted to give a measure of contribution of a unit strength of electromagnetic field to the meter reading.

ISSN:0041-1450    

DOI:10.1080/00411458108204342

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

Case's approach to the solution of the one-dimensional equation of transport is mathematically reformulated by expanding the phase or scattering function for the given problem to be solved as a spectral Integral over the complete set of eigenfunctions for a previously solved transport problem. The fundamental equation of our approach is a singular integral equation (involving a spectral Integral over the spectrum of the solved problem) whose kernel depends upon the difference between the phase function of the problem to be solved and that of the solved problem. Several examples are given which illustrate the use of the new formalism. Finally, the new formalism is used to give a clear statement of the inverse problem.

ISSN:0041-1450    

DOI:10.1080/00411458108204343

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

The spectral representation of the linear transport problem is applied to two additional examples. In the first example, we obtain the dispersion relations, normalization coefficients and eigenfunctions for any order N of scattering by using the eigenfunctions for isotropic scattering as the basis. In the second we obtain the dispersion relations, normalization coefficients and eigenfunctions for N + 1 order scattering by using the eigenfunctions for Nth order scattering as the basis. New identities relating quantities referring to different orders of scattering are obtained as well as identities involving spectral integrals and the polynomials hl(ν). Independent calculations are carried out to verify relations obtained using the spectral representation.

ISSN:0041-1450    

DOI:10.1080/00411458108204344

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor