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This book covers the latest problems of modern mathematical methods
for three-dimensional problems of diffraction by arbitrary
conducting screens. This comprehensive study provides an
introduction to methods of constructing generalized solutions,
elements of potential theory, and other underlying mathematical
tools. The problem settings, which turn out to be extremely
effective, differ significantly from the known approaches and are
based on the original concept of vector spaces 'produced' by
Maxwell equations. The formalism of pseudodifferential operators
enables to prove uniqueness theorems and the Fredholm property for
all problems studied. Readers will gain essential insight into the
state-of-the-art technique of investigating three-dimensional
problems for closed and unclosed screens based on systems of
pseudodifferential equations. A detailed treatment of the
properties of their kernels, in particular degenerated, is
included. Special attention is given to the study of smoothness of
generalized solutions and properties of traces.
This book describes new, highly effective, rigorous analysis
methods for electromagnetic wave problems. Examples of their
application to the mathematical modelling of micros trip lines,
corrugated flexible waveguides, horn antennas, complex-shaped
cavity resonators and periodic structures are considered. Special
attention is paid to energy dissipation effects. Various physical
models and methods of analysis of dissipation are described and
approximate formulas and computer-based calculation results for
dissipation characteristics are given and compared with
experimental data. Ways of decreasing dissipation in waveguides and
resonators are discussed. The book will be of interest to
physicists and engineers working on the theory and design of
microwave and millimetre-wave components and devices. Designers in
microwave engineering will find here all the information they need
for choosing the correct waveguide (resonator) for a stipulated
dissipation characteristic. The numerical algorithms and formulas
can be directly applied to CAD systems. The book is also relevant
for students of electromagnetism and microwave circuits.
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