Search results for "Residue theorem"

Regularity of solutions of cauchy problems with smooth cauchy data

1988

Full-wave analysis of industrial microwave applicators: TM modes

2004

In this paper, full-wave analysis of the TE modes of an industrial cylindrical microwave applicator is presented. The dispersion characteristics and fields configurations are shown. These results are obtained by a numerical simulation based on the residue theory. The authors have obtained particular modes called loop modes, which have a complex propagation constant that describes a loop within the complex plane. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 46–50, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20203

Principal Values of Cauchy Integrals, Rectifiable Measures and Sets

1991

The extensive studies started by A. P. Calderon in the sixties and continued by many authors up today have revealed that the Cauchy integrals $$ {C_{\Gamma }}f(z) = \int_{\Gamma } {\frac{{f\left( \zeta \right)d\zeta }}{{\zeta - z}}} $$ behave very well on sufficiently regular, not necessarily smooth, curves F, see [CCFJR], [D] and [MT].

The General Stokes’s Theorem

2012

Let ω be a differential form of degree k - 1 and class C 1 in a neighborhood of a compact regular k-surface with boundary M of class C 2. The general Stokes’s theorem gives a relationship between the integral of ω over the boundary of M and the integral of the exterior differential dω over M. It can be viewed as a generalization of Green’s theorem to higher dimensions, and it plays a role not unlike that of the fundamental theorem of calculus in an elementary course of analysis. Particular cases of the general Stokes’s theorem that are of great importance are the divergence theorem, which relates a triple integral with a surface integral and what we know as the classical Stokes’s theorem, w…