Phase Optimization Problems

1 Introduction2 Formulation of physical problems2.1 Forming fields of given structure2.2 Antenna synthesis problems2.3 Phase optimization problems in waveguides and open resonators3 Mathematical formulation of the problems3.1 Variational problems with no amplitude-phase restrictions on sought functions3.2 Variational problems with amplitude-phase restrictions on sought functions3.3 Homogeneous optimization problems4 Analytical solutions4.1 A general class of Hammerstein nonlinear integral equations with free phase4.2 Particular case: one-dimensional Fourier transform4.3 Particular case: discrete Fourier transform4.4 Particular case: Hankel transform4.5 Generalized nonlinear integral equation concerned regularized problems5 Numerical methods, algorithms, and results5.1 Theoretical results5.2 Methods of Newton type5.3 Method of opposite directions5.4 Method of generalized separation of variables5.5 Homogeneous problems6 Nonstandard inverse problems of diffraction theory6.1 Introduction6.2 Diffraction on impedance surfaces. "Invisible" bodies and screens6.3 Metallic short-periodical arrays6.4 Creation of fields with circular polarizationAfterword: Ethical aspects of scientific work

Olena O. Bulatsyk is a scienti¿ c researcher at the Department of Numerical Methods in Mathematical Physics at the Institute of Applied Problems in Mechanics and Mathematics (IAPMM) in Lviv, Ukraine. She received her M.S. degree in mathematics from Lviv State University in 1997 and her Ph.D. degree in mathematical modelling from IAPMM in 2004. Dr. Bulatsyk has authored over 10 scientific publications and is a member of the IEEE and AMS.Boris Z. Katsenelenbaum studied at Moscow State University. He received his Ph.D. and D.Sc. degrees from the Institute of Radio Engineering and Electronics (IRE)/ USSR Academy of Sciences (Moscow) in 1948 and 1960, respectively, where since 1954 he has held numerous positions at the latest being that of Chief Scientist. From 1962 to 1985, he served also as a Professor at the Moscow Institute of Physics and Technology, from which he received his professor diploma in 1965. Prof. Katsenelenbaum has written ten books and a lot of articles on various problems of high frequency electrodynamics and diffraction theory, and received the Ukrainian State Award for Science and Technology in 1989. Since 1998 he has been living in Nahariya, Israel.Yury P. Topolyuk is a senior scientific researcher at the Department of Numerical Methods in Mathematical Physics at IAPMM in Lviv, Ukraine. He received his M.S. degree in 1984 and his Ph.D. degree in applied and numerical mathematics in 1994, both from Lviv State University. Dr. Topolyuk has authored over 40 scienti¿ c publications. He is a member of the IEEE and AMS.Nikolai N. Voitovich is the head of the Department of Numerical Methods in Mathematical Physics at IAPMM in Lviv, Ukraine. He received his Ph.D. degree in 1968 and his D.Sc. degree in 1982, both in radiophysics, from IRE (Moscow) and Kharkiv State University, respectively. From 1961 to 1971 he worked at IRE, then took up a position at the IAPMM. Prof. Voitovich has authored six books and over 150 scienti¿ c papers, and received the Ukrainian