Abstract. The book presents a short description of generalized Rieman function z(1/2,x) of the complex argument x and the five-place table of its values in the region abs(x)=[0:0.001:1.750; 1.750:0.005:4.000;  4.00:0.01:10.00], arg(x)=[0^o:5^o:50^o; 50^o:10^o:90^o].

Abstract. The book presents a new method for solving various diffraction and scattering problems (acoustic, electrodynamics, quantum mechanics etc.).The method is based on developing the  diffracted field in the form of a series of the eigenfunctions of auxiliary homogeneous problems in which the spectral parameter is usually not the frequency. The scheme of different variants of the method is described.   The method is essentially effective for the analysis of resonant systems, in particular, of open resonators and waveguides. It permits one to represent the exact solution in unbounded domains in the form of discrete series, without additional integral with respect to the spectral parameter, and use the variational technique for solving homogeneous problems. A lot of  new problems are solved by the method.   Rigorous mathematical treatment of the main versions of the method is given in Appendix.

Abstract. The diffraction theory of synthesis of the antennas being closed semitransparent surfaces is proposed and developed. In the synthesis problems complete or amplitude only directivity pattern is given. The approach is based on applying the generalized eigenoscilation method which permits to calculate immediately the shapes of external and inner surfaces as well as transparency distribution of inner one, without the need to solve the direct problem. In the book, the bases of the theory are described, the theory is applied to resonant antennas, resonant field transformators, and non-resonant antennas with semitransparent surfaces. Variational methods for solving the synthesis problems according to given amplitude pattern are presented and applied. Three-dimensional vector problems are considered as well.

Abstract. Problems of antenna synthesis according to amplitude directivity pattern are formulated and solved in the book. The problems are considered as variational one and have been reduced to nonlinear integral or matrix equations. The iterative and gradient methods are used for solving these problems. Special attention is paid to question of inuniqueness of solutions and their branching.   The problems are considered when both amplitude and phase distributions of the current or field are unknown (amplitude-phase synthesis), as well as only one of these distributions is given (amplitude synthesis and phase synthesis). The following systems is investigated: linear antennas and arrays, flat antennas and arrays, cylindrical (ringed) antennas and arrays, hybrydic antenna systems, quasi-optical field-forming and radiation systems, conform resonant antennas, etc.   The numerical methods are described and results of their applying are presented.

Abstract. The book is a renewed and extended version of book [2]. It contains also new treatments of the method as well as results of solving new physical problems by usage of the generalized eigenoscillation concept. New theoretical results are mostly involved in the chapters on the variational technique and on the mathematical justification of the method.

Abstract.This is an elementary textbook on the numerical methods for solving the following problems: approximation of the functions; nonlinear equations in one variable; numerical integrating; ordinary differential equations.

Abstract. The book is devoted to the optimization problems arising in various applications of the wave field theory which are based on the use of phase distributions as the optimization functions. Freedom of a choice of phase can be caused by two factors. First, this is a phase field distribution which can be used in cases when only its intensity distribution is the subjectof interest, what is the case in the antenna synthesis problems or in theproblems of energy transmission. Second, the phase functions can describe thecorrection which should be provided by appropriate devices (phase correctors) for creating fields of the desired structure. The multielement phase fieldconverters are samples of such devices.

This line of investigation is not sufficiently enough presented in the iterature, first of all, because of nonlinearity of mathematical problems arising there. They have, as a rule, nonunique solutions changing their quantity as the physical parameters vary. This fact is often a feature for practice as it provides an additional freedom of choosing a solution from an existing set with the purpose of satisfying certain additional requirements.

Nonlinearity of the problem complicates its solving and demands addition investigation of the process of solution branching with changing physical parameters, what leads to the necessity of developing special numerical methods and justifying them.

In the book a special class of analytically solvable nonlinear integral equations arising in such problems is described and analyzed in detail. Such cases are seldom in practice and can, in particular, be used in the illustrative purposes while studying theory of nonlinear equations.

The book involves also nonstandard inverse problems that extend the scope declared by the book title. In particular, the problems related to minimization of the back scattering are considered as well. A nonstandard afterword regarding etical aspects of the scientific work concludes the book.

The book is intended for experts working in the field of research, design and optimization of the radiating and transmitting systems, and also for the mathematicians interested in the theory of nonlinear integral equations. It will be also useful for the students and graduate students in appropriate fields.

[Errata]