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.,


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 change-of-variables 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 Holder-continuous 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 tangent-plane 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

Distribution Statement : APPROVED FOR PUBLIC RELEASE