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Phase Optimization Problems. Applications in Wave Field Theory

  • ID: 2180289
  • Book
  • March 2010
  • 319 Pages
  • John Wiley and Sons Ltd
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This is the only book available in English language to consider inverse and optimization problems in which phase field distributions are used as optimizing functions. The mathematical technique used relates to nonlinear integral equations, with numerical methods developed and applied to concrete problems. Written by a team of outstanding and renowned experts in the field, this monograph will appeal to all those dealing with the investigation, design, and optimization of electromagnetic and acoustic radiating and transmitting devices and systems, while also being of interest to mathematicians working on the theory of nonlinear integral equations.
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1 Introduction

2 Formulation of physical problems

2.1 Forming fields of given structure

2.2 Antenna synthesis problems

2.3 Phase optimization problems in waveguides and open resonators

3 Mathematical formulation of the problems

3.1 Variational problems with no amplitude–phase restrictions on sought functions

3.2 Variational problems with amplitude–phase restrictions on sought functions

3.3 Homogeneous optimization problems

4 Analytical solutions

4.1 A general class of Hammerstein nonlinear integral equations with free phase

4.2 Particular case: one–dimensional Fourier transform

4.3 Particular case: discrete Fourier transform

4.4 Particular case: Hankel transform

4.5 Generalized nonlinear integral equation concerned regularized problems

5 Numerical methods, algorithms, and results

5.1 Theoretical results

5.2 Methods of Newton type

5.3 Method of opposite directions

5.4 Method of generalized separation of variables

5.5 Homogeneous problems

6 Nonstandard inverse problems of diffraction theory

6.1 Introduction

6.2 Diffraction on impedance surfaces. "Invisible" bodies and screens

6.3 Metallic short–periodical arrays

6.4 Creation of fields with circular polarization

Afterword: Ethical aspects of scientific work
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Olena Bulatsyk
Boris Z. Katsenelenbaum
Yury P. Topolyuk
Nikolai N. Voitovich
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