
Accession Number : ADA141748
Title : On the Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains.
Descriptive Note : Final technical rept.,
Corporate Author : DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST
Personal Author(s) : Dallas,A G
PDF Url : ADA141748
Report Date : Apr 1984
Pagination or Media Count : 190
Abstract : Various standard results concerning manifolds in euclidean spaces, coordinate systems, and functions defined on such manifolds are developed and organized. For example, conditions are identified under which the image of a manifold is again a manifold. A development of Lebesgue measure and integration on a manifold is presented. Included is a changeofvariables formula for the transformation of an integral over a manifold to integration over a second manifold suitably related to the first. Classes of regular domains are defined. Special attention is given to those regular domains possessing a Holdercontinuous exterior unit normal field, or Lyapunov domains. Slightly modifying the standard presentations, geometric and analytic properties of the boundary of a Lyapunov domain are derived, including the identification of certain canonical tangentplane coordinate systems. (Author)
Descriptors : *Vector spaces, *Electromagnetic scattering, *Electromagnetic radiation, Maxwells equations, Moving targets, Coordinates, Time dependence, Lyapunov functions, Transformations(Mathematics), Vacuum
Subject Categories : Theoretical Mathematics
Electricity and Magnetism
Optics
Distribution Statement : APPROVED FOR PUBLIC RELEASE